System Dynamics Modeling and Development of a Design Procedure for Short-term Alternative Energy Storage Systems THESIS

Transcription

1 System Dynamics Modeling and Development of a Design Procedure for Short-term Alternative Energy Storage Systems THESIS Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University By Joshua John McDonough Graduate Program in Mechanical Engineering The Ohio State University 2011 Master's Examination Committee: Professor Marcello Canova, Advisor Professor Yann Guezennec

2 Copyright by Joshua John McDonough 2011

3 Abstract Recovering and storing a vehicle s kinetic energy during deceleration and the subsequent use of the stored energy during acceleration has lead to significant increases in vehicle efficiency. Current production hybrid electric vehicles (HEVs) convert the energy and store it using electric machines and electro-chemical batteries. While these systems can be configured to provide substantial benefits in addition to kinetic energy recovery, significant limitations exist which hinder the performance and market penetration. Converting mechanical energy to electricity then storing it chemically leads to considerable losses during storage. The path must be followed in the opposite direction during release, compounding the losses. Current HEV batteries, while very effective at storing large quantities of energy, have longevity driven power limitations which drive up cost and weight. As a result of these limitations, investigations have been made into alternative means to recover and store kinetic energy on board vehicles. This thesis investigates two such methods of energy recovery and storage, a hydraulic system with accumulator energy storage and a purely mechanical system with flywheel energy storage. Both systems are of parallel hybrid architecture and offer high power capacity at relatively low cost. The hydraulic system consists of a pump/motor to convert mechanical work to fluid power and a high-pressure accumulator to store the energy. The mechanical system transmits the vehicle s kinetic energy to a flywheel through changing the ratio of a continuously variable transmission linked between the flywheel ii

4 and the drivetrain. System dynamics models are created for each of the systems components and coupled to allow for analysis over simulated drive cycles. An iterative design method is proposed for both the hydraulic and mechanical systems, based on drive cycle analysis, performance in simulation, and system properties, such as mass and estimated cost. The systems are compared and contrasted with each other in order to evaluate the relative strengths and weaknesses of the various kinetic energy recovery methods. iii

5 Dedication This document is dedicated to my family and fiancée. iv

6 Acknowledgments I would like to thank the many people who made this research possible. First, thank you to my advisor Professor Marcello Canova for his guidance and direction throughout the work. Thank you to Professor Giorgio Rizzoni for the opportunity to perform my graduate research at the Center for Automotive Research. Additionally I would like to thank Dr. Fabio Chiara for his assistance and insight throughout the project, General Motors for sponsoring the project, and Professor Yann Guezennec for teaching excellent hybrid vehicle classes and serving on my defense committee. Also making my graduate school education possible was the teaching assistant opportunity provided by the department of mechanical and aerospace engineering. Thank you to the faculty and staff who made that experience possible. I truly enjoyed my time as a TA. Thank you to my family for their inspiration and continued support and for instilling passions for engineering and automobiles. Finally, I cannot thank my fiancée, Arden, enough for her love and support. Her encouragement was always there when I needed it. v

7 Vita July, Born Coffeen, Illinois May, B.S. Mechanical Engineering, Rose-Hulman Institute of Technology, Terre Haute, IN. August, 2009 to present...graduate Teaching and Research Associate, Department of Mechanical Engineering and Center for Automotive Research, The Ohio State University Publications McDonough, J., Jebakumar, K., Chiara, F., Canova, M., Koprubasi, K., Raghavan, M. System Dynamics Modeling of Alternative Energy Storage Systems for Hybrid Vehicles. ASME Dynamics Systems and Control Conference, Bolletta, A., Chiara, F., Canova, M., McDonough, J., Koprubasi, K., Raghavan, M. A Design Procedure for Alternative Energy Storage Systems for Hybrid Vehicles. ICE International Conference on Engines & Vehicles, 2011 Fields of Study Major Field: Mechanical Engineering vi

8 Table of Contents Abstract... ii Dedication... iv Acknowledgments... v Vita... vi List of Tables... x List of Figures... xii Chapter 1: Introduction Motivation Kinetic Energy Recovery Hybrid Electric Vehicles (HEVs) Alternative Energy Storage Systems for Hybrid Vehicles Mechanical Energy Storage Hydraulic Energy Storage Design Considerations References Chapter 2: State of the Art Introduction Mechanical Energy Storage Systems Hydraulic Hybrid Energy Storage Systems Drive Cycle Analysis Methodologies for Energy Storage System Design Conclusions References Chapter 3: System Dynamics Modeling for Alternative Energy Storage Systems Introduction Conventional Vehicle Component Models Modeling Scheme for Alternative Energy Storage Systems Model of Mechanical AESS vii

9 3.3.2 Model of hydraulic AESS Conclusion References Chapter 4: Proposed Method for Design of Short-Term AESS Introduction Drive Cycle Analysis Generation of Vehicle Based Drive Cycle Statistics Statistical Weighting Process Definition of Target System Behavior Preliminary AESS Design Procedure Mechanical Energy Storage System Design Hydraulic Energy Storage System Design Correlations between Design Parameters and Physical Properties Mechanical ESS Correlations Hydraulic ESS Correlations Combining the Correlations to Form Properties Vehicle Simulator for Evaluation Overview of Vehicle Simulator High Level Torque Split Control Strategy Vehicle Information Needed for Simulation Cost Function Definition and Design Optimization Design Method Conclusions References Chapter 5: Application of Design Method to Mechanical and Hydraulic AESS Introduction Vehicle Details and Cycle Statistics Preliminary Design Procedure Mechanical ESS Preliminary Design Hydraulic ESS Preliminary Design Evaluation of Preliminary Designs Evaluation Procedure Mechanical ESS Design Evaluation viii

10 5.4.3 Hydraulic ESS Design Evaluation Design Optimization Mechanical ESS Design Optimization Hydraulic ESS Design Optimization Validation on Alternate Drive Cycle Mechanical ESS Design Validation Hydraulic ESS Design Validation Conclusions References Chapter 6: Conclusions and Future Work Conclusions Future Work References ix

11 List of Tables Table 1. CVT Model Inputs Table 2. CVT Model Outputs Table 3. CVT Model Parameters Table 4. Shape-factor K for different planar stress geometries Table 5. Data for Different flywheel rotor materials Table 6. Frictional Loss Test Conditions Table 7. Frictional Loss Test Results Table 8. Clutch and Flywheel Model Inputs Table 9. Clutch and Flywheel Model Outputs Table 10. Clutch and Flywheel Model Parameters Table 11. Pump/Motor Model Inputs Table 12. Pump/Motor Model Outputs Table 13. Pump/Motor Model Parameters Table 14. Accumulator Model Inputs Table 15. Accumulator Model Outputs Table 16. Accumulator Model Parameters Table 17. PRV Model Inputs Table 18. PRV Model Outputs Table 19. PRV Model Parameters Table 20. Reservoir Model Inputs Table 21. Reservoir Model Outputs Table 22. Reservoir Model Parameters Table 23. Sample of Possible Drive Cycle Statistics Table 24. Sample Velocity Based Statistics for Regulatory Cycles Table 25. Sample Vehicle Parameters Table 26. Relevant Braking Statistics for Mid-Sized SUV on FTP-75 Cycle Table 27. Mechanical ESS Design Parameters Table 28. Mechanical ESS Design Constraints Table 29. Hydraulic ESS Design Parameters Table 30. Hydraulic ESS Design Constraints Table 31. Required Vehicle Information for Simulation Table 32. Vehicle Details Table 33. Design Relevant Drive Cycle Statistics for 2009 Saturn VUE on Synthetic Cycle Table 34. Mechanical ESS Design Constraints Table 35. Mechanical ESS Design Parameters Table 36. Mechanical ESS Preliminary Design Parameters x

12 Table 37. Hydraulic ESS Design Constraints Table 38. Hydraulic ESS Design Parameters Table 39. Hydraulic ESS Preliminary Designs Table 40. Cost Function Weights Table 41. Mass of Mechanical Components Table 42. Volume of Mechanical Components Table 43. Mechanical ESS Preliminary Design Results Table 44. Mechanical ESS Preliminary Design Cost Function Values Table 45. Mass of Hydraulic Components Table 46. Volume of Hydraulic Components Table 47. Hydraulic ESS Preliminary Design Results Table 48. Hydraulic ESS Preliminary Design Cost Function Values Table 49. Optimized Mechanical ESS Design Parameters Table 50. Comparison of Optimized Design to Weighted Mean xi

13 List of Figures Figure 1. Chevrolet Volt Range Extension Hybrid Powertrain Layout [4]... 4 Figure 2. Specific Power versus Specific Energy for Various Short-Term Energy Storage Systems [5]... 9 Figure 3. Flow of Power for Flywheel Mechanical Energy Storage System [5] Figure 4. Toroidal CVT Variator Example [11] Figure 5. Comparison of Toroidal CVT Technology with other Automotive Transmissions [5] Figure 6. Toroidal CVT Variator Behavior [26] Figure 7. Component Details for Jaguar with FHSPV [7] Figure 8. Sample Hydraulic Launch Assist Drivetrain Layout [12] Figure 9. Component Sizes over Various Driving Cycles [14] Figure 10. Comparison of Motor Power Distributions between UDDS and US06 [14].. 30 Figure 11. Cumulative Braking Energy vs Power, FTP-75 Cycle [15] Figure 12. Braking Energy Distribution over Speed FTP-75 Cycle [15] Figure 13. Energy Dispersion over Braking Events for a Real World Cycle [40] Figure 14. Information Flow in the Vehicle Simulator Figure 15. Block Diagram Representation of a Forward Vehicle Simulator Figure 16. Engine Model Figure 17. Sample Fuel Consumption Map for the Engine Model Figure 18: Torque Converter Model Figure 19. Wheel and Tire Model Figure 20. General Layout of Renewable Energy Storage System for Parallel Hybrid System Figure 21. Overview of Control Hierarchy for RESS Figure 22. Mechanical Hybrid Powertrain Layout Figure 23. CVT Model Figure 24. Normalized CVT Efficiency Figure 25. Scheme of flywheel to drivetrain power chain Figure 26. Block Diagram of Clutch and Flywheel Model Figure 27. Wet Clutch Coefficient of Friction [12] Figure 28. Hydraulic Hybrid Powertrain Layout Figure 29: Hydraulic diagram of the ESS Figure 30. Hydraulic Pump Model Figure 31. Axial Piston Pump Figure 32: Flow and Overall Efficiency Map of P1 028 Axial Piston Pump Figure 33: Identification of Pump Flow Model xii

14 Figure 34: Pump Volumetric Efficiency Model at Max. Displacement (Left) and at Variable Displacement (Right) Figure 35: Pump Mechanical Efficiency Model Figure 36. Block Diagram of the Displacement Controller Logic Figure 37. Bladder-Type Accumulator Figure 38. Block Diagram of the Accumulator Model Figure 39. Poppet Valve Model Figure 40: Discharge Coefficient Curve for the Pressure Relief Valve Figure 41. Block Diagram of the PRV Controller Logic Figure 42. Block Diagram of the Accumulator Model Figure 43. Proposed AESS Design Flowchart Figure 44. US FTP-75 Test Cycle Velocity Profile [1] Figure 45. Velocity and Power Profiles for Mid-sized SUV over FTP-75 Cycle [2] Figure 46. Sample Power Sign Changes on FTP-75 Cycle [2] Figure 47. Distribution of Braking Event Energy, FTP-75 Drive Cycle Figure 48. Net Traction and Braking Power FTP-75 Cycle Figure 49. Energy per Braking Event FTP Figure 50. Maximum Braking Power per Event FTP Figure 51. Energy Distribution for Energy Storage Capacity FTP Figure 52. Energy Distribution for Maximum Braking Power Figure 53. Event Maximum Power compared to Event Energy FTP Figure 54. Effect of Energy Storage Capacity on Total Energy Storage Figure 55. Effect of Maximum Power on Total Energy Storage Figure 56. Effect on Maximum Speed on Total Energy Storage Figure 57. Mechanical ESS Design Configuration Figure 58. Hydraulic ESS Design Configuration Figure 59. Pre-charge pressure Energy Storage Relationship Figure 60. Sample CVT Torque to Mass Correlation (Torotrak CVT) Figure 61. Sample CVT Torque to Volume Correlation (Torotrak CVT) Figure 62. Sample Pump Length (Parker P1 18cc/rev, End Port Design) Figure 63. Sample Pump Width and Height (Parker P1 18cc/rev, End Port Design) Figure 64. Pump Displacement to Volume Correlation Figure 65. Pump Displacement to Mass Correlation Figure 66. Accumulator Mass Correlation Figure 67. Accumulator Outer Dimensions (Bosch HAB-5X) [10] Figure 68. Accumulator Actual Volume Correlation Figure 69. Accumulator Maximum Fluid Volume, Adiabatic Compression [10] Figure 70. Accumulator Fluid Volume Correlation (1400 PSI Pre-charge) Figure 71. Accumulator Fluid Volume (5000PSI Max, Varying Pre-charge Pressure). 152 Figure 72. Reservoir Mass Correlation Figure 73. Diagram of Vehicle Simulator Figure 74. AESS Brake Control Flowchart Figure 75. AESS Traction Torque Control Flowchart Figure Saturn VUE xiii

15 Figure 77. Sample of Synthetic Driving Cycle Figure 78. Accumulator Energy Figure 79. Mechanical ESS Vehicle Speed Profile Synthetic Cycle Figure 80. Engine Torque and Speed on Synthetic Cycle Figure 81. Flywheel Speed Synthetic Cycle Figure 82. ESS State of Energy Synthetic Cycle Figure 83. CVT Ratio Synthetic Cycle Figure 84. Clutch Mode Synthetic Cycle Figure 85. Power Split at Coupling Point Synthetic Cycle Figure 86. Clutch Slip Example Low Numerical Gear Ratio Figure 87. Clutch Slip Example High Numerical Gear Ratio Figure 88. Desired and Actual Speed Trace Synthetic Cycle Figure 89. Engine Torque and Speed over Synthetic Cycle Figure 90. Hydraulic Pump/Motor Torque and Speed Figure 91. Hydraulic Pump/Motor Flowrate Figure 92. Hydraulic Pump/Motor Displacement Figure 93. Hydraulic Accumulator Pressure Figure 94. Hydraulic Accumulator and Reservoir Volumes Figure 95. Hydraulic Accumulator State of Energy Figure 96. Mechanical ESS Design Parameter Interaction Plot Figure 97. Mechanical ESS Design Parameters Main Effects Plot Figure 98. Main Effects Plots for Cost Function Value Figure 99. Interaction Effects for Hydraulic Design Parameters Figure 101. Mechanical ESS Vehicle Speed over 75% Urban 25% Highway Cycle Figure 102. Mechanical ESS Power Split at Coupling Point over 75% Urban 25% Highway Cycle Figure 103. Flywheel Speed over 75% Urban 25% Highway Cycle Figure 104. Mechanical ESS State of Energy over 75% Urban 25% Highway Cycle Figure 105. CVT Ratio over 75% Urban 25% Highway Cycle Figure 106. Clutch Mode over 75% Urban 25% Highway Cycle Figure 107. Hydraulic ESS Vehicle Velocity over 75% Urban 25% Highway Cycle Figure 108. Hydraulic ESS Torques at Coupling Points over 75% Urban 25% Highway Cycle Figure 109. Hydraulic ESS State of Energy over 75% Urban 25% Highway Cycle Figure 110. Accumulator Pressure over 75% Urban 25% Highway Cycle Figure 111. Hydraulic Accumulator and Reservoir Volumes over 75% Urban 25% Highway Cycle Figure 112. Hydraulic Pump/Motor Displacement over 75% Urban 25% Highway Cycle xiv

16 Chapter 1: Introduction 1.1 Motivation In 2009, the United States alone consumed million barrels of oil per day for transportation [1]. As the price of oil and fuel economy standards for automobile manufacturers increase, great demand is placed on ways to reduce vehicle fuel consumption. In the United States, CAFE standards for vehicle fuel economy are set to increase by 29% for passenger cars and over 24% for light trucks between 2011 and 2016 [2]. Aside from government regulation, consumers are demanding higher fuel economy due to the rising fuel prices, causing OEMs to constantly look for ways to meet both the demand and regulation while maintaining performance, consumer acceptance and remaining competitive in the market. The increasing cost for energy and the desire to meet government regulations has caused automotive OEMs to investigate the application of traditionally non-automotive technologies to vehicles in the hopes improving fuel economy and overall vehicle efficiency. Many of these technologies involve fitting the vehicle with a means to supply traction force in addition to the internal combustion engine. Such vehicles are commonly referred to as hybrid vehicles, and are gaining increasing OEM focus and market share as external pressure and consumer preference increase demand for vehicles with higher fuel 1

17 economy [3]. Hybrid vehicles offer ways to increase vehicle efficiency by recovering normally wasted energy and/or allowing the engine to operate in a more efficient manner. 1.2 Kinetic Energy Recovery A significant portion of a vehicle s fuel is spent accelerating from rest. The kinetic energy of the vehicle is then dissipated by resistive forces and the use of traditional friction brakes during the subsequent deceleration. This inherent energy loss caused by friction braking leads to significantly higher fuel consumption for vehicles with conventional powertrains during city driving when compared to highway only driving despite lower road loads. One method for improving fuel economy is to recovery and store as much of the vehicle s energy as possible during deceleration, then use the stored energy to accelerate the vehicle at a later time. The process of storing the energy is commonly known as regenerative braking. Ideally, regenerative braking could recover all of the energy traditionally wasted by friction brakes leading to significant increases in fuel economy. In order to successfully implement regenerative braking functions on a vehicle, a specific system needed to recover, store and release the energy. To date, several options for regenerative braking have been developed for vehicle use. One such method involves using an electric machine (generator) to convert the vehicle s mechanical energy to electrical during braking and chemically store it in a battery. When necessary, the electric machine draws the stored energy from the battery and provides additional propulsion for 2

18 the vehicle. Alternatively, energy can also be recovered using a hydraulic pump and stored in a high pressure accumulator to be used for hydraulic motoring. Energy can also be stored mechanically using a rotating disc (flywheel) of sufficient inertia. This method requires a means for increasing the flywheel speed while the vehicle speed is decreasing in order to store the energy. To release the energy, the flywheel must decelerate while vehicle speed is held constant or increased. As a result, a continuously variable ratio device is needed between the vehicle s drivetrain and the flywheel. Each method for kinetic energy recovery must provide a torque to the drivetrain in the opposite direction of rotation for normal forward drive operation. Potentially, the braking torque can be applied to either set of drive wheels depending on vehicle architecture and desired configuration. The layout of the regenerative braking architecture does impact potential performance, as well as the design of the vehicle powertrain. Systems can be completely integrated with the powertrain, which is the case for many electric regenerative braking systems, or completely separate with independent operation. Some configurations can allow for additional benefits such as providing direct storage for energy produced by the engine or enabling engine off operation while the vehicle is stopped or at very low speeds. For safety reasons, regenerative braking systems cannot completely replace friction brakes. In cases of potential energy storage system failure or desired deceleration beyond the capability of the regenerative system, friction brakes must still be capable of providing sufficient stopping capability. Also friction brakes are necessary for anti-lock brake functionality as well as traction and stability control implementation. 3

19 1.3 Hybrid Electric Vehicles (HEVs) The most common type of hybrid vehicle on the road today is the hybrid electric vehicle (HEV). HEVs use electric machines along with on-board batteries to store energy and provide electric power assist. Most HEVs also provide limited engine off operation at rest and low speeds. Multiple levels of vehicle hybridization can be found in production ranging from belted starter-alternator mild hybrid systems to full-size, extended range hybrids capable of traveling upwards of 40 miles on battery power alone [4]. The cost and complexity of the systems also vary greatly depending on functionality. Figure 1. Chevrolet Volt Range Extension Hybrid Powertrain Layout [4] The electric machine in a HEV provides the capability to store and retrieve energy from the battery. In order to store energy, the electric machine behaves as a generator and charges the battery by drawing energy from the vehicle. Typically this is done during braking, but in certain configurations can also be performed directly by the engine. When 4

20 traction power is commanded by the electric vehicle, the electric machine behaves as a motor and provides torque to the wheels at the expense of battery charge. HEVs store energy in a high voltage battery pack consisting of multiple battery cells in series which can also be combined in parallel to increase capacity. Mild hybrid systems operate in the 30-50V range while more advanced full-hybrids designs use voltages over 200. Although the most common battery type for HEVs is based on nickel metal hydride technology, OEMs are beginning to switch to lithium ion chemistry for higher power and energy density [5]. Considerations on battery life typically limit the maximum current and therefore the power the battery can supply. As a result, HEV batteries are designed to provide relatively large energy storage but limited power capability. Additional electronic components are necessary for HEV operation. Inverters are needed to convert the AC electric machine power to DC power for the battery. Voltage converters are also necessary to operate other electronic accessories and optimized motor efficiency. The functionality of the power electronics comes at the cost of reduced system efficiency and additional cooling requirements. The benefits of electric hybridization are substantial and well understood. Electric hybrids have the capability of improving vehicle efficiency through regenerative braking, engine off vehicle operation, and allowing for more efficient use of the vehicle s powertrain. Some configurations also allow use of the electric machine to vary the gear ratio between the engine and the wheels, effectively behaving as an electronic continuously variable transmission. Engine efficiency can be improved by using the electric motor to change the torque and speed operating point of the engine, while still 5

21 providing the requested torque to the wheels. In most cases this involved forcing the engine to run at a higher load where efficiency is greater and absorbing the excess power into the battery for future use [5]. If a hybrid electric system is designed with substantial reserve energy capacity in the battery and electric machines which can supply a significant portion of the driver s torque request, the conventional engine can be downsized, allowing for more efficient operation. Engine downsizing can improve both fuel economy and reduce cost for a given technology level. Utilizing all of the benefits that electric hybrid vehicles have to offer, improvements in EPA estimated fuel economy of 7-50 % have been attained. Production examples of electric hybrid vehicles show improvements in fuel economy over their contemporaries of up to 50% in combined city and highway fuel economy. The gains are particularly impressive in urban driving scenarios where the regenerative braking can be used in combination with engine off operation to realize city driving cycle fuel economy improvements of up to 80% [6],[7]. The gains and benefits of hybrid electric vehicles are not without compromises. The added expense of the electric components and battery are significant. For example, the MSRP of a 2011 Toyota Prius over the MSRP of a comparable 2011 Toyota Corolla is over $3,200. On larger vehicles, the premium can be even higher. A 2011 Chevrolet Tahoe Hybrid costs over $6,000 more than a comparably equipped model with a conventional powertrain [8]. The premium in cost for a hybrid electric vehicle may be 6

22 recovered by the consumer, but the outcome depends heavily on the cost of fuel and the number of miles driven by the owner [9]. Hybrid electric vehicles also present several technical challenges that limit effectiveness. The conversion between forms of energy during storage and recovery causes reduced efficiency. The vehicle s mechanical energy is transferred to electrical energy by the electric machine then converted to chemical energy storage by the battery. During each step in the process, losses are incurred, reducing the amount of actual energy stored. The reverse process occurs when the battery s energy is used to propel the vehicle. Estimates for round trip efficiency for hybrid electric systems are close to 50% depending on the operating points and conditions [5]. This limits the effectiveness of the regenerative braking and the opportunities for improving the vehicle fuel economy. The batteries used for energy storage also present challenges. With current battery technology, in order to ensure satisfactory durability and longevity, the battery s power must be limited to less than the maximum capability. The depth of discharge for the battery must also be carefully monitored and controlled. Large swings in the battery s state of charge (SOC) cause reduced life [10]. For this reason, compromises are required in the design process where the battery must be oversized in terms of energy storage capacity in order to provide the desired power capability. This leads to increased costs and system weight. Accurately estimating the battery s SOC is also a challenge in HEV implementation. Over several years, as battery capacity degrades, significant errors in the estimation of a battery s SOC can occur, potentially causing battery damage and reduced system performance. Batteries also display temperature impacted performance. HEVs 7

