Design Methodology for Small Brush and Brushless DC Motors

Transcription

1 Design Methodology for Small Brush and Brushless DC Motors Jérôme Cros, Mehdi Taghizadeh Kakhki, Geraldo C.R. Sincero, Carlos A. Martins, Philippe Viarouge INTRODUCTION Manufacturers of components and sub-systems for large scale applications are constantly improving the quality of their products in order to ensure customer satisfaction. They are facing severe competition constraints and this is particularly true for automotive industry. The offer of new services and functionalities goes well together with the increasing use of electronics and electrical actuators which provide auxiliary functions in a vehicle, improving the functional performances. Given this context, and the constant need for improving the electrical machines, the present chapter focuses on the design methodology for brushed or brushless DC machines as the two mostly used motor types in small accessories for vehicles. This methodology is also applicable to many other machine types. We discuss various winding configurations for the machine armature and the advantages of new motor designs using a concentrated winding. We present a method for the selection of an efficient motor and an analytical dimensioning process using a non-linear constrained optimization approach. Finally, we discuss the application of finite element and time-simulation methods for the validation of the optimal solution. SMALL ELECTRIC MOTORS IN MODERN VEHICLES An electrical actuator is a device designed for moving or controlling another mechanism or system. Table 1 shows a list of automotive accessories using small power actuators, (Cho and Johnston, 1999). Small rotating electric motors are an important part of the electrical system and are used in several feature accessories in a modern car. Over 100 motors are used in a well equipped luxury vehicle (Thiemer, 2001). These machines have very different requirements in terms of power, speed, torque, volume, form and size. The energy conversion from electrical to mechanical in a rotating electrical motor is the result of an interaction between two magnetic fields, one created by permanent magnets (PM) or electromagnets and the other generated by current-carrying conductors (armature AcademyPublish.org - Vehicle Engineering 207

2 winding). The number of magnetic poles in the magnetic field is referred to as machine poles. The current-carrying conductors are mounted in the armature core openings which are referred to as armature slots. Table 1. List of automotive accessories using small power actuators (Cho and Johnston, 1999). starter motor, alternator, radiator motor-fan, air conditioning Power train compressor drive, idle speed control, engine throttle control, transmission shifter, electrically variable transmission, engine coolant pump motor, electrical valve, and ECR actuators. electric power steering system, electro-hydraulic power steering, ABS Chassis systems, brake-by-wire actuators, active suspension actuator, and 2-4 wheels drive actuator. windshield wipers, window lifts, seat adjuster, seat vibrators, sunroof Body actuators, sliding door closers, door lock mechanisms, headlamp adjuster, mirror adjusters, steering column adjuster, HVAC blower, cruise control, headlight wiper motors, power antenna, headlight doors, trunk closer, and auto-leveling system. The two mostly used motor types in small accessories are PM brushed dc motor and PM brushless dc motor. In a PM brushed dc machine, the permanent magnets are mounted on the stationary part of the machine (stator) and the armature is the rotating part of the machine (rotor). DC voltage is applied to the commutator copper segments through carbon brushes pressing against these segments (Hamdi, 1994). The commutator segments are mounted on a cylinder on the rotor shaft and are insulated from each other and also from the rotor shaft. The commutator segments are wired to the ends of the armature coils. In fact, the set formed by the commutator and the brush assembly acts as a mechanical rotary switch. This allows reversing the coil current in the rotating armature maintaining the torque production. Fig. 1 shows a brushed dc machine used as a radiator cooling motor fan. In a PM dc brushless machine, the permanent magnets are mounted on the rotor and the armature is stationary. The armature coils are fed with a power electronic converter and the coil current waveform must be synchronized with the rotor position. These motors are often fed with square-wave currents or voltages when a simplified control system is required. However, similar motors fed with sinusoidal currents and voltages are also becoming increasingly popular since the cost of electronics (including microcontrollers) is rapidly decreasing. Employing a sinusoidal current waveform is more advantageous since it generates less noise and vibration. However, it requires several current sensors and increases the complexity of the control system. The power converter acts, therefore, as an electronic commutator and is generally integrated inside the motor. It avoids the problems associated with a mechanical brushcommutator assembly including the mechanical wear and EMI compatibility (Torrey and Kokernak, 2002) and results in a more efficient and reliable machine. The cost of 208 AcademyPublish.org - Vehicle Engineering

3 production for PM brushless machine is higher compared to the brushed dc machine but it allows for variable speed operation without an additional electronic converter. It is usually used in more expensive luxury cars. Fig. 2 shows a 5-phase brushless dc machine with an external rotor for a radiator cooling motor fan. Fig.1. Brushed DC motor for a radiator cooling motor fan Brush assembly Armature (rotor) Permanent magnet poles (stator) Commutator Fig.2. Brushless DC motor for a radiator cooling motor fan Armature (stator) Permanent magnet poles (rotor) Power electronic converter AcademyPublish.org - Vehicle Engineering 209

