MODELLING, OPTIMIZATION AND VERIFICATION OF POWER SPLIT INFINITELY VARIABLE TRANSMISSIONS

POLITECNICO DI BARI DOTTORATO DI RICERCA IN INGEGNERIA DELLE MACCHINE XX Ciclo Curriculum:Macchine a fluido (SSD ING-IND/08) Sede di Bari MODELLING, OPTIMIZATION AND VERIFICATION OF POWER SPLIT INFINITELY VARIABLE TRANSMISSIONS Salvatore Schembri Volpe Relatori: Dott. Ing. Giuseppe Carbone Prof. Ing. Michele Napolitano Dott. Ing. Enrico Sedoni Controrelatori: Prof. Ing. Massimo Borghi Coordinatore: Prof. Ing. Michele Napolitano A.A. 2008-2009

One must still have chaos in oneself to be able to give birth to a dancing star. F. Nietzche on Earth, I will keep on running on Air, I will keep on flying on Water, I will keep on rowing and the Fire inside me, will always keep on burning SSV to Lucia and to all of my Family

Abstract The author presents an optimization procedure to design infinitely variable transmission architectures which allows them to achieve a significant reduction of power recirculation and, hence, an increase in mechanical efficiency. The focus of this thesis is on infinitely variable transmissions used in off-highway vehicles and in particular on input coupled and output coupled architectures. The optimized solutions have been analyzed in depth, with particular attention to the power flowing through the infinitely variable unit, which strongly influences the overall efficiency of the transmission. The major result of this study is that also the so far neglected output coupled solution, if properly optimized, guarantees very good performance over the entire range of vehicle speed. The analysis then shows that the particular choice of either input or output coupled architecture by itself, or of a mixed solution, strictly depends on the specific application under consideration and that none of them should be discarded a priori. Robust control systems playing a crucial role in order to guarantee human operator safety and overall vehicle performance in different working conditions, a virtual verification process is described focusing on the Model Based Engineering, which allows to reduce the number of prototypes and, hence, lower costs and development time.

Preface This work has been carried out as part of a collaboration program between the Politecnico di Bari and Case New Holland - Product Development. This being so, the academic research has been applied to the industrial automotive context, with particular focus on the Global Product Development process of power split infinitely variable transmissions for off-highway, agricultural and construction equipment vehicles. The thesis aims to show an original and effective approach, based upon a design optimization procedure and a virtual verification methodology, which turned out to significantly improve the transmission performance, reducing the time to market and the costs related to the product development. Therefore, this study not only provided an original contribution for the conceptual and performance analysis of infinitely variable transmissions, but also constitutes a valid and helpful tool for the design engineers in order to improve product quality and reliability, with a significant impact on the time to market and on the product cost. Chapter 1 provides a general introduction on the thesis work. Chapter 2 provides an overview on agricultural and construction equipment vehicles, highlighting the main technological features such as the Power Take Off, the hydraulic and electronic systems, with a general description of the general requirements during working conditions. Particular attention has also been devoted to the Global Product Development process. Chapter 3 provides a general survey on continuously and infinitely variable transmissions, describing the state-of-the-art technological solutions available and their general advantages and drawbacks. Specific attention is also paid on the suitability of each solution to the off-highway vehicles. Chapter 4 focuses on power split infinitely variable transmissions. A thorough analysis of power and torque flows is provided, with particular attention to the problem of power recirculation. Both the input and output coupled architectures have been analyzed, highlighting the potential benefits of mixed solution. An effective approach to the design phase is then presented by means of an optimization procedure to minimize power recirculation through the variable speed unit. This process allows to achieve a significant reduction of power recirculation and, hence, an increase in mechanical efficiency.

The analysis described in this chapter has been accepted for publication on the ASME Journal of Mechanical Design. Chapter 5 provides a general overview of a virtual verification process based upon Model Based Engineering. Following the optimization procedure described in Chapter 4, the optimized product specifications are used to develop a dynamic model of the physical system which allows to perform closed-loop simulations. May, 2009

Contents 1 Introduction 3 2 Fundamentals of agricultural machines 7 2.1 Transaxle and Power Take Off... 7 2.2 Hydraulic systems...... 8 2.3 Electronic systems... 10 2.4 Performanceandtypicalworkingoperations... 11 2.5 Global Product Development for agricultural and construction equipment machines... 13 3 Introduction to Continuously and Infinitely Variable Transmissions 16 3.1 CVUtypesandprinciples... 17 3.1.1 Hydrodynamictorqueconverter... 17 3.1.2 MechanicalCVUs... 18 3.1.3 HydrostaticCVUs... 21 3.1.4 ElectricCVUs... 24 4 Design optimization of power split IVTs 27 4.1 PrinciplesofpowersplitIVTs... 27 4.2 KinematicanalysisofapowersplitIVT... 30 4.2.1 Inputcoupledequations... 32 4.2.2 Outputcoupledequations... 35 1

4.3 Power flowanalysis... 36 4.3.1 Input coupled power flows... 37 4.3.2 Output coupled power flows... 41 4.4 DesignoptimizationofpowersplitIVTs... 45 4.4.1 Optimizationproblemformulation... 46 4.4.2 Numerical implementation of the optimization process...... 48 4.4.3 Theoptimizationalgorithms... 49 4.4.4 SimulatedAnnealing... 51 4.4.5 Results... 53 4.5 Optimizationconclusions... 56 5 Virtual verification of power split IVTs 61 5.1 Current scenarios for off-highwayvehicles... 62 5.2 Model-Based Design... 64 5.3 PlantModel... 65 5.3.1 Theactuationsystems... 67 5.3.2 Drivelinemodel... 70 5.4 ModelandSoftwareintheLoop... 71 5.5 HardwareintheLoop... 72 5.5.1 HILsimulationsandautomatictestsequences... 75 6 Conclusions 81 7 Acknowledgements 83 8 Nomenclature 88 2

Chapter 1 Introduction Automotive manufacturers are facing significant challenges arising from the continuous evolution of the market demand, lawmakers decisions in terms of polluting emissions and new compelling technologies. In particular, the product development process has to deal with tighter cost and time targets in order to increase profitability, gain and maintain a sustainable competitive advantage versus competitors: customer needs have to be properly understood and translated into effective and efficient technical solutions, matching cost targets and minimizing the time to market. Agricultural and construction equipment machines are of utmost importance for the world s nutrition and housing needs, with a technology content evolving to high sophisticated mechatronic systems in the developed countries. The tractor and the harvester remain still the most important machines and their transmission system is a key component representing about 35-40% of the total tractor first cost. In the last few decades, a growing attention has been devoted to the environmental issue. Governments are continuously setting tighter limitations for polluting emissions to reduce green-house gases. In order to fulfil these requirements, automotive manufacturers are obliged to dramatically reduce fuel emissions while increasing vehicle performance and comfort. Continuously Variable Transmissions (CVTs) have been widely introduced in the au- 3

tomotive industry, in particular in the off-highway market, thanks to their many advantages in terms of fuel economy, reduced emissions and human operator comfort. About 100 years ago, battery-driven electrical drives allowed already a continuously variable speed control and low noise levels, though the main problem was the poor capacity for stored energy. Early developments of hydrostatic drives have been introduced in mid 60s, at the same time agricultural engineers invented a friction drive CVT for a self-propelled plough in which the speed control was obtained by the radii of friction contacts. Recently, off-highway vehicle manufacturers have introduced hi-tech CVTs on almost all the lines of product, with a small exception for the low power machines in which the cost of such a complex transmission cannot be justified. The scientific literatureoffers a high number of contributions focusing on CVTs. Carbone, Mangialardi and Mantriota have analyzed the dynamic performance of metal V- belt CVTs and toroidal traction drives [1, 2], in particular for road vehicles [3, 4]. Renius [5] has performed a very useful and detailed analysis of the market demand evolution for agriculture machines, focusing on several state-of-the-art CVT technologies. The CVU can generally be realized using different technological solutions: hydrostatic transmissions with variable displacement units, belt or chain drive, toroidal traction drives, electric groups (generator-inverter-motor). Several technological solutions for CVUs offer the possibility to obtain a zero output speed with a non zero input speed even without any PGT connection: in this case, the CVU can actually be thought of as an Infinitely Variable Unit (IVU). Examples of IVU can be hydrostatic transmissions with at least one variable displacement unit, or hybrid electric transmissions with generator, inverters and motors. Generally, both CVUs and IVUs present a lower efficiency compared to that of a fixed ratio mechanical transmission, therefore a direct CVT transmission, i.e., a transmission in which all the input power flows through the CVU, presents a poor overall efficiency and a significant heat dissipation. Furthermore, direct CVTs adopting CVU do not allow to obtain a zero output speed with a non-zero input one (the so-called zero active speed). 4

Power split IVTs are a particular CVT typology that offers the possibility to obtain a zero active speed: they can generally be obtained by coupling either a CVU or a IVU, a Planetary Gear Train (PGT) and a fixed ratio gear. The total power is split into two parts, one flowing through a constant ratio mechanical path and one through the variable speed unit. Therefore, adopting power split IVT architectures, the negative effects in terms of power dissipation will influence a reduced amount of total power; nonetheless a continuously variable output speed can be obtained over a wider speed range, in particular with multiple-range architectures. As a main consequence, power split IVTs present an overall efficiency higher than that of a direct CVT, due to the higher efficiency of the mechanical path. This thesis focuses on applications of virtual modelling and numerical simulations to the entire Global Product Development (GPD) process of power split infinitely variable transmissions for agricultural and construction equipment machines, introducing a thorough conceptual analysis of different architectures. The power and torque flows through the variable speed units have been deeply investigated, since they are strictly related to the overall transmission efficiency. Particular attention has been devoted to the effects of the transmission gear ratios, especially for complex, multiple ranges architectures, for they strongly influence the amount of power recirculation through either the CVU or IVU. Anovel,effective approach for the design optimization process of power split IVTs for agricultural and construction machines has been developed by the means of different state-of-the-art optimization algorithms, which turns out to potentially increase the transmission efficiency, significantly improving the overall vehicle performance. Robust and effective control system playing a crucial role, the Model Based Design approach will be finally described, in order to implement a virtual verification process before production. The number of prototypes required to develop and test the control strategies can be reduced adopting numerical models which are used to perform in-the-loop simulations with the control system. As resulting benefits, the overall vehicle performance can 5

be tested and improved earlier within the GPD process; a very high number of working scenarios can be safely simulated, including failure dangerous conditions; a significant reduction of costs and time can be achieved. 6

Chapter 2 Fundamentals of agricultural machines 2.1 Transaxle and Power Take Off The complete tractor transmission, also referred to as transaxle, can be schematically represented as in Fig. 2-1, [6], showing a combination of the vehicle speed change gearbox, the rear axle with brakes, the Power Take Off (PTO) and, if required, arrangements for the front axle drive and for the drive of auxiliary units. The PTO has a crucial importance for agricultural machines for it is the only way to make the tractor to be a mobile power supply [21]. It is represented by a mechanical shaft generally located on the rear of the tractor which is frequently adopted to connect the machine with several kind of devices, such as trailers, ploughers, haying tools, by means of a mechanical joint. In some cases, a PTO is available also on the front of the vehicle. In general, the PTO has to be able to drive hydraulic pumps and any other auxiliary component, also with non-zero vehicle speed, Fig. 2-2. In standard applications, the PTO speed is completely independent from the driveline output speed for it takes its motion directly from the primary shaft, typically using an engagement clutch followed by spur gears for different output PTO speeds. Generally, 7

Figure 2-1: Side view of a tractor transmission the PTO presents two standard output speeds, namely 540 and 1000 rpm at 2000 rpm of engine speed. In some cases, a so called economic ratio can be found, with the aforementioned output speeds with the engine rotating at about 65% of its maximum power speed. Modern tractors also offer a synchronized PTO which takes its motion from the output driven shaft of the transmission, therefore the angular speed is synchronous with the tractor wheels speed. This kind of application is especially useful for those kind of trailers that need to work as drivers. 2.2 Hydraulic systems Following the historic development of the mechanical system, the adoption of hydraulic systems of growing complexity is one of the key feature of the modern agricultural and construction machines, starting in 70s and 80s, making a heavy use of hydraulic components in order to activate and control main components, such as the loader, the steering system, the four-wheel drive mode, the power take-off, the range shift system, the clutches and the brakes. Fig. 2-3 shows a sample scheme of the hydraulic circuit of a 8