23 must be designed with systems capable of preventing the battery from experiencing extreme temperature. As a result of these technical challenges and limitations, other forms of energy storage for vehicles are being investigated including forms of mechanical and hydraulic storage. 1.4 Alternative Energy Storage Systems for Hybrid Vehicles While electrical energy storage systems offer many benefits, opportunities to store energy in other forms should also be investigated and understood, in order to evaluate the feasibility as a cost effective alternative to electric systems. Two of the most promising candidates for non-electric energy storage are mechanical, in the form of a rotating disc (flywheel), and hydraulic, via bladder-type accumulators. The capability of flywheelbased energy storage has become a possibility due to the development of new CVT designs that allow for the transfer of energy into and out of the flywheel. Hydraulic energy storage systems have the advantage of using commonly available, cost-effective and well understood components with potential for low cost. 8

24 Figure 2. Specific Power versus Specific Energy for Various Short-Term Energy Storage Systems [5] In addition to the cost benefits, hydraulic and flywheel mechanical energy storage systems also have higher specific power than batteries. Figure 2 shows the specific power and specific energy for some short-term energy storage systems. Hydraulic and flywheel mechanical systems also have the advantage of relatively little performance degradation over time regardless of the depth of discharge in terms of energy storage capacity. Due to these reasons it is important to consider these technologies for vehicle hybridization Mechanical Energy Storage The concept behind mechanical energy storage is relatively simple. The goal is to transfer the vehicle s kinetic energy to a rotating disc (flywheel) mounted on board the 9

25 vehicle. The flywheel increases its rotational speed as the vehicle speed decreases accordingly. Figure 3 shows this simple flow of energy between the flywheel and vehicle and the results of the energy flow. Figure 3. Flow of Power for Flywheel Mechanical Energy Storage System [5] While the concept is simple, the practical implementation is more difficult. With strictly mechanical coupling between the flywheel and vehicle, the ratio of speeds between the portion of the conventional drivetrain to which the flywheel system is attached and the actual flywheel itself must be allowed to change. As energy is traded from the vehicle to the flywheel through conventional powertrain components, the rotating speed of the conventional components must smoothly decrease, while the rotational speed of the flywheel must smoothly increase. This results in a need for a constantly changing and variable speed ratio between the flywheel and the drivetrain. This can be accomplished in a couple of different ways. A conventional gearbox could be used, with clutch plates which allow for constant slippage while flywheel speed is changing. However, this involves very inefficient operation of the flywheel system and very high clutch wear. The other option is to use a device which allows for constantly varying input-output ratios. 10

26 This is typically know as a continually variable transmission and is seeing increased popularity for replacing stepped gear automatic transmissions for non-hybrid vehicle use. Changing the CVT ratio, which in turn forces a change in the flywheel speed, allows energy transfer between the flywheel and vehicle. CVTs exist in multiple designs. The simplest designs involve two variable diameter pulleys with a belt between them. The pulleys are split and allow for varying diameters depending on the radius where the belt is riding. The ratio is changed as the pulley diameter is altered through sliding the halves of the pulley together and apart. This is typically done in unison for both pulleys to keep tension on the belt. For higher torque applications, chain type metal belts are used. Toroidal CVTs offer another method of continuous ratio change. This design uses dished discs connected by metal rollers to transmit torque. The metal rollers are allowed to pivot, effectively changing the ratio between two discs. Half-toroidal designs restrict roller pivoting to one direction from center while full-toroidal designs allow the roller to pivot over center for wider ratio spread capability. Torque is transmitted while the rollers spin by using traction fluid that resists shear forces while compressed between the rollers and discs. Some current production CVTs use the half-toroidal design, while full toroidal designs have primarily been seen in prototype applications such as motorsports [11]. Figure 4 shows the basic structure of a full-toroidal cvt. 11

27 Figure 4. Toroidal CVT Variator Example [11] The flywheel itself can vary widely in design and material depending on the system s capability. Typically flywheels fall into two categories, low speed (<20,000 rpm) and high speed (>30,000 rpm). Low speed flywheels can be produced from steel or other low cost materials and primarily use conventional ball bearings. This offers the opportunity for low cost energy storage. High speed flywheels use composite materials with high tensile strength to enable speeds above 30,000 rpm. Bearings can be high precision ball bearings or magnetic bearings which suspend the flywheel and offer low friction. Flywheel energy storage requires an enclosure surrounding the flywheel for safety purposes. The surrounding also offers the possibility to create a vacuum around the flywheel for reduced windage. Potential benefits to flywheel energy storage include low cost, high power, high durability, and low weight when compared to electrical systems. Limitations for flywheel based mechanical energy storage include limited low energy density compared to batteries and limited energy storage duration due to inherent losses from the rotating 12

28 components. Flywheel systems can also offer superior overall efficiency of storage and release of up to 70% [12] Hydraulic Energy Storage Hydraulic energy storage revolves around storing high pressure fluid in an accumulator which can later be released to perform work. When vehicle deceleration is desired, a pump is used to send fluid from a low pressure reservoir to a high pressure accumulator. To provide acceleration assist, the pump behaves as a motor and changes the potential energy of the pressurized fluid into mechanical work. Hydraulic controls in the form of solenoid operated valves regulate the fluid flow to and from the pump. Traditional hydraulic components can be used to create the system. Bladder type steel hydraulic accumulators offer fluid storage at pressure up to 350bar. The external of an accumulator is typically steel and cylindrical in shape with domed ends. On the inside, a rubber liner is used to separate the gas charge from the working fluid. As fluid enters the fixed volume, the gas inside of the bladder must compress, causing an increase in pressure. Since the fluid and the gas must have equal pressure, the fluid pressure increases with gas pressure. Recently, hydraulic accumulators made of composite material have been design to hold even higher pressures at significantly less weight than traditional steel designs at higher cost. In addition to an accumulator hydraulic energy storage systems also need a low pressure reservoir to house fluid that is not inside of the 13

29 accumulator. The reservoir must have sufficient volume to allow for the accumulator to reach maximum pressure. Hydraulic pumps are commonly used in industrial settings in many capacities and are available in a wide range of designs. Simple fixed displacement pumps offer low cost and high reliability at the expense of limited operating conditions. Variable displacement pumps allow for precise control over torque output for a given speed and higher system efficiency, but increase cost and complexity. Hydraulic controls are necessary to route fluid flow and dictate the system behavior. With the need for the hydraulic pump to behave in both pump and motoring modes with always positive vehicle velocity, fluid direction through the pump needs to be re-routed to allow for the pump to always rotate in the same direction. Control valves are also needed to prevent backflow when the system is not functioning. Pressure release valves are necessary to prevent over pressurizing the accumulator or reservoir. Benefits of hydraulic energy storage include durability, proven components and high power capability. Depending on the system design, low cost can be achieved. The drawbacks include heavy components and limited energy storage when compared to electrical systems. 1.5 Design Considerations Also of great significance when discussing multiple options for vehicle energy storage is the design of the system. Difficult decisions must be made in both system architecture 14

30 and component specifications which will ultimately decide the overall effectiveness in practice. With the magnitude of importance that resides in the design, great need is placed on methods for configuring alternative energy storage systems for maximum performance at minimum cost, both financially and in terms of system weight and space. While the ultimate test of a design s validity resides in the real-world performance, OEMs neither have the time nor the resources to build working prototypes of each and every feasible design configuration. This has given rise to analysis lead design, which causes design decisions to be based on available data and performance in simulation. In order to evaluate a design in simulation, a prescribed velocity versus time profile is needed as a guide for the vehicle to follow. Common drive cycles include the regulatory cycles as well as real-world driving data collected by logging actual vehicles in use. These drive cycles become the basis for comparison of results such as fuel economy, performance, and component efficiency. Designs are revised according the results of these simulations and subsequently OEMs invest significant resources into hardware based development. The typical process of running simulations to optimize fuel economy over a range of cycles can be expedited with good preliminary system design. This can be accomplished with prior knowledge of the characteristics of the driving cycles. For instance, knowing the maximum braking power for a given drive cycle will help set a bound on the maximum useful power absorption of the regenerative braking system. Taking into account the frequency and distribution of cycle statistics such as energy, power, 15

31 acceleration, for braking and acceleration periods offers potential to begin simulations with designs that are closer to optimal. Presently, design methods exist for optimizing the design of hybrid electric vehicles. These methods take into account the specific design targets and constraints of the electrical components as well as all of the possible configurations. However, significantly fewer methods exist for designing short-term energy storage systems, specifically hydraulic and mechanical systems. The short-term systems provide radically different constraints on the design and can potentially operate in very different conditions in terms of when and how the kinetic energy is both recovered and returned to the vehicle. As a result, the following work provides an analysis based design method for mechanical and hydraulic short-term energy storage systems (ESS) which allows for the maximization of performance while minimizing system mass, volume, and cost. 16

32 1.6 References [1] U.S. Energy Information Administration. [2] CAFE Standards. National Highway and Traffic Safety Administration [3] HEV Sales by Model. U.S. Department of Energy Alternative Fuels and Advanced Vehicle Data Center. [4] Tortosa, N. Karbon, K. Aerodynamic Development of the 2011 Chevrolet Volt. SAE International Technical Paper [5] Guzzella, L., Sciarretta, A. Vehicle Propulsion Systems Introduction to Modeling and Optimization (2nd ed.). Springer: New York. [6] Simopoulos, G., et al. Fuel Economy Improvements in an SUV Equipped with an Integrated Starter Generator. SAE Paper [7] 2011 Ford Fusion Sales Brochure. [8] Car Price Comparison. [9] Greene, D., et al. Future Potential of Hybrid and Diesel Powertrains in the U.S. Light-Duty Vehicle Market. (2004). U.S. Department of Energy. [10] Adams, J., et al. Approach to Validation Plan Development for Advanced Battery Systems in Vehicle Applications. SAE International Technical Paper [11] Cross, D., Brockbank, C. Mechanical Hybrid System Comprising of a Flywheel and CVT for Motorsport and Mainstream Automotive Applications. SAE International Technical Paper [12] Boretti, A. Improvements of Vehicle Fuel Economy Using Mechanical Regenerative Braking. SAE International Technical Paper

33 Chapter 2: State of the Art 2.1 Introduction This chapter contains a review of current research and development of non-electric energy storage for vehicles, specifically hydraulic and flywheel mechanical systems with a focus on short-term storage systems. Attention is also given to drive cycle statistical analysis and current HEV design procedures. 2.2 Mechanical Energy Storage Systems Investigation into the concept of storing energy in a rotating disc for passenger cars was spurred by rising gasoline prices in the 1970 s. Dr. Andrew Frank from the University of Wisconsin investigated the idea of using a very large flywheel to store substantial amounts of energy and allow engine off operation of the vehicle [1]. University of Wisconsin research showed fuel economy improvement of up to 33% were possible using a large steel flywheel underneath the vehicle to buffer the engine s energy output. The flywheel energy was transmitted using a 4-speed manual gearbox and hydrostatic CVT [1]. While promising, several drawbacks limited the potential for production use. Even though engine downsizing could negate much of the additional weight of the flywheel itself, a very heavy containment structure would be needed to contain the large flywheel 18

34 in the event of a crash. The efficiency of the system was severely hindered by the design s hydrostatic CVT. High losses in the flywheel due to bearings and windage were significant and present over the entire cycle. More recently, investigations have begun using higher speed flywheels (20,000rpm and greater) to obtain higher energy density. Advances in technologies such as lighter, compact, and more efficient continuously variable transmissions (CVTs) have allowed new configurations for storing energy in flywheels. New designs have allowed flywheels to be coupled to the drivetrain in parallel with the engine to produce very high round trip efficiencies in regard to storing and releasing energy. Higher speed operation reduces the flywheel mass and eliminates some of the packaging issues with large, low speed flywheels. The introduction of kinetic energy recovery in Formula 1 racing in the 2009 season has spurred the development of regenerative braking systems with high power density. Out of this development spawned a high speed flywheel system with a full toroidal CVT capable of flywheel speeds exceeding 60,000rpm and 60kW of power with a total system weight of only 25kg [26]. The technology developed for Formula 1 has begun to infiltrate the realm of production vehicles beginning with the CVT. Flybrid Systems under the license from a toroidal CVT designer, Torotrak LLC, has been working with OEM car manufacturers to bring the technology of the Formula 1 flywheel hybrid system to production vehicles. Torotrak and Flybrid have published several papers touting the benefits of flywheel energy storage for vehicle fuel economy, showing the energy 19

35 recovered from braking can provide up to 21% of the energy needed to propel a vehicle over the US-FTP75 cycle [2]. The advancement in CVT technology in terms of specific torque output and efficiency has made flywheel energy storage more promising. At the heart of this improvement in CVT technology is the development of full-toroidal traction drive CVTs. Figure 5 shows a plot of torque capacity and weight of toroidal CVTs (T-CVT) compared to production CVTs as well as other transmission types. T-CVTs have much lower weight for a given torque capacity than conventional push-belt CVTs, placing near manual transmissions in terms of torque capacity per unit mass. Figure 5. Comparison of Toroidal CVT Technology with other Automotive Transmissions [5] Traction drive is accomplished through the use of the variator rollers which transmit torque between the toroidal discs within the transmission. The variators change the input 20

36 speed to output speed ratio by changing the alignment of their axis of rotation. The result is the effective radius of where the force is being transmitted changing. Changing the radius effectively changes the speed ratio. Figure 6. Toroidal CVT Variator Behavior [26] Torque is transmitted without metal to metal contact by the use of elasto-hydrodynamic traction fluid which resists shear while under compression. With a fluid film between the variators and the discs, metal to metal contact is prevented, allowing for adequate transmission life [5]. Traction fluids have allowed the T-CVT to become a possibility and much development has gone into optimizing them for T-CVT use [6]. Current applications of flywheel hybrid systems include prototype production vehicles such as the Jaguar XF with FHSPV (Flywheel Hybrid System for Premium Vehicles). The project is being lead by a consortium of automotive companies including Jaguar Land Rover, Ford, Prodrive, Torotrak, Xtrac, Flybrid Systems, and Ricardo. The system 21

37 has a parallel configuration and is capable of providing 60kW power while improving fuel consumption by 20% [3]. Figure 7 shows the system uses a T-CVT coupled to the rear axle with a high speed flywheel for energy storage. The system is capable of storing over 400kJ of energy and flywheel speeds of up to 60,000rpm. Figure 7. Component Details for Jaguar with FHSPV [7] Very recently a paper was published on the topic of design of mechanical flywheel systems for implementation in automotive vehicles. Topics discussed included possible configurations, design, and CVT control for a specific case of a vehicle decelerating from 100km/h to 60km/h. The effects of gearing between the flywheel and vehicle were 22

38 investigated and guidelines were provided for selecting proper gearing to maximize energy storage in the flywheel. Assumptions were made with regards to the initial sizing of the system as well as the operating limits of the system. Not included in the paper were energy losses due to rolling resistance and aerodynamic resistance during deceleration. The final conclusions showed the F1 style system, with proper design, could be successfully implemented and controlled in road cars [8]. While the majority of research into flywheel mechanical hybrids for road cars has been done in simulation, the recent advancements in technology offer an efficient and lightweight solution to regenerative braking. 2.3 Hydraulic Hybrid Energy Storage Systems In the late 1970 s hydraulic hybrids were investigated by Buchwald et al. in their work on parallel hybrid systems for urban bus applications. Their research showed great potential for braking energy recovery and reduction in fuel consumption through engine downsizing and regenerative braking [4]. More recent research has focused on both series and parallel systems for energy recovery and improvements in average engine operating efficiency. In the mid 2000 s research and development on series hydraulic hybrids was performed by the EPA along with Eaton Corporation and others on a project involving hybridization of a UPS delivery truck. The goals were reducing emissions and fuel consumptions through recovering braking energy and optimizing engine operation. The high amount of 23

39 urban driving and frequent stops made the delivery truck an excellent application for hydraulic hybrid technology. The results were 60-70% increases in fuel economy and 40% reduction of carbon dioxide. With the reasonable cost of hydraulic technology, the payback period for the cost of the hybrid delivery truck over a conventional version was estimated at 3 years [9]. Research at the University of Michigan on series hydraulic hybrids for 5-ton trucks has also shown in simulation that substantial gains in fuel economy of up to 68% are possible in urban driving conditions [10]. In the simulations, engine shut down was employed and regenerative braking was maximized though accumulator energy control. The research also addressed some of the challenges related to the relatively low energy density of the hydraulic accumulator used in the vehicle. Allowing the SOC to reach relatively low levels before recharging with the engine allowed better use of the limited energy storage capacity. While gains from series hydraulic hybrid systems can be significant on large vehicles where the powertrain is a relatively small portion of the overall vehicle weight and the primary operating environment contains limited highway operation, the gains are less significant on smaller vehicles with more frequent highway use. As a result, lower cost and lighter parallel hydraulic launch assist (HLA) designs have been considered for smaller vehicles. HLA systems typically have less power capability and energy storage than series hybrid configurations, but have the advantage of less weight added to the vehicle and lower cost of components while still retaining the regenerative braking functionality. 24

40 Modeling and demonstration vehicle research on HLA systems for small and mid-sized vehicle applications has shown improvements of anywhere from 10% to over 30% are possible [11],[12]. Ford Motor Company Advanced Powertrain along with the U.S. EPA fitted a hydraulic pump/motor in parallel with the conventional drivetrain in a mid-sized SUV for demonstration purposes. In additional to demonstrating improvements in fuel economy, it also showed the ability to smoothly blend conventional brake operation with regenerative braking from the hydraulic system [11]. Simulation performed at Anglia Ruskin University in 2008 showed gains of 7-10% were possible with only regenerative braking and no engine off operation [12]. In this work, the system was sized to recovery the amount of energy equal to the vehicle s kinetic energy when stopping from 60km/h to 0km/h. The model uses an axial piston pump/motor clutched to the drive axle along with a piston-style high pressure accumulator. Very short urban cycles were used to estimate the results. Figure 8 shows the drivetrain layout for the design used for simulation. 25

41 Figure 8. Sample Hydraulic Launch Assist Drivetrain Layout [12] Recent research promoted by the Center for Compact and Efficient Fluid Power has focused on developing new technologies for improving the performance of hydraulic systems for hybrid vehicles. Topics include hydraulic control strategies, developments in variable displacement pump/motor efficiency, advanced accumulator energy storage, and noise and vibration reduction. Future projects include implementation of parallel hydraulic hybrid systems on a light-duty truck and a passenger car [13]. The advantages for hydraulic hybrids are the high power density of fluid power and the well known technology. Unfortunately, low energy density offsets some of the advantages. However, advancements in component technologies such as lightweight 26

42 composite accumulators have allowed hydraulic hybrids to better compete with other hybrid technologies. 2.4 Drive Cycle Analysis Methodologies for Energy Storage System Design The design procedure of a vehicle typically begins with an analysis of the intended uses. This is no less true with hybrid vehicles, of any type. Knowing, or at least having an approximate knowledge of the duty cycle, velocities, accelerations, and grades the vehicle must traverse allows the design to best accomplish its intended goals of performance, emissions, and fuel economy. Traditionally, vehicles have been designed to worst case scenario standards. Engines and transmission components were sized for peak output in order to meet acceleration and grade-ability targets. With these targets met, the designers could safely assume the more moderate conditions of the regulatory and real-world driving cycles would be easily met. With the advent of hybrid vehicles and the ability to draw power from more than one source, the design space has opened up greatly, causing an increase in the number of design decisions to be made. Even relatively simple parallel hybrid vehicle designs introduce numerous options for powertrain configuration, power capability, energy storage capacity, and speed range of operation. The once popular metrics of top speed, acceleration times, and grade-ability are of little use in designing an alternate power source. Instead, new statistics surrounding available braking energy, braking power, and speeds at which energy is available for recovery are needed to generate optimum design 27

43 solutions. As a result, more specific investigation into the characteristic statistics of the energy and power requirements for both traction and braking over traditional drive cycles has been performed in order to assist with design. The following paragraphs will discuss some of the recent analysis. It should be noted that the majority of the work on drive cycle analysis has been performed for HEVs and electric technologies, but the analysis can also be applied to non-electric forms of energy storage. Argonne National Laboratory published a paper on the influence of drive cycles on plugin hybrid vehicle design [14]. The paper begins with discussion on the importance of using analysis tools to determine the approximate power and energy metrics for a certain vehicle and a given drive cycle. In this work, Argonne National Laboratory s Powertrain Systems Analysis Toolkit (PSAT) is used to determine the power and energy requirements. Figure 9 shows the resulting requirements of power for the different system components. 28

44 Figure 9. Component Sizes over Various Driving Cycles [14] In the paper, the engine was sized to meet grade-ability, thus is constant for all cycles. However, the required ESS power which is related to the regenerative braking power and the required motoring power for all electric operation each varied for each driving cycle. Note that, due to the large difference in vehicle energy and power demand of each cycle, the motor peak power varies by up to a factor of 3. While peak values are important, if the hybrid system power source can be augmented by the engine, the distribution and frequency of the power capability needed also become important. Figure 10 shows the distribution for motor power between two cycles. 29

45 Figure 10. Comparison of Motor Power Distributions between UDDS and US06 [14] Looking at the distribution for UDDS, there is little need to size the electric motor above 20kW and reductions in cost and weight could be realized by sizing less than the peak without significant penalties for that particular cycle. However, in the case of the US06 cycle a large percentage of the motor usage is near peak, warranting sizing for peak operation. The conclusion drawn from the Argonne National Laboratory paper is that driving cycle statistics should be an important factor in design and multiple tradeoffs exist between performance, cost, fuel economy, and emissions. A more detailed analysis of driving cycles with regard to hybrid braking system design is presented in [15]. The paper begins with basic longitudinal vehicle dynamics and uses the equations to arrive at information about the energy and power of braking events over a 30

46 range of cycles. Important statistics about the distribution of energy and power are calculated and presented. In addition to distribution plots, cumulative distribution plots were also shown. Figure 11 shows the percentage of energy that is not recoverable from minimum to maximum braking power. Figure 11. Cumulative Braking Energy vs Power, FTP-75 Cycle [15] From the above curve, it is very easy to see where the marginal gains for increasing power are high, and at what point the gains begin to diminish. This is extremely helpful from a design perspective because it allows the designer to quickly estimate the effects of changing the braking power on the system s ability to recover energy. Also in [15] are distributions with respect to vehicle velocity. Figure 12 shows the distribution of energy with respect to vehicle speed. 31

47 Figure 12. Braking Energy Distribution over Speed FTP-75 Cycle [15] Looking at Figure 12, for this particular drive cycle, the majority of the braking energy available is located at vehicle speeds below 50km/h. The usefulness of this information stems from the fact that the capability of the energy storage systems typically vary with speed either due to efficiency differences or mechanical limitations. Relevant conclusions from the paper include the limited amount of energy that is available at very low and very high speeds and the idea that most of the braking energy is concentrated in a relatively small power range. Some investigation into drive cycle analysis and the subsequent design of flywheel hybrid energy storage systems has been done by Flybrid Systems LLP [16]. In [16] a real world cycle is taken from a specific automaker and analyzed with respect to braking energy distribution. Both the change in kinetic energy and the amount of recoverable energy (change in kinetic energy minus road loads) are shown in Figure

48 Figure 13. Energy Dispersion over Braking Events for a Real World Cycle [40] The real world cycle shows the majority of the braking events for a 1800kg vehicle are in the 100kJ to 500kJ range. While the analysis in [16] addresses energy, it does not address the power considerations under the assumption that the system in question has sufficiently high power capabilities. Current practice for hybrid design includes running countless full vehicle simulations over a variety of cycles in order to sufficiently sample the design space and allow for optimization based on the constraints such as cost, fuel economy, performance, and durability among others. Clearly, the type of drives cycles which are used for simulation will heavily impact the results. Due to this, research into methods for randomly generating appropriate drive cycles based on real world driving data is being performed. At Ohio State University s Center for Automotive Research, real world drive cycle data 33