4 Table 2 and 3 show examples of PM brushed dc motors and PM brushless dc motors for different applications in vehicles. Starter Motor Poles Slots Brushes Speed 2565 rpm Power 150 W 500 W Input Voltage 1000 rpm 2000 rpm 500 W 1.5 kw 2000 rpm 1820 rpm 1800 rpm 120 W 120 W 1.2 kw 12 V 12 V 12 V 12 V 12 V 12 V Table 2. Structure of PM dc motors applied on some of vehicle accessories Electrohydraulihydraulic blower Electro- Heater Radiator Wiper Application Fan ABS Power Fan Table 3. Structure of PM brushless dc motors applied on some vehicle accessories Application Electrohydraulic Water Radiator Radiator Heater Fan Fan blower Power Pump Fan Steering Poles Slots Number of Phases Speed 2500 rpm 2000 rpm rpm rpm rpm Power 250 W 350 W 120 W 1500 W 500 W Dc Bus Voltage 12 V 12 V 12 V 42 V 42 V Trends in Small Motor Design for Automotive Applications In the current economic context and due to severe competition, all kinds of electrical machines should be constantly improved to reduce their costs and improve their performance. This evolution has become possible thanks to more efficient and precise calculation methods which allow the designer to further elaborate the optimization of the structures. This is also due to technological advancements in materials, electronics, manufacturing techniques and new technical specifications that lead to new developments and new designs. For instance, the 42V Powernet voltage modification has important consequences on existing electrical equipment, mainly for brushed dc motors present in many systems and 210 AcademyPublish.org - Vehicle Engineering

5 accessories. The higher input voltage may lead to current commutation problems, electromagnetic interferences and, even, ring fire on brushed dc motors, among other problems (Thiemer, 2001; Torrey and Kokernak, 2002; Hamdi, 1994). In this context, many existing motors need to be improved. It is also interesting to evaluate new design solutions that might be more appropriate for the new electrical system specifications. Integration of the equipment in a new car design adds new constraints and should meet new requirements. Designers will have to pay attention to a number of aspects such as frame size, cost, noise, lifetime, ambient conditions, and quantities which vary from one vehicle model to another. New designs of electrical motors can benefit from new manufacturing techniques, for example, new winding methods which reduce the copper volume and copper losses in significant proportions. The use of new materials may have important consequences on the machine structure. For instance, the design of electromagnetic devices with soft magnet composite (SMC) materials can offer several advantages over conventional laminated materials. It can facilitate the implementation of new structures with fewer parts, reduced size and weight (Hultman and Jack, 2003). DESIGN METHODOLOGY The design methodology allows the designer to find a compromise between material properties, device dimensions, the cost of production and assembling processes, and application constraints. It begins with the analysis of the application specifications and a topological research to find a machine structure well-adapted for the given application. The topological research is, in fact, the process of the pre-selection of machine structures which have the best potential to meet the requirements of a given application. It allows the designer to limit the number of solutions before proceeding to a dimensional and geometrical optimization. Fig. 3 shows a general flowchart for this type of methodology. Topological Research This approach relies on the designers knowledge and experience (expert rules) and does not need any particular Computer Aided Design (CAD) tools other than analytical models. This approach enables the designer to find geometries of electrical machines which take advantage of particular properties and performance of magnetic materials or windings. This helps also in reducing the size of the optimization problem. For example, Soft Magnetic Composite (SMC) materials may be an interesting choice for the type of magnetic material, however, they may impose some specific constraints for the motor geometry in regard to the pressing process. Nevertheless, compared to laminated material, SMC materials have isotropic properties which allows the design of original structures of magnetic circuits with different mechanical assemblies. This may improve AcademyPublish.org - Vehicle Engineering 211

6 the production process. This type of decision can not be easily formulated in an optimization problem and all possible options should be studied individually. The selection of a winding configuration, the choice of the number of poles and slots in a machine, or brush and commutator segment numbers in the case of a brushed dc machine, are also other examples of parameters to determine in a topological research before proceeding to a dimensional and geometrical optimization. Fig.3. Design optimization methodology Analysis of application specifications Topological Research Selection of the structure Axial or radial air-gap, number of poles, number of slots, winding configuration, etc. Global optimization of a given structure Dimensioning Multi-physical modeling Optimization Prototypes and Tests Classical Machine Dimensioning Method In this classical approach, the main dimensions of the machine are derived directly from the application specifications using simplified analytical formulas and expert factors determined by experimental data from many years of design experience (Hamdi, 1994). It may also employ Computer-Aided-Design (CAD) tools like Finite Element (FE) magnetic field calculations to complete the analysis and to validate the structure. Fig. 4 shows the diagram of a complete CAD environment for electrical machine design. It should bring together a multitude of coupled physical models to reproduce all the physical phenomena typically appearing in an electrical machine. It is also possible to perform several iterations with this CAD procedure. However, this is generally done by the designer when comparing and analyzing different solutions without using a specific 212 AcademyPublish.org - Vehicle Engineering