Figure 2-2: Example of a mechanical PTO, CNH all rights reserved. light tractor. In recent applications, hydraulic circuits are also employed in combination with other mechanical devices to realize continuously variable transmissions. Combine and forage harvesters typically adopt hydro-mechanical transmissions characterized by multiple hydrostatic units and very prolonged piping systems. Construction equipment machines can operate only thanks to hydraulic systems able to actuate telescopic arms and loaders. There are two principal typologies of hydraulic circuits: Open Center and Closed Center. Open center circuits, normally adopt such a pump so as to get a constant flow rate and a variable pressure. The pump is directly actuated by the engine shaft and continuously pressurizes the oil, regardless from the components activated. Closed center circuits, on the other end, normally adopt pumps which provide a constant pressure and variable flow rate. In both cases, the hydraulic circuit only absorbs engine power when some hydraulic components is actuated, in particular for auxiliary ones. 9

Figure 2-3: Hydraulic circuit of a 100hp tractor. CNH all rights reserved. 2.3 Electronic systems Starting from the mid 80s, electronic systems showed a strongly growing presence on offhighway vehicles. A high number of Electronic Control Units (ECUs) has been adopted on board for different purposes: (i) to properly measure and process physical signals, (ii) to better detect and respond in different working conditions, (iii) to automatically control the engagement and disengagement of mechanical components. ECUs allow to control in closed loop the proper sequences of transmission ranges, especially in loaded conditions, according to the engine speed and to the output vehicle speed requested by the human operator, as it is in the case of infinitely variable transmissions. In general, electric systems are adopted to actuate any hydraulic component related to the driveline ranges, i.e. multi-disc clutches, synchronizers, brakes, infinitely variable units, engine speed request. The transmission can indeed be automatically controlled by taking into account the engine speed, the load torque acting on the wheels, the traction load, the vehicle speed and tire slipping. 10

Figure 2-4: Forces decomposition during towing operations 2.4 Performance and typical working operations Agricultural and construction machines are mainly meant to provide the following functions: Provide a traction towing force and guarantee loading operations; Supply mechanical power by the means of the PTO; Supply hydraulic power thanks to the auxiliary components and to the loader. In particular the towing force is one of the crucial aspects since it allows the operator to work in different scenarios, on different ground conditions and with different working devices, Fig.2-4.One of the key requirements for a tractor is indeed represented by the traction load curve at fixed maximum engine power. The maximum traction load to be guaranteed is generally associated to the Gross Vehicle Weight (GVW) of the ballasted tractor, so as to obtain a behavior as the normalized one shown in Fig. 2-5, representing the so called Nominal Working Cycle, wherethe 11

(b) Engine Power (a) Traction Load maximum traction load can be saturated either by the tires adherence limits or by any other maximum sustainable load within the transaxle. 1 0.8 0.6 0.4 0.2 0 0 0.5 1 1.5 2 2.5 Ground Speed 1 0.8 0.6 0.4 0.2 0 Ground Speed Figure 2-5: Normalized traction load (a) at maximum rated normalized engine power (b) Table 2.1 shows other typical agricultural applications with their relative vehicle working speed. Ground speed Application 0, 2 2 km/h Digging 2 5 km/h Rotary harrows, hoeing 5 10 km/h Plowing, packing 10 50 km/h Mowing, sprinkling, transportation Table 2.1: Ground speed as function of agricultural application Focusing on the rated engine power, typically four main tractor families can be distinguished which differ in terms of diesel engine type, number of vehicle missions to be accomplished, and comfort level required for the human operator, see Table 2-6. 12

Figure 2-6: Major classification of tractors 2.5 Global Product Development for agricultural and construction equipment machines Global Product Development (GPD) process represents the key strategy at the basis of all Research & Development (R&D) efforts in developing new concepts and technologies to match customer needs and improve product quality and vehicle performance maintaining profitability. The starting point is represented by the voice of the Customer, who has to actively interact with marketing department, namely the Brand, and specific product platforms to express needs and requirements: these information have to be thoroughly understood andtranslatedintoeffective design concept and technical specifications [20]. Generally, the GPD process for automotive industry can be divided in five main steps, as shown in Fig. 2-7. Once the customer needs have been properly collected and analyzed, the first step is represented by the Program Planning. At this stage, the product platforms and the marketing department share the potential programs to match the targets that have been set by the Customers, defining the key strategies, the overall program duration - which constitutes the Time To Market (TTM) - and the program milestones. The engineering departments have to be involved as well since this phase is strictly related to the Concept 13

Figure 2-7: Main steps of the Global Product Development process for automotive industry. Development which represents the early design process either of a new product or a core feature. In this phase, all the ideas and concepts addressing the targets are taken into consideration so as to create a set of potential technical solutions. Next step is represented by the Feasibility Analysis, during which engineers and platforms thoroughly evaluate advantages and drawbacks related to any potential solution arisen from the concept development. Different considerations and constraints are taken into account, namely costs, legislation, potential markets, competitors offer, available and patented technologies, manufacturing and logistic constraints. The output from this phase can be thought of as the Company s answer to the Customer in terms of feasible and appropriate product design concepts. If this output is considered appropriate in terms of quality, feasibility and profitability, the program can be considered approved (Program Approval) and the GPD process can move ahead. The Optimization phase consists in all of those actions and analyses meant to properly define product specifications and features so as to match customer expectations and to maximize the added value. For the specific applications of agricultural and construction 14

equipment machines, the value added is certainly represented by reduced fuel consumption, low emissions, improved vehicle performance, maximum human operator comfort. In this step, very important is the What-If analysis, which is basically meant to thoroughly investigate as many design solutions as possible, in order to guarantee the optimal product performance given the related design constraints. Product design specifications have then to be validated and tested in order to ensure product quality and safety prior to manufacturing: this happens in the Verification phase. Physical and virtual prototypes are verified and tested; also, the control logics and the relative control software are developed and validated. Last step is the Implementation, in which the product design is frozen and released to manufacturing plants that are now allowed to produce the product (OK to Build) and then forward it to the various Dealers (OK to Ship). Virtual analysis and numerical simulations turn out to be of utmost importance during the overall aforementioned process. Product and feature models allow to speed up the early GPD phases so as to be able to detect any potential failure in significant advantage with respect to the latest steps; the optimization phase can be managed in a rigorous and effective way implementing Design of Exploration activities so as to deeply investigate and maximize the product performance by varying the design parameters over a wide range of acceptable values; dangerous and unsafe working conditions can be tested and analyzed minimizing the risks for employees and for the Customer itself. From an economic point of view, the cost associated to a design problem heavily increases in the latest step of the GPD: too late problems can determine the need of extra prototypes, significantly increasing the time and the costs. In this work, applications of numerical simulations will be shown following the baseline of the GPD process, starting with the model and the analysis of a new product, then showing the benefits obtained from an effective optimization procedure in terms of vehicle performance, and finally illustrating a state-of-the-art approach for control system development and test, which significantly supports product robustness and reliability. 15

Chapter 3 Introduction to Continuously and Infinitely Variable Transmissions The transmissions adopted in the automotive industry can generally be split into two main families: stepped and stepless transmissions. The former category represents the most popular solution, especially for European car market; the latter is based on Continuously Variable Transmissions (CVTs) and recently has been widely introduced in the automotive industry, in particular in the off-highway market, thanks to their many advantages in terms of fuel economy, reduced emissions and human operator comfort. Focusing on agricultural machines, CVTs with automatic controls have been introduced in Europe in 1996 for standard tractors, opening a new era of power train design principles. A CVT is a power transmission device which allows to continuously vary the speed ratio between two finite extremes thanks to the adoption of a Continuously Variable Unit (CVU) connected between two mechanical shafts. When the speed ration can be continuously varied between two values including the zero output speed with a non-zero input one, the CVU can be referred to as an Infinitely Variable Unit (IVU). Infinitely Variable Transmissions (IVTs) are particular kind of CVT that offer the possibility to continuously vary the output velocity including the possibility to obtain a zero output speed wit a non-zero input speed. Therefore, an IVU can be thought of as 16

Figure 3-1: Main typologies of continuously variable units. an IVT when adopted by itself. This chapter provides a general survey of the known available technologies in terms of continuously and infinitely variable units, describing the working principles and the main advantages and drawbacks, with specific reference to off-highway applications. 3.1 CVU types and principles In general, four main CVU typologies can be considered as fundamentals, differing for the physical principle adopted, ratio control system and field of application: hydrodynamic torque converter; mechanical; hydrostatic; electric, see Fig. 3-1, [5]. 3.1.1 Hydrodynamic torque converter The hydrodynamic torque converter has recently achieved the highest production volumes for cars and construction machinery, offering the lowest production cost. On the other hand, this technology presents two major weak points for off-highway applications: (i) 17

the maximum efficiency is not generally poor, but is available only within a very limited range of transmission ratios; (ii) the speed ratio cannot be controlled in Closed Loop as it is automatically related to the load. A solution to diminish point (i) is to add a free wheeling element or even a clutch blocking the unit, but this would reduce the system effectiveness in terms of continuous output velocity thus requiring a higher number of additional conventional ranges. Weak point (ii) cannot be significantly improved. These are the main reasons why the torque converter have not been successfully adopted, in particular on agricultural machines. 3.1.2 Mechanical CVUs Mechanical CVUs allow the closed loop ratio control by the means of variable effective radii, whereas the torque is transmitted by the mean of the traction force between the friction contacts. Furthermore, the efficiency is significantly high with respect to the other CVT types. Therefore, mechanical CVUs can be successfully employed in the offhighway markets, though generally limited to the low to medium power applications. An example of mechanical CVT transmission for agricultural machines is shown in Fig. 3-2. In general, two main traction types CVUs are available : V-Belt CVUs and toroidal traction drives. V-Belt CVUs The gear ratio variation is obtained by two fixed sheaves with opposing two movable sheaves so that their relative movement allows to change the belt pitch radius at the input and output shafts, Fig. 3-3. The torque is generally a function of the normal force, the friction coefficient and the radius, namely T = μf N r. The normal force F N is generally obtained using a hydraulic actuation driven with electro valves. In terms of friction, these CVUs are normally lubricated by oil, therefore the maximum usable friction coefficient (steel/steel) ranges between 0.06 and 0.12 depending on the type of fluid. High values can be obtained with special "traction fluids" whereas lower values are 18

Figure 3-2: Continuously variable transmission realized with a mechanical CVU, Munich Research Tractor 1988. obtained for instance with rape seed oils. In general, V-Belt CVUs present the best potential efficiency, likely the highest efficiency among the different CVU concepts. If the clamping forces are properly controlled and adjusted to the actual torque load, mechanical full load efficiencies up to 95% can be achieved over a wide range of speed ratio. Actual values are generally smaller due to the losses in the hydraulic actuation and control system. If a simple variable displacement pump is used, the efficiency can be reduced down to 90%, whereas a significant improvement to 92.5% can be obtained using a variable displacement pump [5]. In terms of drawbacks, these CVUs present two significant limitations: (i) the CVU transmission range is limited between two finite values, thus it is not possible to obtain a zero output CVU velocity with a nonzero one; (ii) the transmission output speed range is generally limited, especially with respect to the combination between forward and reverse ranges; (iii) it is not possible to obtain an effective active zero output speed (power-zero) condition. 19

Figure 3-3: V-Belt chain CVT, concept of PIV As will be shown in the next chapter, the main consequence of weakness (i) is that V-Belt CVUs cannot be used for output coupled power split architectures. Toroidal traction drives Toroidal traction drives make use of power rollers, whose rotating axis is able to modify its position and to change the input and the output contact points. Two main classifications are available: "Full" and "Half" toroidal CVUs, Fig. 3-5.A typical advantage of toroidal CVUs is the potential for high torque capacity with compact design due to the parallel power flow. The slip is generally higher than in the case of chain drive CVUs, and the same applies for drilling friction. In general, half toroidal present a higher efficiency with respect to full-toroidal case, although in both cases the efficiency drops at high loads and at high speed reductions. Also, like in the case of V-Belt CVUs, the transmission ratio is limited between two finite 20