49 has been recorded and used to generate a Markov chain model which can then be used to generate random drive cycles where the length of the cycles along with the percentage of urban and highway driving are specified by the user [17]. Varying amounts of traffic can also be programmed into the generator for better coverage of the various conditions the vehicle will encounter. These types of developments allow the hybrid vehicle designer to evaluate and optimize the design over cycles which closely replicate the actual driving patterns. Drive cycle analysis gives the designer a portion of the input needed. Obviously, other design constraints are needed to arrive at a product which is feasible to produce and will function as intended. Much of the research and investigation into proper design of energy storage systems has been focused on electrical systems. A need is present to develop a methodology by which to design and size hydraulic and mechanical flywheel energy storage systems for light duty vehicles. 2.5 Conclusions Based on current literature and research progress, mechanical and hydraulic energy storage systems present an effective way to employ regenerative braking. The benefits have been researched and the systems are understood. What is lacking is a design procedure for short-term energy storage systems. Current conventional vehicle design methods where the components are sized for the worst case scenario of vehicle use, do not apply to designing energy storage systems 34

50 since the ESS is not the primary provider to traction force nor the sole provider of braking force. Current HEV energy storage system design methods do apply to a limited extent, however, due to the difference in nature between the long-term and short-term energy storage systems only certain aspects apply. Methods of HEV design where the battery limitations are taken into account are not valid for systems where such limitations are not present. Additionally, the HEV electrical system can take on multiple configurations and provide additional features not offered by short-term forms of energy storage. In most cases, the energy storage capacity of a battery in a HEV is at least an order of magnitude greater than the energy storage offered by mechanical and hydraulic means; however, the mechanical and hydraulic systems offer potentially higher power. HEV design methods also account for the necessity of ensuring a particular HEV design is charge sustaining. Short-term energy storage systems with relatively limited energy storage capacity do not have the charge-sustaining constraints. Furthermore, battery based electrical energy storage systems have very high energy density which allows for numerous braking events to be stored before the battery reaches its maximum state of energy. This allows the HEV to selectively discharge the stored energy throughout the drive cycle. Short-term energy storage systems, by definition, do not have this capability due to the lower energy density of the system. In order to maximize the effectiveness of the short-term energy storage system s limited energy storage capacity the system must be charged and discharged more frequently in order to prevent the case where braking energy is available for storage, but the system cannot 35

51 accept additional energy. This means the design of the short-term systems must be based on the individual braking events. These intrinsic differences lead to the necessity of design methods specifically for mechanical and hydraulic short term energy storage systems and the specific advantages and constraints they provide. The proposed method involves braking event by braking event analysis in terms of energy and power, coupled with statistical weighting, in order to best size the system. This approach leads to considerable reduction in the effort needed to not only arrive at appropriate system sizing, but also reduces the amount of testing and verification that is necessary. 36

52 2.6 References [1] Frank, A. Beachley, N. Evaluation of the Flywheel Drive Concept for Passenger Vehicles. SAE Technical Paper [2] Cross, D., Brockbank, C. Mechanical Hybrid System Comprising of a Flywheel and CVT for Motorsport and Mainstream Automotive Applications. SAE International Technical Paper [3] Flybrid Systems. FHSPV Press Release. September [4] Buchwald, P., et al. Improvement of City Bus Fuel Economy Using Hydraulic Hybrid Propulsion System A Theoretical and Experimental Study. SAE Paper [5] Brockbank, C. Burtt, D. Developments in Full Toroidal Traction Drive Infinitely and Continuously Variable Transmissions. SAE International Technical Paper [6] Newall J, Nicolson D, Lee A, Evans S; Development and Assessment of Traction Fluids for Use in Toroidal IVT Transmissions ; SAE 2002 World Congress; March 2002; Detroit; Michigan; USA [7] Squatriglia, C. KERS Comes to Cars as Jaguar Tests Flywheel Hybrid. [8] Moro, D. et al. Guidelines for Integration of Kinetic Energy Recovery System (KERS) based on Mechanical Flywheel in an Automotive Vehicle. SAE International Technical Paper [9] U.S. Environmental Protection Agency. World's First Full Hydraulic Hybrid in a Delivery Truck. [10] Kim, Y., Filipi, Z. Simulation Study of a Series Hydraulic Hybrid Propulsion System for a Light Truck. SAE International Technical Paper [11] Kepner, R., "Hydraulic Power Assist A Demonstration of Hydraulic Hybrid Vehicle Regenerative Braking in a Road Vehicle Application," SAE Technical Paper ,

53 [12] Toulson, E. Evaluation of a Hybrid Hydraulic Launch Assist System for use in Small Road Vehicles. IEEE International Symposium on Industrial Electronics, ISIE [13] Center for Compact and Efficient Power. Hydraulic Hybrid Passenger Vehicle, Test Bed 3: Highway Vehicles. [14] Kwon, J. et al. Impact of Drive Cycles on PHEV Component Requirements. Argonne National Laboratory. SAE Technical Paper [15] Gao, Y. et al. Design and Control Principles of Hybrid Braking System for EV, HEV and FCV. IEEE Vehicle and Propulsion Conference, [16] Cross, D. Hilton, J. High Speed Flywheel Based Hybrid Systems for Low Carbon Vehicles. IEEE Hybrid and Eco-Friendly Vehicle conference, [17] Gong, Q. et al. An Iterative Markov Chain Approach for Generating Vehicle Driving Cycles. SAE International Technical Paper

54 Chapter 3: System Dynamics Modeling for Alternative Energy Storage Systems 3.1 Introduction This chapter contains the low-frequency dynamic models developed for aiding in performance prediction and design methodology development for alternative energy storage systems. First, lumped parameter models for conventional vehicle components and vehicle dynamics are presented. This is followed by the development of models for components specific to both the mechanical and hydraulic storage systems. The goal of these models is to provide time averaged prediction of behavior during vehicle operation. 3.2 Conventional Vehicle Component Models In order to evaluate the behavior of conventional and hybrid vehicles, it is important to correctly understand the energy flows in the powertrain components. Doing so allows for evaluation and understanding of where efficiency can be improved. For this reason, a brief description of the models utilized to describe the vehicle energy flows is presented here. Combining these models to form a simulator is necessary for easily evaluating the behavior. Figure 14 shows the outline for the simulator subsystems and the information that is passed from one sub-system to another. 39

55 Figure 14. Information Flow in the Vehicle Simulator. Vehicle Dynamics The vehicle dynamics model is represents the longitudinal motion of the vehicle as well as the longitudinal load transfer between axles. The model results from an equilibrium equation, where the acceleration of the vehicle is a result of a balance between the force generated at the road/wheel interface by each individual tire due to traction and braking torque and the resistive forces acting on the vehicle (tire rolling resistance, aerodynamic force and grade). The resulting equilibrium equation is: M veh dv dt veh F wheel F roll F aero F grade (3.1) where M veh is the equivalent vehicle mass (which include the inertial effects of the rotating masses), V veh is the vehicle longitudinal velocity and F wheel represents the tractive and braking force generated by each tire. The resistive forces are expressed as follows: F F F roll aero grade r M 0 0.5C A M veh x veh g r M f 1 air g sin V veh 2 veh gv veh (3.2) 40

56 where C x is an aerodynamic friction coefficient, r 0, r 1 are rolling friction coefficients (determined experimentally), A f is the vehicle frontal area and α is the road slope angle (positive is uphill). Driver The driver model determines the position of accelerator and brake pedal for tracking the prescribed velocity profile. It is based on a PID feedback controller that generates signals between -1 and +1. Positive values mean that the measured speed is lower than the desired one, therefore are intended as accelerator signals (a, between 0 and 1); negative values mean the opposite and represent braking signals. The sign of the braking signal is reversed so that the brake signal b is also between 0 and 1. Supervisory Controller The supervisory controller block contains an overarching control logic that commands the main powertrain components in relation with the vehicle operating conditions and the driver commands. Specifically, the supervisory controller commands the following: Engine torque Torque converter lock-up clutch Transmission gear shifting. The control logic implemented is largely based on static maps, which must be calibrated based on vehicle data. Powertrain Components A more detailed representation of a forward-looking vehicle energy simulator is shown in Figure 15, adapted from 0. 41

57 Figure 15. Block Diagram Representation of a Forward Vehicle Simulator. Engine Model The engine model is purely static; hence it neglects crank-angle dynamics and torque oscillations due to the alternating inertia and combustion cycles. A conceptual sketch of the engine model is shown in Figure

58 Figure 16. Engine Model 0 The engine torque is applied to the crankshaft and flywheel, lumped together in a single rotational inertia, which is also subject to the load torque, coming from the rest of the powertrain 0. This constitutes the mechanical interface between the engine and the drivetrain. The torque that the engine generates is calculated using a table interpolation based on the maximum available torque at the current engine speed and the percentage of load desired (which corresponds to throttle opening in traditional gasoline engines and to amount of injected fuel in diesel engines). The fuel consumption is estimated using another table interpolation, as a function of torque and speed. A sample fuel consumption map is shown in Figure

59 Figure 17. Sample Fuel Consumption Map for the Engine Model. The engine torque is given by: Where T ice α T ω T ω T ω ice,max T ice,max ω and ω ice,min ice,min (3.3) T ice,min represent respectively the maximum torque and the friction torque of the engine, both functions of the engine speed. Given the throttle input and the measured crankshaft speed, the net torque is calculated and applied to the equivalent inertia, which represents the crankshaft and the flywheel: J ice d T dt ice T load (3.4) 44

60 In the scheme shown in Figure 15, the load torque is represented by the torque converter pump. The output shaft is then used to connect the engine to the rest of the driveline components. Note that, being the torque map obtained with steady-state testing, it does not take into account the effect of the equivalent inertia, which may become significant during large and rapid transients in the engine speed. Torque Converter The torque converter is a fluid coupling device that is used to transmit motion from the engine to the transmission input shaft. It is capable of multiplying the engine torque (acting as a reduction gear), and, unlike most other mechanical joints, provides extremely high damping capabilities, since all torque is transmitted through fluid forces rather than friction or pressure. It is traditionally used in vehicles with automatic transmissions to avoid the need of automatically engaging and disengaging a mechanical clutch. A torque converter (Figure 18) is composed by three elements: a pump, connected to the engine shaft, a turbine, connected to the transmission, and a stator which does move. The fluid in the torque converter is moved by the pump because of engine rotation, and drags the turbine and therefore transmits torque to the transmission. The torque at the turbine is generally higher than the torque at the pump (i.e. the engine torque), thanks to the presence of the stator. The torque difference is higher when the speed difference between the pump and the turbine is higher; at steady state, the two elements tend to rotate at the same speed and the torque difference tends to zero. 45

61 Figure 18: Torque Converter Model 0 The torque converter model is based on a torque-speed map that for calculating the torques exerted by the fluid on the turbine and the pump. In particular, torque characteristics are usually represented in graphical form, as graphs of torque ratio and capacity factor versus the speed ratio 0, 0. The speed ratio and the torque ratio are defined as: SR t, p Tt TR T p (3.5) The capacity factor, which is an indicator of the maximum torque that can be transmitted by the torque converter, is defined as: K t T p p (3.6) In the vehicle modeled here, detailed data on the transmission components were not available; therefore, the three parameters above described have been determined from commonly available maps for the torque converter. 46

62 The operation of the unlocked torque converter can be split into two phases: multiplication mode and torque coupling mode. The multiplication mode occurs when the engine speed exceeds transmission input speed by a significant amount. As the name might suggest, the torque at the output shaft of the converter is actually larger than the input torque (i.e. the input torque is multiplied). The coupling operating mode occurs when the engine speed and the transmission input speed are nearly equal (i.e., there is a small slip between the turbine and the pump). In a forward-oriented model, the turbine and impeller speed are given. For this reason, the determination of the torque converter operating mode (coupling or multiplication) is made by detecting and comparing the two speeds. In particular, coupling occurs when their difference is below a given threshold. Gearings and Differential Gearings are purely mechanical components, with no inputs, outputs or controls. In forward-oriented simulators, such components are simply modeled as static functions. The external interfaces are two mechanical connections representing input and output shafts. The simplest model possible for gearings only accounts for the speed and torque ratios, without considering the losses due to friction. However, for energy analysis and in general for more accurate predictions, a lossy gear model must be introduced, to account for power losses in the gearing. Given the fact that the speed ratio is fixed by kinematic constraints, the power loss implies the reduction of the torque at the output shaft, taken into account by the gear efficiency: 47

63 T out out g in 1 T g in (3.7) where g is the gear ratio. In this case, the subscripts in and out refer to the shaft of input and output power flow, since the loss must reduce the output power. The identification of the shafts is based on the sign of the product The power loss is calculated as T 1 Gearbox loss in in T, which is positive at the input shaft. P and is always positive. Functionally, a gearbox is transmission whose ratio (and possibly other characteristics, such as efficiency) can be changed through the supervisory controller. The model implemented for the gearbox is the simplest possible, and consists in a lossy gear with variable gear ratio and variable efficiency (which depends on gear ratio, speed, and input torque). The variable gear ratio signal deriving from the gear selection index is filtered with a 1 st order transfer function that mimics the delay involved in the actual procedure of gear shifting. This model captures the essential functionality common to manual gearboxes and automatic transmissions, and can be used for both cases. Wheels and Brakes The wheels represent the link between the powertrain and the external environment. The wheel model includes the motion of the wheel and the effect of the brakes, calculating the forces at the interface between tire and road surface. The traction force is calculated given the powertrain torque, the brake signal and the vertical load on the wheel. 48

64 In the vehicle simulator, a very simplified modeling approach is used, that is a perfect rolling model in which the torque applied to the wheel shaft is completely transformed into traction force considering pure rolling motion between the tire and the soil, and neglecting tire deformation. The quasi-static model does not take explicitly into account wheel slip and relaxation length; however, it assumes that the dynamic response of the tire can be approximated by a first order delay and that the maximum force generated at the road/terrain interface is proportional to the vertical load on the wheel 0. Figure 19 shows a schematic of the model. Figure 19. Wheel and Tire Model. The brakes are modeled as an additional torque that reduces the net torque acting on the tire. The brake torque is proportional to the brake input signal (which represents a normalized pressure). Therefore the net torque acting on the wheel is: T wheel T shaft T brake (3.8) 49

65 Where T shaft is the torque at the driveshaft, and T brake T represents the braking brake,max torque (calculated as a function of the maximum available braking torque). The brake command is equivalent to the normalized pedal position, and varies between 0 and 1. Given the effective rolling radius R wheel of the tire, the effective traction force generated at the wheel is computed as: F wheel T R wheel wheel (3.9) Which, inserted into Equation 10, allows for computing the vehicle longitudinal velocity. The corresponding wheel speed is: wheel V R veh wheel (3.10) 3.3 Modeling Scheme for Alternative Energy Storage Systems From an energy system standpoint, the presence of an AESS introduces an additional degree of freedom in the determination of the propulsive power to move the vehicle. Since the propulsive power can be provided by either the engine or the AESS or a combination of both, it is possible to define a power split that optimizes specific objective functions along the vehicle operations (such as fuel economy). Depending on the architecture of the hybrid vehicle, the AESS can perform additional tasks, such as vehicle launch, regenerative braking, or potentially crankshaft energy harvesting. 50

66 In order to define a flexible modeling environment to characterize different hybrid vehicle configurations, a standard representation can be adopted to define the power and energy flows through the AESS. In particular, the system is composed by three fundamental elements: Power connection node: this element, physically represented by a clutch/transmission component, allows one to physically connect the AESS to the vehicle powertrain, enabling for a bi-directional flow of power; Energy converter: this element converts the power flows at the summation node into a suitable form of energy that can be stored. For instance, an electric motor/generator is required to convert mechanical energy into electrical energy that can be stored in an electrochemical battery. The conversion process occurs with energy losses, which must be correctly accounted for in order to conduct energy analysis; Energy storage: this element is able to store energy and release it when required by the control system. From a dynamic system standpoint, the amount of energy stored at a given time represents the state variable of the system. The following work will focus on modeling systems which can store energy in mechanical (flywheels) and potential (hydraulic accumulators or pneumatic accumulators) form. Since each energy conversion process occurs with losses, it is critical to define a vehicle system layout and a suitable choice of components so that maximum roundtrip energy efficiency can be achieved for storing and releasing energy. As stated previously, the 51

67 focus will be on the analysis of parallel hybrid systems, as the one shown in Figure 20. Such solution is very common today for micro-hybrid or mild-hybrid architectures, where the maximum energy/power capacity of the AESS is relatively small, compared to the corresponding engine outputs. This allows the AESS to perform limited functions, such as energy recovery, vehicle launch and engine torque assist. Prime Mover Transmission Energy Storage Device Energy Conversion Device Power Summation Wheels Figure 20. General Layout of Renewable Energy Storage System for Parallel Hybrid System. 52

68 Vehicle Level Controller Torque Request Subsystem Controller Torque Command Energy to Storage Medium Energy Conversion Device Energy to Powertrain Figure 21. Overview of Control Hierarchy for RESS. From a control standpoint, the secondary energy storage system can be utilized by applying commands to the connection node and to the energy converter. This is consistent with the majority of the energy storage systems for hybrid vehicles. The AESS control is realized in a hierarchical fashion, as shown in Figure 21. The vehicle level controller (which represents the supervisory energy management strategy) requests a torque (positive or negative) to a subsystem controller. The subsystem controller then applies the system constraints (in terms of speed, torque, energy/power limitations) and provides a command (generally, a torque) to the energy converter. The subsystem controller may be integrated into the vehicle level controller and implemented in a variety of fashions. Constraints on the storage medium and energy conversion device can be integrated into the controller to ensure feasible operating conditions. 53

69 With reference to a mechanical energy storage system, such as a flywheel coupled to the vehicle driveline through a clutch and a CVT, the energy conversion (mechanical to mechanical) would be done by controlling the clutch pressure and the CVT system. The equivalent gear ratio of the CVT would have to be controlled in order to provide the desired torque to the powertrain, consequently extracting energy from the flywheel (the storage medium). In the case of a hydraulic system, a variable displacement motor/pump is considered as the conversion device, transforming the energy stored in the accumulator (in the form of pressurized hydraulic fluid) into mechanical energy at the shaft. In this case, the motor/pump displacement is used to control the torque request from the supervisor based on the pressure differential (available energy) and the operating conditions of the system Model of Mechanical AESS The architecture considered for the mechanical hybrid vehicle is based on a parallel configuration 0, where the mechanical ESS is located between the transmission and the drive axle, as shown in Figure 22. The continuously variable transmission couples the ESS to the transmission output shaft, allowing for transferring torque to the drivetrain. This configuration allows for minimal changes in vehicle design and allows for standard drivetrain components to be used. 54

70 Fuel Tank Fuel Energy Engine ICE Power Flywheel + Clutch Transmission Flywheel Power ICE Power CVT CVT Power Mechanical Power Summation Braking Power Combined Power Drive Axle Power to Wheels Figure 22. Mechanical Hybrid Powertrain Layout Continuously Variable Transmission The purpose of the CVT is to adjust the speed ratio (N CVT ) between the driveshaft and the flywheel in order to store and discharge energy. In general, increasing the ratio numerically forces the vehicle to transfer mechanical power to the flywheel. On the other hand, reducing the ratio numerically has the opposite effect. If the ratio is increased while the vehicle is decelerating, energy that otherwise would have been dissipated as heat by 55

71 the mechanical brakes is used to accelerate the flywheel. If the ratio is decreased during vehicle acceleration, the energy stored in the flywheel is transferred back to the vehicle. A functional block diagram of the CVT is shown in Figure 23. The speed ratio, in combination with the rotational speed of the drivetrain, is used to determine the speed of the CVT side of the clutch. The torque is passed from the clutch and flywheel system, modified as an effect of the speed ratio and the CVT efficiency, and sent to the drivetrain. Figure 23. CVT Model In the following mathematical formulation, the notation adopted to indicate the direction of the torque and volumetric flow is as follows: the torque is considered positive if directed towards the drivetrain, negative if directed from the drivetrain. The torque out of the CVT is a function of the speed ratio, input torque, and efficiency: (3.11) Where N is the speed ratio and is the mechanical efficiency of the CVT, defined as: CVT, T 0 * 1 (3.12) CVT, T 0 CVT 56

72 CVT efficiency is considered a function solely of input torque, scaled as a function of maximum torque, based on a full toroidal design 0. Figure 24 shows the approximation for CVT efficiency as a function of maximum input torque. Figure 24. Normalized CVT Efficiency The angular velocity of the clutch side of the CVT is defined as: (3.13) Where is the angular velocity of the clutch side of the CVT and is the angular velocity of the drivetrain. 57

73 Flywheel Fixed Gear 1 CVT 2 3 Drivetrain N 1 N 2 Figure 25. Scheme of flywheel to drivetrain power chain A feed forward controller is used to prescribe the CVT ratio necessary to command the desired torque at the mechanical power summation node. The feedforward controller for the CVT ratio has been developed in the simplified assumption that the clutch is fully engaged and no slip is observed between the clutch plates. In this hypothesis, the system to consider is sketched in Figure 25. The flywheel (whose angular velocity is indicated by 1 ) is coupled by means of a fixed gear (with gear ratio N 2 ) to the input shaft of the CVT (whose variable gear ratio is indicated by N 2 ). The output shaft of the CVT is connected to the drivetrain, whose angular velocity is indicated by 2. Given a desired Torque at the driveshaft (T des ), the following equation can be written for the power at the driveshaft: 58

74 (3.14) Equation (14) states that the desired power at the driveshaft power summation point is provided solely by the power due to the inertia torque of the flywheel (frictional losses on the flywheel bearings are neglected for simplicity). Given the definition of the gear ratio of the fixed gear and of the CVT, summarized below: (3.15) the following expression for the rate of change of the gear ratio of the CVT can be obtained: (3.16) At this point, knowing the angular velocity of the flywheel 1, the angular velocity of the driveshaft 3, the rate of change of the driveshaft speed and, imposing a desired torque, the rate of change of the CVT is calculated by means of equation 16. In order to be consistent with the notation previously introduced, equation 16 is rewritten in the following way: (3.17) where N CVT is the speed ratio of the CVT, T des is the desired torque to the drivetrain, I fly is the inertia of the flywheel, ω DT is the rotational speed of the drivetrain side of the CVT, 59

75 and N gear is the gear ratio for any additional gearing between the CVT and flywheel. Equation 17 can be integrated to give N CVT as a function of time. It should be noted that the actual torque will be slightly less than desired due to the frictional losses in the flywheel and the efficiency of the additional gearing (neglected for simplicity). The CVT ratio integration is limited to ratios between the minimum and maximum, determined by the specific CVT design considered. In order to account for the actual dynamic response of the actuator performing the CVT ratio variation, the output of the CVT feed forward controller is properly filtered. In detail, it is assumed that the CVT ratio change presents a dynamic response typical of a second order over-damped system. As a secondary effect, the dynamics of the CVT ratio actuator enhances the stability of the numerical solution obtained, enabling the simulation solver to converge even for particularly abrupt requests of CVT ratio change. Table 1. CVT Model Inputs Inputs Speed Ratio (Control) Drivetrain speed (Exogenous) Clutch Torque (Exogenous) Units [Nm] [r/min] [Nm] Table 2. CVT Model Outputs Outputs Drivetrain Torque Clutch Speed Units [Nm] [r/min] 60

76 Table 3. CVT Model Parameters Parameters Units Maximum Ratio [-] Minimum Ratio [-] Maximum Torque [Nm] Mechanical Efficiency [-] Mass [kg] Clutch and Flywheel System The main function of the flywheel is to provide a mechanical means to store braking energy. The clutch is needed for coupling the flywheel and drivetrain when the CVT is at the limit of its speed ratio range, particularly while accelerating the flywheel from rest and disengaging while the flywheel is rotating and the vehicle is at rest. Figure 26 shows the functional block diagram for a clutch and flywheel system: Figure 26. Block Diagram of Clutch and Flywheel Model The speed of the CVT side of the clutch is specified by the CVT model. Output torque depends on multiple variables and parameters inside of the model as described below. Energy Considerations 61

