DESIGN OF COMPACT PERMANENTMAGNET SYNCHRONOUS MOTORS WITH CONCENTRATED WINDINGS


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1 DESIGN OF COMPACT PERMANENTMAGNET SYNCHRONOUS MOTORS WITH CONCENTRATED WINDINGS CSABA DEAK, ANDREAS BINDER Key words: Synchronous motor, Permanent magnet, Concentrated winding. The design and comparison of three permanent magnet motors for a constant power of 45 kw at rot/min rated speed, and rot/min maximum speed, with concentrated windings and different kinds of water jacket cooled stator and PM rotor is presented. Motor A and motor B have surface mounted magnets and equal tooth widths with coils wound on each tooth, but different number of stator slots, while motor C has buried magnets and unequal tooth widths and coils wound on each second tooth. The simulation results show that motor A has the smallest current rating and the highest power factor but has the biggest cogging torque and torque ripple at load. Motor B produces the smoothest torque and smallest cogging torque but also the highest total losses. Motor C yields the lowest total losses and has the better thermal behavior but has the lowest power factor and the highest current rating. 1. INTRODUCTION Modern variable speed drives demand compact electrical motors with high power and torque density, which produce at the same time small losses. As an alternative for the squirrel cage asynchronous motor, which is used nowadays in the middle power range, three inverterfed permanent magnet motors were designed with help of finite element program FEMAG for a constant power of 45 kw and 230 V phase voltage at rot/min rated speed and rot/min maximum speed. In order to increase the torque density and to reduce the losses, the so called modular synchronous machine with concentrated tooth coil windings is applied due to the short winding overhangs, which lead to reduced copper losses and reduced axial length [1 3]. The three models were designed with identical number of poles (2p = 24), stator inner and outer diameter and active length (Table 2). Differences are in the stator and rotor geometries. Motor A and B have surface mounted magnets and equal tooth widths with coils wound on each tooth, while motor C has buried Darmstadt University of Technology / Department of Electrical Energy Conversion, Darmstadt, Germany, "Csaba Deak" Rev. Roum. Sci. Techn. Électrotechn. et Énerg., 52, 2, p , Bucarest, 2007
2 184 Csaba Deak, Andreas Binder 2 magnets and unequal tooth widths with coils wound on alternate teeth. The basic design for the motors is described and the calculated steady state electromagnetic performance as well as the thermal behavior is evaluated, showing that motor A has the smallest current rating and the highest power factor but has the biggest torque ripple. Motor B produces the smoothest torque but also the highest total losses, while motor C has the best thermal utilization and the lowest total losses, but has the lowest power factor due to the higher current rating. 2. BASIC DESIGN 2.1. MOTOR GEOMETRY Three different stator and two different rotor designs were considered and optimised in order to determine the better solution for the power & torque demand (45kW/430 Nm at 1000 rot/min 45kW/143 Nm at rot/min) and the thermal demands of Thermal Class F (limit of average winding temperature 145 C). The geometries and the winding configurations are presented in Fig. 1, where U, V and W are the three phases, while + and are the wounding directions of the coils. The identical stator outer diameter, active iron length and the shaft diameter allow the application of an identical water jacket cooling system as well as identical end shields, bearings, shafts, position sensors and motor mounting, simplifying thus a lot the manufacturing process of the prototypes. The identical stator inner diameter and the identical pole number give the advantage, that the two rotors can be eventually interchanged in order to test the behaviour of the different statorrotor combinations. a c b Fig. 1 Geometry and winding configurations: a) motor A; b) motor B; c) motor C.
3 3 Permanent magnet synchronous motors with concentrated windings STATOR DESIGN Motor A has 24 semiclosed slots with constant tooth width and coils wound on each tooth (Fig. 1a) resulting in eight coils per each phase, all connected in parallel [1]. Round copper wire is used for the windings. The number of slots per pole and phase is q = 0.5 which means a ratio of 2/3 between the coil width and the pole pitch and thus a rather low pitching factor k p of for the fundamental. The distribution factor k d is unity due to the toothwound coils and multiplied with the pitching factor it gives the winding factor k w [2]. The deep and narrow slots produce a big slot stray flux, leading to a rather low power factor, but are necessary in order to compensate the low winding factor with a high current loading A, thus an increased number of turns per phase (Table 1). Motor B has 18 semiclosed slots with constant tooth width and coils wound on each tooth (Fig. 1b) resulting in six coils per phase. The number of slot per pole and phase is q = 3/8 which means a ratio of 8/9 between the coil width and the pole pitch and thus a big winding factor k w of for the fundamental. This configuration produces two subharmonics of the air gap field at load, which results in a higher harmonic leakage causing a lower power factor. Due to the winding arrangement, three coils have to be connected in serial and then connected in parallel with the other three coils. In this case each phase conductor consists of 5 internal wires (strand in hands). The big disadvantage is the occurrence of additional copper losses due to the 1 st order current displacement. This effect is totally eliminated in motor A due to the fact that all coils are connected in parallel and thus the phase conductors consist of only one wire per turn. Motor C (Fig. 1c) has 24 open slots and unequal tooth widths [1]. The alternate teeth have parallel sides to carry prefabricated coils. The appropriate width of the intermediate teeth allows increasing the coil pitch so that a ratio close to unity between coil width and pole pitch and thus a high winding factor can be obtained [1, 2]. This is 0.98 for the fundamental (Table 1). Each slot holds one coil side of one phase, which means that the number of slot per pole and phase is q = The resulting four coils per phase are connected in parallel, so no 1 st order current displacement occurs. Profiled copper wire is used for the windings, thus an increased slot fill factor of 59% is achieved. The deep and narrow slots together with the big sub harmonic air gap field at load, which will occur at a q = 0.25 configuration, cause a low power factor, but give a good field weakening capability [2].