Figure 3-4: Measured mechanical efficiency of a V-belt CVU with a variable displacement pump for the actuation system. Courtesy of P.I.V. values. These are the most significant limitations for off-highway vehicles, in particular for power split IVTs. 3.1.3 Hydrostatic CVUs Hydrostatic CVUs are formed by the combination of at least one hydrostatic pump and at least one hydrostatic motor, [5]. Moreover, at least one unit must have a continuously variable displacement. Since these circuits allow to obtain a zero output speed with a non-zero input one, they can be referred as IVUs. A simple scheme of a hydrostatic circuit is shown in Fig. 3-6, [6].In general, these circuits work with a fully reversible variable displacement pump (1) that is connected to the input shaft, and a fully reversible motor (2) that can have constant of variable displacement according to the design architecture adopted and is connected to the output shaft. The charge pump (3), with the safety valve (4), always feeds the low pressure pipe passing through the filter (5) and one of the check valves (6). The surplus oil leaves the low pressure pipe automatically thanks to the flush valve (7) arriving at the tank through the pressure relief valve (8) and the cooler (9). 21

Figure 3-5: a) Half toroidal and b) Full toroidal CVU geometry Figure 3-6: Typical hydrostatic circuit adopted as IVU. Symbols ISO 1219-1. 22

The charging system is often adopted in order to replace oil leakage maintaining a minimum pressure in the low pressure pipe (namely 20bar), to control oil temperature, to control fluid contamination, to serve as an auxiliary power and to enable high pump speeds. The pressure relief valves (10) are safety elements. If the charging system fails, an emergency re-filling of the circuit is operated by the suction check valves (11), which however are not used in general. If a blow out takes place for a long period of time, the fluid temperature can rise to very high values exceeding the IVU limits, determining dangerous failures. That s one of the main reasons why modern systems adopt pressure limitation without blow out: the pump will decrease its displacement automatically once a pressure signal exceeds a given limit. For these systems, the torque transmitted is directly related to the circuit pressure and to the displacement of the units, therefore, if the pressure in the circuit is saturated by either the relief valves or the pump itself, also the maximum transmittable torque will be saturated. Therefore, for off-highway vehicles, pressure relief valves can constitute the limit to the maximum towing force defined in Sec. 2.4. The transmission ratio can be effectively controlled in closed loop by varying the variable displacement of either unit according to the input speed, the desired vehicle ground speed and the load conditions. Different strategies can be adopted in order to optimize vehicle performance and guarantee safe working conditions, Fig. 3-7, shows a standard concept of pump and motor displacement as a function of the ground speed, [5]. Hydrostatic IVUs present a lower efficiency if compared to mechanical CVUs and generally turn out in heavier and more voluminous solutions: these are the main reasons why these solution are not frequently adopted for passenger cars. However, they are successfully employed for off-highway vehicles and mobile machinery, especially in the medium to high power ranges, where the overall vehicle weight is not a crucial design constraint. Moreover, this kind of transmissions allow the possibility to obtain the complete set of power split Infinitely Variable Transmission (IVT) possible architectures, which provide 23

Figure 3-7: Sample pump and motor displacement variation as a function of the ground speed. higher performance, as will be described in the following sections. Fig. 3-8, shows two typical connections between hydrostatic IVUs and the gearbox for a tractor and a wheel loader transmission, respectively.in order to cover the entire speed range, the IVU is connected to a stepped gearbox with generally 2, 3 or 4 forward ranges and no more than 2 reverse ones. Dual clutch systems and synchronizers can be adopted in order to automatically control the range shift together with the variation of the overall IVU ratio. 3.1.4 Electric CVUs Electric CVUs constitute an upcoming technology that present significant advantages in terms of reduced noise level, reduced maintenance costs, high effectiveness of control systems with low energy required for the ratio control, environmental sustainability. A significant set of critical points still limit the adoption of such systems on a wide basis: safety aspects related to the high voltage required; high costs of the required components; limited efficiency related to the high number of energy conversions; high volumes and weights associated to the batteries. Toyota Prius, Fig. 3-9, constitutes one of the best 24

Figure 3-8: Typical connections between a hydrostatic IVU and stepped gearboxes: a) tractor, b) wheel loader machines. example of electric CVU adopted for hybrid passenger cars. 25

Figure 3-9: Toyota Prius transmission: first commercial hybrid car CVT working with an electric IVU, 1997. 26

Chapter 4 Design optimization of power split IVTs This chapter focuses on the analysis of power split infinitely variable transmissions, focusing on the main concepts and applications. Particular attention will be devoted to the problem of power recirculation, providing a thorough conceptual analysis of power and torque flows, in particular through the variable speed unit, for different possible transmission architectures. Then, a novel and effective approach to optimize transmission performance is presented, showing the benefits obtained in terms of overall transmission performance. 4.1 Principles of power split IVTs Power split IVTs are a particular CVT typology that offers the possibility to obtain a zero output speed with a non-zero input one; IVTs can generally be obtained by coupling acvu,aplanetarygeartrain(pgt)andafixed ratio gear. The total power is split into two parts, one flowing through a constant ratio mechanical path and one through either the CVU or the IVU. In general CVUs and IVUs have a lower efficiency compared to the constant ratio path, thus, adopting power split IVT architectures, their negative 27

effects in terms of power dissipation will influence a reduced amount of total power; nonetheless a continuously variable output speed can be obtained over a wider speed range, in particular with multiple-range architectures. As a main consequence, power split IVTs present an overall efficiency higher than that of a "direct" CVT, due to the higher efficiency of the mechanical path.fig. 4-1 shows one possible basic configuration Figure 4-1: Principles of a power split IVT. for a power split IVT, [5]. In general, the IVU output speed can be reversed according to the working conditions, this meaning that the power flow through the IVU can be reversed flowing from right to left. In this case, the power is superimposed to the system input power and therefore must be transferred through the mechanical path again to the right of the system. This condition is typically referred to as power recirculation, which can strongly affect the overall IVT efficiency. If the value of the power recirculating through the IVU is low compared to the input power, the total system efficiency is still higher than the one of a direct CVT, otherwise, significant power and heat dissipation will occur, deteriorating the overall system performance. Depending on the link between the driving/input shaft, the variable speed unit, and 28

the driven/output shaft, Input Coupled (IC) or Output Coupled (OC) architectures can be obtained, Fig. 4-2.The IC and OC architectures can be thought of as mirrored one to Figure 4-2: Basic concept of Input (A) and Output (B) coupled concept for power split IVTs, [5]. each other, although their operational behavior is completely different in terms of power recirculation and system efficiency. Renius [5] has performed a qualitative steady state analysis showing the IVT efficiency for the two cases assuming a mechanical efficiency of 97% for each gear meshing and a constant IVU efficiency of 85%, Figs. 4-3 and 4-4.It can be noticed that the best values efficiency are obtained when all the power is transmitted through the mechanical path: this condition is usually referred to as the lockup point. Also, the power split region without power recirculation is characterized by the higher efficiency and limited power and heat dissipation. In the following sections, a thorough kinematic analysis of input and output coupled architectures is provided with a deep focus on the power and torque flows through the IVU. An effective optimization procedure is the presented to determine the optimal set of transmission gear ratios that minimize the power recirculation according to the specific vehicle nominal working cycle and in compliance with the major design constraints. This analysis constitutes a very helpful tool for the designer for it provides a detailed benchmarking between the IC and OC concepts and avoids the traditional trial and error approach to determine the gear ratios, in particular for multiple ranges architecture with a high number of degrees of freedom, that minimize power recirculation and improve 29

Figure 4-3: Power and efficiency charateristics for an input coupled power split IVT. vehicle performance. 4.2 Kinematic analysis of a power split IVT A general useful scheme of input and output coupled power split IVTs can be obtained using the schematic diagram of Fig. 4-5. Yan and Hsiech [8] have performed a preliminary analysis of both concepts with particular reference to a Differential Transmission (DT); they state: "if an output-coupled DT is used as an IVT and the output of the DT has zero speed, we have a case that the member of the PGT adjacent to the CVU also has zero speed. This is physically impossible when the input member of the DT is in motion". Thus, Yan and Hsiech concluded that only the input coupled architecture can be applied to an IVT. This conclusion is only partially 30

Figure 4-4: Power and efficiency characteristics of an output coupled power split IVT. correct as it holds true solely for the particular case of CVUs that do not allow a zero output speed with a non-zero input speed, as in the case of expandable-pulley CVUs. Therefore, observing that IVUs allow one to obtain the so called lockup point, occurring when the IVU output speed is zero with a non-zero input speed, the conclusion given by Yan and Hsiesh does not apply when a IVU (e.g., a hydrostatic transmission) is adopted as a CVU. Also notice that IVTs present the Power-Zero condition when the output speed is zero with a non-zero input speed. It follows that if a IVU is used as an IVT without any PGT, the lockup and power-zero conditions will coincide. The consequence is that the output coupled concept can be reassessed for IVT applications. Examples of IVUs are hydrostatic transmissions with one or two variable units (pump/motor); hybrid architectures composed by an electric circuit with a generator, a 31

Figure 4-5: Circuit schematic diagrams of input coupled (a) and output coupled (b) architectures motor and an inverter. Therefore, both the IC and OC architectures are analyzed in this work, which provides a novel contribution on the efficient implementation of an OC IVT. In order to cover the entire vehicle speed range, the great majority of IVT transmissions presents multiple range architectures. In this paper, the authors will concentrate on a dual range, fully synchronized IVT transmission for agricultural machines [10], which is frequently adopted for off-highway transportation. This choice will not limit the generality of the analysis and methodology adopted for both the IC and OC architectures. 4.2.1 Input coupled equations The conceptual transmission stick diagram of Fig. 4-6 shows a dual range IC IVT architecture, in which the outlet power is always transmitted by the Carrier (C), in first range, and by the Sun (S2), in second range. By expressing the speed ratio of the PGT in a frame of reference fixed to the carrier, two Willis [5] transmission ratios can be evaluated in terms of the various angular speeds, as: and τ wa = ω 5 ω C ω 1 ω C (4.1) 32

Figure 4-6: Input coupled power-split architecture. CNH, all rights reserved. τ wb = ω 5 ω C ω S2 ω C, (4.2) where ω i represents the angular speed of the i th gear. The angular speed of the ring 5 is related to the input speed through the IVU, so that: ω 5 = τ FRG τ IV U ω 1 = τ IV U ω 1, (4.3) τ FRG being the fixed ratio of the gears before and after the IVU and τ IV U the IVU transmission ratio. From Eqs. (4.1-4.3), the IVT transmission ratio in first and second ranges are obtained as: τ I IV T = ω C ω 1 = τ wa τ IV U τ wa 1 = τ 1 τ IV T (4.4) and 33

τ II IV T = ω S2 = [τ wa (τ wb 1) + (τ wa τ wb ) τ IV U ] = τ 2 τ IV T, (4.5) ω 1 τ wb (τ wa 1) respectively. In Eqs. (4.4) and (4.5) the first and second range gear ratios are defined as τ 1 = ω C /ω I and τ 2 = ω S2 /ω II, respectively ω I and ω II are the corresponding output angular speeds, and τ IV T the global transmission ratio, τ IV T = ω out /ω IN. The specific IVU under evaluation is a hydrostatic transmission made up by reversible variable displacement pump and a reversible bidirectional fixed displacement motor. Furthermore, two independent clutches respectively connect the carrier and the sun to the transmission final reduction in order to obtain a synchronized range shift without any power or speed discontinuity. In standard applications, during the vehicle s acceleration the variable unit displacement is varied from negative to positive values in first range and from positive to negative values in second range. constraint results for the transmission ratios: Therefore the following design τ wa τ wb < 0. (4.6) Also, defining τ IV T_s = ω out_s /ω in the transmission ratio at the range shift point, the synchronization condition requires the output speeds in first and second ranges to be equal, with the same IVU ratio, i.e., τ IV U_s I = τ IV U_s II. (4.7) Since τ IV T_s I = τ IV T_s II, using Eqs. (4.4,4.5) and (4.7), the following constraint for τ wb is obtained as: τ wb = τ wa τ 1 τ IV T_s 1. (4.8) (τ 1 τ 2 ) τ IV T_s 34