7 optimization method. In fact, this classical methodology is often confined to the comparison of all the solutions resulting from a topological design approach. Fig.4. Computer-Aided- CAD Environment Design (CAD) with Environment coupling with ofcoupling physical of physical models models. Thermal Modeling Heating transfer Dilation, dissipation Mechanical Modeling Assembly, parts movement Joule Losses Iron Losses Strength, Vibration B(H) curve Electrical Circuit Modeling Current & voltage waveforms Flux densities Magnetic Modeling Magnetic flux Global Optimization The aim of global optimization is to find the optimal dimensions for a suggested structure taking into account all kind of application constraints and material properties. The term Global refers to the fact that this approach takes into account all different physical phenomena and their interactions. A Global optimization approach needs also physical models, but unlike the classical approach, it uses the dimensional parameters as design variables and the application specifications are considered as constraints. The main challenge is to define an optimization problem with a given objective, variables, and linear and non-linear constraints (geometrical, electrical, thermal and mechanical). The choice of an optimization tool and optimization method (such as gradient-based methods, evolutionary algorithms, etc.) does not depend on the optimization problem. Any method could be used as far as convergence towards a solution is possible and all constraints are validated using modeling methods. Both analytical and finite element models could be used to evaluate the performance of the electrical machine. Optimization with Analytical Models Analytical models are widely used in a global optimization process since they allow us to take into account many physical phenomena and their mutual interactions. They are simple to implement and fast in terms of simulation time. However, they need simplifying assumptions which affect their accuracy and limit their utility in applications with complex geometry and material non-linearities. Optimization with Analytical Models Corrected with Finite Element Models Finite Element (FE) models are used to analyze the performance of the electromagnetic structures before their final realization. They are more precise than analytical models and AcademyPublish.org - Vehicle Engineering 213

8 are generally used as a reference for the validation of analytical models. Finite element models are used for field calculation, thermal and mechanical modeling, etc. Optimization schemes with analytical models corrected by finite element models are becoming increasingly popular since they benefit from advantages associated with both analytical models and field calculation tools. In this approach, for each intermediate optimal design solution, the electrical parameters generated by the analytical model are compared to those obtained by a 2D or 3D finite element computation (Cros et al., 2008). If there is a significant difference between these two sets of parameters, correction factors are applied to the analytical models to improve their accuracy. Figure 5 shows the flowchart for a design methodology using this approach. Optimization with Finite Element Models (Direct Method) Two dimensional (2D) and three dimensional (3D) finite element based methods may lead to more efficient tools for field calculation, allowing for a more precise evaluation of the machine characteristics. Currently, however, an iterative optimization process using finite element models may result in unpractical computation times in the case of electrical machine design. With the new technological advancements in data processing and computation speed increase, this approach will be progressively more interesting and will become possibly predominant in the future. Fig.5. Flowchart of the design methodology Load and power specifications Torque-speed characteristic and energy requirements Selection of motor main parameters Slot and pole numbers Brush and commutator segment numbers Selection of a winding configuration Position of phase coils in armature slots Iterative geometric design calculation 2D FE magnetic computations Analytic electrical equivalent model Correction factors for electrical model Performance calculation and validation Commutator model for time simulation 214 AcademyPublish.org - Vehicle Engineering

9 ARMATURE WINDING CONFIGURATION In conventional DC motors, three main types of rotor armature windings may be identified: lap winding, wave winding, and frog-legs winding (Hamdi, 1994). These windings are made with simple coil elements which are always interleaved. The ratio between the axial length of the end-windings and the axial length of the armature magnetic circuit is then relatively high. All these winding types differ primarily on the method used to connect the terminals of the simple coils to the commutator. For a lap winding, the number of parallel paths is equal to the number of poles. A wave winding has only two paths in parallel, regardless of the number of poles. The frog-leg winding method combines lap winding and a wave winding placed on the same armature, in the same slots, and connected to the same commutator bars. Figure 6 presents a conventional lap winding armature of a permanent magnet brush DC motor used in an automotive application. One can notice that the yoke has a relatively high number of slots and is made of laminations. The significant copper volume of the end-windings is typical of a lap winding with a small axial motor length. To avoid the interleaving of the coils, it is possible to directly wind the armature simple coils around each tooth of the rotor magnetic circuit (Cros and Viarouge, 2002). This kind of winding is called a concentrated winding but may be also called a non-superposed winding. As shown in Fig. 6, this technique considerably reduces the copper volume of the endwinding, the total copper losses and the total axial length of the motor (Cros and Viarouge, 2003). In small power applications using permanent magnet motors with reduced axial length, concentrated windings are progressively replacing other types of armature windings. Fig.6. Comparison of armature end-windings a) lap winding b) concentrated winding Armatures with concentrated windings have always a small number of slots with wide openings and large tooth sections. They can be realized with a laminated material but they are also well adapted to the use of soft magnetic composite (SMC) materials due to the reduced mechanical constraints during the molding process. With such materials, it is possible to insert the end-windings in the active part of the rotor magnetic circuit and expand the tooth tips to perform an axial concentration of the air-gap magnetic flux into AcademyPublish.org - Vehicle Engineering 215