4 186 Csaba Deak, Andreas Binder 4 Table 1 Winding parameters Motor A B C Number of turns per coil Number of parallel connections Number of strand in hands Number of turns per phase Connection of phases Y Y Y Wire diameter/dimensions (mm) Slot fill factor Winding factor (of fundamental) Resistance per phase (at 145 C) (mω) ROTOR DESIGN High energy NdFeB permanent magnets are used with a remanence of B R = 1.1 T (150 C) and a coercive field strength of H cb = 712 ka/m. The rotors of motor A and motor B are identical with magnets mounted on the rotor surface and fixed with a bandage (Fig. 1a, b). In order to reduce the cogging torque and the torque ripple at load, the pole coverage of the magnets was reduced to 77% of the pole pitch [1]. In order to reduce the losses in the magnets due to air gap field space harmonics, segmented magnet poles are considered (Table 2). Motor C is designed with buried magnets, so no bandage is necessary (Fig. 1c). The iron contour above the magnets allows an optimisation of the air gap geometry by an appropriate modelling of the rotor surface and thus a nearly sinusoidal rotor field is obtained [1], if slot opening influence is neglected. The variable air gap has a minimum of δ 0 = 0.5 mm in the pole axis (Table 2). 3. ELECTROMAGNETIC PERFORMANCE 3.1. NOLOAD OPERATION The open circuit air gap flux density and the cogging torque are determined by 2D numerical calculation at noload. From the noload field distribution (Fig. 2) it can be seen, that the intermediate teeth of motor C have a flux concentration at the stator bore due to their small width at the wedges. This means that this small area is saturated already at noload. The flux density distribution in the air gap (Fig. 3) for four pole pitches shows that motor A and motor B have a mainly trapezoidal air gap flux density. The influence of the small interpole gaps as well as of the semiclosed slot openings is clearly visible, as well as the influence of segmentation of the surface magnets. The slot openings produce the biggest
5 5 Permanent magnet synchronous motors with concentrated windings 187 distortion of the radial air gap flux density distribution, considered in the middle of the air gap. Due to the open slots, thus bigger slot openings and the unequally distributed slots, this effect is much bigger for motor C causing a high harmonic content of the air gap field even if the rotor surface optimisation yields a nearly sinusoidal rotor field [1]. * teeth with coils Table 2 Motor dimensions Motor A B C Stator outer diameter (mm) Stator bore diameter (mm) Active length (mm) Stator yoke height (mm) Number of stator slots Stator tooth width (mm) * Stator slot opening (mm) Air gap (mm) (=δ 0 ) Bandage (mm) Number of poles Magnets / pole Magnet height (mm) Magnet width (mm) Pole coverage ratio α m (%) Rotor yoke height (mm) Shaft diameter (mm) The gaps between the magnet segments of one pole do not have an influence on the air gap field as it was the case with motor A and motor B, because of the smooth rotor iron surface. The cogging torque of a motor depends on the ratio between the number of slots and poles, the stator/rotor geometry and also on the pole coverage of the magnets. Here unskewed stator and rotor are considered. The influence of the pole coverage on the cogging torque and on the torque ripple at load at rated current and field oriented control (I sd = 0) was examined in [1] for motor A for a pole coverage varying between 55% and 100%, resulting in a minimum ripple at 77 % pole coverage. The cogging torque of motor A is reduced by 40% compared to 100% pole coverage ratio and is 5.3% of the rated torque. With the same pole coverage, Motor B has a much smaller cogging torque of 0.7% of rated torque while motor C produces a cogging torque of 1.9% of the rated torque (Fig. 4).