Figure 4-7: Output coupled power-split architecture. 4.2.2 Output coupled equations The conceptual stick diagram for the OC architecture is shown in Fig. 4-7, where the IVU is linked to the final gears through the carrier and the sun, in first and second ranges, respectively.following the same approach as in Sec. 4.2.1, the ring angular speed will now be defined as ω 5 = τ IV U ω C, and ω 5 = τ IV U ω S2, in first and second range respectively. The corresponding IVT transmission ratios are: and τ I IV T = ω C ω 1 = τ wa τ IV U + τ wa 1 = τ 1τ IV T, (4.9) τ II IV T = ω S2 ω 1 = and the synchronization condition yields: τ wa (τ wb 1) τ wb (τ wa 1) + (τ wb τ wa ) τ IV U = τ 2 τ IV T ; (4.10) 35

τ wb = τ 1 τ 2 τ wa + τ 1 τ 2 τ IV T_s (τ wa 1). (4.11) (τ 1 τ 2 ) 4.3 Power flow analysis Power split IVTs basically present three possible power flows, as analyzed by Yan and Hsiech [8] and Mantriota [11, 12, 13], for the IC case, Fig. 4-8. Here, a thorough power flow analysis is provided also for the OC architecture Fig. 4-9. Figure 4-8: Power flow types for the IC architecture Figure 4-9: Power flow types for the OC architecture ThetypeIIIpowerflow is the only one which guarantees that the power crossing the IVU is equal to or smaller than the input power [11]. Since IVUs have a lower 36

efficiency with respect to PGTs, higher efficiencies are obtained with lower power fractions flowing through the variable path, the optimum being obtained at the lockup point [5]. Thus, type III regions enjoy a high transmission efficiency and a low heat dissipation. Moreover the size of IVU components is strictly related to maximum power and torque to be guaranteed during working conditions, so that type III flows generally lead to more compact technological solutions. The IVT efficiency, η IV T, is a weighted function of the mechanical efficiency, η M, and of the IVU efficiency, η IV U, the weights being the power fractions flowing through the IVU and the PGT, P IV U /P IN and 1 P IV U /P IN, see Table 4.1. Type I η IV T = η M ³1 P IV U ³ Type II η IV T = η 1 M 1 P IV U P IN P IN Type III η IV T = η M ³1 P IV U P IN + η 1 P IV U IV U P IN + η IV U P IV U P IN + η IV U P IV U P IN Table 4.1: Expressions of η IV T as function of possible types of power flows It is noteworthy that type I, II and III flows occur for P IV U /P IN < 0, P IV U /P IN > 1 and 0 <P IV U /P IN < 1, respectively. Fig. 4-10 shows the IVT efficiency versus P IV U /P IN for different values of η IV U, and fixed η M =0.95. Maximum possible efficiency is thus obtained for lockup conditions where P IV U /P IN =0, η IV T = η M.The main focus of this work is therefore on power recirculation, which is strictly related to the overall transmission efficiency. 4.3.1 Input coupled power flows Considering the IC architecture and defining T i,j thetorqueexertedfromthei th element to the j th one, the following equations can be written for the control volume 2 (CV2) shown in Fig. 4-11, in first range: T 12,1 + T 6,5 + T C =0 (4.12) 37

1 η M 0,9 0,8 0,7 η IVT 0,6 0,5 0,4 0,3 0,2 η IVU = 0.8 η IVU = 0.75 η IVU = 0.7 0,1 0-2 -1.5-1 -0.5 0 0.5 1 1.5 2 P /P IVU IN Figure 4-10: η IV T as a function of the ratio P IV U /P IN ; η M =0, 95. Figure 4-11: Control volumes for the IC architecture. 38

and T 12,1 ω 1 + T 6,5 ω 5 + T C ω C =0. (4.13) In order to have type III power flow, the following conditions must be satisfied simultaneously: T 12,1 ω 1 > 0; T 6,5 ω 5 > 0; T C ω C < 0. (4.14) In Eqs. (4.12) and (4.13), T C is the load torque acting on the carrier shaft and ω C the corresponding angular speed. Rearranging Eqs. (4.12) and (4.13) and using the kinematic conditions (4.1-4.6) evaluated in Sec. 4.2.1, one has: and T 6,5 = T 12,1 = µ 1 τ IV T T C (4.15) τ IV U 1 µ τ IV T τ IV U T C. (4.16) τ IV U 1 Considering the inequalities in Eqs. (4.14), rearranging Eqs. (4.15) and (4.16) and substituting the expression of the IVT ratio from Eq. obtained in first range for: (4.4), type III power flow is τ IV U > 0. (4.17) Likewise, in second range, Eqs.(4.12) and (4.13) can be rewritten as: and T 12,1 + T 6,5 + T S2,4 =0 (4.18) T 12,1 ω 1 + T 6,5 ω 5 + T S2,4 ω S2 =0, (4.19) 39

respectively. Therefore, using the expression of the IVT ratio (4.5), the condition for type III power flow in second range is: τ IV U < 0. (4.20) Considering the control volume CV1 in Fig. 4-11 containing the IVU, and being T 5,6 = T 6,5 and T 1,12 = T 12,1, the ratio between the power flowing through the IVU and the input power can be derived as: P IV U P IN = τ IV U (τ IV T 1) τ IV T (1 τ IV U ). (4.21) Rearranging Eqs. (4.4) and (4.21), eliminating τ wb using the constraint Eq. (4.8), the power ratios in first and second ranges can be written as: and I P IV U = τ wa +(1 τ wa ) τ 1 τ IV T (4.22) P IN (τ wa 1) τ 1 τ IV T P IV U P IN II = τ 2 τ IV T_s τ IV T τ 1 τ IV T_s 1 (τ wa 1) + τ 1 τ IV T_s (τ wa 1) τ wa τ 2 τ IV T τ 1 τ IV T_s 1, (τ wa 1) (4.23) respectively. From Eq. (4.22), it can be observed that for an IC architecture, the power ratio is theoretically infinite at zero output power, meaning that a significant heat dissipation occurs at nearly zero speed. The analysis is completed studying the torque behavior at the input and output shafts of the IVU as a function of the output load torque T out and of the IVT gear ratio τ IV T. Considering that power is transmitted through the carrier in first range and through the sun in second range, power conservation can be respectively applied for both ranges as T C,3 ω C = T out ω out, T S2,4 ω S2 = T out ω out, ω out being the output angular speed. Therefore 40

T C,3 = T out ω out /ω C = T out /τ 1 (4.24) and T S2,4 = T out ω out /ω S2 = T out /τ 2. (4.25) Using Eqs. (4.24) and (4.25) in the torque and power-balance equations, the torques at the output shaft of the IVU in first and second ranges, can be written as: µ TIV I 1 1 U,out = T 5,6 = T out τ 1 τ wa 1 (4.26) and " # TIV II 1 1+τ 2 τ U,out = T 5,6 = T out IV T_s τ 2 τ 1 τ IV T_s 1, (4.27) (τ wa 1) respectively. Finally, by applying the power conservation between the input and output shafts of the IVU, the corresponding torques at the IVU input shaft can be obtained as: T I IV U,in = T 12,13 = T out 1 τ 1 τ wa +(1 τ wa ) τ 1 τ IV T_s τ wa 1 (4.28) and T II IV U,in = T 12,13 = respectively. T out τ 2 τ 1 τ IV T_s 1 µ 1 τ 2 τ IV T_s 1 τ wa 1+τ 1 τ IV T_s + τ 2 τ IV T 1+τ 1 τ IV T_s, (4.29) 4.3.2 Output coupled power flows For the output coupled architecture shown in Fig. 4-12, using the same approach as in Sec. 4.3.1, the torque and power balance equations in first range and steady state conditions can be written applying the power conservation theorem to CV 1, to give: 41

Figure 4-12: Control volumes for the OC architecture. 42

T IN + T 6,5 + T 10,C =0 (4.30) and T IN ω 1 + T 6,5 ω 5 + T 10,C ω C =0, (4.31) respectively. The conditions for type III power flow can be written as: T IN ω 1 > 0; T 6,5 ω 5 < 0; T 10,C ω C < 0, (4.32) T 10,C being the load torque acting on the carrier. Note that in second range, Eqs. (4.30-4.32) are still valid, provided that T 10,C and ω C are replaced by T 8,S2 and ω S2 respectively. Considering the kinematic conditions (4.9,4.10) evaluated in Sec. 4.2.2, one has: µ T 6,5 = 1 τ IV T τ IV U τ IV T 1 T 10,C (4.33) and T IN = µ 1 τ IV U τ IV T T 10,C. (4.34) τ IV U τ IV T 1 Thus, using Eqs. (4.32-4.34), with the definition of speed ratios provided in Eqs. (4.1) and (4.2), and applying the design constraint, Eq. (4.6), the condition for type III power flow in first range reduces to: τ IV U < 0. (4.35) Likewise, substituting T 10,C with T 8,S2 in second range, one has: τ IV U > 0. (4.36) Following the same approach as in Sec. 4.3.1, the power ratios in first and second ranges 43

canbewrittenas: I P IV U = τ wa (τ wa 1) τ 1 τ IV T (4.37) P IN τ wa and respectively. II P IV U = 1+τ 2 τ IV T + τ 1τ IV T 1 τ 2 τ IV T_s P IN τ 1 τ IV T_s 1, (4.38) τ wa Furthermore, the corresponding torques at the output and input shafts of the IVU can be written as: and µ TIV I 1 τ 1 τ IV T U,out = T 5,6 = T out, (4.39) τ 1 τ wa T II IV U,out = T 5,6 = T out 1 τ 2 T I IV U,in = T 8,9 = T out 1 τ 1 " # τ 1 τ IV T 1 τ 2 τ IV T_s τ wa τ 1 τ IV T_s 1, (4.40) τ 1 τ IV T + τ wa (1 τ 1 τ IV T ) τ wa, (4.41) T II IV U,in = T 10,11 = T out τ 2 respectively. " τ 1 τ IV T 1 τ 2 τ IV T_s +(1 τ 2 τ IV T ) # τ wa τ wa τ 1 τ IV T_s τ wa τ 1 τ IV T_s 1, (4.42) Unlike the IC case, the torque at the output shaft of the IVU depends also on the IVT transmission ratio. Nonetheless, from Eq. (4.37) it can be observed that the power ratio at zero speed has a unit value, this meaning that the OC architecture behaves like a purehydraulic direct transmission near power-zero condition, with no power recirculation. Table 4.2 provides a useful summary of conditions to have type III power flow for 44

both the IC and OC architectures. 1st Range 2nd Range IC τ IV U > 0 τ IV U < 0 OC τ IV U <0 τ IV U > 0 Table4.2:ConditionstohavetypeIIIpowerflow for the IC and OC architectures. 4.4 Design optimization of power split IVTs The power flow analysis carried out in Sec. 4.3 has shown different possible working scenarios pointing out recirculation conditions through the IVU and their negative effects in terms of overall transmission efficiency, fuel consumption and heat dissipation. Standard designs of mechanical transmissions typically rely on a trial and error approach. The main inputs to this process are the vehicle nominal working cycle, the number of ranges, the engine power and torque curves. The outputs are then the corresponding transmission ratios: following this methodology, given a nominal engine speed, each gear ratio corresponds to a specific output speed and thus can be determined uniquely, according also to pre-existing components. A verification process with design and layout constraints will follow next. For an IVT transmission, it is clear that each range has an infinite number of output speeds, depending on the IVU ratio; therefore the aforementioned iterative approach results in a heavy computational load also because the number of degrees of freedom to be evaluated is much higher than for a standard mechanical transmission. Here, an effective approach to transmission design has been implemented by means of optimization algorithms, which allow one to explore a wide range of designs and to optimize the overall transmission efficiency. As will be shown in the next sections, the design of complex IVTs, such as the one under evaluation, can improve significantly thanks to a more effective way of evaluating design data and parameters with respect to 45