10 the teeth. Such modification takes advantages of the isotropic properties of magnetic composite materials and partially compensates its low permeability. This axial insertion of the end-windings reduces the volume of copper and the total axial length of the motor. Concentrated Armature Windings of Brushed DC Motors The concentrated winding technique is too often associated and restricted to windings with a short pitch, i.e. windings with lower performances than those of classical winding structures. The concentrated windings with a short pitch are then limited to sub-fractional power applications with low voltage supply, where the performance in terms of torque to current ratio is not critical. In the case of the brushed DC motor, the simplest motor widely used for mirror adjustment and door latch is using a concentrated winding armature because its production cost is very low. This motor has 2 poles, 3 armature slots, 2 brushes, 3 commutator bars and a winding with a short pitch of 120 electrical degrees. Fig. 7(left) shows the diagram of a developed surface of this drum armature. This developed diagram is made by unrolling the periphery of the armature and commutator into a plane. This motor, which is well adapted for low voltage and low power applications, presents several drawbacks: the current commutation is not efficient, because the number of segments on the commutator and the number of coils per parallel path are very small (Fig.7, right). The commutation voltage between two consecutive segments is relatively high r in important Electro-Magnetic Interferences (EMI). because the internal voltages in the parallel paths of the winding are unbalanced, the path currents are different and there is a circulating current in the armature which is generated by the third harmonic of the no-load emf in each coil. This current decreases the motor efficiency and increases the noise and the torque ripple. the winding coefficient associated to a short pitch of 120 electrical degrees is small and equal to. The performance in terms of torque to weight ratio and torque ripple is low. Fig.7. Diagram of an armature with 3 slots, 2 poles and a single layer concentrated winding with a short pitch of 120 electrical degrees (3 coils); Diagram of the parallel coil paths (right) N S V V 216 AcademyPublish.org - Vehicle Engineering

11 Fig. 8 (left) shows an evolution of the machine of Fig. 7 by using a multi-layer concentrated winding. This new winding configuration increases the number of commutator bars and of armature coils. In Fig. 8 (right), each coil has been identified by 2 numbers. The coils having the same first number (e.g., coils 1.1 and 1.2) are wound around the same tooth and have the same no-load voltage. These coils are connected to different bars of the commutator to get coil paths perfectly balanced. The current commutation in the coils wound on a same tooth is achieved, simultaneously, by different brushes. Consequently, the multi-layer winding improves the commutation when compared to a single layer winding because the number of turns per coil and the coil inductance are reduced for the same operating point (same values of DC supply voltage, DC current and rated speed). Employing an armature with a multi-layer concentrated winding is an interesting solution for applications which need more power and higher voltages. Fig.8. DC motor with 3 slots, 2 poles and a multi-layer concentrated winding using 6 coils (left); Diagram of the parallel coil paths (right). 3.1, , , N N S V V Comparison: Lap Winding versus Concentrated Winding The drive of an automotive electrical motor fan, which is a typical application of the permanent magnet brushed DC motor, is chosen to compare a conventional lap winding armature with a multilayer concentrated winding one. The conventional motor has 20 armature slots with 20 simple coils, 4 stator poles and 4 brushes. This type of motor has been adopted by a lot of manufacturers in the world. The winding of the rotor is overlapped with a short pitch of 1 to 5. Fig. 9 shows the developed diagram of this structure with coil connections on the 20 commutator segments. The coils having the same first number (e.g., coils 1.1 and 1.2) have the same no-load emf and are in phase. Fig. 10 shows the parallel coil paths for the same machine. Manufacturers sometimes make simplifications to minimize the cost. For example, the number of brushes can be reduced while adding equalizer connections on the commutator as shown in Fig. 11. AcademyPublish.org - Vehicle Engineering 217

12 Fig.9. Diagram of a lap winding machine having 20 rotor slots, 4 stator poles and a lap winding and a short pitch from 1 to N S N S V Fig.10. Diagram of parallel coil path connections for the machine presented in Fig V It is possible to design an equivalent motor using a multilayer concentrated winding armature by using the same permanent magnet stator, the same commutator and the same number of brushes (2 or 4 brushes). In fact, one avoids the interleaving of the endwindings by regrouping simple coils which have the same emf phase on the same tooth of the armature. This leads to a new armature with only 5 big teeth and 4 simple coils superposed on the same tooth (Fig. 12). The simple coils can be concentrated around the tooth to minimize turn length and the copper volume in the end-winding. The connections of the terminals of the simple coils to the commutator segments and the parallel coil paths are always identical in both machines (i.e. machines in Fig. 9 and Fig. 12). The width of 218 AcademyPublish.org - Vehicle Engineering

13 the tooth tip influences the electromotive force and can be modified to obtain the same pattern of the no-load magnetic field in the air-gap. Fig.11. Diagram of a machine with 20 rotor slots, 4 stator poles, 20 commutator segments, 2 brushes with a lap winding and a short pitch from 1 to N S N S N S N S V Fig.12. Diagram of a multilayer concentrated winding machine with 5 rotor slots, 4 stator poles, 20 commutator segments 5.1, , , , , , , , , , N S N S V It is also possible to make such a concentrated winding armature with only 2 brushes by using equalized connections on the commutator as shown in the conventional armature of Fig. 11. In this case, the number of coils can be also reduced to facilitate the manufacturing process (Fig.13). Fig. 14 (right) shows a new concentrated winding armature made of a soft magnetic composite (SMC) material that can replace a 20 slots lap winding armature (Fig 14, left) made of a stack of laminations in a 180 W/12V motor fan application. The stator, the brushes and the commutator are the same for both motors. These machines have similar performance (torque and efficiency) and Table 4 summarizes a comparative analysis on the material weights. The use of a concentrated winding provides an important weight AcademyPublish.org - Vehicle Engineering 219

