Design of a Cost-Efficient High-Speed High- Efficiency PM Machine for Compressor Applications A. Gilson, S. Tavernier, M. Gerber and C. Espanet Moving Magnet Technologies Besançon, France adrien.gilson@movingmagnet.com F. Dubas and D. Depernet ENERGY department FEMTO-ST Institute Belfort, France Abstract This paper presents a high-speed 3 kw 80 krpm surface-mounted permanent magnet (SMPM) motor for compressor applications. The design procedure using finite element analysis (FEA) is presented with a particular focus on the efficiency calculation. The paper also aims to give general indications to provide a cost-efficient solution. A prototype is built and experimental results are given and compared to the simulations. Keywords Finite element analysis; high-speed motors ; machine design; permanent magnet machines I. INTRODUCTION High-speed permanent magnet machines are increasingly used in a wide range of applications such as machine tools, gas turbine and compressors [1 3]. Their important power density, high reliability and efficiency have been found to be very suitable for demanding applications. In the automotive industry, fuel cell compressors [4] and electrically-assisted turbochargers are particularly located in high temperature environments that need great integration levels. Therefore, the demand for both high-speed and highly efficient machines has become significant. However, another important aspect of this growing field of applications is the need to handle the costs of manufacturing. Consequently, design guidelines and compromises have to be found to achieve both high efficiency and simple manufacturing. A good knowledge of the different losses is necessary to achieve this task. The present work investigates the design of a high-speed high-efficiency 3 kw 80 krpm machine dedicated to air compression. The machine is calculated using FEA and the results are used to evaluate the losses. The best configuration in terms of efficiency is proposed and a prototype is built to compare the results. II. MACHINE DESIGN The machine topology was determined using essentially manufacturing consideration. The number of phases was set to 3 to be compatible with standard inverters. A 2-pole rotor magnet rather than a 4-pole was chosen to enable an easy magnetization process and reduce the inverter frequency. A low number of slots have been selected to make the winding process easier. 6 slots were chosen rather than 3 to prevent rotating forces resulting from unbalanced magnetic pull (relevant at high rotational speeds). Finally, a high supply voltage of 400 V is used for this machine to be compliant with the voltage level currently used in fuel cell electric vehicle (FCEV) or hybrid electric vehicle (HEV). The resulting prototype is presented in Fig.1. A. Stator design As shown in Fig. 2, the stator core is made of riveted teeth wounded independently and assembled together afterwards. It enables simpler manufacturing, short end-windings and a high copper filling factor even for semi-closed slots. A NO20 (0.2 mm thickness) stator lamination material was selected to minimize the stator iron losses. Fig. 1. 3 kw 80 krpm prototype. (a) (b) Fig. 2. Stator overview. (a) Concentrated winding on a tooth (b) Stator assembly in the cooling jacket. 978-1-4673-7151-3/15/$31.00 2015 European Union
(a) Fig. 3. Rotor. (a) Nd-Fe-B ring magnet (b) Partially assembled rotor (without bearings) with shaft, retaining sleeve, and magnet (not visible). B. Rotor design The rotor is made of different components as shown in Fig. 3. The 2-pole magnet is a single ring made of sintered Nd-Fe-B diametrically magnetized. Although the magnet segmentation is a well-known way to dramatically reduce the PM eddycurrent losses [5], it will be shown that this costly operation won t be necessary in this machine design. The rotor requires a high strength sleeve to retain the magnet because of the high circumferential speed which is above 80 m/s in the final design. Nickel/cobalt based superalloys, titanium alloys, high-strength non-magnetic stainless steel, carbon or glass fiber are usually used for that matter. A Ti-6Al-4V titanium alloy was chosen because of its high tensile strength and low density. The sleeve thickness was calculated according to [6] and made as thin as possible to limit the additional inertia and support the stress at rated speed with a 20% over-speed. Although the acceleration time is not the main topic of this study, a low inertia is usually required in high-speed compressor applications to improve the dynamic response. C. General design High-speed hybrid ceramic ball bearings were selected for their simplicity and cost effectiveness. For high speed applications, active magnetic bearings or foil bearings can also be used but require respectively a dedicated control drive and a very specific and tough mechanical calculation process. In order to reach higher current density, a water-cooling system is integrated to effectively remove the heat generated by the stator and winding losses. Two types of position sensors are built-in the prototype. A set of 3 Hall effect sensors to drive the motor in block commutation mode and a sin/cos encoder to allow field oriented control (FOC) of the machine. III. SIZING PROCESS AND LOSS EVALUATION The calculation of the efficiency of the machine is carried out using different loss models. The input values needed to calculate these losses are evaluated using the 2D FEA software Flux2D for various set of geometrical parameters. For this study, the following parameters have been selected: the air gap length, the magnet thickness, the tooth width, the stator yoke width, the external diameter and the stack length. Several combinations of parameters were selected and the associated designs were calculated using FEA and the loss models described further. However, even if no rigorous (b) optimization process has been