77 The flywheel energy storage capability is based upon its mass moment inertia and its rotational speed. The total kinetic energy that can be stored in the flywheel is calculated according to the following relation: (3.18) where is the mass moment of inertia of the flywheel and is its angular velocity; the higher the moment of inertia of the flywheel and the higher its maximum rotational velocity, the higher the energy storage of the system. However, both the moment of inertia and the maximum rotational velocity directly affect the overall weight of the system. In details, the mass moment of inertia of a mechanical flywheel rotating around a certain axis is calculated according to the following formula: I fly V 2 dr dv (3.19) r r where r is the radius vector of the generic infinitesimal portion of the body with respect to the axis of rotation, ρ( r ) is the mass density at the same point and d( r ) is the actual distance from the axis of rotation. The integration is performed over the volume V of the flywheel. In order to maximize the moment of inertia of the system, high values of the density of the material are required, especially in points of the body far from the axis of rotation, in case the density of the body is not homogeneous. However, this determines an increase of the mass of the system, calculated according to the following relation: m V dv (3.20) r r 62

78 In order to understand the energy storage capability of the flywheel system, it is useful to identify which parameters affect the maximum energy density of the system. This variable can be calculated according to the following formula: e mech max K (3.21) Where e mech-max is the maximum energy density per unit of mass of the flywheel, is the density of the flywheel, K is a factor depending on the geometrical shape of the flywheel (Table 4), and is the maximum stress allowed in the flywheel (Table 5). Table 4. Shape-factor K for different planar stress geometries Table 5. Data for Different flywheel rotor materials 63

79 It is worth observing that the maximum tensile strength of the flywheel is directly linked to its maximum rotating velocity, its geometry and the eventual tensile strength applied at the inner and outer radius. Assuming that no tension is pre-applied at the inner and outer radius of the rotating body, the centrifugal force is the only one acting on it. The centrifugal force depends upon the rotational speed squared. Low speed flywheels (under 20,000 rpm) are typically manufactured from steel [10]. Composite materials and magnetic bearings allow speeds in excess of 40,000 rpm [10]. All the factors mentioned before must be considered when the design of the system is performed, including the determination of the shape and the materials used for the components. Clutch and Flywheel Losses The flywheel and clutch system experiences frictional losses during operation. Sources for loss include flywheel windage, bearing friction, and clutch slip. For the purposes of the model, the flywheel windage and bearing friction are lumped into one term that varies with flywheel speed, while losses due to clutch slip are handled by the equations describing the torque transmitted during slip conditions. Windage Losses Typically, the flywheel is incased in a structure for safety purposes. Especially for high speed flywheels where windage losses are significant, the casing is put under a vacuum. Using a vacuum reduces the windage losses, but does not completely eliminate them. Studies performed by the University of Texas at Austin are used as the basis for windage 64

80 loss calculation [10]. Table 6 and Table 7 summarize frictional the loss test conditions and the power loss results respectively of the low speed flywheel system under vacuum considered in [10]. Table 6. Frictional Loss Test Conditions Test Conditions Bearing Type Size Dynamic Load Rating Axial Preload Maximum Speed L10 Life Calculation Rolling element angular contact ball bearing 17mm bore 11.6 kn 267 N 18,000 rpm 70,700 hrs Table 7. Frictional Loss Test Results Test Results Bearing rpm Windage rpm 122 watts 140 watts 76 watts 95 watts Bearing Friction The bearings which the flywheel rotates on also provide a source of frictional loss. High speed flywheels typically use magnetic bearings with near zero frictional losses, but with a tradeoff of the magnetic bearings consuming electrical power. Low speed flywheels typically use conventional roller ball bearings, which allow operation above 20,000rpm. 65

81 Data on frictional moment for bearings is readily available from manufactures such as SKF. Based on loading, rotational speed, and the type and size of bearings used, online estimates can be used to calculate the frictional moment [11]. The torque loss from the online estimate can be divided by the rotational speed to give a linear approximation for bearing loss as a function of speed. Estimates by the SKF online calculator are slightly lower than those found in [10] using similar conditions. For the purpose of the model, the results of [10] were extrapolated linearly as a function of flywheel speed to give b fly, torque loss per rotational speed. Clutch Slip Losses The power loss during clutch slip is equal to the torque being transmitted multiplied by the speed differential between the two sides of the clutch. (3.22) Where is the torque at the clutch, is the speed difference between the two sides of the clutch. Modes of Operation The clutch and flywheel system can operate in two different operating modes, lockup and slip (or non-lockup). Under lockup condition, both the CVT and flywheel sides of the clutch are rotating at the same speed. As opposite to this operation, under slip condition, the two sides of the clutch are rotating at different speeds, thus dissipating energy by friction. Output torque of the clutch and flywheel system depends on the mode of operation. Lockup Condition 66

82 Under lockup, the CVT side clutch speed (input) is equal to the flywheel speed and the output torque of the system is a function of the rate of change of the flywheel speed: (3.23) Where b fly is the frictional resistance of the flywheel to rotation due to bearings and windage losses. Slip Condition During slip conditions, the CVT side clutch speed is not equal to the flywheel speed. For this mode, output torque is the reaction torque on the clutch plate. The reaction torque for the clutch varies as a function of the control input, clutch pressure, and physical properties of the clutch. Equation 24 describes the clutch reaction torque: (3.24) Where A clutch is the clutch mating area, r clutch is the effective radius of the clutch, n c is the number contacting clutch plate surfaces, P clutch is the clutch pressure, and µ(δω) is the coefficient of friction as a function of the speed differential between the two sides of the clutch (CVT side and flywheel side). The effective radius for the clutch is a function of the inner and outer radii of the contacting clutch surfaces: (3.25) For a wet clutch, the coefficient of friction (µ) varies with speed differential as shown in Figure 27 [12]. The friction can either be ascending or descending depending on 67

83 temperature, type of fluid, and friction material used. For modeling purposes, one type of behavior should be chosen and implemented. Figure 27. Wet Clutch Coefficient of Friction [12] Under slip conditions, the reaction torque of the clutch is also acting on the flywheel, causing it to change speeds, altering the slip speed. The flywheel changes speed as a function of clutch torque according to the Newton Second Law: (3.26) Switching Between Modes of Operation A fully functional model must be capable of changing between lockup and slip modes depending on the operating conditions of the system. Practical conditions for lockup to be 68

84 met are sufficiently small Δω, and enough pressure to transmit the torque without incurring slip. To determine the maximum torque that can be transmitted without slip, a modified version of the clutch slipping torque can be used: (3.27) where is the static coefficient of friction for the clutch plate friction material. If the torque the flywheel is trying to transmit under lockup conditions is greater than the maximum torque calculated in equation 26, the system changes to slip mode until both conditions are again satisfied. Table 8 to Table 10 are a summary of the inputs, outputs, and parameters for the clutch and flywheel system. Table 8. Clutch and Flywheel Model Inputs Inputs Clutch Pressure (Control) Clutch speed (Exogenous) Desired Torque (Exogenous) Units Pa r/min Nm Table 9. Clutch and Flywheel Model Outputs Outputs Units Output Torque Nm Flywheel Speed r/min Clutch Operating Mode - 69

85 Table 10. Clutch and Flywheel Model Parameters Parameters Units Clutch Area [m 2 ] Clutch Effective Radius [m[ # of Clutch Plate Surfaces [-] Slipping Coefficient of Friction [-] Static Coefficient of Friction [-] Flywheel Rotational Friction [Nm/(rad/s)] Maximum Δω for Lockup [rad/s] Mass [kg] Model of hydraulic AESS The architecture considered for the hydraulic hybrid vehicle is based on a parallel configuration where the hydraulic ESS is located between the transmission and the drive axle, as shown in Figure 28. The hydraulic pump/motor couples the ESS to the transmission output shaft, allowing for transferring torque to the drivetrain. 70

86 Fuel Tank Fuel Energy Engine ICE Power Accumulator Transmission Fluid Power Hydraulic Pump Pump Power ICE Power Mechanical Power Summation Fluid Power Braking Power Combined Power Reservoir Drive Axle Power to Wheels Figure 28. Hydraulic Hybrid Powertrain Layout Figure 29 shows a hydraulic scheme of the system. In its simplest form, the system includes a low-pressure reservoir tank (T01), a variable displacement pump/motor (P01), and a high-pressure accumulator (A01, A02). A logic element (LE01) is inserted to enable a two-directional flow. Further, a pressure relief valve (RV01) is introduced to limit the maximum pressure of the system. 71

87 Figure 29: Hydraulic diagram of the ESS 72

88 Hydraulic Pump/Motor The main function of a basic pump/motor is to produce the requested torque by moving fluid from the reservoir to the accumulator (pump mode) or from the accumulator to the reservoir (motor mode). In order to control the torque and flow rate during utilization, a variable displacement pump/motor must be used. A functional block diagram of the pump/motor is shown in Figure 30. The pump/motor model determines the volumetric flow rate to and from the reservoir and accumulator as a function of the speed and displacement of the pump. The pressure signals received from the accumulator and reservoir are used to calculate the torque output. Figure 30. Hydraulic Pump Model In the following mathematical formulation, the notation adopted to indicate the direction of the torque and volumetric flow is as follows: Torque: positive if directed towards the drivetrain (motor), negative if directed from the drivetrain (pump) 73

89 Flow: positive if directed from the reservoir to the accumulator (pump), negative otherwise (motor). Modeling flow and torque outputs of positive displacement pumps and motors is a wellestablished theory. In general, the pump/motor torque is given by the following equation: T * P P D (3.28) pump/ motor acc res m Where D is the pump displacement (cm 3 /rev) and system, defined as: Similar, the volumetric flow rate is given by: * m is the mechanical efficiency of the m, T 0 * 1 (3.29) m, T 0 m Q pump D N (3.30) * m * v * * Where the product contains the volumetric efficiency of the pump: m v 1, T 0 * (3.31) v v v T 0 The above model, however, is defined so that the displacement is an input and the torque is one of the outputs. However, this representation is in contrast with the I/O scheme shown in Figure 30, where a torque command is given as input. Hence, equations (28)- (31) must be further elaborate to impose that, whenever possible, it is: T T pump/ motor command (3.32) Given the above, Equation (28) can be used to determine the displacement required: 74

90 D T command command * Pacc Pres (3.33) m Combining with (30), the volumetric flow rate is given by: Q T * * command * pump Dcommand N m v N v (3.34) Pacc Pres In general, the mechanical and volumetric efficiency of a pump can be obtained from the technical data and information available from manufacturers. In order to define a model for the pump/motor efficiency, a commercial variable displacement axial piston pump was considered [15]. The pump was chosen in order to match the maximum speed of the drivetrain shaft (through a single-stage gear reduction) and the maximum pressure of the accumulator. Figure 31 shows the pump and its main technical characteristics. Model P1/PD Series, 28cc Displacement 28 cm 3 Max. Outlet Pressure Max. Nominal Torque Min/Max Speed 280 bar 250 Nm 600rpm / 3200 rpm Weight 18 kg Figure 31. Axial Piston Pump The flow and efficiency maps are represented in Figure 32. It is important to observe that the maps are generally provided only at maximum displacement and with the device operating in pump mode. Therefore, a simple procedure was established in order to 75

91 extrapolate the efficiency behavior of the pump/motor to cover the entire range of operating conditions. Figure 32: Flow and Overall Efficiency Map of P1 028 Axial Piston Pump First, the volumetric efficiency of the pump was determined from the flow characteristics. For a piston pump, the characteristic curves can be reasonably approximated by the following model: Q pump D N k P (3.35) Where k leak represents a loss coefficient due to leakage phenomena (modeled by using the Hagen-Poiseuille formula for viscous flow losses). By applying the above model to the flow map of Figure 32, the loss coefficient is determined for each pump speed value. Figure 33 shows the results of the model identification. leak 76

92 Pressure [bar] Data Model Ideal Characteristic Flow Rate [l/min] Figure 33: Identification of Pump Flow Model Although in general k leak f N, the leakage coefficient has been assumed constant (specifically, averaged over the speed range available) as a first approximation. Based on the available data, such reduction leads to a mean squared error less than 15%. The volumetric efficiency of a pump is defined as: Qpump v (3.36) Q id Where Q id D N. Combining (35) and (36) results into: k leak P v 1 (3.37) D N Which allows one to build the volumetric efficiency map of the pump at maximum displacement conditions (Figure 34, left). In order to extrapolate the behavior to reduced displacement values, it is assumed (as commonly done in industrial practice) that the leakage losses are independent from the pump displacement. This results in the volumetric efficiency map shown in Figure 34 (right), which can be implemented in a pump model as a 2D look-up table as function of the pressure and speed. 77

93 v [%] Pressure [bar] v [%] Pressure [bar] Speed [rpm] Figure 34: Pump Volumetric Efficiency Model at Max. Displacement (Left) and at Variable Displacement (Right) The mechanical efficiency of the pump was calculated from the overall efficiency map (Figure 32) and the volumetric efficiency model: m (3.38) The resulting curve is generally a function of the pressure, pump speed and displacement. However, the dependence on speed and displacement was neglected for simplicity. A simple (exponential) correlation was therefore introduced to approximate the mechanical efficiency of the pump as a function of the sole pressure input. Figure 35 shows the results of the model identification. v 78

94 m [%] Pressure [bar] Figure 35: Pump Mechanical Efficiency Model Finally, it is worth observing that a slight penalty in efficiency is generally present when the pump is used as a motor, although this term is typically not explicitly accounted for in the OEM efficiency maps. In the model, an additional efficiency of 97% has been introduced to penalize the operations of the system in motor mode. In order to complete the pump/motor model, simple control logic was introduced in order to adapt the pump displacement in relation with the torque demand. This allows one to respect the standard I/O representation for energy-based modeling of powertrain components, where the energy converter outputs a torque based on a speed input and a torque command from the supervisory controller. The displacement control logic is based on a simple feed-forward scheme. The requested torque to the pump/motor is generally supplied as long as the displacement necessary to provide the torque is within the range of the variable displacement pump. The desired displacement is determined based on the instantaneous accumulator and reservoir pressures, as shown in Equation (33). The resulting displacement command is saturated when hardware limitations occur, i.e., based on the following conditions: 79

95 the maximum/minimum displacement available is reached the reservoir or the accumulator are empty Figure 36 shows a simple block diagram of the displacement control logic. Figure 36. Block Diagram of the Displacement Controller Logic Table 11 through Table 13 summarize the model inputs/outputs and parameters. Table 11. Pump/Motor Model Inputs Inputs Torque Command (Control) Pump Speed (Exogenous) Accumulator Pressure (Exogenous) Reservoir Pressure (Exogenous) Units Nm r/min bar bar Table 12. Pump/Motor Model Outputs Outputs Torque Volumetric Flow Rate Units Nm l/min Table 13. Pump/Motor Model Parameters Parameters Units Maximum Displacement cm 3 /rev Mass kg Volumetric Efficiency - Mechanical Efficiency - 80

96 Accumulator The accumulator is used to store the fluid in the high-pressure portion of the system. The hydraulic accumulator is a pressure vessel containing the charge gas which is separated from the hydraulic fluid by a piston, bladder, or diaphragm. For industrial or motive applications, bladder type hydro-pneumatic accumulators are typically used. As fluid flows in and out of the accumulator, the gas acts as a spring, storing and delivering energy to the system as required. Gaseous nitrogen is widely used as the charge gas in hydraulic accumulators because of its availability, low-cost, consistency of composition and freedom from oxidation and contamination [17]. Information on the capacity and pressure characteristics of hydraulic accumulators can be easily found from various OEMs [18],[19]. A bladder accumulator consists of a welded or forged pressure vessel (carbon steel or stainless steel shell), and ports for gas and fluid inlet. The gas and fluid sides are separated by a bladder. The capacity of the accumulators and the operating pressure range, are typically standardized, and reported in the table below. 81

97 Max. Pressure: 3000psi (200bar) Size (gallon/liter) Diameter (mm) Max. Flow (gpm) Mass (kg) 0.25 / / / / / / / Max. Pressure: 5000psi (345bar) Size (gallon/liter) Diameter (mm) Max. Flow (gpm) Mass (kg) 0.25 / / / / / / Figure 37. Bladder-Type Accumulator [19] When the accumulator is empty (uncharged), all the hydraulic fluid is contained in the reservoir chamber and the accumulator pressure is equal to the pre-charge pressure of the gas. The OEMs specify a general maximum ratio of the system maximum pressure to the pre-charge pressure, which is generally 4:1. This allows one to determine the pre-charge pressure and the correspondent mass of nitrogen gas contained in the accumulator. The accumulator model predicts the system pressure in relation with the rate of volume variation due to the fluid flows. Changes in system pressure allow fluid to enter or exit the accumulator body. Figure 38 shows a block diagram of the accumulator model. 82

98 Figure 38. Block Diagram of the Accumulator Model During compression of the charge gas, a certain amount of energy is lost to the surrounding environment through irreversible heat transfer, which is identical in value to the net heat transported to the accumulator wall. For modeling purposes, the gas is considered as a closed system exchanging work with the hydraulic fluid and the accumulator wall. Applying the continuity equation to the hydraulic fluid side and assuming incompressible conditions, the volume occupied by the fluid is given by: dvl dt Q Q (3.39) pump prv If V is the accumulator volume, the volume occupied by the gas is V g V V. This l allows one to apply the energy balance to the gas system, as follows [20]-[22]: m g du dt dv p haw T Tw (3.40) dt where h is a convection heat transfer coefficient (calibration parameter) and A w represents the surface area of the walls (which depends on the volume of the accumulator occupied by the gas). 83

99 In order to account for the compressibility effects, a real gas model must be used. In this case, the internal energy per unit of mass u is given by: p du cvdt T p dv dt (3.41) v Where v is the specific volume (per unit mass) of the gas charge. For a real gas (N 2 ), the Beattie-Bridgeman equation of state can be used to relate the p-v- T characteristics [23]: p RT v 1 2 A v B 2 v (3.42) Where: A A 0 B B 0 c / vt 1 a / v 1 b / v 3 (3.43) All parameters in this formula are empirical constants specific for nitrogen gas and are given below [23]: A a 9.342e B e 4 3 b 2.467e m / kg 3 c m / kg K R m m 3 3 m 3 m / kg Pa / K / kg Pa / kg 3 / kg 3 (3.44) By differentiating Eq. (42) with respect to T and combining with Eq. (41), the following equation can be obtained: 84

100 dt dt 1 m c g v ha T p g T T w dt v dv dt (3.45) Equation (45) is the energy equation for the nitrogen gas, which is numerically integrated with known volumetric flow rate to give the temperature time history at each time step. This temperature is then substituted into Eq. (42) to give the accumulator pressure history for a process cycle. Note that the gas pressure and liquid pressure inside the accumulator must be equal to each other. Since the accumulator model is characterized by two states (volume and temperature), two initial conditions must be given. In this case, it is assumed that the accumulator is initially empty (hence, t V V g 0 ), and that the initial temperature is equal to 25 o C. Table 14 to Table 16 summarize the model inputs/outputs and parameters. Table 14. Accumulator Model Inputs Inputs Pump/Motor Volumetric Flow Rate PRV Volumetric Flow Rate Initial Volume Occupied by Gas (I.C.) Initial Gas Temperature (I.C.) Units l/min l/min l 0 C Table 15. Accumulator Model Outputs Outputs Units Fluid Volume l Accumulator Level % Gas Temperature 0 C Accumulator Pressure bar 85

101 Table 16. Accumulator Model Parameters Parameters Units Accumulator Volume l Accumulator Diameter mm Accumulator Mass kg Pre-Charge Pressure bar Heat Transfer Coefficient W/m 2 K Specific Gas Constant J/kg-K Real Gas Model Parameters See Eq. (17) Pressure Relief Valve (Flow Restriction) A pressure relief hydraulic valve (PRV) must be incorporated into the system in order to limit the maximum pressure of the accumulator. The PRV is a solenoid-operated poppet valve, which controls the stem position in order to maintain the pressure of the system within range. This valve is modeled as a simple, steady-state flow restriction that connects the accumulator to the low-pressure tank. A block diagram of the valve model is found below in Figure 39. Figure 39. Poppet Valve Model 86

102 Discharge Coefficient [-] The liquid flow through the PRV is modeled through the correlation for friction losses in turbulent incompressible flow conditions: Q prv 2 pacc ptan k Cd (3.46) Where is the reference area of the valve and C d the discharge coefficient, which is a function of the stem position. The two parameters must be identified from experimental data or information from the OEM. Generally, the reference area is a constant term that corresponds to the maximum opening area of the valve. The functional relation between the discharge coefficient and the valve position can be determined from the datasheets provided by product catalogues (which generally report the pressure losses vs. flow characteristics of the valve). Figure 40 shows the discharge coefficient curve considered for the valve model, as a function of normalized valve position Normalized Position [-] Figure 40: Discharge Coefficient Curve for the Pressure Relief Valve The position of the PRV is operated by a simple flow controller, which activates the valve when the pressure of the accumulator exceeds an upper threshold value (P max ). 87

103 When the PRV position control is activated, a combination of a PI regulator and a feedforward compensator control the position of the valve in order to reach and maintain a desired pressure of the accumulator. The controller is then deactivated when the pressure reaches a lower threshold value (P min ). Figure 41 shows a simple block diagram of the controller logic. Figure 41. Block Diagram of the PRV Controller Logic The parameters of the controller have been calibrated in order to quickly reduce the accumulator pressure once the upper threshold is reached, while minimizing the chattering effects caused by the switching logic. Table 17 to Table 19 list the inputs, outputs and parameters of the PRV model. Table 17. PRV Model Inputs Inputs Accumulator Pressure Reservoir Pressure Units bar bar Table 18. PRV Model Outputs Outputs Units PRV Flow Rate l/min PRV Position - 88

104 Table 19. PRV Model Parameters Parameters Units Valve Reference Area m 2 Discharge Coefficient Curve - Hydraulic fluid density kg/m 3 Upper Pressure Threshold bar Lower Pressure Threshold bar Position Controller Parameters N/A Reservoir (Tank) The hydraulic tank stores the fluid in the low-pressure portion of the system, and is used as the supply for the pump. The tank is typically realized in polymer or steel, and its characteristics can be found on datasheets of fluid power components manufacturers 0. Similar to the accumulator, the reservoir is a pressurized vessel where a gas chamber is separated from the liquid by a bladder. The capacity of the reservoir and its pressure range are typically available from the datasheets. Since the reservoir operates at low pressure conditions, the mass of the component is typically in the range of 5-10kg, depending on the material. In general, the manufacturers recommend sizing the capacity of the reservoir based on the maximum capacity of the pump (one liter capacity per one liter per minute flow). The model of the reservoir can be seen as a simplified version of the accumulator model. Figure 42 shows a block diagram representation of the system. 89

105 Figure 42. Block Diagram of the Accumulator Model Applying the continuity equation to the hydraulic fluid side and assuming incompressible conditions, the volume occupied by the fluid is given by: V l t t V Q Q pump prv dt (3.47) 0 0 In this case, it is important to specify the initial condition V 0, which represents the volume initially occupied by the hydraulic fluid. Similar to the accumulator, the volume occupied by the gas is V g V V, where V is the tank volume. l Due to the limited pressure range of the reservoir, a simplified modeling approach can be here adopted, by assuming a simple, steady-state isentropic transformation to characterize the filling and emptying process of the tank. By applying the isentropic model to the gas chamber, it is possible to determine the pressure of the tank: γ t V t p p g 0V g, 0 (3.48) Where V 0 and p 0 are the volume occupied by the gas and its pressure at the initial condition, and is the specific heats ratio (which, for pure nitrogen, is 1.39). Since V V g V l, the above expression can be further elaborated as follows: 90

106 p t V V t p V V p V (3.49) l 0 0 precharge Where p precharge is the pre-charge pressure of the reservoir (parameter). This allows for obtaining the final expression for the tank pressure: p t V p precharge (3.50) V V Table 20 to Table 22 summarize the model inputs/outputs and parameters. l t Table 20. Reservoir Model Inputs Inputs Pump/Motor Volumetric Flow Rate PRV Volumetric Flow Rate Initial Volume Occupied by Gas (I.C.) Units l/min l/min l Table 21. Reservoir Model Outputs Outputs Units Fluid Volume l Reservoir Level % Reservoir Pressure bar Table 22. Reservoir Model Parameters Parameters Units Reservoir Volume l Reservoir Mass kg Pre-Charge Pressure bar Specific Heats Ratio - Initial Volume of Hydraulic Fluid l 91