14 reduction of 58 % when compared to the lap winding armature. The armature winding resistance and the overall armature weight are nearly equal. The magnetic material weight of the soft magnetic composite armature is increased because the tooth tips are axially expanded to concentrate the air-gap magnetic flux into the teeth. Fig.13. Diagram of a machine with 5 rotor slots, 4 stator poles, 20 commutator segments and 2 brushes with a rotor winding made of concentrated windings wound around the teeth 5.1, , , , , N S N S V The superior performance of the multi-layer concentrated winding (for current commutation) has also been confirmed in another study in the case of a 36V supply (Cros and Viarouge, 2003). The long duration experimental tests at rated operation have shown that there is no degradation of the commutator and brushes. Fig 14: 180 W Motor fan with 4 stator poles: lap winding, 20 rotor slots (left); concentrated winding, 5 rotor slots (right) 220 AcademyPublish.org - Vehicle Engineering

15 Table 4. Comparative characteristics of 180W DC radiator cooling motor (Cros and Viarouge, 2003) Armature winding structure Lap winding Concentrated winding Number of rotor slots Number of stator poles Number of brushes Commutator segments Brushes Magnetic circuit material Weight Laminations 422 g SMC 480 g Copper Weight 130 g 55 g Total Weight without Shaft and commutator 552 g 535 g Synthesis of Efficient Brushed Dc Motor Structures with a Concentrated Winding The main requirement for an efficient winding armature is the maximization of the winding coefficient kb which can be defined as the ratio between the fundamental component of the magnetic flux embraced by a coil and the total magnetic flux per pole. This coefficient must be near to unity to maximize the no-load emf amplitude with the lowest number of turns (cros et al., 2002). Its value is less or equal to unity. Fig. 15 shows the winding coefficient value of several armatures versus the number of slots per pole. Fig.15. Variation of the winding coefficient for structures with a concentrated winding winding coefficient (kb) 1 0,95 0,9 0,85 0,8 0,75 0,7 0,65 0,6 0,55 0,5 0,45 0,6 0,8 1 1,2 1,4 1,6 1,8 Number of slots per pole (s/2p) One can see that the structures which offer the best winding coefficients are those which have a number of slots nearly equal to the number of poles. It is always preferable to choose a high number of stator poles to reduce the mass, however, this number should be chosen based on a compromise considering the external diameter and the speed. The pole AcademyPublish.org - Vehicle Engineering 221

16 number has an impact on the number of commutator segments and also on the number of armature coils. To obtain an efficient brushed DC motor with concentrated winding, we must select a machine of 2p stator poles and S rotor teeth which respects the following condition: S 2 p a with a 1or 1or 2 or 3 (1) With brushed DC motors with concentrated windings, the use a number of commutator segments (Z) greater than the number of slots is better to minimize current commutation problems. In this case, there is a plurality of simple coils wound around the same tooth. The terminals of each coil are connected to different segments for simultaneous commutation by different brushes. This type of coil arrangement will allow perfectly balanced parallel paths and avoids any circulating current between these parallel circuits. The number of segments (Z) is generally equal to the Least Common Multiple (LCM) of S and 2p: Z LCM ( S,2 p) (2) Generally, the number of brushes (2B) is equal to the number of stator poles (2p), as shown by Eq. 3 and N of coils are wound around each tooth (Eq. 4). Consequently, the number of coils per parallel path N pa is obtained by Eq. 5. 2B 2 p Z N S N pa Z 2 p (3) (4) (5) In automotive applications the performance of the motor is sometimes compromised in order to minimize the manufacturing costs. For example, it may be interesting to reduce the number of brushes (2B) and the number of coils per tooth (N), particularly in cases of higher number of stator poles. By employing equalizer connections, this simplification could be easily realized and the winding would be always well balanced. However, this modification will affect the life expectancy of the brushes because the current to be commutated by each brush will increase. Table 5 presents the main parameters of brushed DC machines for small power applications which respect the former expressions. The possible simplifications for each structure are shown in gray-colored cells. 222 AcademyPublish.org - Vehicle Engineering

17 Table 5. Main parameters for DC motor structures with a well balanced concentrated winding 2P Poles number S slots Z commutator segments N coils per tooth Npa coils/path B brushes kb winding coefficient Another possible simplification is to divide the number of commutator segments Z by two (Eq. 6) and to reduce the number of coils per tooth. This simplification will result in an unbalanced emf in the different coil paths between brushes but the level of this unbalance is inversely proportional to the number of coils in each parallel path. The main parameters of this kind of machine are presented in table 6. LCM ( S,2 p) Z 2 (6) Table 6. Main parameters for downgraded DC motor structures with concentrated winding 2P Poles number S slots Z=LCM(S,2P)/ commutator segments N coils per tooth 2B brushes kb winding coefficient Synthesis of Efficient Brushless DC Motor Structures with Concentrated Windings The selection of a particular combination for the number of poles and the number of slots in the armature of a brushless dc motor is done in the same manner. First, the number of rotor poles 2p is chosen based on the operating speed and the rotor external diameter. This number should be maximised to reduce the mass of the motor, however, it should be chosen on the basis of a compromise with respect to the electric frequency in order to limit the magnetic losses. According to the data shown in Fig. 15, the number of slots should be close to the number of poles to maximize the winding factor and consequently the motor performance. The various combinations of slots and poles which allow for the realization of balanced windings can be determined by Eq. 7 for the case of three-phase armatures. GCD(S,2p) is the Greatest Common Divisor between the number of slots (S) and the number of poles (2p) and k is an integer. AcademyPublish.org - Vehicle Engineering 223