6 188 Csaba Deak, Andreas Binder 6 a b c Fig. 2 Calculated noload field distribution: a) motor A; b) motor B; c) motor C.
7 7 Permanent magnet synchronous motors with concentrated windings 189 a b c Fig. 3 Calculated radial component of air gap flux density distribution at noload: a) motor A; b) motor B; c) motor C.
8 190 Csaba Deak, Andreas Binder 8 Cogging torque [N m] Rotor position Fig. 4 Cogging torque at α m = 77% LOAD OPERATION The three motors are designed for power converter operation with a fundamental r.m.s. phase voltage of 230 V. They have to generate a steadystate torque of 430 Nm at rot/min rated speed and 143 Nm at maximum speed of rot/min. This requires a high current loading A, which leads to a rather big synchronous reactance and a low power factor at field oriented control, where only qcomponent current I sq is applied. In order to determine the necessary currents at rated and maximum speed for given torque, the current I s and angle γ (angle between qaxis and I s ) are varied until the demanded torque and the maximum phase voltage is reached. The power factor can be improved if also a negative d component current I sd is supplied to the windings (Fig. 5). This will shift the current phasor I s towards the voltage phasor U s. At constant phase current I s, I sq is reduced due to I sq =I s I sd and thus U s is shifted towards the qaxis, reducing the angle ϕ between phase current and voltage. By increasing γ, U s will be reduced due to the increased I sd while the power factor cosϕ will increase [1]. Varying γ between 0 and 35 el, the torque will increase at the beginning, and then it decreases again. The reason for this behaviour is the reluctance torque, which is prominent, when also dcomponent current is applied. The voltage decreases with increasing γ and reaches the value 230 V at 16 el for motor A, 20 el for motor B and 18 el for motor C, respectively. At these angles the torque still has
9 9 Permanent magnet synchronous motors with concentrated windings 191 the requested value and the power factor is increased by 0.1 compared to operation with γ = 0 el. The results of the simulated steady state electromagnetic performance are presented in Table 3 for rated speed and Table 4 for maximum speed respectively. a b c Fig. 5 Phasor diagrams at rated speed: a) motor A; b) motor B; c) motor C. Table 3 Electromagnetic performance at rated speed Motor A B C Speed (rot/min) Phase voltage (V) Frequency (Hz) Phase current (A) Angle γ ( el) Power factor Torque (Nm) Torque ripple (of rated torque) Current loading (A/cm) Current density (A/mm 2 ) Thermal load A J (A/cm A/mm 2 ) Ohmic losses (at 145 C) (W)* Iron losses in stator (W)* *Calculated for sinusoidal voltage and current supply.
10 192 Csaba Deak, Andreas Binder 10 Table 4 Electromagnetic performance at maximum speed Motor A B C Speed (rot/min) Phase voltage (V) Frequency (Hz) Phase current (A) Angle γ ( el) Power factor Torque (Nm) Torque ripple (% of rated torque) Current loading (A/cm) Current density (A/mm 2 ) Thermal load A J (A/cm A/mm 2 ) Ohmic losses (at 145 C) (W)* Iron losses in stator (W)* *Calculated for sinusoidal voltage and current supply. Analysing the torque ripple at rated speed (Fig. 6) results, that motor B has the smoothest torque with the smallest ripple, while motor A and motor C produce similar torque ripple amplitudes. Additional losses, which occur in the windings due to 1 st and 2 nd order current displacement and in the magnets due to flux pulsation are calculated at sinusoidal and voltage source inverter supply. A PWM operation with 3 khz inverter pulse frequency was simulated (Table 5). Fig. 6 Torque ripple at rated speed.