107 3.4 Conclusion The development of dynamic models of the AESS components for both the mechanical and hydraulic systems allows for integration into the powertrain model of the conventional vehicle to produce a hybrid driveline. With modular components, multiple configurations can be easily created with standard interfaces between the models. The scalability of the above models allows for the design space to be explored easily by simply changing the component parameters. Appropriately combining the mechanical and hydraulic models respectively allows for prediction and analysis of the system s behavior over varying conditions during drive cycles. Also, the interactions between the components due to design changes can be studied. For example, changing the gearing between the CVT and flywheel will impact the efficiency of both the clutch and the CVT. By modeling the components and linking their behavior, these types of analysis can be performed with the end goal of evaluating and optimizing design of the system parameters. In lights of the development of a design procedure of short-term energy storage systems, the models provide a crucial tool to evaluate the relative performance of designs when the design parameters within the models are altered. The models developed in this chapter will be used to evaluate designs which are based on statistical processing of drive cycles. 92

108 3.5 References [1] Bayar, K., Bezaire, B., Cooley, B., Kruckenberg, J., Schacht, E., Midlam-Mohler, S., and Rizzoni, G. Design of an Extended-Range Electric Vehicle for the EcoCAR Challenge, Proc. of the ASME 2010 IDETC/CIE Conference, 2010 [2] Koprubasi, K. Modeling and Control of Hybrid-Electric Vehicle for Drivability and Fuel Economy Improvements, Ph.D. dissertation, The Ohio State University, [3] Serrao, L. A Comparative Analysis of Energy Management Strategies for Hybrid Electric Vehicles, Ph.D. dissertation, The Ohio State University, [4] The Ohio State University 2006 Challenge X Team, Final design and vehicle technical specifications, challenge x 2006 fall technical report, The Ohio State University, Tech. Rep., [5] Arnett, M., Bayar, K., Coburn, C., Guezennec, Y., Koprubasi, K., Midlam- Mohler, S., Sevel, K., Shakiba-Herfeh, M., and Rizzoni, G. Cleaner diesel using model-based design and advanced aftertreatment in a student competition vehicle, in SAE World Congress. Detroit, MI, USA: SAE, [6] Rizzoni, G., and Srinivasan, K. Powertrain Dynamics, Lecture notes, The Ohio State University. [7] Kotwicki, A. Dynamic models for torque converter equipped vehicles, SAE Technical Papers, no , [8] Body, W., and Brockbank, C. Simulation of the fuel consumption benefits of various transmission arrangements and control strategies within a flywheel based mechanical hybrid system. Torotrak (Development) Ltd. [9] Samie, F., and Gecim, B. Comparison of Efficiency Measurements and Simulation Results for Automotive Traction Drives. SAE Paper [10] Hearn, C. and Flynn, M.. Low Cost Flywheel Energy Storage for a Fuel Cell Powered Transit Bus. Vehicle Power and Propulsion Conference, Sept 9-12, VPPC IEEE [11] SKF Product Website. ->Products ->Calculations -> Frictional moment - power loss. 93

109 [12] Yang, Y., Lam, R., and Fujii, T. Prediction of Torque Response During the Engagement of Wet Friction Clutch. SAE Paper [13] Bolund, B., Bernhoff, H., and Leijon, M. Flywheel Energy and Power Storage Systems. Renewable and Sustainable Energy Reviews, 11 (2007) [14] Toulson, E. Evaluation of a Hybrid Hydraulic Launch Assist System for use in Small Road Vehicles, Proc. of IEEE Symposium on Industrial Electronics, [15] Wu, B., Lin, C., Filipi, Z., Peng, H., and Assanis, D. Optimal Power Management for a Hydraulic Hybrid Delivery Truck, Vehicle System Dynamics 2004, Vol. 42, Nos. 1-2, pp [16] Parker Hannifin, Service Information Bulletin P1/PD Series 18cc, 28cc, 45cc Medium Duty Axial Piston Pumps - Variable Displacement. [17] Sun, Z., and Miao, H. Hydraulic Assist Power System, Proc. of ASME IMECE, [18] HYDAC US, Bladder Accumulators Catalog, 2010; [19] Bosch Rexroth Group US, Bladder-type Accumulators, 2010 [20] Otis, D. Predicting Performance of Gas Charged Accumulators, Fluid Power Controls and System Conference, University of Wisconsin-Madison, [21] Green, W. Accumulator Time Constants and The Index Method: Some Comparisons Based On Experimental Power, 35 th National Conference on Fluid Power, [22] Pourmovahed, A., Beachley, N., and Fronczak, J. Modeling of a Hydraulic Energy Regeneration System Part I: Analytical Treatment, Journal of Dynamic Systems, Measurement and Control, Vol. 114, [23] Sonntag, R., Borgnakke, C., and Van, G. Wylen, Fundamentals of Thermodynamics, 5 th Edition, John Wiley & Sons Inc., New York, [24] Bosch Rexroth Group US, Hydraulic Tank Data Sheet,

110 Chapter 4: Proposed Method for Design of Short-Term AESS 4.1 Introduction The following chapter proposes a methodology to conduct preliminary design and sizing of the main components of mechanical and hydraulic energy storage systems. The goal of this method is to begin with basic drive cycle information and based on the constraints and attributes of the system create a preliminary set of design parameters. Afterward, the design can be optimized until a set of parameters which best match the desired performance in terms of effectiveness, cost, weight, and volume is reached. Current methods for design of energy storage systems focus on long-term energy storage batteries and the advantages and limitations imposed by systems with batteries. In cases where short-term energy storage is desired in order to take advantage of the benefits of mechanical or hydraulic energy storage, a method for designing such an energy storage system is needed. Figure 43 shows the flowchart for the proposed method laid out in this chapter. The design procedure begins with selecting a relevant drive cycle. This cycle should be representative of the typical user s behavior. Regulatory cycles are also useful if the desire is to optimize the benefit over regulatory testing. Beginning with vehicle velocity profile and its accompanying grade profile along with basic vehicle parameters, relevant cycle statistics can be generated. These braking event statistics tell the designer under 95

111 what conditions braking energy is available for recovery. Weighting methods can then be applied to these statistics in order to arrive at initial AESS design targets. Multiple weighting methods can be used for comparison purposes. Once design targets are known, it is possible to decide on preliminary design parameters using component constraints and engineering fundamentals. Using correlations based on specifications of currently manufactured AESS components, estimates of mass, volume, and cost can be produced and applied to the estimated vehicle parameters. Knowing both the AESS design parameters and the new estimated vehicle parameters, simulations can be performed which predict the performance of the design over a given cycle or cycles. The simulations reveal the actual performance of the individual design over a given drive cycle. Finally, a cost function is used to weight the performance in simulation and system attributes such as mass, volume, and cost in order to revise the design parameters until a design which minimizes the cost function is achieved. The weights which are applied in the cost function depend on the relative importance of the design attributes including the performance. A section of this chapter will be devoted to each step in the design process. The end result is a design procedure which is tailored to short-term energy storage systems. Applying the procedure results in a design which emphasizes capturing and releasing as much of the available braking energy as possible while maintaining low mass, volume, and cost. 96

112 Cycle Profile Vehicle Parameters Drive Cycle Analysis Cycle Statistics Weighting Method Statistical Weighting Process Design Targets Design Constraints Preliminary Design Procedure AESS Design Parameters Design Parameter Optimization Cost Function Feedback Adjusted Design Parameters Drive Cycle Vehicle Simulation Adjusted Vehicle Parameters Parameter to Attribute Correlations Composite Efficiency System Attributes (mass, vol, cost) Weighting Factors Cost Function f(mass, Volume, $, Efficiency) Figure 43. Proposed AESS Design Flowchart 97

113 4.2 Drive Cycle Analysis The foundation of design begins with knowing the purpose or use of the object to be designed. In this case, the starting point for AESS design needs to be the speeds and conditions that will characterize the typical operation of the vehicle. A common method for describing a vehicle s operating conditions is a velocity versus time profile also known as a drive cycle. These profiles are used both for government regulation as well as manufacturer internal evaluation and product testing. They can be generated in a number of ways including being based on real-world driving data and can range from being entirely urban type driving with frequent stops to high speed highway driving for long distances at constant speed. Typical passenger cars must be designed and optimized to operate efficiently over a wide range of potential drive cycles; however, typically emphasis is placed on regulatory cycles which can provide a proxy for performance over a range of cycles. Starting with the velocity versus time profile for a driving cycle, a variety of design relevant statistics can be derived. Figure 44 shows the velocity profile for the US FTP-75 test cycle. This particular cycle is used for regulatory purposes and is therefore an important cycle for design considerations. 98

114 Figure 44. US FTP-75 Test Cycle Velocity Profile [1] Accompanying the velocity profile can be a grade profile, which represents the elevation change of the vehicle over the cycle. Based on the grade of the cycle, the loading seen by the vehicle may vary significantly. The majority of regulatory cycles assume level grade, however, it represents a significant influence on vehicle behavior. Fundamentally, two types of statistics can be derived from the velocity and grade profiles. The first type is information about the drive cycle that is vehicle independent. Statistics such as maximum, minimum, and mean velocity, acceleration statistics, number of stops, time spent at rest, and other information that is solely a function of the velocity, grade, and direct functions of those are independent of the vehicle s parameters (mass, physical dimensions, etc). The other type of statistics is based on vehicle parameters and allow for statistics based on energy and power to be derived. Knowing the drive cycle along with the vehicle s physical parameters allows for information such as instantaneous power to be calculated and used in generation of statistics. These vehicle specific 99

115 statistics provide more detailed information for design purposes than velocity and grade only. Table 23 lists a sampling of the statistics available for each type. Table 23. Sample of Possible Drive Cycle Statistics Information Used Statistics Available Velocity and Grade Only - Velocity (mean, min, max, etc) - Grade (mean, min, max, etc) - Acceleration (mean, min, max, etc) - Deceleration (mean, min, max, etc) - # and duration of stops Velocity and Grade + Vehicle Parameters - Traction power (mean, min, max) - Braking power (mean, min, max) - Traction energy necessary - Braking energy available - Road load loss estimation Velocity based statistics are easily generated by either analyzing the velocity itself or taking the derivative of the velocity to generate the acceleration profile. Table 24 shows basic statistics from three regulatory driving cycles. Table 24. Sample Velocity Based Statistics for Regulatory Cycles US06 FTP Highway FTP Urban Mean Velocity [mph] Mean Acceleration [m/s 2 ] Mean Deceleration [m/s 2 ] Max Speed [mph] Max Acceleration [m/s 2 ] Max Deceleration [m/s 2 ] # of Stops Cycle time [s] Cycle Length [mi] # of Stops/mi

116 While the statistics in Table 24 are relevant to vehicle design, they become immensely more relevant when paired with vehicle parameters. For example, desired maximum deceleration sheds light on the deceleration a regenerative braking system must be capable of providing in order to capture all available energy, however, the actual power or torque necessary to achieve this level of deceleration is a function of the vehicle s parameters such as mass and road loads. For the purposes of AESS design, the velocity based statistics must be coupled with vehicle parameters and longitudinal vehicle dynamics to arrive at statistics which are immediately applicable to design, such as energy, power, and torque Generation of Vehicle Based Drive Cycle Statistics In order to arrive at corresponding statistics of energy, power, and torque for a given drive cycle, the longitudinal dynamics of the vehicle must be considered. These dynamics include the road loads such as aerodynamics resistance, rolling resistance, grade effects, and inertial forces. While multiple methods of describing these road loads are possible, the same models proposed in the Vehicle Dynamics section of Chapter 3 can be solved in reverse to arrive at the necessary traction or braking force for a given vehicle velocity and acceleration or deceleration. These methods are discussed at length in [1] and are considered sufficient for the purposes of this analysis. For the analysis presented below, the following assumptions where used: Air density was assumed constant 101

117 Rolling resistance was calculated assuming the same tire at all locations on the vehicle and on a level road The grade was assumed to be level Vehicle inertial loads were considered to be the vehicle mass + 10% to account for the effect of rotating drivetrain components Additionally, the following vehicle parameters were used: Table 25. Sample Vehicle Parameters Mid-sized SUV Data Vehicle mass [kg] 1680 Frontal area [m 2 ] 2.64 Drag coefficient 0.42 Using the vehicle dynamics described in Chapter 3 along with the sample vehicle parameters and FTP-75 drive cycle, the power profile in Figure 45 can be created. 102

118 Figure 45. Velocity and Power Profiles for Mid-sized SUV over FTP-75 Cycle [2] From power, torque can be easily calculated with the knowledge of the rolling wheel radius of the drive wheels. Energy, on the other hand, must be based on the integral of the power over time. With the power known, the time over which the power is integrated must be systematically determined. To assist in this, the power can be broken down into three distinct phases. P > 0 is traction power where the vehicle powertrain must provide propulsion P < 0 is braking power where the some method of providing a torque opposite the direction of drivetrain rotation must be provided P = 0 is where the vehicle is either: o At rest (velocity is zero) o Coasting and the road loads are exactly matching the traction force 103

119 Defining energy as the integral of power between two time points (t 0 and t 1 ), (4.1) In discrete time, the integral becomes the summation of the power multiplied by the time step over successive time steps between the end points (4.2) Where is defined as (4.3) The amount of braking energy is therefore, the integral when the calculated power is negative. This calculation has the potential to give insight into the amount of braking energy that is available for recovery through regenerative braking but heavily depends on the time points chosen for the integration. In order to distinguish between traction and braking, the sign of the power term should be consistent over the time span. Keeping the sign of the power constant between t 0 and t 1 leads to the creation of discrete events over which the power is either positive or negative. If the power term is then integrated over those bounds, the energy (positive or negative) for that specific event is known. Negative energy events correspond to braking energy available for recovery while positive energy events correspond to the energy that must be supplied by the powertrain. In terms of regenerative braking, the negative events have tremendous implications for the energy storage capacity needed. Figure 46 shows a section of the FTP-75 cycle power profile 104

120 and the points where the sign of the power switches from either positive to negative (green point) or negative to positive (red point). Figure 46. Sample Power Sign Changes on FTP-75 Cycle [2] 105

121 For short term energy storage systems with relatively small absolute energy storage capability, the goal is not to store energy over extended periods of time, but rather recover the available energy as quickly and effectively as possible and release it during the following acceleration and before the next storage opportunity occurs. If the energy is not released soon enough, the available energy in the following braking event may not be able to be captured. Hence, rather than creating a single statistic for the cycle as a whole, a more informative approach is to look at the cycle power event by power event to better assess the desired traits of a short-term AESS [13]. By analyzing a cycle on a per power event basis, statistics for power and energy can be generated for each individual event. Combining the statistics from each individual event over the entire cycle allows for the events themselves to be characterized in respect to the other events in the cycle in order to form a distribution of the statistic on a per event basis. For example, inspecting the distribution of braking energy per event is useful for designing the energy storage capacity of a system. If the maximum braking energy available in an event over the entire cycle is much greater than the average braking energy per event, it might be desirable to design closer to the mean energy available in order to reduce system weight and cost. However, if the distribution is grouped near the maximum value, then designing to the maximum value may be well justified. Figure 47 shows an example of the normalized frequency for braking energy available per event on the FTP-75 cycle with the x-axis normalized by the maximum value. The distribution for the FTP-75 cycle shows the energy is spread out among events with 106

122 varying amounts of energy. However, with the controlled nature of the regulatory cycles, the normalization value for the maximum braking energy per event is relatively low. Figure 47. Distribution of Braking Event Energy, FTP-75 Drive Cycle Similar normalized distributions can be generated for all of the relevant power and energy statistics. Of particular interest, excluding the aforementioned braking energy per event, are metrics such as average and peak braking power, vehicle speed during braking, and deceleration rate during braking. These distributions will become the basis for creating design targets. However, a systematic method for choosing the appropriate 107

123 location within the distribution is still needed. The following subsection will address this need. 4.3 Statistical Weighting Process Once the distributions of the relevant energy and power metrics are known, the task becomes extracting the proper AESS design targets from the statistical information. The ideal targets will provide the design which minimizes the end cost function, however, without complete exploration of the design space these ideal targets cannot be known. Instead, several statistically based methods are proposed, which can be compared in parallel in order to provide the starting point for refined optimization based on the cost function. The weighting methods proposed are: Maximum Values Mean Values Weighted Mean Values Mean Values Weighted with Maximum Power Distribution Maximum values are arrived at by examining all of the events and selecting the maximum values of the statistics. These are the normalization values used for the distribution profiles. This method is favored when a large percentage of the events are characterized with values near the maximum. This method also ensures that the storage system is potentially capable of recovering all of the available braking energy. 108

124 Mean values are arrived at by finding the average of a statistic such as braking energy over all of the events. The equation describing this calculation for a given statistic, is (4.4) Weighted mean values are arrived at by weighting the statistics by their frequency of occurrence. This shifts the mean value towards the most common values, effectively compensating for a trend in the distribution profile. The following equation describes the calculation of weighted mean values: (4.5) If the distribution of a particular statistic is thought to be more important than the others, the other statistics can be weighted by the same distribution. In such a case, the subscript of the weighting variable is changed (from i to j): (4.6) One such weighting which might be of interest is the maximum power distribution. Weighting all of the relevant statistics by the maximum braking power distribution could potentially skew the targets to allow for more energy to be captured without going to the extreme of maximum values targets. For AESS designs, this may allow for the energy and power statistics to be paired. The benefit is that the energy storage is increased to capture the energy in high power events. Otherwise, the energy storage capacity may be undersized for the higher power braking events. 109

125 As a sample of this process, the following design targets were generated for the FTP-75 cycle braking events of a mid-sized SUV using the methods listed above. Table 26. Relevant Braking Statistics for Mid-Sized SUV on FTP-75 Cycle Maximum Values Mean Values Weighted Mean Weighted Mean with Max Power Dist. Energy [kj] Maximum Power [kw] Mean Power [kw] Maximum Deceleration [m/s 2 ] Mean Deceleration [m/s 2 ] Maximum Velocity [m/s] Mean Velocity [m/s] The statistics in Table 26 can be used as design targets for generating preliminary design AESS design parameters. The next section will cover the process of turning design targets into component sizes which are capable of achieving those targets. 4.4 Definition of Target System Behavior The purpose of the alternative energy storage system (AESS) is to replace as much of the engine s output as possible with energy that was recovered through regenerative braking. From this perspective, an efficiency for the AESS can be defined as the total energy 110

126 transferred to the vehicle from the AESS divided by the total energy available for recovery. Equation 4.7 describes this efficiency of energy return: (4.7) Both the numerator and denominator of 4.7 can be broken down further. The energy available for recovery is the braking energy plus any energy that is absorbed by the AESS. (4.8) It is important to note, that for a given vehicle, its properties, and drive cycle the energy available for recovery is constant. The split between braking energy and absorbed energy may differ, but the sum is constant since the vehicle must follow the prescribed path. The returned energy can be described as the energy which is sent from the AESS to the vehicle. Any difference between the initial and final energy stored by the AESS must be accounted for by adding the difference of the final energy minus the initial energy. (4.9) Where is the energy sent to the vehicle from the AESS, is the energy stored by the AESS at the end of the cycle, and is the energy stored by the AESS at the beginning of the cycle. In order to increase the efficiency of energy return, the only option is to increase. The energy sent to the vehicle from the AESS is a function of the energy absorbed by the AESS and the average efficiency in storing and releasing. 111

127 (4.10) Where is the efficiency from moving energy from the vehicle to the AESS, is the efficiency from moving energy from the AESS to the vehicle, and is the energy absorbed by the AESS from the vehicle. represents the time averaged value for the efficiency. Three methods exist for improving : the quantity of energy absorbed, the storage efficiency can be improved, or the releasing efficiency can be improved. Both the storing and releasing efficiencies are a function of not only the design parameters, but also the state variables in the system at the time such as speed. The energy into the AESS multiplied by the average storage efficiency can be described as the stored energy. Looking at the stored energy on an event by event basis, rather than over the entire cycle, the stored energy is the integral of the braking power over the duration of the braking event. (4.11) Where is the power absorbed by the AESS, is the ending time of the event, and is the beginning time for the event. is subject to the constraints of the system and cycle. It cannot be larger in magnitude than the braking power required by the vehicle; otherwise the vehicle will deviate from the intended profile. The system constraints such as maximum torques must be upheld as well. Also influencing the energy stored by the AESS in one event is the maximum energy storage capacity of the AESS system. The energy stored in one braking 112

128 event cannot exceed the maximum energy storage capacity. In terms of controlling the design, the design parameters affect both the maximum energy storage capacity as well as the maximum power level of the AESS. In fact, it is possible to estimate the quantity of energy which the AESS will be able to store over an entire cycle based on the vehicle s parameters. In order to estimate the energy available for recovery by the AESS, the methods of cycle analysis discussed earlier in this chapter must be first used to generate a profile of the total traction and braking power. This is shown in Figure 48 for the FTP-75 cycle and the aforementioned mid-sized SUV. Figure 48. Net Traction and Braking Power FTP-75 Cycle From the power profile, the positive and negative events can be divided and the negative events can be used to better understand the regenerative braking opportunities within the cycle. 113

129 Figure 49. Energy per Braking Event FTP-75 The braking events can also be characterized by their maximum power. 114

130 Figure 50. Maximum Braking Power per Event FTP-75 One analysis that can be performed is to group the events by their individual energy. This information can be normalized and compiled to form Figure 51. The y-axis represents the percent of the cycle s total recoverable braking energy that is characterized by a certain range of energy storage capacity. For example, over 25% of the cycle s energy available for recover comes from events that are 60-70% of the maximum energy event (212kJ). 115

131 Figure 51. Energy Distribution for Energy Storage Capacity FTP-75 The same procedure can also be performed for maximum power per event. Figure 52 shows the distribution of braking energy in the various power ranges. 116

132 Figure 52. Energy Distribution for Maximum Braking Power It is seen that for the FTP-75 cycle, the events which compose over 30% of the available braking energy have a maximum power value between 90% and 100% of the absolute maximum braking power. Note, this does not indicate that a maximum braking power is needed to recover that energy; only the maximum power is needed if all of the braking energy is to be potentially recovered. For example, a design with a maximum power of 70% of the normalization value may still be able to recover the vast majority of the energy in events where the maximum power is higher than 70%. 117

133 Figure 53. Event Maximum Power compared to Event Energy FTP-75 The correlation between maximum power per event and event energy can be looked at to determine the relationship. A relatively wide spread is seen in this cycle, higher power events may be high or low energy. The reverse is also true, but a general trend is seen between the maximum power and braking energy of an event. Lastly, constraints may be placed on the power integration calculation such as limitations on maximum energy stored, maximum power, and maximum speed to arrive at estimates for the total quantity of energy which could be stored by the AESS over the entire cycle. Once this is done, the design targets based on the four preliminary designs can be shown on the figure to give insight into the design s potential for storing energy. The first example shown is the constraint on maximum energy storage. The figure is created by assuming the AESS can store energy in each event up to its maximum value 118

134 with no restrictions on power or speed. Any amount of energy over the maximum is discarded and not considered stored. Figure 54. Effect of Energy Storage Capacity on Total Energy Storage Diminishing returns be seen due to the change in slope of the graph from low energy storage capacity to high. At the higher levels of energy storage, one additional unit of energy storage no longer returns as much total energy storage. Notice the weighted mean with maximum power distribution s slightly higher design target. This could potentially allow for higher efficiency of energy return. Next, a constraint is placed on maximum power. The energy storage capacity is assumed to be sufficient and no limitations were placed on speed. The result is Figure

135 Figure 55. Effect of Maximum Power on Total Energy Storage The maximum power design target shows even more diminishing returns. In this case, increasing the maximum power does continue to increase the theoretically recovered energy. The mean, weighted mean, and weighted mean with maximum power distribution design targets are grouped closely together. This location provides the majority of the braking energy with only ~45% of the maximum power. Lastly, the constraints on power and energy can be lifted and speed used as the limiting factor instead. With the integration of power constrained to only when the vehicle is below the target maximum speed, the following figure is produced. 120