the standard approach. As a practical application, the case of an agricultural vehicle has been considered in the present work. Given specific design requirements and constraints, an optimization process has been implemented to evaluate the optimal set of transmission parameters, namely τ 1, τ 2 and τ wa. A nominal working cycle in maximum power conditions has been considered as shown in Fig. 4-13. 1 (a) P IN /P MAX 0.5 0 0 0.5 1 1.5 2 2.5 τ IVT 1 (b) T IN /T MAX 0.5 0 0 0.5 1 1.5 2 2.5 τ IVT Figure 4-13: Nominal working cycle: (a) normalized torque; (b) normalized power P IN /P max 4.4.1 Optimization problem formulation An analytical form for the optimization process can be obtained by choosing the objective function to be minimized as: Z Ψ (τ wa, τ 1, τ 2 )= f [(τ wa, τ IV T,τ 1, τ 2 )] 2 ρ (τ IV T ) dτ IV T, (4.43) I 46

where I = τ IV T_Min ; τ IV T_Max, f = PIV U /P IN_Max and ρ is the Probability Density Function (PDF) of τ IV T. All design requirements have led to the formulation of optimization constraints. The maximum allowable speed and torque values, in particular at the input and output shafts of the IVU, have to be guaranteed at each point within the integration domain I; thus, the resulting constraints for the input and output coupled cases can be written for a fixed value of the synchronization ratio τ IV T_s as: T IV U_in (τ wa, τ IV T,τ 1, τ 2 ) T IV U_in MAX (4.44) and T IV U_out (τ wa, τ IV T,τ 1, τ 2 ) T IV U_out MAX. (4.45) In terms of the maximum allowable speed, for the generic i th driveline shaft, the followingconstraintshavealsotobesatisfied ω i ω MAX. (4.46) Therefore, for each value of τ IV T I, adomaind τ IV T can be defined as: D τ IV T = {(τ wa, τ 1, τ 2 ) T IV U_in MAX T IV U_in ; (4.47) TIV U_out MAX T IV U_out ; ω i ω MAX }. Since the inequalities in Eqs. (4.44), (4.45) and (4.46) have to be verified simultaneously within the entire interval I, the final optimization constraints can be derived imposing the condition that: (τ wa, τ 1, τ 2 ) D = \ τ IV T I D τ IV T. (4.48) 47

4.4.2 Numerical implementation of the optimization process In order to numerically implement the optimization problem definedinsec. 4.4.1,the integral in Eq. (4.43) has been discretized as: NX Ψ D = fi 2 (τ wa, τ IV T,τ 1, τ 2 ) w i, (4.49) i=1 where the integration interval I has been uniformly divided into N sub-intervals of equal amplitude τ IV T,andw i represents a weighting function related to the machine working cycle, defined as: w i = ρ i τ IV T = t i t tot, (4.50) 0.14 0.12 0.1 0.08 w i 0.06 0.04 0.02 0 0 0,5 τ IVTs 1 1,5 2 2,5 τ IVT Figure 4-14: Weighting function w i versus speed distribution where t i is the amount of time in which the vehicle speed lies in the interval I i = [τ IV T_i,τ IV T_i + τ IV T ] and t tot is the overall vehicle lifetime, thence P N w i =1, (see 48

Fig. 4-14). Three state of the art global optimization algorithms have been used to solve the present design optimization for both IC and OC architectures, namely Differential Evolution (DE) [14, 15], Simulated Annealing (SA) [16] and Nelder & Mead (NM) [17]. All these algorithms belong to the category of Direct Search methods, since they do not make use of derivative information. 4.4.3 The optimization algorithms Numerical algorithms for constrained nonlinear optimization can be broadly categorized into gradient-based methods and direct search methods. Gradient-based methods use first derivatives (Gradients) or second derivatives (Hessians) of the objective function. Examples are the sequential quadratic programming (SQP) method, the augmented Lagrangian method, and the (nonlinear) interior point method. Direct search methods do not use derivative information. Examples are Nelder & Mead, Genetic algorithm and Differential Evolution, and Simulated Annealing. Direct search methods tend to converge more slowly, but can be more tolerant to the presence of noise in the function and constraints. Therefore, when the objective function is nonlinear and non-differentiable, as it is in the problem under evaluation, direct search methods are the methods of choice. For all of these methods, the key feature is the strategy that generates variations of the parameter vectors. Once a variation is generated, a decision must be made whether or not to accept the newly derived parameters. All standard direct search methods, such as NM, use the greedy criterion to make this decision. Under the greedy criterion, a new parameter vector is accepted if and only if it reduces the value of the objective function. Although the greedy decision process converges fairly fast, it runs the risk of becoming trapped in a local minimum. Parallel search techniques, in turns, like genetic algorithms and evolution strategies (DE) have some built-in safeguards to forestall misconvergence: by running several vectors simultaneously, superior parameter configurations can help other 49

vectors escape local minima. Another method which can extricate a parameter vector from a local minimum is the Simulated Annealing (SA) which relaxes the greedy criterion by occasionally permitting an uphill move. Such moves potentially allow a parameter vector to climb out of a local minimum. As the number of iterations increases, the probability of accepting an uphill move decreases. In the long run, this leads to the greedy criterion. In general, an effective optimization technique should fulfill two basic requirements: (i) the method should converge to a global minimum regardless of the initial condition; (ii) the convergence should be fast. Differential Evolution Differential Evolution is a parallel, direct search minimizer of multidimensional functions. The method presents globally and locally correlated step sizes, which self-adapt over time in relation to the location of the population of individuals in the search space. The method uses m parameter vectors u G = {x 1,x 2,...,x m }, as a population for each generation G. The initial population is generally assumed randomly by adding normally distributed random deviation to the initial solution. Then, the key feature of the DE method is to generate trial parameter vectors: DE generates new parameter vectors by adding a weighted difference vector between two population members to a third member. In fact, unlike stochastic techniques such as Genethic Algorithms and Evolutionary Strategies, where the perturbation occurs in accordance with a random quantity, DE uses weighted differences between decision space vectors to perturb the population. A sample algorithm can be the following: Step 1 i =1; Step 2 Randomly select r 1,r 2,r 3 {1, 2,..., m} such that x 1 6= x 2 6= x 3 6= i where i is the index of the currently selected individual in the population; Step 3 Generate an offspring u i,g+1 from the selected parents x r1.x r2,x r3 and from 50

the current individual x i,g.namelyu i,g+1 = x i,g +K (x r3,g x i,g )+F (x r1g x r2,g ), K and F being two control parameters. The coefficient K is responsible for the level of combination that occurs between x r3,g and the current individual x i,g,whereasf is responsible for scaling the step size resulting from the vector subtraction x r1g x r2,g. Typically, in single objective problems, if the new individual u i,g+1 evaluates better than the current individual x i,g, than the current individual is replaced by the new one. However, in multi-objective problems, individuals cannot directly replace the parents without without either a dominance comparison with the current parent, or a sort of all the offspring with all the parents, with respect to their dominance level. This feature prevents the method to converge to local minima. 4.4.4 Simulated Annealing In this algorithm, each point x of the search space is analogous to the state of a physical system, whereas the function f(x) to be minimized is analogous to the internal energy of the system in the state x. Therefore, the goal is to bring the system from an arbitrary initial state to a state with them minimum possible internal energy. At each step, the SA algorithm considers some neighbors x 0 of the current state x, and decides between moving to state x 0 or staying in x. The probabilities are chosen so that the system ultimately tends to move to the states of lower energy. The process is then iterated until the system energy falls below a given threshold or the computational budget has been exhausted. The probability of making the transition from the current state x to x 0 is specified by an acceptance probability function P (e, e 0,T), that depends on the energies e = f(x) and e 0 = f(x 0 ) of the two states, and on a global time-varying parameter T called temperature. One essential requirement for the probability function P is that it must be nonzero when e 0 >e, meaning that the system can move to the new state even if it presents a higher energy than the current on. This, in fact, is the feature that prevents the SA method 51

from becoming stuck into a local minimum. On the other end, when the time-varying temperature T approaches to zero, the probability function P must tend to zero as if e 0 >e, and to a positive value if e 0 <e.in particular, when T goes to zero, the method reduces to the greedy algorithm. Given these properties, the evolution of the solution x crucially depends on the temperature T since it is sensitive to coarser energy evolution when T is high, whereas to finer variations when T is low, where T is gradually decreased during the simulation. Nelder & Mead Differently from DE and SA, the Nelder & Mead method belongs to the class of directsearch methods. For a function of n variables, the algorithm maintains a set of n +1 points forming the vertices of a polytope in n dimensional space. At each iteration, n +1points x 1,x 2,..., x n+1 form a polytope. The points are ordered so that f (x 1 ) f (x 2 )... f (x n+1 ). A new point is then generated to replace the worst point x n+1. P Let c be the centroid of the polytope consisting of the best n points, c = 1 n n i=1 x i; atrialpointx t, is generated by reflecting the worst point through the centroid, x t = c + α (c x n+1 ),beingα a positive parameter. If the new point x t is worse than the second worst point, f (x t ) f (x n ), the polytope is assumed to bee too large and needs to be contracted. Thus a new trial point is defined as: x c = c + γ (x n+1 c), if f (x t ) f (x n+1 ); x c = c + γ (x t c), if f (x t ) <f(x n+1 ). where 0 <γ<1. If f (x c ) <Min[f (x n +1),f(x t )] the contraction is successful and x c replaces x n+1, otherwise another contraction is carried out. 52

In general, NM is not a true global optimization algorithm. However, in practice it tend to work reasonably well for problems that do not present many local minima and strong nonlinearities. 4.4.5 Results The results obtained from the optimization process are compared versus those resulting from the standard design approach in order to highlight the benefits obtained in terms of power recirculation and machine size reduction. The torque and power results are normalized with respect to the maximum recirculating value provided by the standard design approach, unless otherwise specified. For the IC architectures the three optimization algorithms have provided almost identical results. Fig. 4-15 shows the effects of the optimization process on power recirculation compared to the standard approach: a considerable reduction can be observed during the entire vehicle working cycle, resulting in a lower amount of heat generation, in particular near power-zero conditions, and thus improved transmission efficiency. Figs. 4-16 and 4-17 show the normalized torque behavior respectively at the input and output shafts of the IVU. An important overall decrease of the torque at the IVU input shaft is observed whereas the torque at the output shaft shows a significant improvement only in second range. For the sake of completeness, the relationship between the IVU ratio, τ IV U,and the overall transmission ratio, τ IV T, has been analyzed and compared versus that provided by standard gears for both architectures, in order to evaluate the type of power flow obtained from the optimization process along the entire working cycle. Fig. 4-18 shows how all optimization algorithms provided lockup points in first and second ranges for lower output speeds with respect to the standard ratios, leading to a wider operating region with type III flow. Fig. 4-19 shows how the OC optimal solution presents a significantly lower amount of power flowing through the IVU, mainly in second range. Important benefits obtained from the optimization process are also evident in Figs. 4-20 and 4-21 in terms of the 53

0.5 Normalized P IVU 0-0.5 Standard approach Differential Evolution Simulated Annealing Nelder & Mead Range I Range II -1 0 0,5 τ IVTs 1 1,5 2 2,5 τ IVT Figure 4-15: Normalized P IV U for the IC architecture torques at the input and output shafts of the IVU. As a matter of fact, the DE and SA algorithms turned out to outperform the NM one, not only in terms of the optimal solution provided, but also for the reduced level of computational complexity; furthermore, the NM algorithm presented poor convergence properties for the OC problem, due to its nonlinearity, see [18, 19]. Standard DE SA NM IC (time) 52.9 % 69.7 % 69.7 % 69.7 % IC (vel.) 46.7 % 60.0 % 60.0% 60.0 % OC (time) 38 % 40.6 % 35.7 % 23 % OC (vel.) 33 % 50 % 40 % 10 % Table 4.3: Time and speed percentages with type III flow for IC and OC Table 4.3 shows the percentages of time and speed with type III power flow over the entire vehicle working range; in particular, times have been computed according to the 54