11 11 Permanent magnet synchronous motors with concentrated windings 193 Table 5 Additional losses in windings and in magnets [W] Motor A Motor B Motor C Speed (rot/min) Supply Sinus Winding Magnets Supply Inverter Winding Magnets COMPARISON OF THE ELECTROMAGNETIC PERFORMANCES Comparing the designed motors A, B and C, based on noload and load calculations, we can see that motor A has the smallest current rating and the highest power factor at rated speed but has the biggest thermal load due to I 2 R losses as well as the biggest cogging torque and torque ripple at load. Motor B produces the smoothest torque at all investigated operating points but has also the highest total losses due to increased additional eddy current losses especially at high frequencies. This is a major setback for the thermal behaviour. Regarding the current rating and the power factor, motor B stands between motor A and C. Compared to motor A, motor C produces smaller cogging torque and torque ripple but needs a 20% higher current at rated speed. Nevertheless due to the 30% smaller phase resistance it generates smaller ohmic losses and has a lower thermal load at both points of operation. The bigger slot openings cause a bigger harmonic distortion of the air gap field, even if the rotor field is almost sinusoidal due to the rotor outer contour optimisation, so that the power factor of motor C is the lowest at rated speed. The currents at maximum speed of motor B and motor C for 143 Nm are almost the same as the current of motor A due to the higher synchronous reactance, which allows a better field weakening ability. The fractional slot configuration leads to increased losses in the magnets especially at higher speed which could cause an overheating of the magnets. In the considered cases the lowest magnet losses occur for motor C at both rated and maximum speed while in motor B the surface mounted magnets and the bigger slot openings due to lower slot number than motor A shows the highest losses in the magnets. 4. THERMAL ANALYSIS An identical waterjacket cooling system at 45 C is designed for all three motors with a circumferential spiral cooling duct with 14 turns and with a heat
12 194 Csaba Deak, Andreas Binder 12 transfer coefficient of α K = W/m 2 K, which corresponds to 9 l/s water flow rate and 1.66 m/s water velocity [1]. A 2D thermal calculation was performed with help of finite element program ANSYS to verify the thermal behaviour of the motors, first without any resin impregnation in the slots. Due to the symmetrical heat distribution, only two magnet poles are simulated for motor A and motor C and four magnet poles for motor B with the corresponding stator segments. Due to the smaller slot fill factor (lower heat transfer) and bigger copper losses, motor A would excessively heat up without resin impregnation with a maximum temperature of above 200 C in the windings while motor C would reach a maximum temperature of above 300 C which is more than the temperature limit of the isolation. To avoid this, the coils are embedded in resin. For simulation, a heat conduction average value of resin and air of W/mK has been used. In this way the maximum temperature is reduced to 144 C (Fig. 7a) and 203 C respectively (Fig. 7b). The heat transfer of motor C is the best due to the high slot fill factor and so the temperature does not exceed 110 C (Fig. 7c) at rated and maximum speed (Table 6). a c b Fig. 7 Temperature distribution at rated speed: a) motor A; b) motor B; c) motor C.
13 13 Permanent magnet synchronous motors with concentrated windings 195 Table 6 Calculated winding temperatures Motor A Motor B Motor C Speed (rot/min) ϑ Hotspot ( C) (max. 155 C) ϑ average ( C) (max. 145 C) Speed (1/min) ϑ Hotspot ( C) (max. 155 C) ϑ average ( C) (max. 145 C) Motor B on the other hand exceeds the temperature limit at both rated and maximum speed due to the additional 1 st order losses caused by current displacement. 5. CONCLUSIONS Three permanent magnet motors were designed with concentrated tooth coil windings for a constant power of 45 kw and 230 V phase voltage at rot/min rated speed and rot/min maximum speed. Due to the high electromagnetic utilisation and the fractional slot winding design, the power factor of these models ranges only between , but it is improved by 0.1 with help of negative d current supplied to the windings. The models are designed with identical number of poles, stator inner and outer diameter and active length. Motor A and motor B have surface mounted rotor magnets and equal tooth widths with coils wound on each tooth, while motor C has buried magnets and unequal tooth widths with coils wound on alternate teeth. The calculated electromagnetic performance at noload and load operation shows, that motor C has a better thermal utilisation, smaller cogging torque and torque ripple at load, yields lower total losses at rated speed due to the smaller phase resistance but has a smaller power factor and 20% higher current rating than motor A. Motor B produces the smallest torque ripples but also the highest total losses due to increased additional eddy current losses which lead to high temperatures in the windings at high speed, exceeding the thermal limits of the insulation. Motor A and motor C are currently built as prototypes (Figs. 8, 9).
14 196 Csaba Deak, Andreas Binder 14 a Fig. 8 Built prototype stators (under construction): a) motor A; b) motor C. b a b Fig. 9 Built prototype rotors (under construction): a) motor A; b) motor C.
15 15 Permanent magnet synchronous motors with concentrated windings 197 The two motors will be tested in order to verify and evaluate the calculation results. Then the two rotors will be interchanged and the new statorrotor combinations will be tested also. Received on 16 July 2006 REFERENCES 1. C. Deak, A. Binder, Highly utilised permanent magnet synchronous machines with toothwound coils for industrial applications, Proc. Electromotion 05, Lausanne, Switzerland, Sept. 2005, CDROM. 2. T. Koch, A. Binder, Permanent magnet machines with fractional slot winding for electric traction, Proc. ICEM 02, Brugge, Belgium, Aug. 2002, CDROM. 3. D. Ishak, Z. Q. Zhu, D. Howe, Permanentmagnet brushless machine with unequal tooth widths and similar slot and pole numbers, IEEE Transactions on Industry Applications, 41, 2, March/April 2005, pp
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