18 S 3k GCD( S,2 p) (7) The number of slots per pole and per phase is defined by the following equation in the case of a machine with mph phases. S pp S 2 p mph (8) Table 7 gives a list of the various structures of three-phase machines for which it is possible to obtain balanced concentrated windings. The number of slots per pole and per phase (Spp) and the winding coefficient kb are listed in each table cell. The winding coefficient kb is the performance indicator for each solution. The gray-colored cells indicate the most efficient structures which present a winding coefficient higher than 0.9. There is an optimal value of Spp that allows for the maximization of the winding coefficient kb, for each phase-number. These target values are respectively equal to 1/3 for a 3-phase motor, 1/5 for a 5-phase motor and 1/7 for a 7-phase motor. However, it is not possible to realize a polyphase structure with a number of slots equal to the number of poles (S=2p). We can choose however a structure with a number of slots nearly equal to the number of poles, e.g., S=2p ±1 or S=2p ±2. These structures have the advantage of minimizing the cogging torque without slot skewing (Cros et al., 2002). Indeed, the number of pulsations of the cogging torque for a complete mechanical turn corresponds to the Least Common Multiple between the number of slots and the number of poles. Therefore, the frequency of the cogging torque is very high and its amplitude is low. Table 7. Combinations of number of slots (S) and poles (2p) allowing for the realization of three-phase machines with balanced concentrated windings 2p S 3 1/ /4 1/2 1/8 1/4 3/ /2 9 3/ / / / / / / /10 1/ / / /2 3/ / / / /4 1/2 3/ /14 1/ / / / / /2 4/ / / /16 1/8 3/ /4 5/ / / /2 9/ / /2 1/20 1/10 3/ / /4 3/ / / / /2 1/22 1/ / / / / / / / / /8 1/4 3/ AcademyPublish.org - Vehicle Engineering

19 Method for the Determination of the Winding of a Three-Phase Machine After the selection of the number of slots and poles, the next step is to determine the winding configuration and the position of the coils in the slots. Generally, for a threephase machine, it is preferable to apply a method similar to the one used for the design of large synchronous machines with a fractional number of slots per pole and per phase. This method is based on the decomposition of the number of slots per pole and per phase (Spp). For values below unity, Spp must be reduced to a fraction of two non divisible integers b and c, as shown in Table 7. b Spp (9) c A repeatable winding sequence is a list of integer numbers which characterizes the distribution of the larger and smaller pole-phase coil groups in the armature. This repeatable sequence can be derived from Spp and Eq. 9. The list has c numbers made of 0 and 1. The number of 1 s in the repeatable sequence is equal to b and the number of 0 s is equal to b-c. The initial repeatable sequence can then be described as follows: c cb b (10) The configuration of the whole winding structure is derived from 3 consecutive repeatable sequences under c rotor poles. If c is an even number, the same configuration can be repeated as a periodic distribution of coils. If c is an odd number, this distribution is antiperiodic and the direction of the conductors in the coils should be reversed. For a given structure, one can determine an optimal sequence to find the winding that has the highest performance (and the highest winding coefficient). This optimal sequence is derived from the initial one and has the most regular distribution of the number 1 s among the number 0 s. To illustrate this winding determination method, we present an example with a threephase machine which has 18 slots and 16 poles. The configuration of the whole winding can be determined in eight steps as shown in Fig. 16. In the first step, the Spp fraction is reduced to 3/8 and the initial repeatable sequence of the winding is found to be composed of five 0 s and three 1 s. Then, the repeatable sequence is reproduced three times (step 4). In the fifth step, the usual phase sequence AC'BA'CB' is associated to the whole sequence ( A characterizes the return conductor corresponding to conductor A). The conductors associated to number 1 in the sequence are selected to make the first layer of winding (step 6). Generally, this layer of winding cannot be directly realized to form a concentrated winding. In the seventh step, the second layer of the winding is obtained by reproducing and shifting the initial layer by a tooth or a slot width. The direction of each conductor must be also reversed. The final configuration of the winding of a three-phase machine with 18 slots and 16 poles can be checked in the last step. The figure shows only AcademyPublish.org - Vehicle Engineering 225