0.4 0.2 Normalized T IVU IN 0-0.2-0.4-0.6-0.8 Range I Standard approach Differential Evolution Simulated Annealing Nelder & Mead Range II -1 0 0,5 τ IVTs 1 1,5 2 2,5 τ IVT Figure 4-16: Normalized T IV U_IN for the IC architecture specific vehicle duty cycle, whereas speeds have been evaluated as the ratios between the speed range with type III flow and the overall vehicle speed range. It is noteworthy that, for the OC case, the NM algorithm provided a very limited portion of the working cycle with type III flow, as shown in Fig. 4-22. Fig. 4-23 shows a very interesting comparison between the IC and OC optimized solutions in terms of the power flowing through the IVU (normalized by the maximum power obtained from the standard approach in the IC case). For τ IV T close to zero, the OC unit provides no recirculation and behaves like a direct CVT, since all of the power is transmitted through the IVU, as can be inferred from Eq. (4.37) for τ IV T =0,acrucial feature during vehicle acceleration with high loads. Furthermore, it is noteworthy that theocsolutionenjoystypeiiipowerflow where the IC does not; thus, a power split IVT with very limited power recirculation may be designed by adopting a mixed IC-OC solution. 55

1.2 1 Normalized T IVU OUT 0.8 0.6 0.4 0.2 0 Standard approach Differential Evolution Simulated Annealing Nelder & Mead -0.2-0.4 Range I Range II -0.6 0 0,5 τ IVTs 1 1,5 2 2,5 τ IVT Figure 4-17: Normalized T IV U_OUT for the IC architecture 4.5 Optimization conclusions Thischapterdescribedaneffective optimization procedure and a thorough kinematic analysis of a dual range synchronized power split infinitely variable transmission, based upon an infinitely variable unit. The novel result is that, beside the input coupled architecture, which has been deeply investigated in the scientific literature, the output coupled concept has been reassessed to show that both IC and OC solutions, if properly optimized, can give satisfactory performance and that only the particular application or duty cycle of the system under analysis allows the designer to opt for either solution by itself or even for a mixed one. However, the OC solution requires a unit capable of providing a speed ratio equal to zero, in order to be effective from a practical point of view; therefore V-Belt continuously variable transmissions or toroidal traction drives cannot be used since they provide limited speed ratios between two non-zero values. The OC architecture is shown to have better performance in terms of power recirculation at low 56

1 0.5 Traditional approach Differential Evolution Simulated Annealing Nelder & Mead 0 τ IVU -0.5-1 Lockup Points 1st range Lockup Points 2nd range -1.5-2 Range I Range II -2.5 0 0,5 τ IVTs 1 1,5 2 2,5 τ IVT Figure 4-18: Analysis of τ IV U as a function of τ IV T for the IC architecture speed ratios, although the torque load on the IVU may be significantly higher if compared to the IC solution. The IC architecture, in turns, has a more general applicability and performs better close to range shift regions. Although the present study is limited to a sample dual range transmission used for agricultural vehicles, the optimization procedure presented, may constitute a powerful tool for the designer to determine the optimal architecture and the set of gears which minimize power recirculation, increase efficiency, and reduce the IVU maximum torque values thus allowing more compact and economical components. 57

0.4 0.2 0 Normalized P IVU -0.2-0.4-0.6-0.8 Standard approach Differential Evolution Simulated Annealing Nelder & Mead -1 Range II Range I -1.2 0 0,5 τ IVTs 1 1,5 2 2,5 τ IVT Figure 4-19: Normalized P IV U for the OC architecture 0.4 0.2 0 Normalized T IVU IN -0.2-0.4-0.6-0.8 Range I Range II Standard approach Differential Evolution Simulated Annealing Nelder & Mead -1 0 0,5 τ IVTs 1 1,5 2 2,5 τ IVT Figure 4-20: Normalized T IV U_IN for the OC architecture 58

1 Normalized T IVU OUT 0.9 0.8 0.7 0.6 0.5 0.4 0.3 Standard approach Differential Evolution Simulated Annealing Nelder & Mead 0.2 0.1 Range I Range II 0 0 0,5 τ IVTs 1 1,5 2 τ IVT Figure 4-21: Normalized T IV U_OUT for the OC architecture 1 0-1 Lockup Points 1st Range Lockup Points 2nd Range τ IVU -2-3 -4 Range I Range II Standard approach Differential Evolution Simulated Annealing Nelder & Mead -5 0 0,5 τ IVTs 1 1,5 2 2,5 τ IVT Figure 4-22: Analysis of τ IV U as a function of τ IV T for the OC case. 59

0.4 0.2 0 Normalized P IVU -0.2-0.4-0.6 Input Coupled Output Coupled -0.8-1 Range I Range II -1.2 0 0,5 τ IVTs 1 1,5 2 2,5 τ IVT Figure 4-23: Comparison between the IC and OC optimized solutions with the DE algorithm 60

Chapter 5 Virtual verification of power split IVTs Chapter 4 provided a thorough analysis of the different concepts of power split IVTs for agricultural and construction equipment machines. The optimization procedure presented, not only provides a valid tool to the design engineer to opt for the most appropriate architecture and to minimize power recirculation, but also constitutes an effective strategy to approach the Optimization phase within the Global Product Development process. In fact, the system under consideration, namely the power split IVT, could be benchmarked versus possible alternatives and optimized according to the required working scenarios so as to better fulfill Customer needs. Hence, the output from this phase is the finalized design of the power split IVT which has been conceived and dimensioned in order to optimize the overall performance. Therefore, the Optimization phase ends up with the product design specifications. As a next step along the GPD, this chapter will provide a general overview of an effective approach to the virtual Verification of power split IVTs based on numerical simulations. Following the Optimization phase, the released and optimized product specifications will be used to realize a dynamic, functional model of the product system, which allows the designers to simulate realistic working scenarios, including dangerous failure 61

conditions arising from accidental vehicle misuse or faults. Particular attention will be devoted to the Closed Loop simulations which allow to simulate also the behavior of the control systems on board, which play a crucial role in order to guarantee system robustness and safety in different working conditions. 5.1 Current scenarios for off-highway vehicles Innovative technological concepts for agriculture and mobile machinery make a wide use of multi-domain, complex solutions, which combine together different physical components to achieve the required product targets. This is of course the case of power split IVTs for agricultural and construction machinery, where the mechanical gearbox can be coupled to hydrostatic IVUs, and the overall transaxle is automatically actuated using electrovalves that control the clutches, the synchronizers, the PTO and all the auxiliary components of the vehicle. Therefore mechanical, hydraulic and electric components are used together, each of them with its specific dynamic characteristics. The other hand, the human operator has to manage a very high number of vehicle functionalities, specific for each possible working condition and involving engine speed and torque, ground velocity, tools and implements. In order to improve comfort and, at the same time, maximize productivity minimizing the costs, the great majority of these operations are automatically actuated and controlled in closed loop by the means of Electronic Control Units (ECUs). Moreover, vehicle reliability and safety have to be verified and guaranteed in any possible working condition. Fig. 5-1 shows a sample network of ECUs and communication busses for a high rated power tractor. These considerations proof the utmost importance of effective and robust closed loop control systems, which have to guarantee a better working accuracy with a higher quality, a reduced energy input, an improved driver comfort, health and safety, as well as a contribution to environment protection. Moreover, precision farming operations make a 62

Figure 5-1: Network of Electronic Control Units and CAN busses for a tractor. CNH all rights reserved. heavy use of very sophisticated control strategies that have also to provide a clear and robust man-machine interface. Traditional control system development relies on hand written software code that can only be tested once the vehicle prototypes are available. The entire software debugging and optimization processes have thus to be performed by downloading the code into the ECU and by physically connecting it to the real vehicle. Then, the code developer can execute a limited set of maneuvers in order to evaluate and enhance the control code behavior. This approach results in very poor safety conditions since any bug present in the control software, can potentially turn out into dangerous conditions not only for those appointed to test and verify the ECU, but also for the final Customer. Moreover, only a very limited set of working scenarios can be physically reproduced and in a very long time: no fault condition can be investigated to check control software robustness. As a further consideration, hand written control software can result poorly readable and 63

shareable among different control engineers. From an economic point of view, this approach results extremely costly since requires a high number of physical prototypes to initiate the control system development and verification, and any potential failure that determines irrecoverable damages to the prototype, turns out in even higher costs and delays. Furthermore the Time To Market results extremely high since all the part procurement to build the physical prototypes are needed before being able to start all the product verification and optimization process. In this chapter, an effective approach to the product verificationphasewillbede- scribed, which relies on a virtual methodology to verify overall product performance with specific focuses on safety and reliability issues. This methodology is typically referred to as Model-Based Design. 5.2 Model-Based Design Model-Based Design (MBD) constitutes an extremely powerful and effective tool to approach the product verification process, mainly supporting control system development, [22]. In order to avoid the aforementioned negative scenarios related to the traditional hand-written software code, the idea behind MBD is to simulate the physical system to be controlled, namely the plant, aswellasthecontrollogics. In this way, the Verification phase of the GPD can be approached requiring a dramatically lower number of prototypes since concurrent engineering can be implemented adopting virtual methodologies. With specific reference to the control system, Model-Based Design is mainly composed by four main steps: 1. Model in the Loop - the model of the control system is simulated versus the plant; 2. Software in the Loop - the software of the control system is automatically generated and simulated versus the plant; 64

3. Hardware in the Loop - the real ECU, namely the hardware, is simulated versus the plant model. The following sections will describe in deeper detail the aforementioned steps, focusing on the plant model of the driveline of a dual clutch, automatically synchronized, hydromechanical power split IVT for a 230hp tractor with four forward and two reverse ranges. The transmission stick diagram is shown in Fig. 5-2, [24]. Figure 5-2: Power split IVT with hydrostatic IVU, CNH patented technology 5.3 Plant Model The starting point for the plant model is represented by the output from the Optimization phase of the GPD process. The transmission kinematic stick diagram will be characterized by the optimal gear ratios as resulting from the process described in Sec. 4; furthermore, the gears and shafts inertias, the design data of the hydrostatic IVU, the actuation system electrovalves characteristics and all the design parameters of the components of the driveline to be controlled will complete the set of input data to the 65

plant model. For this specific application, given the number of extra design constraints which have not be considered in the optimization process, the driveline system released and considered here, has joined only a portion of the benefits described in Sec. 4 The software packages adopted to model the plant are compliant with Matlab R and Simulink R platforms for they represent the widely adopted tool to develop and simulate the control models. The system has been modelled following a lumped-parameter approach, since only derivatives with respect to time have been considered; furthermore, the overall model results one dimensional since only the longitudinal vehicle dynamic has been considered in order to preserve a sustainable level of computational complexity. One of the key requirements for the plant model is in fact related to the possibility to be simulated in Real Time, in a synchronous way with the real ECU so as to allow all the in-theloop simulations. Therefore, the minimum acceptable time step for the model is 1ms so as to be consistent with the sample rate of the ECU, namely 1kHz for off-highway applications. As a direct consequence, all physical phenomena characterized by a proper dynamic faster than 1kHz have to be simplified or functionally emulated. The transmission power losses have been modelled as a function of the angular velocity and the torque transmitted; furthermore, the volumetric and mechanical efficiency of the hydrostatic IVU have been considered as functions of the pump angular velocity, hydrostatic circuit pressure and pump swash angle. Following a top-down approach, the inputs to the plant model are the actuation signals coming from the ECU, whereas the outputs are all the physical signals associated to the sensors installed on the driveline, and a set of extra outputs that although are not controlled in closed loop, result useful to further investigate the behavior of the system. Fig. 5-3 shows a list of the main inputs and outputs of the model. 66