conducted, large parametric analyses enable us to assume that the presented design is close to an optimum in terms of efficiency. A. Stator iron losses The iron losses are calculated by (1) using the Bertotti model [7]. The selected input data for the calculation are the peak value of the flux density in the middle of a tooth and the stator yoke. (1) where is the stacking factor,, and respectively hysteresis, eddy-current and excess component of the losses. For a sinusoidal flux density, these coefficients are respectively given by (2), (3) and (4). (2) 6 (3) / / (4) where and are respectively hysteresis and excess coefficients, the peak value of the flux density, the thickness of the sheet, the conductivity of the material and its density. Manufacturer s data are used to obtain and for the appropriate values of and. B. Rotor eddy-current losses Rotor eddy-current losses are calculated in the rotor yoke, magnets and sleeve using transient FEA. Since the slot opening is small and the air gap tends to be large for that design, losses induced by the stator slotting permeance harmonics are very low. However, the space-harmonics of the armature magnetomotive force (MMF) could lead to important eddycurrent losses in the magnet and the sleeve. Consequently the losses will be evaluated consistently. Fig. 4 shows the current density distribution in the selected rotor at rated speed and torque with a sinusoidal current supply. The maximum value of the current density is about 2 A/mm 2 and the loss close to 3 W which is acceptable for the rotor dimensions. The current density at the sleeve/magnet interface is almost continuous because the electrical conductivities of the two selected materials are really close. Fig. 4. Current density in the rotor and sleeve at rated speed and torque.
TABLE I. SKIN DEPTH IN THE COPPER FOR DIFFERENT FREQUENCIES TABLE II. LOSSES AT RATED SPEED AND TORQUE Harmonics 1 5 7 11 13 Skin depth (mm) 1.81 0.81 0.68 0.55 0.50 C. Copper loss The machine is wye-connected with series phase winding and the relatively high supply voltage leads to a reasonable wire diameter. Equation (5) is used to calculate the skin depth and Table I displays the results for a fundamental frequency of 1333 Hz, a copper electrical resistivity of 1.72 10-8 Ωm and a relative permeability of 1. (5) 0 where is the electrical resistivity, the frequency, the relative permeability and the vacuum permeability. Table I shows that the skin effect is nonexistent for a wire of diameter 1 mm up to the 13th harmonic which is the case for the selected design. As a result, the skin effect can be neglected and the use of Litz wire is assumed to be unnecessary. Consequently, the copper losses are simply given by (6). 6 (6) where is the resistance of a single coil and the root mean square value of the current. The resistance of a coil is found geometrically by looking at the available surface in the slot and the average path around a tooth. D. Mechanical losses Mechanical losses are divided into bearing losses and windage losses. The latter are caused by the air friction in the air gap and are calculated thanks to (7) and (8) according to [8][9]. (7) where is the skin friction coefficient, is the density of the fluid, the radius of the rotor, is the rotational speed and the length of the rotor. The coefficient is obtained using (8). 1 lnre (8) where Re is the Reynolds number, and b are empirical constants respectively equal to 2.04 and 1.768 according to [8]. The solution of this equation can be expressed by (9): Re / (9) where is the Lambert function. A more detailed approach of the windage loss is analyzed in [10] where the friction of a rotating disk is also given. For the selected design, these losses have been found to be lower than 5 W at rated speed. Bearing loss is evaluated by (10) where A and α are determined experimentally [9]. (10) Method Mode I Mode II Unit Stator iron FEA/Analytical 35.1 35.1 W Rotor sleeve FEA 1.6 3.2 W Rotor magnet FEA 1.5 8.1 W Rotor yoke FEA 0.0 0.1 W Copper Analytical 47.6 48.0 W Bearings Experimental 17.8 17.8 W Windage Analytical 4.2 4.2 W Total - 107.8 116.5 W Efficiency a - 96.5 96.3 % In a first approach, a linear dependence is assumed between the bearing loss and the rotational speed. Consequently the expression is more simply defined by (11). (11) where is the friction torque measured on the machine at low speed and no load. E. Simulation results Calculated losses for the selected design at rated speed and torque are presented in Table II. The different values are derived from the previous equations. Since is difficult to evaluate beforehand, the bearing loss figure presented in the table comes from the experimental measurement of. In order to understand the impact of non-sinusoidal supplied currents. Two different simulation results are presented in the table. Mode I is a purely sine wave and mode II contains 7.8% of 5 th harmonic and 3.4% of 7 th harmonic. These values were measured afterwards on the machine. The most significant difference is found in the rotor where the losses increase from 3.1 W to 11.4 W. IV. MEASUREMENTS The experimental setup is presented in this section. Some details are given about the control electronics and the different test benches. A. Electronic The machine is driven by a 2-stage driver. As shown in Fig. 5, the first one is a 3-phase interleaved step-down buck chopper which adapts the voltage level at the output, and the second one is a 3-phase 2-level voltage source inverter (VSI) driving the motor. Two control modes are implemented: Pulse Amplitude Modulation mode (PAM): the chopper adapts the voltage level at the input of the inverter which is used in full-wave mode; Pulse Width Amplitude Modulation mode (PWAM): the motor is driven with field oriented control mode, the chopper adapts the voltage at the input of the inverter which is only used to apply the references in (d, q) frame.