20 the winding for 8 rotor poles and this distribution repeats itself for the next 8 poles. Fig. 16. Determination of the concentrated winding of a three-phase machine with 18 slots and 16 poles (periodic symmetry of the winding under 8 poles) Step 1 : 18 3 S pp Step 2 : Initial repeatable sequence : Step 3 : Optimal repeatable sequence for highest winding performance : Step 4: Step 5: A C B A C B A C B A C B A C B A C B A C B A C B Step 6 : A A A B B B C C C Step 7 : A A A B B B C C C Step 8 : A A A A A A B B B B B B C C C C C C N S N S N S N S ANALYTICAL DESIGN AND FORMULATION OF AN OPTIMIZATION PROBLEM An iterative design process for brushed or brushless surface mount PM motors requires a small computation time for estimation of steady state performances and constraint evaluations in regard to the application requirements. Generally, the optimization problem is formulated with a reduced number of variables, an analytical dimensioning process, and several rapid modeling methods for comparison of different possible solutions. Fig.17 presents a general flowchart of a design method based on the iterative optimization process. The main motor performance requirements impose several non-linear constraints for the design method. These are the torque (Te), the motor speed (N), the supply voltage (UDC), the operating temperature (Tw) and the minimal efficiency ( µ 8. Other constraints for the maximal motor size are also added by using two parameters: the maximum external diameter (Dext_max) and the maximum axial length of the motor (Lmax). Before beginning the optimization process, one selects the motor structural parameters i.e. the number of slots (S) and the number of poles (2p), by taking account of the winding type and the number of phases (mph). Such a decision should also consider the 226 AcademyPublish.org - Vehicle Engineering

21 motor size and the winding performance, represented by the winding coefficient (kb), as discussed in the preceding sections. Table 8. Main specification parameters Torque (N.m) Speed (rpm) DC voltage (V) Maximal external Diameter (m) Maximal motor length (m) Working temperature ( C) Minimal efficiency Te N UDC Dext-max Lmax Tw Different kinds of permanent magnet, soft magnetic and conductive materials can be selected and characterized by their respective parameters like the magnetic saturation threshold for the laminations or the residual induction (Br) for the permanent magnets (Hamdi, 1994). The residual induction and the copper resistivity (ρ) are adjusted according to the motor operating temperature. The maximal flux density B sat in the softmagnetic material is fixed to avoid magnetic saturation. Several technological constraints should also be considered. These parameters impose a limit for certain parameters like the maximal copper filling factor kr and the minimal air-gap thickness. Generally, the filling factor does not exceed 0.35 in a small motor and the air-gap thickness is around 1 mm. Table 9 summarizes main material characteristics and technological parameters. Fig.17. Flowchart of the analytical design method of the motor structure Motor structure parameters Number of armature slots: S Number of permanent magnet poles: 2p Number of phases: mph Winding performance coefficient: kb Non-linear constrained optimization method Design Variables Table 9 Specification and realisation Constraints Tables 7 & 8 Iterative process Analytical design model Table 10 Performance Modelling AcademyPublish.org - Vehicle Engineering 227

22 A small number of variables including geometrical dimensions, current and magnetic flux densities are computed by a non-linear constrained optimization procedure that takes account of the performance criteria and the specifications constraints of the motor application. These design variables are listed in Table 10. It should be noted that one may use several similar variables (Bmag) to impose different flux densities in various parts of the magnetic circuit. Fig. 18 illustrates a number of geometrical stator parameters and Table 11 shows several equations which can be used to compute the main characteristics of the motor during the iterative design process. Table 9. Material parameters and technological constraints Iron Maximal flux density (T) Bsat Lamination (< 1.8 T) and SMC (< 1.4T) Residual induction (T) Br Ferrite < 0.4 T and NdFeB bonded (< 0.7 T) Copper resistivity (Ω.m) ρ Air-gap thickness (m) e > 0.75 mm Copper filling factor kr < 0.35 Table 10. Main design variables Total copper section (m 2 ) Current density (A/m 2 ) Armature (airgap) diameter (m) Armature length (m) Magnet thickness (m) Scu J D L la Permanent magnet arc ratio ß 0 1 Iron flux density (T) Bmag Bmag Bsat Fig.18. Sectional view of a permanent magnet motor with external armature eca etb t De ecr Dint e Dext la 228 AcademyPublish.org - Vehicle Engineering

23 Table 11. Analytical design model for a brushless DC motor with concentrated winding Parameter Analytical expression Constraint relation Specific armature loading (A/m) Air-gap flux density (T) Electromagnetic Torque (Nm) Tooth angular width (rad) Tooth tips thickness (m) Armature yoke thickness (m) Permanent magnet yoke thickness (m) A J Scu D Ba Inner Rotor : B r la 2 D D ln D 2 ( e la ) External Rotor : B r la 2 D 2 ( e la ) D ln D T 2 k b sin(β ) 2 D L B A a 2 θ B a 2 B m ag S etb D Ba 2 t 4 Bm ag S eca D B a 4 p B m ag ecp Slot diameter (m) De External armature : D B a 4 p B m ag 2 4 A D 2 etb D 2 etb S kr J (1 t ) 2 Inner armature : 2 4 A D 2 etb D 2 etb S kr J (1 t ) 2 External diameter (m) Dext External armature : D e 2 eca Inner armature : D 2 ( e la ecp ) Inner diameter (m) Dint External armature : D 2 ( e la ecp ) One turn length per coil for an external armature Number of turns per coil Lturn Inner armature : D e 2 eca B a 2 L 1 D e D 2etb S B sat 4 Ns 30 U D C A D p m ph 4 2 S T N Phase Resistance Rph S Lturn Ns 3 Scu RMS Phase current Iph 1 Scu J N s 2 S RMS No-load flux θ T per phase N s m ph p I Total Copper losses Loss 2 mph Rph Iph T T e Dext Dext max D int D int max AcademyPublish.org - Vehicle Engineering 229