Figure 5-3: List of main inputs and outputs of the plant model, CNH all rights reserved. 5.3.1 The actuation systems The outputs from the ECU are the current signals which have to energize and actuate the mechanical components of the driveline. The major task of the model of the actuation systems is thus to simulate the electrovalves which convert an electric signal, namely the current, into a mechanical one, namely a force or a pressure. The resulting signals will then be provided to the models of the mechanical components of the system, namely the clutches, the synchronizers and the hydrostatic IVU. The clutches actuation is modelled considering four main inputs: the clutch current, the dump-valve current, the clutch-hydraulic-circuit supply pressure and a correction factor for the actuating current which takes into account the engine angular velocity. As shown in Fig. 5-4, the current signals I A and I B actuate the clutch A and B, respectively and are multiplied by a corrective factor which takes into account the angular velocity of the internal combustion engine, in order to prevent the possibility to pressurize and actuate the clutches when the engine is off. The current I DUMP actuates the dump-valves which act as safety devices since, in dan- 67

Figure 5-4: Actuation system for clutches A and B. gerous situations, they open the clutches depressurizing the hydraulic circuit in such a way as completely disconnect the driveline from the final semi-axles and the vehicle itself. The output from the clutch actuation system are the clutch hydraulic chamber pressure and the normalized pressure of the discs which is converted into a torque according to the clutch geometry and the friction between the discs. If the dump-valve is active, the chamber pressure will drop to 1 bar and the normalized force will be zero. The synchronizers actuation is slightly more complex since each synchro can engage two different gears, namely the first and the third range, the second and the reverse one, the fourth and the reverse two. Therefore, for each synchronizer, two independently actuated solenoids can pressurize the left and right chamber of a double effect cylinder which is then linked to the synchro by the mean of a fork. When the left chamber is pressurized, the synchro will move rightward, and viceversa. In order to reset the synchro in neutral position, both the chambers are simultaneously pressurized: the geometry of the system will guarantee the equilibrium condition between the left and right active 68

areas only when the synchro is in the central position. One of the key features of the synchronizers is the interlock system, which basically consists in a Poka-Yoke device that prevents to simultaneously engage multiple synchronizers, with different driving speed, on the same driven shaft. A set of pins connected to the synchronizers forks is used to allow the actuation of only one synchronizer per driven shaft, locking the others in their neutral position. Fig. 5-5 shows the logic truth-table of the interlock system.in order to emulate this logic, a state machine has been used to Figure 5-5: Truth table for synchronizers interlock system showing the possible simultaneous engagement. CNH all roghts reserved compute and limit the synchro positions and the contact forces, taking into account the position of all synchronizers, according to the aforementioned truth table. The hydrostatic IVU is actuated by the means of the current signal I HST which energizes an electrovalve that moves a hydraulic piston controlling the swash plate of the variable displacement pump. In this application, the current signal will be converted into 69

a normalized swash angle which will be fed to the model of the hydrostatic unit. 5.3.2 Driveline model All of the physical signals coming from the actuation system module are fed to the overall model of the driveline mechanical components, namely, the clutches, the sycnhronizers and the hydrostatic IVU. Fig. 5-6 shows the overall layout of the driveline model realized in Simulink R and SimDriveline R.All the branch connections represent the mechanical Figure 5-6: Driveline model layout. CNH all rights reserved. shafts of the transmission, that are characterized by their respective inertias. Each mechanical component is modelled adopting specific library blocks that are parameterized according to the design data. It is interesting to notice a logic consistency with the transmission stick diagram in Fig. 5-2.The synchronizers are treated as special clutches, using the same library block but with completely different actuation dynamic. 70

The simulated quantities in the driveline model are captured using specific bus connections which collect the set of information to be provided to the control modules to execute closed loop simulations. 5.4 Model and Software in the Loop Once the plant model is complete, it can be interfaced to the model of the control system in order to run closed loop simulations. This is the step of MBD referred to as Model in the Loop (MIL) since the control logics and strategies are modelled and simulated versus the plant model, Fig. 5-7.During the MIL phase, no legacy code is used since all Figure 5-7: Model in the Loop simulation the control strategies are implemented and engineered using specific software packages, in particular making a wide use of state machines. Generally, the human operator behavior is taken into account by implementing specific time histories, typically referred to as stimuli, which can be simulated adjusting and refining the strategies. Therefore, different scenarios can be easily and safely emulated on a standard computer, allowing the control engineers to perform a what-if analysis which, at the end, will provide a robust and optimized control logic. Hence logic constitutes an implementation of the control system specifications that have been virtually simulated against the product dynamic specifications, namely, the plant. 71

After MIL simulations have been performed, the verified and tested control model needs to be translated into legacy code, that will in the end be embedded into the real ECU. The legacy code is thence automatically generated using specific software packages that will allow the control engineer to take care of the scaling of all the control variables used, the memory allocation, the frequency of the ECU and so forth. The automatically generated software can still be interfaced with the plant model and used to run Software in the Loop (SIL) simulations on a standard PC, Fig. 5-8.During Figure 5-8: Software in the Loop simulations thesilphase,thesamescenariosasofthemilcasecanbesimulatedandverified so as to detect any potential weakness or failure of the legacy code that has been generated. Once the control software has been verified and tested, it can be compiled and downloaded into the real Electronic Control Unit. 5.5 Hardware in the Loop Hardware in the Loop (HIL) simulations represent the last and most important step in the virtual verification process. During this phase, in fact, the real ECU, namely the hardware, is tested using a specific test bench in which the physical systems to be controlled are real-time simulated. Here, real-time deals with the fact that the simulation of one or more component is performed in such a way that the input and output signals 72

show the same time-dependent values as the real, dynamically operating component, [25]. From a computational point of view, this requirement set the limit to the maximum frequency that can be simulated in real time, therefore the time-scale of the processes and components to be simulated is limited in order not to increase the computational complexity. Furthermore, HIL test benches also allow the possibility to include some extra hardware components within the control loop, such as electro valves, engine injectors, park brakes, displays and so forth. TheadvantagesofHILsimulationsareingeneral: Design and testing of the control hardware and software without the need to operate the real process and thence without the need of the physical prototype, in particular for complex systems; Safe verification of extreme and dangerous working conditions in the lab; Safe test and verification of faults and failures of sensors, actuators and any hardware/software component on the overall system; Possibility to frequently reproduce experiments, using automatic test sequences to explore the system behavior with multiple combination of boundary conditions and parameters; Easy operations with different man-machines interfaces; Dramatic cost and time reduction to achieve a low Time To Market and sustain profitability. Fig. 5-9 shows the simplest configuration of a HIL test bench architecture, with only one ECU. A host PC, which controls the overall test bench, is linked to a real-time simulator either via LAN connection or optics fiber; the simulator is the core of the test bench since it is composed by the real-time processors, where the plant model is 73

simulated, and by a set of electric boards with different functionalities, such as electric power supply, Fault Insertion Unit (FIU), interface with the real physical loads and sensors.the simulator is then connected to the ECU by means of the real wiring harness Figure 5-9: Sample configuration for a Hardware in the Loop test bench of the vehicle under consideration and of a set of electronic boards which are used to convert electronic signals into numeric ones and viceversa. A DSpace R Double Mid Size, HIL simulator has been used for the application under consideration, as shown in Fig. 5-10.The electrovalve actuators are installed on the back of the simulator cabinet, whereas the break-out box in the front provides easy and flexible access to the electric scheme of the system, Fig. 5-11.Since the tractor presents different ECUs controlling specific portions of the entire system, the ones to be verified have been physically connected to the real-time simulator whereas those which are not tested can be emulated and interfaced to the rest of the ECU network using CAN-busses. This application will focus on the IVT Driveline Control Logic (DCL) ECU. 74

Figure 5-10: DSpace Hardware in the Loop simulator. CNH all rights reserved 5.5.1 HIL simulations and automatic test sequences The plant model used for MIL and SIL simulations is compiled and downloaded on the real time processor of the test bench in order to start HIL simulations. The time-step adopted is 1ms witha4thrungekuttasolver,soastoguaranteeapropertrade-off between the computational complexity of the processes to be simulated and the ECU sample frequency. In terms of computational complexity, the real time processor typically spends 20-30% of the simulation time-step on the plant model execution, whereas the remaining part is dedicated to the lead time of the communication process between the real-time processor and the hardware implementation, that typically requires 0, 6 0, 7ms in order to guarantee an effective interface with the ECU. Once the test bench is set, a sequence of test cases is implemented in order to automatically launch a series of simulations, investigating different working conditions and 75

Figure 5-11: Physical loads (a) and wiring harness pin-out (b) of the HIL simulator. CNH all rights reserved scenarios, including nominal and failure conditions. A typical test case is composed by the following information: 1. Test ID 2. Test name 3. Test description 4. List of steps to be executed 5. Test procedure 6. Expected result 7. Result 8. Notes Fig. 5-12 shows a simple test case with the aforementioned information, analyzing in particular the vehicle acceleration and deceleration from maximum speed.the first step 76

Figure 5-12: Sample test case for vehicle acceleration to maximum speed is the vehicle Key-ON operation, which needs to be verified by measuring the battery voltage on specific channels of the HIL simulator; the engine is then started after pushing the clutch pedal, therefore the clutch switch and the engine speed are measured so as to check if the engine reaches the angular speed requested. In order to select the output ground speed, the operator can input 3 memory settings, referred to as "Range Selector Switch", so as to quickly choose among three pre-set values, especially during working operations that require frequent change of speed. In this sequence, the maximum output speed is associated to third memory set, thus, in step 4, the operator selects the range selector switch no.3 and the ground output speed of 50 km/h. The operator selects the Forward mode in step 5 and then releases the clutch pedal in step 6 following a given variation law for the pedal. Using the so-called shuttle-lever, the operator can manually select the desired percentage of target velocity, as definedinstep4: inthiscasethe operator moves the shuttle-lever to 100% so as to achieve the vehicle maximum ground speed. Then the shuttle lever is moved back to 0% in step 9 so as to decelerate the vehicle to power-zero condition. It is important to notice that during the entire maneuver, the vehicle is automatically accelerated and decelerated by the ECU, that controls the transmission ratio of the IVU and the proper sequence of clutches and synchronizers engagement.fig. 5-13 shows the HIL execution of the aforementioned maneuver. Note that the clutch actuation currents 77

2000 1000 Engine Speed [RPM] 0 160 165 170 175 180 185 190 195 1 0.5 Clutch A Cur Clutch B Cur 0 160 165 170 175 180 185 190 195 1 Synchro F1-F3 pos 0 Synchro F2-R1 pos Synchro F4-R2 pos -1 160 165 170 175 180 185 190 195 1 0 τ IVU -1 160 165 170 175 180 185 190 195 40 20 Output speed [km/h] 0 160 165 170 175 180 185 190 195 Time [s] Figure 5-13: HIL simulation of test case 1. 78

have been normalized between 0 and 1. Also, the synchronizer positions have been normalized between -1 and 1 so that normalized position -1 will correspond to range 1 for the synchronizer I-III, to range R1 for the synchronizer R1-II and to range R2 for the synchronizer R2-IV. Another very important requirements for IVT transmissions, is the possibility to continuously guarantee the synchronization between the vehicle and the driveline speeds when the cutches are open. This is for instance the frequent case in which the human operator pushes the clutch pedal, completely disconnecting the driveline from the vehicle, which generally decelerates due to drag torques and rolling resistances. In this conditions, the ECU has to actively control the IVU ratio, the engine speed and the synchronizers actuation so as to continuously follow the vehicle speed, in order to guarantee that the proper range and relative clutch is smoothly and safely engaged once the pedal is released. In fact, if the driveline speed does not follow the vehicle speed when the clutches are open, a huge torque bump due to inertial phenomena can affect the engine shaft with potentially dangerous consequences. Fig. 5-14 shows the test case implementation for a synchronization verification: the vehicle is accelerated up to 45km/h, then the clutch pedal is depressed until the vehicle speed drops to 20 km/h and then the pedal is released. Fig. 5-15 shows the result of the aforementioned synchronization maneuver. As can be noticed, the vehicle is accelerated on flat ground up to 45km/h then, at time t = 47s the operator pushes the clutch pedal and the vehicle starts decelerating.during the deceleration, the driveline controller continuously vary the IVU transmission ratio, τ IV U, and the synchronizers engagement so as to follow the vehicle speed. When the clutch pedal is released at t =74s, the vehicle speed reached 20 km/h so the second range is safely engaged since the synchronizer F2 and the driveline transmission ratios were properly set. The vehicle is then smoothly accelerated again up to 45km/h as specified in the test case. 79