136 Figure 56. Effect on Maximum Speed on Total Energy Storage In this case, the design target for the weighted mean with maximum power distribution is slightly lower than the mean and weighted mean. The majority of the braking energy appears to be in the 20-50% range, which corresponds to 5.0 to 12m/s. Increasing the maximum speed beyond 50% gives little improvement in total energy stored. It should be noted that through this definition of goals for the AESS, the focus is on both storing and releasing energy. The compromises between the designs can be seen and used to help understand the potential benefits. However, interaction between the design targets was not analyzed in this section. Handling the complexity of some parameters changing and affecting others along with the influence of control and changing efficiencies within the specific systems will be addressed in Chapter

137 4.5 Preliminary AESS Design Procedure To begin the optimization process, an initial set to design parameters detailing the components of the system are needed. These parameters are based on the design targets from the relevant cycle statistics, individual component constraints imposed by physical limitations, and engineering judgment. The following subsections will outline the preliminary design procedure for both the mechanical and hydraulic energy storage systems Mechanical Energy Storage System Design Multiple options for configuring a parallel mechanical ESS exist. Possible configurations include connecting the ESS either between the engine and transmission input, between the transmission output and final drive reduction, or aft of the final drive reduction. Connecting between the engine and output shaft has the added complexity and potential benefit of variable gear reduction. The option of connecting the system between the transmission output and final drive reduction benefits from the additional gearing provided by the final drive ratio. For this design method development, the case where the mechanical ESS is connected in parallel between the transmission output and final drive reduction is the focus, however, if the variations are taken into consideration, the design method remains applicable. For a parallel mechanical energy storage system consisting of a flywheel, CVT, clutch, and gears (as shown in Figure 57), the list of the main design parameters is presented in Table

138 Gears CVT Gears Drivetrain Flywheel Clutch Figure 57. Mechanical ESS Design Configuration Table 27. Mechanical ESS Design Parameters Design Parameter Flywheel - Inertia - Maximum speed Gears - Flywheel to CVT - CVT to driveshaft Clutch - Diameter - Number of friction surfaces - Available pressure Before the preliminary selection of the design parameters can commence, the main physical limitations of the components must be understood since they will impose design constraints on the system. For the mechanical system, the main physical limitations can be found in the flywheel, CVT, and clutch. The flywheel is limited to a maximum speed due to limits of material strength and bearing type. In detail the radial tensile strength on the flywheel structure is mainly due to the centrifugal force due to the rotation of the flywheel around its axis: 123

139 (4.12) where r is the radius vector of the generic infinitesimal portion of the body with respect to the axis of rotation, ρ( r ) is the mass density at the same point and is the flywheel velocity. The maximum radial tensile strength of the flywheel depends upon the geometry of the flywheel and the physical structure of the material. Some data on typical values of maximum tensile strength of material used in the construction of flywheels are summarized in [3] and [4]. The clutch, based on its design parameters, can only transmit up to a maximum torque during lockup mode. Typically the maximum clutch torque is based on the maximum static coefficient of friction for the material. (4.13) Where T clutch,max is the maximum clutch torque, R c is the effective clutch radius, N fs is the number of friction surfaces A c is the friction surface area, static is the static coefficient of friction between the friction material and reaction plates, and p clutch is the hydraulic pressure of the clutch operating fluid. The CVT mechanical performance is limited in the form of maximum speed and ratio spread capability. The minimum and maximum CVT speed ratios must be used as constraints in system design. The CVT maximum torque capacity must also be respected. Table 28 lists the constraints for the mechanical ESS. 124

140 Table 28. Mechanical ESS Design Constraints Design Constraints - Maximum Flywheel Speed - Maximum CVT Speed - Maximum CVT Ratio - Minimum CVT Ratio - Maximum CVT Torque - Maximum Clutch Torque Once the design constraints are understood, the constraints and parameters must be coupled to the design targets. Coupling through use of mathematical relationships allows for intuitive alteration of the design parameters until the design targets are met within the constraints. The primary design targets are designated as desired energy storage, desired power capability, and desired speed operation range. Desired Energy Storage The main storage device in a mechanical ESS is the flywheel. The flywheel must be capable of storing a prescribed quantity of energy which becomes available due to vehicle deceleration. The energy is stored my means of a rotating mass with a specified inertia. The equation for flywheel kinetic energy is presented below: (4.14) Where E fly is the flywheel kinetic energy, I fly is the flywheel inertia, fly,max and fly,min are the maximum and minimum flywheel speeds, respectively. As previously mentioned, the maximum flywheel speed is dependent on the flywheel material and type of bearings used. Low speed flywheel systems with steel flywheels and conventional ball bearings typically have a maximum speed of around 20,000 rpm. High 125

141 speed flywheel systems use composite material flywheels with magnetic bearings to achieve speeds in excess of 40,000 rpm. Minimum flywheel speed is a self-imposed value, in order to extend the range of vehicle speeds when the mechanical energy storage system can operate with the clutch locked. More information on this subject will be covered in the section below where the vehicle speed range of operation is discussed. Desired Power Capability The power that can be absorbed or provided by the ESS is a function of the flywheel speed and acceleration, provided that the torque capacity of the system is sufficient. By differentiating the energy equation to derive an expression for power one can obtain the following equation: (4.15) The flywheel speed is a function of the vehicle speed, gearing, and CVT ratio: (4.16) where V veh is the vehicle speed, r w is the drive wheel ratio, g FD is the final drive ratio.g CVT is the CVT to driveshaft gearing g fly is the flywheel to CVT gearing and N CVT is the CVT ratio. By differentiating equation 11 the following expression is obtained: (4.17) 126

142 By combining the gear ratios into a single term ( ) and rewriting the equation for power in terms of CVT ratio and vehicle speed the following expression for flywheel power can be obtained: (4.18) Given a vehicle speed, a rate of change of vehicle speed (prescribed by the desired speed trace) and tire radius, the flywheel power is a function of flywheel inertia, CVT ratio and its rate of change, and the gear ratios of the system. On the other hand, the torque constraints of the system (clutch, CVT, shafts, etc) must be met in order to transmit the desired power. The necessary coupling points torque can be calculated by knowing the desired vehicle deceleration (or acceleration): (4.19) Where is the torque at the coupling point (between transmission output and final reduction gearing), M eff is the effective vehicle mass, is the vehicle speed, and is the road load force. In steady state conditions, the torque at the driveshaft can be equated to the torques at different locations in the system based on the gearing between them. By performing this calculation, the maximum torque on each side of the CVT can be obtained and compared to the CVT rated torque capacity. (4.20) 127

143 The torque that the clutch can transmit during lockup is a function of the clutch design and clutch hydraulic pressure: (4.21) Where T clutch,max is the maximum clutch torque, R c is the effective clutch radius, N fs is the number of friction surfaces A c is the friction surface area, static is the static coefficient of friction and p clutch is the hydraulic pressure of the clutch operating fluid. Based on a desired maximum coupling point torque, available clutch pressure, and coefficient of friction for the clutch plates, the necessary size and number of friction surfaces can be calculated. Range of Vehicle Speed Operation For optimum system efficiency, the system must be operated with the clutch in lockup mode in order to prevent excessive energy losses due to clutch slip. Under these conditions, based on the range of CVT ratios available, flywheel speed is limited based on vehicle speed and gear ratios of the intermediate gearings. From equation 11 the following expression of the flywheel speed as a function of vehicle speed can be obtained: (4.22) For a given vehicle speed, there exists a maximum and a minimum flywheel speed based on minimum and maximum CVT ratios: 128

144 (4.23) The nature of these constraints becomes apparent when considering the actual operation of the energy storage system. In fact, in order to store mechanical energy, the flywheel speed must increase when the vehicle decelerates. In practice this is accomplished by appropriately increasing the CVT ratio in a smooth fashion. In details, as also equation 13 shows, the mechanical power is transferred to the flywheel by acting on the rate of change of the CVT ratio. This term, within brackets in equation 13, must be positive to transmit energy to the flywheel, counteracting the effect of the negative vehicle acceleration term. As the CVT ratio is increased and the flywheel accelerates, the vehicle decelerates due to the inertial torque applied to the flywheel. At a certain vehicle speed, the CVT ratio will be at its maximum limit and the clutch must be disengaged to prevent the flywheel from slowing down with the vehicle. This specific value of the vehicle speed also serves as the speed at which the clutch can be re-engaged to provide acceleration assistance. Unlike the deceleration condition, the clutch can be slipped to provide acceleration from vehicle stop, at the cost of a lower operating efficiency due to an initial clutch slip operation. At the other extreme of the operating range, the vehicle speed can become sufficiently high as to prevent the flywheel from being engaged, even at the lowest CVT ratio available. Under these conditions, it is beneficial to limit the minimum speed of the flywheel in order to extend the range of vehicle speed where the clutch can be fully engaged. 129

145 The speed constraints can also be regarded in terms of energy storage capability. In details, the maximum and minimum flywheel speeds are directly related to the amount of energy that can be recovered and stored. Flywheel inertia affects the speed of the flywheel in order to store a given amount of energy. By combining equation 9 with equation 18 of flywheel speed as a function of vehicle speed, the following general equation for the variation of the flywheel energy can be derived: (4.24) By properly simplifying equation 19 the following expression can be obtained: (4.25) Equation 20 must be coupled with the constraint on the maximum flywheel speed: (4.26) Where is the maximum allowable flywheel speed. Using the derived expressions, values for each of the design parameters can be attained. An example of applying this method to the mechanical ESS is shown in Chapter Hydraulic Energy Storage System Design Multiple options for configuring a parallel hydraulic ESS exist. Possible configurations include connecting the ESS either between the engine and transmission input, between the transmission output and final drive reduction, or between the final drive reduction and 130

146 drive wheels. Connecting between the engine and output shaft has the added complexity and potential benefit of variable gear reduction. The option of connecting the system between the transmission output and final drive reduction benefits from the additional gearing provided by the final drive ratio. For this design method development, the case where the hydraulic ESS is connected in parallel between the transmission output and final drive reduction is the focus, however, if the variations are taken into consideration, the design method remains applicable. For a parallel hydraulic energy storage system consisting of a pump/motor, accumulator, reservoir, and gears (as shown in Figure 58), the list of the main design parameters is presented in Table 29. Pump/ Motor Accumulator Reservoir Gears Drivetrain Figure 58. Hydraulic ESS Design Configuration 131

147 Table 29. Hydraulic ESS Design Parameters Design Parameter Accumulator - Volume - Maximum pressure - Pre-charge pressure Reservoir - Volume - Pre-charge pressure Pump/Motor - Maximum displacement - Maximum pressure Gears - Pump to driveshaft Before the preliminary selection of the design parameters can commence, the main physical limitations of the components must be understood since they will impose design constraints on the system. For the hydraulic system, the main physical limitations can be found in the pump/motor and accumulator. The pump is limited to a maximum pressure differential as well as maximum and minimum speeds. The accumulator is limited by maximum pressure and pressure ratio between the operating pressure and the pre-charge pressure. Table 30 lists the constraints for the hydraulic ESS. Table 30. Hydraulic ESS Design Constraints Design Constraints - Maximum pump pressure - Maximum pump speed - Minimum pump speed - Maximum accumulator pressure - System pressure to accumulator precharge pressure ratio 132

148 Once the design constraints are understood, the constraints and parameters must be coupled to the design targets. Coupling through use of mathematical relationships allows for intuitive alteration of the design parameters until the design targets are met within the constraints. The primary design targets are designated as desired energy storage, desired power capability, and desired speed operation range. Desired Energy Storage The energy storage device in a hydraulic ESS is the hydraulic accumulator. The potential energy stored in an accumulator can be calculated as the integral of the work done on the gas in the accumulator by the hydraulic fluid. For a bladder type gas charged accumulator, the pressure of the gas is a function of the instantaneous volume. As a first approximation, by neglecting the heat transfer to the surroundings and assuming adiabatic gas compression, the following expression for the energy stored in the accumulator can be derived: (4.27) Where E accumulator is the accumulator potential energy, P o is the accumulator pre-charge pressure, V min, V max and V acc are the initial volume, the final volume and the total volume of the accumulator, V is the fluid volume in the accumulator and is the specific heat ratio of the pre-charge gas. In this case, the main physical constraint is represented by the maximum accumulator pressure: (4.28) 133

149 Where P acc,max is the maximum accumulator pressure. The integral in 22 can be evaluated over the range of available pre-charge pressures in order to find the maximum energy storage capacity for a given total accumulator volume and maximum pressure. The optimum pre-charge pressure must satisfy the constraint of the accumulator maximum pressure ratio (system pressure to pre-charge pressure) limitation. Figure 59 shows the effect of pre-charge pressure on the energy stored in the accumulator (the example refers to a bladder-type accumulator with total volume of 20 liters and maximum pressure of 350bar). Figure 59. Pre-charge pressure Energy Storage Relationship 134

150 Desired Power Capability The power that can be absorbed or provided by the hydraulic ES system is a function of the hydraulic pump speed, maximum pump displacement, and accumulator pressure. In details: (4.29) Where P pump,max is the maximum pump power, P pump is the pressure differential across the pump, D pump,max is the maximum pump displacement and pump is the pump speed. Maximum pump displacement is dependent on the specific pump model chosen. The pressure differential across the pump is the difference between the accumulator pressure and the reservoir pressure: (4.30) The pump speed is a function of the pump gearing, final drive reduction, and vehicle velocity: (4.31) Where V veh is the vehicle velocity, r w is the tire radius, g FD is the final drive ratio and g pump is the gear ratio between pump and driveshaft. For a given vehicle speed, the torque demand on the pump can be found as a function of the desired acceleration or deceleration of the vehicle according to the following expression: (4.32) 135

151 where is the effective vehicle mass and is the road load force. The desired pump torque can be compared to the available pump torque (physical constraint): (4.33) If the available torque matches or exceeds the desired pump torque for a given vehicle speed, the target power can be met (assuming pump speed constraint is met). Range of Vehicle Speed Operation Due to limitations on pump speed, consideration must be given to the desired range of vehicle speed operation for the system. The pump speed is directly related to vehicle speed through the following equation: (4.34) The constraints on maximum and minimum pump speed limit the range of vehicle speed operation for a given gear ratio between the pump and the drivetrain. Using the derived expressions, values for each of the design parameters can be attained. An example of applying this method to the hydraulic ESS is shown in Chapter Correlations between Design Parameters and Physical Properties Once a set of physical parameters are developed, correlations between the parameters and the physical properties of the design such as mass, volume and cost are needed in order to evaluate the system performance in simulation and to evaluate the effectiveness of the design. The basic premise in this approach is to use information derived from the 136

152 manufactured components to determine how the physical properties scale with the design parameters. In many cases, datasheets which show the change in physical properties between common product lines can be used to create the correlations. From these correlations, estimates of the physical properties can be made. In some cases, the estimates can be quite accurate if the products are well developed and established. In other cases, especially in estimates of cost the accuracy may depend heavily on information not considered in this section such as economies of scale in production. The following section presents methods for correlating the parameters to properties for both the mechanical ESS and the hydraulic ESS. Samples will be shown; however, the actual correlations may vary significantly if the same type or technology level of components is not chosen. Accurate information is used where possible, however, in some cases, such as cost, limited information is available and significant simplifying assumptions must be made Mechanical ESS Correlations Mass, volume and cost estimates must be made for the flywheel and its containment structure, the CVT, the clutch, and gears connecting the components. Mass and volume will be looked at individually for each element and the total values for the system will be the sum of the parts. For simplification, the clutch will be assumed to be incorporated into the CVT. Cost will be simplified as a function which scales with energy storage and power capability of the system. 137

153 Flywheel and Containment Structure Mass and Volume The mass of the flywheel itself is dependent on the inertia and radius of gyration based on the following formula: (4.35) The radius of gyration depends on the shape of the flywheel. For a solid disc, (4.36) Where r is the outer radius of the disc For a thin cylindrical shell:, where r is the radius of the shell. Knowing the target inertia for the system and the radius of gyration for the shape of the flywheel allows the resulting mass to be calculated. In order to determine the mass of the containment system, it must be observed that the main function of the system is to absorb the energy of the flywheel in the event of a catastrophic failure of its structure, avoiding the projection of the pieces of the system far from the AESS. In case this event happens, it is reasonable to assume that the energy that must be absorbed by the containment system is a fraction of the actual kinetic energy carried by the flywheel itself. For this reason, the mass of the flywheel containment structure can be approximated as proportional to the maximum energy stored by the flywheel. In order to develop a reasonable correlation, a review of significant technical literature has been performed. A containment system designed by the University of Texas Austin comprised of an aluminum housing, steel shell, and metallic honeycomb layer 138

154 weighed 235kg in order to contain a flywheel with 3370 kj of energy [4]. Based on this design, in first approximation, this ratio of containment weight to flywheel energy has been used to determine a relationship of 0.070kg of containment structure weight per kj of flywheel energy. The volume of the containment structure depends on the volume of the flywheel. Knowing the radius and width of the flywheel allows for a reasonable estimation of containment structure to be a cylinder with radius approximately 50mm larger than the flywheel to be contained. This additional volume allows for the three piece containment system structure. CVT Mass and Volume Transmissions are typically designed to a torque limitation. As torque increases, the size and weight of the transmission must increase to transmit the desired torque. This provides grounds to base CVT mass and volume on torque capacity. Limited information is available for mass and volume for CVTs due to limited mass production at higher torque levels. A small amount of information is available from Torotrak for full toroidal CVTs. Torotrak CVTs have a 6.25 ratio spread and a range of torque capacities from 100Nm to 450Nm. Using the information available, a correlation can be developed between CVT torque capacity and CVT mass [5],[6]. Plotting the data (torque and mass) for the three Torotrak examples is shown in Figure 60. A linear correlation between torque capacity and CVT mass has been found to match the data very well. 139

155 Mass (kg) y = x Torque Capacity (Nm) Figure 60. Sample CVT Torque to Mass Correlation (Torotrak CVT) Other sources for CVT mass estimates include Nissan and Hyundai CVTs which are currently in production. JATCO Ltd. supplies belt type CVTs to Nissan for vehicles with a range of displacements from under 1.8L up to 3.5L. However, component weights are not published by JATCO and the components supplied to Nissan also include a torque converter in the design [7]. CVT volume can also be estimated based on data available from Torotrak. Based on the diameter and length of the transmission, the volume of the smallest cylinder the CVT can fit within, can be used to estimate the volume occupied. Figure 61 shows the correlation between CVT torque capacity and CVT volume. 140

156 Volume (liters) y = 0.031x Torque Capacity (Nm) Figure 61. Sample CVT Torque to Volume Correlation (Torotrak CVT) Gear Set Mass and Volume The mass and volume for additional gearing between the components and the drivetrain can be estimated by the physical size of the gearing. For helical gears, the pitch diameter can be used to estimate the volume for a given width. Mass can be estimated based on material density. For a 15cm diameter steel (7.87g/cc density) gear with a width of 3cm, the mass is 4.2kg with a volume of 530cc. Coupling this with a gear of 7.5cm diameter and same width gives a mass of 1.0 kg and a volume of 132cc. Adding a reasonable mass to consider the housing and lubrication, gives a conservative estimate of 7kg and 1 liter of volume per pair of gears. This estimate is reasonable when compared to off the shelf ground helical gears available for purchase [8]. 141

157 Estimates of Mechanical System Cost For the mechanical system, the energy storage is primarily a function of flywheel size. Therefore as energy storage increases, the additional cost is primarily a due to the added flywheel material and resulting increase in cost for containment. The power capacity will scale with CVT, clutch, and gearing costs. In addition to the costs that scale with energy and power, additional fixed costs will be present due to overhead for design and manufacturing regardless of system size. As a result, the cost model in equation 32 is proposed. (4.37) Where is the price of the mechanical system, is the fixed cost, is the multiplier for maximum power, and is the multiplier for maximum energy storage. Actual values for the coefficients should be based on estimates for the scaling behavior of the component costs. Additional Remarks The above correlations are primarily based on available components and reasonable engineering estimates. Actual weight and volume of a production energy storage system will vary due to vehicle packaging and final system configuration. These estimates are meant to be used in establishing a process which can be revised and improved upon as detailed component information becomes available. 142

158 4.6.2 Hydraulic ESS Correlations Mass, volume and cost estimates must be made for the hydraulic systems components including the pump/motor, accumulator, reservoir, and gearing. Mass and volume will be looked at individually for each element and the total values for the system will be the sum of the parts. Additional to the mass of the components, the mass of the fluid in the system should also be considered. Cost will be simplified as a function which scales with energy storage and power capability of the system. Pump Mass and Volume The main design parameter for pumps is the displacement. Increasing pump displacement increases both the mass and volume of the pump. Using a medium duty, variable displacement axial piston pump designed for mobile applications by Parker Hannifin as the basis for the correlation, pump displacement can be plotted against mass and volume. Example values for pump mass were taken from the appropriate product datasheet [9]. Volume was calculated by using the maximum dimensions in each direction and multiplying to find the smallest box volume the pump would fit inside. Actual pump physical volume is obviously slightly smaller. In Figure 62, the length for a Parker P1 Series 18cc/rev pump is shown as 164.2mm. Figure 63 shows the height and width as 193.3mm ( ) and mm ( ), respectively. The results of computing the volume and plotting against displacement are shown in Figure 64. Plotting published pump mass against displacement gives Figure 65. Both correlations are nearly linear, especially at the lower displacement ranges. The linear correlations 143

159 provide a good estimate for pump mass and volume based on the displacement design parameter. Figure 62. Sample Pump Length (Parker P1 18cc/rev, End Port Design) 144

160 Figure 63. Sample Pump Width and Height (Parker P1 18cc/rev, End Port Design) 145

161 Pump Mass (kg) Pump VJolume (L) Parker P1 Axial Piston Pump Volume Correlation y = 0.12x R² = Pump Displacement (cc/rev) Figure 64. Pump Displacement to Volume Correlation Parker P1 Axial Piston Pump Mass Correlation y = 0.45x R² = Pump Displacement (cc/rev) Figure 65. Pump Displacement to Mass Correlation 146

162 Mass (kg) Accumulator Mass and Volume The nominal accumulator volume chosen for energy sizing purposes can be used to determine the actual volume occupied by the accumulator as well as the accumulator dry mass for a given pressure and material. Off the shelf Bosch Rexroth bladder type accumulators made from steel were used to develop the following relationships [10]. Information for accumulators made of composite materials (produced by Structural Composites Industries and sold by LightningHybrids) [11] was also included for comparison y = 4.0x R² = y = 2.3x R² = PSI 5000 PSI 6000 PSI Composite 50 0 y = 0.48x R² = Nominal Volume (L) Figure 66. Accumulator Mass Correlation As expected, accumulator volume scales linearly with nominal volume (Figure 66). The higher pressure steel accumulators are considerably heavier for a given volume. Due to much higher material strength, the composite accumulators have much lighter weight 147

163 even with higher operating pressure. The data for the 6000 PSI composite accumulator has a perfectly linear correlation due to the mass being based on approximations by the manufacturer (Lightning Hybrids). Using the published outer dimensions for the cylinders, an approximation for the actual ones, cylinder volume can be calculated by multiplying the cross-sectional area by the length of the body of the accumulator. Figure 67 is an example schematic of a bladder type hydraulic accumulator. The dimensions B and C were used to calculate a cylinder volume for estimating the actual volume occupied by the accumulator. Figure 67. Accumulator Outer Dimensions (Bosch HAB-5X) [10] Figure 68 shows the estimated cylinder volume as a function of the nominal accumulator volume. The relationship is linear, but it does depend on operating pressure and type of 148

164 Cylinder Volume (L) construction material. Higher pressures require thicker walls for a given material, increasing the total volume of the accumulator for a given nominal volume y = x R² = y = x R² = 1 Figure 68. Accumulator Actual Volume Correlation y = x R² = Nominal Volume (L) 3000 PSI 5000 PSI Composite Fluid and Reservoir Mass and Volume The necessary reservoir volume is based on the fluid volume needed to fill the accumulator from empty to maximum pressure. This volume also depends on pre-charge pressure which can vary based on design requirements. Tables, such as the one presented on Figure 69, provided by the accumulator manufacturer, give the maximum fluid volume for each accumulator size based on pre-charge pressure and either adiabatic or isothermal conditions. Since the fluid storage will occur rapidly under most conditions, the adiabatic case can be used to estimate the volume of fluid storage for a given accumulator. 149