24 PERFORMANCE ANALYSIS WITH FINITE ELEMENT AND TIME- SIMULATION METHODS The optimal solution must be evaluated by finite element analysis and time-simulation methods to quantify the analytical model error or to validate the performances before prototype realization. One can use a finite element model with step by step time resolution of Maxwell equations. Such modeling method can compute magnetic losses and takes account of magnetic saturation and rotor motion. When significant differences on motor performances are observed between finite element and analytical methods, several correction coefficients for analytical models are derived from these evaluations and another optimization process is performed. With such a method, the convergence of optimal analytical design process is achieved and all the constraints imposed by the application specifications are validated by finite elements or time-simulations (Cros et al., 2008). In the case of the finite element calculation of a brushed DC machine, the collector modeling is based on an equivalent circuit similar to a full bridge converter using a direct coupling method with meshed armature coils (Fig. 19). Specific switches with an arc model must be used to reproduce the conduction sequences between brush and collector segments and to simulate the conduction by the electric arc (Sincero et al., 2010). This approach is powerful for final solution analysis but it is very time consuming. It is possible to estimate commutation phenomena more accurately and analyze influence of some parameters such as the brush angle. To illustrate the performance of such finite element simulation, the comparison of experimental and simulated armature current waveforms for a 3 slots-2 poles DC motor with a concentrated winding is presented in Fig. 20 (Sincero et al., 2010). Fig.19. Simulation scheme for the finite element simulation of a 3 slots-2 poles DC motor with a concentrated winding Another method to model the brush and brushless motor variable speed operation is a time-simulation method (Fig. 21) based on the matrix resolution of the differential electrical equations of armature coils (Sincero et al., 2010). The armature winding coils are modeled by their equivalent circuits composed of self and mutual inductances, 230 AcademyPublish.org - Vehicle Engineering

25 resistances and electromotive forces. These equivalent circuits use constant inductance values and neglect magnetic saturation. The commutator connects the armature coils to the input DC source and by Eq. 11, we determine the armature coil current, which is represented by vector [I]. The electromotive force [E], and the electromagnetic torque T o, are determined by Eqs. 12 and 13: d[ I] d[ ( )] [ V ] [ Rcoil ][ I] [ L] p (11) dt d [ E] K psin(2 f p( )) (12) flux e T [ E] [ I] T0 Tiron T loss mech (13) Where [V] is the matrix of coil voltages, [L] is the coil inductance matrix, R coil is the coil resistance, [λ] is the armature flux vector, [θ] is the vector of the spatial phase angles of the armature coils, p is the pole pair number and Ω is the mechanical angular speed. Fig.20. Experimental & simulated waveforms for rotor coil voltage, armature current and DC supply current. 40 Voltage (V) Current (A) Rotor coil voltage -5 DC Current -30 Rotor Coil current Times (s) The matrix resolution simulation is preferred since it speeds up the time spent on the performance analysis of PM synchronous motors. Besides, it allows comparing different structures by only changing the files that generate the parameter matrices. This approach is more powerful and efficient during a design process where different motors have to be compared. The commutator and the control blocks are the systems that differ between a PMBLDC motor and a PM dc motor in this simulation strategy, although their basic functionalities AcademyPublish.org - Vehicle Engineering 231

26 are the same. Based on information about the rotor position, the gate signals are generated to feed the armature coils with a current that is in phase with the emf. This is necessary to maximize the output torque. However, it is also possible to simulate other types of control strategies. The simulation method for the commutator of both the brushless and brushed motors is detailed in (Sincero et al., 2008). Fig.21. General flowchart of a time-simulation method for brushed and brushless machines t 0 dt The inverter simulation model can neglect the PWM modulation by using the value of the inverter output voltages averaged over one modulation period. The voltages applied to the armature coils are positive or negative depending on the rotor position. During the diode conduction, an amplified current error determines the voltage to be applied in order to maintain a zero current in the phase (Figueroa et al., 2003). This simulation reproduces accurately, among others, the waveforms of the machine coils voltages and currents, the joule and inverter losses, and the torque ripple due to phase commutation effects (Figueroa et al., 2003). The average value over each modulation period can be also used to model the dc-dc converter. This linear variable dc voltage source is connected to the collector model. The real operation is similar to the inverter one: depending on the rotor position, the positive or negative input voltage is applied to the armature coils, which is equivalent to the collector segment contact with the positive or negative brush. The coil under commutation is short-circuited in order to invert its current direction while maintaining the output torque constant. If the current commutation is not completed at the end of the short-circuit interval, an electric arc voltage is generated and applied to the armature coil which generates an arc current until the complete coil current inversion (Sincero et al., 2008). The advantage of this methodology is the accurate estimation of the machine current waveforms, joule and commutation (arc and brush) losses, torque ripple and DC input current. Fig. 22 shows the brushed dc motor model block diagram. 232 AcademyPublish.org - Vehicle Engineering