Figure 5-14: Test case implementation to verify vehicle and driveline synchronization with open clutches. 1 0.5 Clutch A Cur Clutch B Cur 0 20 30 40 50 60 70 80 90 100 110 120 1 0 Synchro F1-F3 pos Synchro F2-R1 pos Synchro F4-R2 pos -1 20 30 40 50 60 70 80 90 100 110 120 1 τ IVU 0-1 20 30 40 50 60 70 80 90 100 110 120 60 40 20 Output speed [km/h] 0 20 30 40 50 60 70 80 90 100 110 120 Time [s] Figure 5-15: HIL simulation of test case 2. 80

Chapter 6 Conclusions This work provides a thorough description of the application of numerical simulations to the Global Product Development process for off-highway machines, with particular emphasis on the benefits obtained for the Feasibility, Optimization and Verification phases. An effective optimization procedure and a thorough kinematic analysis of a dual range synchronized power split infinitely variable transmission, based upon an infinitely variable unit, are provided. The novel result is that, beside the input coupled architecture, which has been deeply investigated in the scientific literature, the output coupled concept has been reassessed to show that both IC and OC solutions, if properly optimized, can give satisfactory performance and that only the particular application or duty cycle of the system under analysis allows the designer to opt for either solution by itself or even for a mixed one. However, the OC solution requires a unit capable of providing a speed ratio equal to zero, in order to be effective from a practical point of view; therefore V- Belt continuously variable transmissions or toroidal traction drives cannot be used since they provide limited speed ratios between two non-zero values. The OC architecture is shown to have better performance in terms of power recirculation at low speed ratios, although the torque load on the IVU may be significantly higher if compared to the IC solution. The IC architecture, in turns, has a more general applicability and performs better close to range shift regions. Although the present study is limited to a sample dual 81

range transmission used for agricultural vehicles, the optimization procedure, presented by the authors, may constitute a powerful tool for the designer to determine the optimal architecture and the set of gears which minimize power recirculation, increase efficiency, and reduce the IVU maximum torque values thus allowing more compact and economical components. Following the product feasibility analysis and optimization, the implementation of a virtual verification process, based upon Model Based Engineering, is presented. Given the high technology content and the complexity of power split infinitely variable transmissions, robust and effective control systems play a crucial role in terms of vehicle performance, safety and human operator comfort. The physical system to be controlled, namely the plant, is thus modelled and simulated according to the design data and specifications defined and finalizedintheoptimization phase, so as to reproduce the behavior under different working scenarios. On the other hand, the control logics and strategies can be modelled in order to perform closed loop simulations. With this approach, the need of physical prototypes is dramatically reduced, minimizing product costs and time to market. Furthermore, dangerous and failure conditions can be easily and quickly simulated so as to verify in advance product robustness and safety. A set of simulations is then presented showing the implementation of specific test cases to evaluate the behavior of an infinitely variable transmission for agricultural machines in nominal and failure conditions. 82

Chapter 7 Acknowledgements Ican tbelieveifinally got to this point...it all started like a personal bet. It has been a long, tough, climbing through exams, projects, challenges, travels, joys and sorrows. And now that I got to the peak, I look behind me and my heart explodes. Everysinglestepwasworth theeffort: finally the Sun. This is definitively the best part of the entire work: I can finally try to acknolewdge all the wonderful people I met on my road and who helped, encouraged and loved me, day by day. I couldn t have reached this point alone. I now want to thank each of you individually, of course in random order...but let me first start by thanking the Lord, who provided me the strength and the faith to approach these long years alone. Every Sunday, I walked out from the Duomo di Modena with a regenerated spirit, ready to start a new week. Thanks for talking to me through Don Giacomo Morandi, who weekly touched my heart, penetrating the deepest of my Soul. I also need to express my gratefulness towards my Company, Case New Holland, for allowing me to pursue this PhD program in combination with my work. I really appreciate the encouragement and the patience demonstrated by my responsibles, especially when I had to cope with multiple academic programs (...). I will do my very best to redeem myself for the times, especially in the last weeks, my attention was split between in-office and out-of-office commitments. 83

Prof. Napolitano, thanks for being a secure Mentor for me. I successfully graduated with you, and immediately started brand new adventures: you followed my steps anywhere, even across the ocean, and continuously supported and helped me, inside and outside the University, preserving a constant link. Thanks also for all the patient and useful corrections and suggestions on our paper and on this thesis. Giuseppe, you grabbed my hand and took me again along the passionating world of scientific Research. I met very few people talented like you, with a deep and unbounded focus on new innovative concepts and creative ideas, perfectly combining the Scientist and the Engineer. It s thanks to your full availability, interest and friendliness if I managed to meetyouineindhoven,discusssomeroughideasandstartourhardworktotransform them in something concrete. Haibo, a Coach, a Teacher, a Friend. We have been sitting ten thousand kilometers far from each other, nonetheless you taught me all I know about our products, about CVTs and the amazing world of agriculture. How many phone conversations, how many suggestions, how many projects discussed together! Thanks a lot for sharing with me your knowledge and your wisdom, you made me feel comfortable every single day in office: whenever I had some problems or doubts, I knew who to call. Enrico when I first mentioned you about my PhD program - I remember we were at the coffee machine - you started nodding before I could even finish my sentence! I could see pride in your eyes, and I felt proud to proceed with this adventure. Had it not been for the IVT project we worked on together, I wouldn t possibly have thought about design optimization. Kezhun 84

thanks for your trust on me. You gave me the necessary autonomy and flexibility to approach my job, without forgetting about the personal life: this has been absolutely important in order for me to proceed with my studies and my after dinner work. It s now the turn of my dearest ones, without whom I would have been lost. Mamma, Papà so far so close! Our daily phone calls made me feel at home. We celebrated together any success, exam, good news...or simply the pleasure to meet each other again whenever I got back home. Mamma, your love constantly supported my steps. I am aware of all of your tears, whenever I had to leave for Washington, Rome, Modena...may all of my efforts and achievements partially mitigate the time I spent away from our household...and the infinite number of shirts you perfectly ironed me in no time whenever I was back home. Papà, you constantly encouraged me in every good or bad moment. Look at how many further bricks I added to our building...each of them paid with sacrifices and passion. Thanks for the great efforts both of you did in order to provide me and Adriano with everything that made us feel comfortable, for your emotional and economical support. Thanks again, because I never missed anything. None of my achievements would have been possible without your prompt and secure back up. Adriano there we go: we followed different paths...and somehow we always happened to be on the same boat! I am proud and happy to row with you in this strange Sea of our lives, sharing our dreams and concerns, looking for something we do not clearly know yet...but we are cocksure it does exist. Thanks for the long chats and discussions, for all the time we had dinner together recalling the wonderful days spent rowing. Thanks for horning anytime you arrived under my window! Thanks to all of my other relatives who have been close to me in one way or another. Thanks to my aunt Elisa, for our weekly phone conversations in which you constantly 85

reassured me for any challenge I had to face; thanks to my grandparents, Tata and Totò, for you never stopped pray for me and feed me with your kind words. Thanks to Anna, Nando and Fabrizio for your constant hospitality during my week ends alone: a safe harbourwhereialwaysfeltathome! ThankstoGianna, Manuela and Vito, though we didn t get in touch so often, I could always rely on your esteem, that made me feel special and proud of my work. I always appreciated our lunches and dinners all together: those are the best moments ever. Stefano my buddy, thanks for the strength of our friendship, that never got weaker even at long distances. Thanks for picking me up anytime I had chance to get back to Bari and I was too tired to drive: it was oxygen for my soul to join you and the rest of us. Thanks to all the "Magnifici Senatoribus del Sacro Poker" : Ricciolinus, Pallatvs, Flatvlentvs, Parmaenisae, Notarvs atque plaebevs Fritzibus: our nights spent playing cards with cigars and "croccantini" are unforgettable. Michele eminent "Conte": I felt the difference since you left the wonderful Emilian lands. Those two years together reinforced our friendship, I will never forget our discussions on the disadvantages of the "Single-Life"...but I wonder if we will change our mind in one year or so...thanks for raising three fingers in the picture we took in Gardaland...though I m still waiting for a reasonable explanation. Paolo, I will keep with me all the e-mails we exchanged in these years. Although we were ten thousand kilometers far from each other, you probably have been one of the person I felt "closer" to me since we got in touch on a daily base. Thanks for all the shipments of wonderful goodies (Irish Spring & Poker gadgets, mostly) you took me. Thanks to all those colleagues of mine with whom I had the pleasure to become friend 86

(...most of them coming from Down-South...). Thanks to Roberto, a guy from Turin who is now able to speak most of Apulian dialects; thanks to Gigi, for your lessons of body building and "Latin-lovery"; thanks Antonio, for the wisdom of your "Qualgh e ddije"; thanks Francesca, your cheerfulness often brightened up our boring days; thanks PFerrac, for introducing the all of us to the local traditional cuisine; thanks Mico, for your patience and proactive support on our HIL test bench; thanks Gianni, for all the questions you answered me about power recirculation and your remarkable knowledge in hydraulics that resulted very helpful in my work. and last, but absolutely not least Lucia my beloved. I have no words to properly thank you for the love, the sweetness, the care you always gave me. You have always supported all the tough calls I made, even when I had to leave our hometown, crossing the ocean, to follow my dreams. Thanks for the extraordinariness of our relationship, which often acted as an unreachable example for the others. Thanks for being able to understand each other without a single word; for our perfect complicity, for the unmeasurable encouragement you have always donated me. Thanks for your extraordinary appetite and gourmet: for appreciating the Fiorentina as it must be, without asking to re-cook it, for enjoying the raw Seafood as well as the Tortellini, thanks for being a fan of Paposcia and of all the goodies from "Bar Pizzicato". Iwillneverbeabletoexpressallofmygratefulnessforthepatienceandtheloveyou demonstrated to me, in particular during the last four years we spent far from each other. I can only promise you that our dreams will shortly come true. Love. Salvatore Schembri Volpe May 2009 87

Chapter 8 Nomenclature C = Carrier shaft CV T = Continuously Variable Transmission CV U = Continuously Variable Unit D = intersection along the entire integration domain I of the local domains D τ IV T D τ IV T = domain of validity of the design constraints ECU = Electronic Control Unit GP D = Global Product Development PTO = Power Take Off MIL = Model In the Loop SIL = Software In the Loop HIL = Hardware In the Loop GV W = Gross Vehicle Weight TTM = Time to Market MBD = Model based design f = P IV U /P IN_Max ratio between IVU power and maximum input power I = integration domain of the objective function Ψ IC = Input Coupled IV T = Infinitely Variable Transmission 88

IV U = Infinitely Variable Unit PGT = Planetary Gear Train DCL = Driveline Control Logic FIU = Fault Insertion Unit P IN = input power to the IVT P IV U = power flowing through the IVU OC = Output Coupled S2 =Sun shaft I A I B I HST I DUMP = Actuation current for clutch A = Actuation current for clutch B = Actuation current for hydrostatic IVU = Actuationcurrentfordumpvalve T i,j = torque exerted from the i th to the j th element T out = output load torque w i = weighting function for the discretized optimization problem η IV T = efficiency of the IVT η IV U = efficiency of the IVU η M = mechanical efficiency of the fixed ratio portion of the power split IVT ρ = probability density function (PDF) τ 1 = transmission ratio of first range τ 2 = transmission ratio of second range τ f = transmission ratio of final reduction gears τ FRG = transmission ratio of the Fixed Ratio Gear τ I IV T = transmission ratio of the IVT in first range τ II IV T = transmission ratio of the IVT in second range τ IV T = overall transmission ratio of the IVT τ IV T_s = overall transmission ratio of the IVT at range shift point τ IV U = transmission ratio of the Infinitely Variable Unit 89

τ IV U = τ IV U τ FRG overall transmission ratio of the IVU and Fixed Ratio Gear τ IV U_s = overall transmission ratio of the IVU at range shift point τ ωa = transmission ratio of the PGT 1-2-3-5 τ ωb = transmission ratio of the PGT S2-4-3-5 Ψ = objective function Ψ D = discrete form of the objective function ω i = angular speed of the i th gear 90

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