165 Figure 69. Accumulator Maximum Fluid Volume, Adiabatic Compression [10] If pre-charge pressure is assumed to be constant, a correlation between available volume (maximum fluid volume) and nominal accumulator size can be determined. Based on a pre-charge pressure of 1400 psi (97 bar) calculations were preformed, assuming adiabatic compression, to estimate the fluid volume in the accumulator at maximum pressure. The following equation for maximum accumulator fluid volume was used: (4.38) Where is the maximum fluid volume, is the nominal accumulator volume, is the pre-charge pressure, and is the maximum accumulator pressure. 150

166 Fluid Volume (liters) To confirm the validity of the above equation, by comparing it with the results of Figure 69, a sample case was examined, under the condition of a maximum pressure of 3000PSI and a pre-charge pressure of 1400PSI. Using Figure 69, the estimate for fluid volume is approximately 255 cubic inches for a 2.5 gallon accumulator. This equates to 4.18 liters of fluid. Using the above equation for adiabatic compression, with a ratio of specific heats of 1.4 for air, gives a fluid volume of 3.97L, a difference of 5%, which is can be attributed also to the error of reading the graphs accurately. For a fixed pre-charge pressure of 1400PSI, the calculations produce the results shown in Figure y = 0.646x y = x PSI y = x PSI 6000 PSI Nominal Accumulator Volume (L) Figure 70. Accumulator Fluid Volume Correlation (1400 PSI Pre-charge) For the more general case where pre-charge pressure can vary, a surface plot can be generated based on the above equation (Figure 71). 151

167 Figure 71. Accumulator Fluid Volume (5000PSI Max, Varying Pre-charge Pressure) Fluid volume does decrease significantly as pre-charge pressure is increased, especially in larger nominal accumulator sizes. For a given pre-charge pressure fluid volume scales linearly with nominal volume. Knowing the aforementioned relationship, allows for estimation of fluid volumes for accumulators sizes which are not available off the shelf. Once fluid volume is known, fluid density can be used to estimate the mass of the fluid in the system. To this purpose, a typical hydraulic fluid such as Mobil Hydraulic Oil M 46 having a density of 0.875kg/liter [12] can be used in the calculation. Volume for the reservoir can be estimated as the same as the fluid volume for the system. Knowing the volume of the reservoir, an approximate mass for the reservoir can be calculated based on material type, wall thickness, and a rectangular cross section. Using a cross section of 25cm x 25cm, the dry mass for the reservoir is shown in Figure 72 for 152

168 Reservoir Mass (kg) aluminum (39 g/cc density, 4mm wall thickness) and steel (7.87 g/cc density, 2mm wall thickness) y = x y = x Reservoir Volume (L) Aluminum (4mm) Steel (2mm) Figure 72. Reservoir Mass Correlation Estimates of Hydraulic System Cost For the hydraulic system, the energy storage is primarily a function of nominal accumulator volume. Therefore as energy storage increases, the additional cost is primarily a due to the increased accumulator cost. The power capacity scales with pump displacement. Cost also scales with pump displacement causing cost to scale with power capacity. In addition to the costs that scale with energy and power, additional fixed costs will be present due to overhead for design and manufacturing regardless of system size. As a result, the cost model in equation 34 is proposed. 153

169 (4.40) Where is the price of the hydraulic system, is the fixed cost, is the multiplier for maximum power, and is the multiplier for maximum energy storage. Actual values for the coefficients should be based on estimates for the scaling behavior of the component costs. Additional Remarks The calculations presented in the previous sections are based upon information related to off-the-shelf components that are not necessarily designed in an optimum way for use on board a vehicle. As a result, careful design may allow for reduction in the mass and/or volume of the system when compared to the total system estimates from summing the results of the above correlations. In addition to the main components of the system, accessories necessary for operation such as hydraulic controls, hydraulic lines, mechanical shafts, etc. will add mass and volume to the system. Other factors such as designing for vehicle safety may also alter the physical properties of individual components Combining the Correlations to Form Properties Once all of the correlations are developed, estimates of mass, volume, and cost can quickly be determined based on the design parameters by adding the masses and volumes for all of the individual components in each system. Sensitivities can also be determined to see the effect of changing just one parameter. Examples of applying these correlations 154

170 to actual designs will be shown in chapter 5. In the scope of the design process, the properties are passed to both the simulation evaluation tool in order to adjust the vehicle mass and to the optimization cost function to determine the optimization value which is a function of system performance, cost, volume, and mass. 4.7 Vehicle Simulator for Evaluation With the end goal of the ESS to be an increase in fuel economy of the vehicle, the resulting design in both its preliminary and optimized state must be evaluated to determine the predicted benefit of adding the system to a vehicle. Due to the high cost of building and testing prototype systems, it is desirable to model the behavior and evaluate in a simulation environment where computer processing can be used to solve the dynamic equations very quickly at relatively low cost. In Chapter 3, models for the various vehicle and AESS components were developed for this purpose. Within the realm of evaluation through modeling and simulation, multiple methods are possible. Two basic categories of vehicle simulations exist, forward and backward. In this context, forward simulation involves controlling the torque production of any possible energy sources to match the desired speed profile, such as a drive cycle. Backward simulation instead begins with the speed profile and calculates the required torque to meet the velocity and rate of change of velocity. Backward simulation works very well when there is only one possible flow path for the torque. Otherwise, dynamic programming along with simplifying assumptions are needed to determine the proper 155

171 split of torque between possible sources, considerably complicating the equation solving process. Due to these reasons, forward simulation will be used to evaluate the AESS systems. Forward simulation is not without its own set of complications in this context. If a full vehicle model (including powertrain, AESS, and vehicle dynamics) is used, with two possible options for torque generation, a decision must be made at each point in time regarding the torque split between the two possible options. A number of control strategies are possible, ranging from simple rule-based to more complicated logic which takes into account vehicle state variables and component efficiencies. The problem with any forward simulation control strategy is that it will always be sub-optimal by some amount. Knowing that full vehicle forward simulation will be sub-optimal, the focus should be on consistent control which will allow for fair comparison between the models. The following sub-sections present the basic outline of the vehicle simulator along with the ESS control strategy used Overview of Vehicle Simulator The simulator uses the system dynamics models presented in Chapter 3 with the AESS connected in parallel configuration between the transmission output and final drive reduction. Figure 73 shows the signal flow path for the simulator. 156

172 Engine Transmission Conventional Drivetrain Torque Driver Torque Request High Level Controller Torque Split Command AESS AESS Torque + Mechanical Torque Summation Vehicle Dynamics Vehicle Speed Figure 73. Diagram of Vehicle Simulator The driver operates on the difference between the actual vehicle speed and the desired vehicle speed from the drive cycle. A torque request signal is sent to a high level controller which decides on the appropriate torque to request from both the engine and the AESS. The torque is then summed at a mechanical summation node before it is sent to the final reduction and the vehicle dynamics block. The component speed signals are fed backward starting from the vehicle dynamics block. Low level controllers exist for the transmission and AESS. The transmission controller decides when to change gears based on a lookup table with speed and torque. The AESS controller modifies the behavior of the AESS in order to deliver the desired torque coming from the torque split command. In the hydraulic ESS, the pump displacement is modified. In the mechanical ESS the clutch and CVT ratio are controlled to provide the torque requested. 157

173 The main outputs of the simulator include all of the state variables for each component in the system. Of particular interest is the quantity of energy stored and released by the AESS. The amount of energy lost to braking is also calculated. Other conventional powertrain variables can be examined, such as fuel consumption and energy losses in the various components. Torque split between the AESS and conventional powertrain can also be plotted and analyzed. Emphasis is placed on the ability of the AESS to recover and release all available braking energy as this represents the potential benefits of the systems, regardless of what the predicted fuel economy benefits may be. As a result, the primary output of the simulator that will be used for cost function analysis will be the percentage of total available braking energy that is both captured and released by the AESS High Level Torque Split Control Strategy The purpose of the high level controller is to decide on the torque split strategy between the conventional powertrain and the AESS. As previously stated, multiple methods of accomplishing this task are possible. For this design method, a simple rule based strategy is proposed in order to allow for consistent behavior between system designs. The basic constraints on AESS use are the physical limitations of the system components. For the mechanical ESS, this is maximum flywheel speed, maximum CVT torque, and the maximum and minimum CVT ratios. For the hydraulic ESS, maximum pump 158

174 displacement and maximum accumulator pressure are the constraints. These limitations will be used to dictate the control strategy. The premise for control of the AESS in regenerative braking is to capture all available braking energy up to the point where the physical limitations are reached. This strategy ensures the largest possible amount of braking energy recovery and the smallest possible amount of friction brake use. In general, for short-term energy storage systems, this is a good strategy so long as the system efficiency doesn t change drastically with the control inputs. If this is true, the main task for the controller is to increase energy stored by maximizing the energy that can be stored at any given time. This is accomplished by using the AESS to the fullest extent anytime energy is available and the constraints are met. In the mechanical ESS, all braking torque command (T req ) will be satisfied by the ESS up to the maximum CVT torque (T max ) until the maximum CVT ratio is reached, at which point the flywheel must be decoupled via the clutch and allowed to freewheel. In the hydraulic ESS, all braking torque (T req ) will be satisfied by the ESS up to the maximum pump torque (T max ) until the maximum accumulator pressure is reached, at which point the bypass valve must be opened to prevent accumulator over-pressurization. Figure 74 shows the control flowchart for the braking torque split. 159

175 Braking Torque Request No Can energy be stored? Yes No ESS Use No Treq > Tmax? Yes Command Treq from AESS Command Tmax from AESS and remainder from friction brakes Figure 74. AESS Brake Control Flowchart With limited energy storage capacity, in order to maximize the amount of energy that can be stored in the next braking event, the AESS system must be quickly depleted between regenerative braking events. Due to this situation, the premise for AESS traction torque control is very similar to the braking control strategy. Any time energy is in the ESS and available for use, the controller will favor it over the conventional powertrain until the energy is depleted. Obviously, the same restraints on torque capacity must be respected. Figure 75 shows the AESS control flowchart for traction torque requests. 160

176 Traction Torque Request No Is AESS Energy Available? Yes No ESS Use No Treq > Tmax? Yes Command Treq from AESS Command Tmax from AESS and remainder from Engine Figure 75. AESS Traction Torque Control Flowchart While the proposed control method is not optimal, it provides a consistent and intuitive strategy for AESS use which caters to the advantages of the systems such as high power capacity and ability to operate from low to high SOE repeatedly without performance degradation Vehicle Information Needed for Simulation Based on the vehicle components models shown in Chapter 3, information about the components is needed to characterize the models in simulation. The following tables list the information needed for all of the conventional vehicle components. 161

177 Table 31. Required Vehicle Information for Simulation Component Engine Torque Converter Transmission Wheels and Tires Vehicle Dynamics Characterizing Information -Maximum brake torque curve - Efficiency map - Idle fuel consumption - Maximum Speed - Mass - Effective Inertia - Fuel lower heating value - K factor over speed ratio range - Torque ratio over speed ratio range - Gear ratios - Efficiency - Shift scheduling (up and down shifts) - Final drive ratio - Effective rolling radius - Coefficient of rolling resistance - Mass of vehicle - Frontal area - Drag coefficient With the above vehicle information and using the aforementioned control strategy, full vehicle simulation is possible. The output of the simulations can then be taken into account by the cost optimization function and used to revise the design. 4.8 Cost Function Definition and Design Optimization Once the design has been evaluated in simulation and the design attributes such as mass, volume, and cost have been estimated the task becomes weighting these factors in a proper manner to assess the overall quality of the design. One method for this assessment is to define a total cost function which weights all of the factors and combines them into a single expression which can be optimized through finding the minimum value. Each 162

178 factor is normalized by a target value. For instance, if the target system price is $2,000, the estimated price for a given design would be divided by $2,000 (the normalization value). The result is an expression which in the most desirable case would be as small as possible, representing an estimated cost less than the target cost. Defining the factors of interest to be the percentage of total braking energy recovered ( ), system mass ( ), system volume ( ), and price (, the following cost function can be written: (4.41) Where the subscript T denotes the target value for each of the factors. The weighting coefficients,,,, and are left to the designer to specify, but in general should sum to equal 1. They allow the relative importance of the different factors to be changed depending on the context of the design. For instance, in some applications such as large trucks, volume and mass may be of very little concern. In such a situation, the and coefficients would be small in comparison to and coefficients. Targets values should also be carefully specified by the designer. One possible source of target values would be an equivalent electrical energy storage system. Target values might also be factors from the initial design before any revisions are made. Using the cost function as defined above, designs can be readily compared. With this comparison method, several tactics can be used to refine the design until a minimum value for is found. Conceptually, the simplest method for performing the optimization would be evaluating the cost function for all possible design parameter 163

179 combinations. While in some cases this may be possible, with many design parameters the task of evaluating the very large number of possible combinations is computationally intensive and can be avoided by systematically narrowing the range where the optimal design is thought to exist. The first tactic involves comparing designs based on the different statistical weighting methods. In terms of the statistical weighting methods shown in Section 4.3, designs based on the maximum values, mean values, weighted mean values, and weighted mean values with maximum power distribution design targets can be evaluated in simulation and compared in terms of cost function value. The design with the minimum cost function value is then selected as the focus of a refinement to further decrease the cost function and improve the design. The refinement process involves varying the main design parameters which affect energy storage capacity, power limitations, and AESS speed range operation in order to find the net effect on the cost function. By iterating the design process with parameter values a small percentage above and below their nominal values, the local gradient of the cost function with respect to the design parameters can be found and used to revise the design. The local revision of the design prevents exhaustive search of the design space for the optimal solution by first narrowing the window of examination. For example, the flywheel inertia can be modified ten percent above and ten percent below the nominal and the cost function evaluated for both cases. If the cost function value is lower with greater flywheel inertia, the flywheel inertia can be increased in steps and re-evaluated until the minimum cost function is found. Refinement can also come from analyzing the simulation outputs. Looking at the behavior of the ESS during simulation can provide 164

180 meaningful information that can lead to design improvements. For example, looking at not only the composite AESS efficiency, but also the one-way storage and return efficiencies might give insight into where the AESS is lacking performance and consequently where the design parameters can be adjusted to improve the performance. Understanding the sensitivity of the design to the cost function weighting coefficients is also of interest. Performing the design method and optimization process for different values of the weighing coefficients in the cost function can help the designer to better understand the influence of these coefficients on the resulting design. Some connections may be intuitive such as lowering the relative weighting of the price and volume will result in a larger, possibly more effective system, however, some trends may not be as apparent, especially if additional factors are included in the cost function. Despite the optimization methods proposed above, the design optimization process is not an exact science. The cost function provides the tool necessary to compare designs, however, the actual process of deciding how to vary the parameters in order to improve the design takes a combination of engineering judgment and understanding of the system behavior. Experimental design techniques can also be applied to make more efficient use of each design evaluation. 4.9 Design Method Conclusions The design method proposed in this chapter begins with knowledge of the base vehicle parameters and drive cycles of concern and provides the process and tools for the design 165

181 of a mechanical or hydraulic ESS which best meets the criteria of the designer. Like any method the quality of the output will heavily depend on the quality and accuracy of the information used during the process. Care should be taken to ensure that the inputs are as accurate as possible. If it is known that some inputs are not accurate or may change due to outside factors, the design process should be revisited once the inputs are better understood. Due to this likelihood, it is suggested that design parameters with very similar cost function values be kept in consideration until confidence in the accuracy of the inputs exists. In some cases additional constraints may also be placed on the design parameters or attributes due to restrictions. A case of this may be a constraint on total system volume due to vehicle packaging. In general, the cost function is only applicable as long as the constraints are met. 166

182 4.10 References [1] Guzzella, L., Sciarretta, A. Vehicle Propulsion Systems Introduction to Modeling and Optimization (2nd ed.). Springer: New York. [2] Bolletta. Alberto. Design of alternative energy Storage Systems for Hybrid Vehicles Based on Statistical Processing of Driving Cycles Information. Thesis. [3] B. Bolund, H. Bernhoff, M. Leijon. Flywheel Energy and Power Storage Systems. Renewable and Sustainable Energy Reviews, 11 (2007) [4] Hearn, C., Flynn, M. et al. Low Cost Flywheel Energy Storage for a Fuel Cell Powered Transit Bus. Vehicle Power and Propulsion Conference, Sept 9-12, VPPC IEEE [5] Brockbank, C. and Burtt, D. Infinitely and Continuously Variable Full Toroidal Traction Drive Transmissions for Transverse Applications in Sub A, A & B Sector Vehicles. Torotrak, Ltd. [6] Torotrak plc. Example Automotive Applications. [7] JATCO Ltd. [8] Quality Transmission Components online catalog. [9] Parker Hannifin. P1/PD Series Medium Duty Axial Piston Pumps. Catalog HY /P1/EN. Effective February 01, [10] Rexroth (Bosch Group). HAB Series 5X Bladder Accumulator Data Sheet. [11] LightningHybrids. Lightweight High Pressure Bladder Accumulators. Accumulator Catalog Sheet. [12] Mobil Hydraulic Oil M 46 Specifications. [13] Bolletta, A., Chiara, F., Canova, M., McDonough, J., Koprubasi, K., Raghavan, M. A Design Procedure for Alternative Energy Storage Systems for Hybrid Vehicles. ICE 2011 International Conference on Engines & Vehicles. 167

183 Chapter 5: Application of Design Method to Mechanical and Hydraulic AESS 5.1 Introduction The following chapter uses the design procedure outlined in Chapter 4 and applies it to both the mechanical and hydraulic energy storage systems. First, the vehicle details are outlined followed by the choice of drive cycle for the design. For this example, the drive cycle chosen is a custom drive cycle synthesized from fleet studies data gathered by the Center for Automotive Research at The Ohio State University. With the vehicle and drive cycle information, preliminary design parameters are generated for the four statistical weighting methods presented in Chapter 4. Next, the four preliminary designs are compared both in terms of design attributes and performance in simulation. The cost function is then defined and calculated for the preliminary designs using a defined set of weights. Based on the cost function value, the best design is chosen and optimized through iteration of the design process. Once the optimized designs are found for both the mechanical and hydraulic systems, the performance of each is examined on a real-world drive cycle to confirm the performance. Throughout the chapter, the results are analyzed and conclusions are drawn. 168

184 5.2 Vehicle Details and Cycle Statistics This section outlines the vehicle that is used in the design process. The vehicle chosen for demonstrating design process is a 2009 Saturn VUE mid-sized SUV. The basic vehicle information is presented in Table 32. Table 32. Vehicle Details Vehicle: 2009 Saturn VUE Weight: 1900kg Engine: 3.5L V6 LZ4 Transmission: 6 speed automatic Transmission ratios: 4.48; 2.87; 1.84; 1.41; 1.00; 0.74 Final drive ratio: 2.77 Tire Size: 0.713m diameter (235/60/R17) Frontal Area: 2.9 m 2 Figure Saturn VUE 169

185 Specific vehicle information necessary for simulation was provided by General Motors. This included detailed engine performance and fuel consumption maps, torque converter data, transmission efficiency, and road load information. The drive cycle chosen for this example is based on fleet studies data of individual users in mixed urban and highway driving. From the fleet studies data, a process of generating synthetic drive cycles which captures the general driving pattern is used to create additional cycles which are statistically representative of actual driving patterns [1]. Figure 77 shows a sample of the driving cycle. The complete cycle is over 60,000 seconds long and covers a distance of over 480 miles. This length was chosen to represent the behavior of a driver over an entire tank of fuel. Figure 77. Sample of Synthetic Driving Cycle Using the synthetic drive cycle coupled with the vehicle information, the relevant cycle statistics were calculated. The statistical methods used were maximum values, mean values, weighted mean values, and mean values weighted with the maximum power 170

186 distribution. The information shown in Table 33 is the basis for the preliminary design procedure. Table 33. Design Relevant Drive Cycle Statistics for 2009 Saturn VUE on Synthetic Cycle Energy [kj] Maximum Power [kw] Maximum Velocity [mph] Maximum Values Mean Values Weighted Mean Mean Weighted with Max Power Dist Looking at the relevant statistics, the maximum values are much greater than both the mean and the weighted mean values. The weighted mean values are significantly higher than the mean values, suggesting a high frequency of very small braking event which do not contain significant energy. 5.3 Preliminary Design Procedure The following sub-sections cover the preliminary design procedure for both the mechanical ESS and hydraulic ESS. For both types, a design example is shown for one set of design targets. Afterwards the design parameters for each of the four preliminary designs are shown. Then, all four preliminary designs are evaluated in simulation and 171

187 compared based on a cost function. The best of the four designs is further refined until a minimum value for the cost function is found Mechanical ESS Preliminary Design The following section covers the preliminary design procedure for the mechanical ESS. This includes the process of using the design targets to generate the initial design parameters. Once the process is shown for one design case, the results of applying the same procedure to each of the sets of design targets is shown in a table for comparison. Before the design procedure can commence, the type of components to be used must be specified. This important step dictates the constraints that must be applied. The mechanical system considered consists of a steel flywheel coupled to a CVT through a clutch and set of gears. The CVT is coupled to the drivetrain between the transmission output and the final drive reduction using another set of gears. The clutch and CVT are used to change the flywheel speed in order to store and release energy. It is assumed that the necessary control actuators are present and do not impose restrictions on the operation. Table 37 and Table 38 list the resulting constraints and parameters which must be specified for the configuration considered, respectively. It is assume that the clutch is designed to accommodate the torque sent to the flywheel, and therefore, the resulting clutch parameters will not be covered in detail. 172

188 Table 34. Mechanical ESS Design Constraints Design Constraints Maximum flywheel speed 2100 rad/s (20,000 rpm) Maximum CVT Speed 420 rad/s (4,000 rpm) Maximum CVT ratio 2.2:1 Minimum CVT ratio 0.4:1 Maximum clutch torque 300 Nm Maximum CVT torque 300 Nm Table 35. Mechanical ESS Design Parameters Design Parameter Flywheel - Inertia Gears - Flywheel to CVT - CVT to driveshaft CVT - Maximum input torque The example sizing exercise shown here is for the design based on the weighted mean with maximum power distribution. A preliminary value of the inertia of the flywheel can be calculated starting from the equation of the mechanical energy: (5.1) For this case, with a minimum flywheel speed of 10,000 rpm and a desired energy of 175kJ, the required inertia is kgm 2. Assuming a minimum flywheel speed of half the maximum flywheel speed over-sizes the inertia by 33% compared to a minimum of zero, but allows for operation at higher vehicle speeds. 173

189 In order to determine the torques at the individual components, the gearing between the components must first be decided. The gearing between the CVT and the flywheel is determined by the maximum flywheel speed and the maximum CVT speed. Dividing the maximum flywheel speed by the maximum CVT speed, will set the highest gear ratio where both conditions are met simultaneously. For this example, a gear ratio of 5:1 between the flywheel and CVT is used. Once the gearing between the flywheel and CVT is determined, the gearing between the CVT and drivetrain can be computed based on the maximum desired vehicle speed for mechanical ESS use. To decide this gear ratio, the case with minimum flywheel speed and maximum vehicle speed must be considered. For this example, the maximum vehicle speed for regenerative braking comes from the design targets as 25mph. During this scenario, the flywheel is at 10,000 rpm and the CVT ratio is at the minimum ratio of 0.4:1. Knowing these values along with the radius of the drive wheels and final drive ratio, the gear ratio between the CVT and drivetrain that will allow for coupling can be determined. For this case, the ratio is 6.0:1. Once the gear ratios are determined, the necessary CVT torque capacity to achieve the desired braking power target can be calculated. Making the assumption that the highest power occurs at the maximum vehicle velocity cycle statistic (25mph), the resulting CVT speed is known. Assuming the worst case scenario where the CVT ratio is at its minimum of 0.4:1, the necessary torque to provide 28 kw of power is calculated to be 134 Nm. Applying this preliminary design procedure to each of the sets of design targets results in the preliminary design parameters shown in Table

190 Design Parameters Table 36. Mechanical ESS Preliminary Design Parameters Max Values Mean Values Weighted Mean Weighted Mean Max Power Flywheel Inertia (kg*m^2) Flywheel to CVT ratio 5.0:1 5.0:1 5.0:1 5.0:1 CVT to driveshaft Ratio 2.1:1 7.2:1 4.6:1 6.0:1 CVT Torque Capacity (Nm) In the next phase of the design process, these preliminary design parameters are evaluated in simulation and compared based on the performance and design attributes Hydraulic ESS Preliminary Design The following section covers the preliminary design procedure for the hydraulic ESS. This includes the process of using the design targets to generate the initial design parameters. Once the process is shown for one design case, the results of applying the same procedure to each of the sets of design targets is shown in a table for comparison. Before the design procedure can commence, the type of components to be used must be specified. This important step dictates the constraints that must be applied. The hydraulic system considered consists of a variable displacement axial-piston hydraulic pump/motor connected through a set of gears to the vehicle between the transmission output and final drive reduction gears. The pump/motor transfers fluid between a steel bladder-type accumulator and a simple fluid storage reservoir. It is assumed that the necessary 175

191 hydraulic controls are present and do not impose restrictions on the operation. Table 37 and Table 38 list the resulting constraints and parameters which must be specified for the configuration considered, respectively. Table 37. Hydraulic ESS Design Constraints Design Constraints Maximum pump pressure [bar] 350 Maximum pump speed [rpm] 3000 Minimum pump speed [rpm] - Maximum accumulator pressure [bar] 350 System pressure to accumulator pre-charge 4:1 pressure ratio Table 38. Hydraulic ESS Design Parameters Design Parameter Accumulator - Volume - Maximum pressure - Pre-charge pressure Reservoir - Volume - Pre-charge pressure Pump/Motor - Maximum displacement - Maximum pressure Gears - Pump to driveshaft With the design constraints in mind, the process of determining the design parameters can begin. To illustrate this process, the steps to use the weighted mean with maximum power distribution design targets to arrive at a hydraulic ESS design are shown. 176

192 The first step in the procedure is to calculate the pre-charge pressure and accumulator volume necessary to store the desired amount of energy. The expression for accumulator energy outlined in Chapter 4 is used. (5.2) The integral can be performed over a range of pressure and volumes until the design target of 175kJ is met. Figure 78 shows the energy stored over a range of pre-charge pressures for a 16.1 liter accumulator. Using a pre-charge pressure of 110bar meets the design target. Figure 78. Accumulator Energy 177

193 Once the accumulator volume and pre-charge pressure are set, the pump gearing can be determined based on the maximum pump speed. Using the maximum velocity of 25mph along with the vehicle parameters, the following relationship can be used to solve for the highest pump gearing which allows for pump operation without exceeding the speed limitation. (5.3) Performing the calculation shows a gear ratio of 2.6:1 will prevent pump over-speed at 25mph. With the gear ratio and pre-charge pressure determined, the pump displacement necessary to achieve the target power level can be found. Making the assumption that the highest power occurs near the highest vehicle speed and consequently, highest pump speed, the displacement can be solved for from the following equation using a power value of 28kW and a maximum speed of 3000rpm. (5.4) Considering the lowest possible pressure (pre-charge pressure), solving for the displacement gives 61 cc/rev as the required pump size to meet the power target. The remaining parameter to determine is the necessary reservoir size. The reservoir must be of sufficient volume to accommodate the maximum fluid volume that can be held in the accumulator. Applying the ideal gas law and adiabatic assumptions, a good estimate of the fluid volume can be calculated. The following expression is the result of those assumptions: 178

194 (5.5) Using the above equation gives a fluid volume of 12.9 liters. Therefore, the reservoir must accommodate at least 12.9 liters of fluid. Following the same procedure for each set of design targets from the four statistical weightings gives the preliminary designs shown in Table 39. Table 39. Hydraulic ESS Preliminary Designs Maximum Values Mean Values Weighted Mean Mean Weighted with Max Power Dist. Accumulator Volume [liters] Pump Displacement [cc/rev] Pump Gear Ratio Pre-Charge Pressure [bar] Reservoir Volume [liters] As expected, the higher power target leads to higher pump displacement, while higher energy targets causes the accumulator volume to increase. Higher maximum vehicle speeds reduce the pump gear ratio, decreasing the torque multiplication from the pump. 179

195 5.4 Evaluation of Preliminary Designs The following section covers the evaluation of preliminary designs for both the mechanical and hydraulic energy storage systems. The cost function is used as the basis for evaluating the preliminary designs. The results from simulation are compared in both cases and conclusions are drawn Evaluation Procedure Once the preliminary design parameters are set the evaluation process can begin. The evaluation process is two-fold. First the design parameters are taken and used to generate estimates of the design attributes of mass, volume and cost. Next, the design parameters and the mass are used to evaluate the design in simulation. Once this is completed, the results of the simulation are coupled with the design attributes through the cost function to arrive at a single value which represents the overall quality of the design. The following sections will step through the evaluation process for both the mechanical and hydraulic ESS preliminary designs. Before performing the evaluations individually for the mechanical and hydraulic designs, it is pertinent to discuss the evaluation techniques that will be applied to each. The cost function definition is similar for both AESS types. Both use the formula shown below, only with potentially different weightings coefficients (a,b,c,d) and normalization (or target) values. (5.6) 180

196 For the purposes of showing the design procedure, the weighting coefficients will remain the same and have been chosen as the following: Table 40. Cost Function Weights Cost Function Weights The choice shown in Table 40 focuses on the efficiency of the system and cost over mass and volume. 50% of the weight is place on the efficiency of the system and 30% is placed on cost in order to emphasize the performance and cost aspects of the systems. The same weight (10%) was given to mass and volume. Changing the weights will significantly affect the design chosen as the best solution. Increasing the weights of mass and volume will results in a smaller, lighter system which may sacrifice efficiency. In general, cost will scale with mass and volume. If the components are larger and heavier, the cost will increase as well. Despite the strong impact of the weighs on the final design parameters, the process remains the same regardless of the weights used. Careful thought should be given to the values of the weights. Various sets of weights can also be used to evaluate several potential designs. Alternatively, the factors in the cost function can be pulled out and treated as constraints with high or low limits. For example, the volume factor could be removed from the cost function and instead be treated as a constraint with a maximum value. In this case all designs with less than a certain volume would be considered acceptable and no additional preference for smaller systems would be given. 181

197 The normalization values for each design type will be from the design using the weighted mean design targets. The weighted mean design targets should provide a conservative design which caters to the statistically most common events. Finally, to gain a better understanding of the effect of the cost function weights, the sensitivity of the design to the cost function weights should be studied. This is crucial to understanding the design space and the influence of the weighting factors. Also similar for each design type will be the calculation of, the efficiency of the system at returning the available braking energy to the vehicle. This efficiency is defined at the energy provided to the vehicle by the AESS divided by the total amount of energy available for recovery. This metric is a proxy for the fuel savings the AESS will be able to provide since it is proportional to the reduction in energy that must be provided by the engine. It is used instead of the actual fuel consumption since engine control and transmission behavior may confound the results if fuel economy is used as the focus. The following equation describes this efficiency calculation: (5.7) In practice, this calculation must be adjusted slightly for any difference in state of energy of the AESS between the beginning and end of the simulation. For instance, if the AESS starts with zero energy, but ends with some available energy it is possible that the energy remaining will be used the next time the vehicle is driven and therefore should be counted toward the returned energy. To rectify this situation, any difference between the final and initial AESS energy state is added to the numerator of the above equation. 182

198 5.4.2 Mechanical ESS Design Evaluation The following subsection will evaluate the preliminary designs for the mechanical ESS. First, the design attributes will be computed for each of the preliminary designs. Next, the design relevant outputs from simulation will be shown for one design case in order to confirm the behavior of the simulation. Finally, the results for the remaining designs will be shown and the cost function calculated for each. As part of the evaluation process, the design parameters must be used to determine approximate design attributes for the system. This process, as described in Chapter 4, will be shown as applied to the weighted mean with maximum power design. Mass Calculations The mass of the mechanical ESS is a combination of masses of the flywheel and containment structure, CVT and clutch, and gear sets. Using the correlations shown in Chapter 4, the breakdown of the masses for the components with the weighted mean with maximum power distribution design targets is shown in Table 41. Table 41. Mass of Mechanical Components Component Mass [kg] CVT 31.3 Flywheel 21.4 Containment 12.3 Gears 14.0 TOTAL

199 Volume Calculations The volume of the mechanical ESS is a combination of the volumes of the flywheel containment structure, CVT, and gears. Using the correlations shown in Chapter 4, the breakdown of the volumes for the components with the maximum values design targets is shown in Table 42. Table 42. Volume of Mechanical Components Component Volume [L] CVT 10.6 Flywheel 6.1 Containment Gears 2.0 TOTAL 18.7 Cost Calculations The cost of the mechanical ESS components primarily scales with the cost of the CVT and the cost of the flywheel and containment structure. Since cost information for flywheels and CVTs are not well established, for this design example an example cost equation will be used to weight the relative costs of increasing the CVT torque and flywheel inertia. (5.8) Where is the maximum CVT input torque in Nm and is the flywheel inertia in kg*m 2. The cost for the maximum values design is $2,910 based on the above equation. The basic structure of the cost calculation uses a fixed cost to estimate the overhead costs along with variable cost depending on the torque capacity of the CVT and the inertia of 184

200 the flywheel. The cost equation shown above was based on estimates of cost increase for similar components. Evaluation in Simulation Once the mass of the system is known, the design parameters along with the systems mass can be used to evaluate the performance of the design in a full-vehicle simulation environment. The behavior of the simulator and control strategy for the mechanical ESS are covered in Chapter 4. The results of using the simulation are shown below. Relevant state variables are plotted against time to verify the proper behavior of the system. The drive cycle used is the aforementioned synthetic cycle. The first confirmation of proper simulation is to ensure that the vehicle follows the desire speed trace. Figure 79 shows the first 500 seconds of the synthetic cycle. Figure 79. Mechanical ESS Vehicle Speed Profile Synthetic Cycle The vehicle matches the speed trace precisely. This confirms the behavior of the driver and response to the driver s inputs. Next, the engine torque and speed are shown. 185

201 Figure 80. Engine Torque and Speed on Synthetic Cycle The engine torque and speed are reasonable and behave as expected. An engine shut-off strategy allows the engine speed to be reduced to zero while the vehicle is at rest. The AESS state variables such as torques, speed, CVT ratio, and energy are shown next. The state of energy of the flywheel is determined by normalizing the current energy in the flywheel by the maximum possible energy storage, in this case 175kJ. Figure 81. Flywheel Speed Synthetic Cycle 186

202 Figure 82. ESS State of Energy Synthetic Cycle Figure 83. CVT Ratio Synthetic Cycle Figure 84. Clutch Mode Synthetic Cycle 187

203 Figure 85. Power Split at Coupling Point Synthetic Cycle From Figure 81 through Figure 85 the behavior of the mechanical ESS can be observed. The flywheel stores vehicle energy during deceleration and releases it on the subsequent acceleration. For this design case and cycle, the full capacity of the flywheel is not utilized. The maximum SOE that is reached is 100%, suggesting that the flywheel is being used to its full capacity. Tabulating the results for all four of the designs produces Table 43. Table 43. Mechanical ESS Preliminary Design Results Maximum Values Mean Values Weighted Mean Mean Weighted with Max Power Dist Mass[kg] Volume [L] Cost [$] Once the design results are known, the values can be normalized by the weighted mean results and a cost function value can be calculated. 188

204 Table 44. Mechanical ESS Preliminary Design Cost Function Values Maximum Values Mean Values Weighted Mean Mean Weighted with Max Power Dist. Cost Function Value Looking at the cost function values, the mean values weighted with the maximum power distribution provides the lowest value. This is due to the relatively large increase in compared to the relatively small increase in mass, volume, and cost over the weighted mean design. To help analyze the designs, the one-way and two-way efficiencies were calculated based on the efficiency of the ESS. The one way efficiency is defined as the percentage of the energy absorbed from the vehicle by the EES that is actually stored in the flywheel. The two way efficiency is defined as the percentage of the energy absorbed that is returned to the vehicle. For the max values design, the one way efficiency is 82.8%, while the two way efficiency is 37.8%. This suggests that the max values design is very inefficient at returning the energy to the vehicle once it is stored in the flywheel. The main cause of the low two way efficiency is operating the clutch in slip mode. The efficiency of the system in slip mode is primarily determined by the efficiency of the clutch. Clutch efficiency is equal to the ratio between input speed an output speed. The longer the portion of time spent in slip mode, the worse the system efficiency will be. Since the flywheel is being used as a launch assisting device, the clutch must be allowed to slip during initial vehicle acceleration. The duration of this slip phase is dependent on a 189

205 number of factors including the design parameters and gearing in particular. Looking at the flywheel speed and clutch mode during one such acceleration event gives insight into the effect of gearing on the duration of clutch slip. Figure 86 shows the system behavior with a low numerical gear ratio similar to what is used in the maximum values design. Notice the clutch is in slip mode from t=510 until t=517, when the CVT can be used to control the flywheel speed. Figure 86. Clutch Slip Example Low Numerical Gear Ratio 190

206 In contrast, the same event is shown for a design with a higher numerical gear ratio between the CVT and drivetrain in Figure 87. With a higher numerical gear ratio, the duration of clutch slip mode is reduced significantly. The slip period now ends before t = 515s, which leads to a much higher two way efficiency. Figure 87. Clutch Slip Example High Numerical Gear Ratio The gearing difference and the larger inertia are the primary reasons for the effectiveness of the weighed mean with maximum power distribution design s low cost function value. 191

207 5.4.3 Hydraulic ESS Design Evaluation The following subsection will evaluate the preliminary designs for the hydraulic ESS. First, the design attributes will be computed for each of the preliminary designs. Next, the design relevant outputs from simulation will be shown for one design case in order to confirm the behavior of the simulation. Finally, the results for the remaining designs will be shown and the cost function calculated for each. As part of the evaluation process, the design parameters must be used to determine approximate design attributes for the system. This process, as described in Chapter 4, will be shown as applied to the maximum values design. Mass Calculations The mass of the hydraulic ESS is a combination of masses of the pump, accumulator, reservoir, fluid, and gears. Using the correlations shown in Chapter 4, the breakdown of the masses for the components with the weighted mean with maximum power distribution design targets is shown in Table 45. Table 45. Mass of Hydraulic Components Component Mass [kg] Pump/motor 30.8 Accumulator 82.9 Reservoir 4.1 Fluid 11.3 Gears 7.0 TOTAL

208 Volume Calculations The volume of the hydraulic ESS is a combination of the volumes of the pump, accumulator, reservoir, and gears. Using the correlations shown in Chapter 4, the breakdown of the volumes for the components with the maximum values design targets is shown in Table 46. Table 46. Volume of Hydraulic Components Component Volume [L] Pump/motor 10.3 Accumulator 28.9 Reservoir 12.9 Gears 1.0 TOTAL 53.0 Cost Calculations The cost of the hydraulic ESS components primarily scales with the cost of the pump and the cost of the accumulator. Based on cost information for off-the-shelf hydraulic components, the following equation for cost will be used. (5.9) Where is the pump displacement in cc/rev and is the accumulator volume in liters. The cost for the maximum values design is $3,340 based on the above equation. Using off-the-shelf component information it was found that accumulators start at 4 liters in size and the incremental cost per additional liter of capacity is approximately $50. Similarly for the hydraulic pump, the minimum displacement for the type of pump used was 18cc/rev. The incremental cost per additional displacement is approximately $

209 The $2450 represents the cost of the 4 liter accumulator plus the 18cc/rev pump along with estimations for the cost of a fluid reservoir and the necessary hydraulic controls. Evaluation in Simulation Once the mass of the system is known, the design parameters along with the system s mass can be used to evaluate the performance of the design in a full-vehicle simulation environment. The behavior of the simulator and control strategy for the hydraulic ESS are covered in Chapter 4. The results of using the simulation are shown below. Relevant state variables are plotted against time to verify the proper behavior of the system. The drive cycle used is the FTP-75 cycle. The first confirmation of proper simulation is to ensure that the vehicle follows the desire speed trace. Figure 88. Desired and Actual Speed Trace Synthetic Cycle The vehicle matches the speed trace precisely. This confirms the behavior of the driver and response to the driver s inputs. Next, the engine torque and speed are shown. 194

210 Figure 89. Engine Torque and Speed over Synthetic Cycle The engine torque and speed are reasonable and behave as expected. An engine shut-off strategy allows the engine speed to be reduced to zero while the vehicle is at rest. The AESS state variables such as torques, speed, pressures, volumes, and energy are shown next. 195

211 Figure 90. Hydraulic Pump/Motor Torque and Speed Figure 91. Hydraulic Pump/Motor Flowrate 196

212 Figure 92. Hydraulic Pump/Motor Displacement Figure 93. Hydraulic Accumulator Pressure 197

213 Figure 94. Hydraulic Accumulator and Reservoir Volumes Figure 95. Hydraulic Accumulator State of Energy Much can be garnered from the behavior of the maximum values designed hydraulic system over the synthetic cycle. Most notably the state of energy of the accumulator does reach the maximum value, showing full utilization of the energy storage system. Figure 92 it is seen that the maximum pump displacement is reached in many occasions. The majority of these instances are due to traction torque assist, however, a portion are during vehicle braking. This is an indication that if the displacement was higher or the pump gear ratio numerically higher, more energy could potentially be recovered. Additionally, 198

214 some engine braking is reducing the amount of energy which can be recovered by the hydraulic system. Using the results of the simulation, a value of the cost function can be calculated. For the maximum values design, the braking energy recovery efficiency is % of all of the energy that would have otherwise been dissipated by the friction brakes was returned to the drivetrain by the hydraulic ESS. Tabulating the results for all four of the designs produces Table 47. Table 47. Hydraulic ESS Preliminary Design Results Maximum Values Mean Values Weighted Mean Mean Weighted with Max Power Dist Mass[kg] Volume [L] Cost [$] Once the design results are known, the values can be normalized by the weighted mean results and a cost function value can be calculated. Table 48. Hydraulic ESS Preliminary Design Cost Function Values Maximum Values Mean Values Weighted Mean Mean Weighted with Max Power Dist. Cost Function Value Looking at the cost function values, the weighed mean design provides the lowest value. This is due to the relatively small decrease in compared to the relatively large 199

215 decrease in mass, volume, and cost over the weighted mean with maximum power distribution design. It is interesting to note that for the same drive cycle, the best mechanical ESS design uses the mean weighted with maximum power distribution while the best hydraulic ESS design uses the weighted mean design targets. This difference is due to the difference in operation and energy density of the systems. The hydraulic system is less sensitive to gearing changes than the mechanical system and also gains more weight when the desired energy storage capacity is increased. 5.5 Design Optimization After the preliminary designs are evaluated, the process of optimizing the designs can begin. The goal of the optimization is to begin with the best of the preliminary designs and refine the design until it can no longer be improved. The preliminary design serves the purpose of eliminating a significant portion of the design space and providing a starting point in the search for the minimum cost function value. This section will focus on the refinement of the design to find the minimum cost function value for both the mechanical ESS and hydraulic ESS. The process that will be used is a full-factorial design with each of the design parameters serving as factors with three levels. The three levels will be the factor at its best preliminary design level, 90% of the preliminary design level, and 110% of the preliminary design level. For example, the accumulator volume for the best preliminary hydraulic ESS design is 11.1L. The levels for the accumulator volume in the full-factorial design will be 10L, 11.1L, and 12.2L. 200

216 With the full-factorial design, each possible combination of levels is evaluated. The benefit of this experimental design is that interaction effects between the design parameters can be studied. For example, changing pump displacement alone might not produce a significant benefit, however, if the gearing is also changed along with pump displacement, then a reduction in the cost function value might be realized Mechanical ESS Design Optimization Starting with the design parameters from the mean values weighted with the maximum power distribution, a full factorial experiment was conducted with the design parameters maximum CVT input torque, flywheel inertia, and CVT to drivetrain gear ratio all at three levels (at, 10% above, and 10% below the nominal design value). Each possible design combination was evaluated in simulation and the results were compared in terms of cost function value. 201

217 Figure 96. Mechanical ESS Design Parameter Interaction Plot Looking at the interaction plots from the results of the simulations, there is little interaction between the parameters with these factor levels. The general trends can be seen in both Figure 96 and Figure 97. The inertia with the lowest cost function value is 0.106, while the cost function value decreases with increasing CVT to drivetrain gear ratio and decreases with decreasing maximum CVT torque. At this point, the results point to further increasing the gear ratio and further decreasing the maximum CVT torque in order to explore the design space further. 202

218 Figure 97. Mechanical ESS Design Parameters Main Effects Plot Eventually, further increasing the gear ratio and decreasing the CVT torque capacity are no longer beneficial. This is due to the reduction of vehicle speed range where regenerative braking can occur and the reduction in power of the ESS. With these results, the question becomes why the reduction in gear ratio is beneficial. The answer is twofold. Increasing the gear ratio allows for energy recovery at lower vehicle speeds when the speed differential between flywheel speed and vehicle speed is the greatest. The second benefit is an improvement in the efficiency of returning energy from the flywheel to the vehicle, particularly during launch assist. Since the clutch must be slipped when the flywheel is used to help accelerate the vehicle from rest, a portion of the flywheel s 203

219 energy is expended in a less efficient manner. Increasing the gear ratio decreases the amount of time the clutch operates in slip mode, therefore increasing the efficiency of releasing the flywheel s energy. Based on the design refinement, the combination of maximum CVT torque and gear ratio is 95 and 8.54:1, respectively. This combination provides a low cost function value while providing good power capability and adequate speed range. Table 49. Optimized Mechanical ESS Design Parameters Mean Weighted with Max Power Dist. Optimized Design Values Flywheel Inertia [kg*m 2 ] Maximum CVT Input Torque [Nm] Flywheel to CVT Gear Ratio 5:1 5:1 CVT To Drivetrain Gear Ratio 6.0:1 8.54: System Mass [kg] System Volume [L] System Cost [$] Cost Function Value Comparing the optimized design with the mean values weighted with the maximum power distribution, the only differences are a slight reduction in the maximum CVT torque and an increase in the CVT to drivetrain gear ratio. This improves efficiency and reduces the cost while maintaining the same mass and volume. 204

220 5.5.2 Hydraulic ESS Design Optimization Starting with the design parameters from the mean values weighted with the maximum power distribution, a full factorial experiment was conducted with the design parameters pump displacement, accumulator volume, and pump gear ratio all at three levels (at, 10% above, and 10% below the nominal design value). Each possible design combination was evaluated in simulation and the results were compared in terms of cost function value. From evaluating all of the combinations, trends can be identified and used to help determine the optimum solution. Figure 98 shows the main effects of the design parameters on the cost function value. From the plots, it can be seen that in all cases, the accumulator volume of 10 liters and a gear ratio of 2.56 provide the lowest cost function value. However, the trend for the pump displacement shows lower displacement improving the design. 205

221 Figure 98. Main Effects Plots for Cost Function Value In addition to the main effect plots, the interactions between the design parameters should be considered. Figure 99 shows the interaction plots for all of the design parameters. The lack of parallel behavior of the lines indicates significant interaction between the design parameters. This means the main effects are not dominant and cannot be solely used to guide in optimization. 206

222 Figure 99. Interaction Effects for Hydraulic Design Parameters Based on in the interaction plots, significant interaction is seen between the pump displacement and the gear ratio. At the higher pump displacements, increasing the gear ratio does not improve the performance, however, at the -10% displacement, increasing the gear ratio has a positive effect on the cost function value. Less significant interaction is seen between the other factors. Following the trend of decreasing the pump displacement along with increasing the gear ratio results in the optimized design parameters and attributes are shown in Table