Battery Buck converter Inverter Motor Command 3 Hall sensors Sin/cos sensor Fig. 5. Simplified diagram of the control electronics. In the present paper and during the measurements, the PAM mode only is used to drive the motor in block commutation mode. B. Mechanical setup Two different methods were used to carry out the measurements. The first one consists in using an eddy-current (EC) brake. A magnet (-poles axially or radially magnetized) is placed onto the rotor shaft to induced eddy-currents in a copper or aluminum plate. The plate is attached to a torque sensor as shown on Fig. 7. The second method consists in measuring the acceleration time and position of the rotor. By using (12), we obtain the torque of the machine. (12) where is the rotor inertia, the rotational speed and the output torque. This technique may produce important errors if is not known precisely. In fact, even if the inertia of a plain cylinder is simple to evaluate, the actual rotor is much more complicated and various elements can modify the inertia such as ball bearings, balancing operation and machining tolerance. To cope with this problem, an additional inertia shown on Fig 6 is added to the rotor. The geometry of this part is simpler and consequently the inertia can be accurately determined. Then, two tests are conducted, with and without the additional inertia. The response time difference enables the calculation of the initial rotor inertia. Fig. 8. Measured loss at no load operation C. Experimental results Fig. 8 shows the no-load losses. This curve contains the mechanical losses and and the iron losses assuming that the rotor magnet produce most of these losses and neglecting the effect of the stator currents on the stator flux density. Fig. 9 and 10 show the peak torque and efficiency measurements on the machine at different supplied voltages. As mentioned before, two methods were used to carry out the tests. The 48 V curves were made using the same EC brake whereas the other curves come from the acceleration time measurement and a different EC brake. Some improvements have to be found to reach higher speed and torque. The power of the EC brake and the stability of the bench have been found to be insufficient to reach 3 kw at 80 krpm. Fig. 6. Titanium alloy disks to be attached to the rotor AXIAL MAGNET COPPER PLATE To drive MOTOR TORQUE METER Torque measurement Fig. 9. Peak torque TEST BENCH Fig. 7. Test bench with EC brake.
teeth which is not taken into account here. Mechanical losses are also difficult to predict in the case of high speed machines. Finally, the future steps of this work are: Loss separation to identify the difference between measurements and simulations. Additional tests have to be conducted to measure independently the mechanical and rotor losses; Adapting the test bench for higher speed and power; Comparison between block commutation driving mode and Field-Oriented Control and the influence of the current waveform on both stator and rotor iron losses. Fig. 10. Efficiency V. CONCLUSION The design of a high-speed and high efficiency SMPM machine for compressor applications has been investigated in this paper. The design process is presented and some guidelines are given to handle the cost of manufacturing such as: Concentrated winding on independent teeth provide an axially compact machine because of the short endwindings and the assembly of the machine can be automated more easily; A 2-pole ring magnet without segmentation to ease the manufacturing, assembly and magnetizing process; A high voltage DC-bus to decrease the wire diameter and avoid the skin effect. Some difficulties were encountered during the measurements of the machine for this range of power and speed: A specific test bench is necessary to measure the machine and most of the rotating torque sensors are not able to reach this level of speed. Vibrations transmitted to the bench can be a problem as well; The measured losses tend to be much higher than the simulated values (around 70 W compared to 120 W without copper losses). The difference may lie in the evaluation of the iron losses and saturation in the stator REFERENCES [1] A. Borisavljevic, Limits, Modeling and Design of High-Speed Permanent Magnet Machines, 2013 edition. Berlin; New York: Springer, 2012. [2] N. Bianchi, S. Bolognani, and F. Luise, Potentials and limits of high speed PM motors, in Industry Applications Conference, 2003. 38th IAS Annual Meeting. Conference Record of the, 2003, vol. 3, pp. 1918 1925 vol.3. [3] C. Zwyssig, J. W. Kolar, W. Thaler, and M. Vohrer, Design of a 100 W, 500000 rpm permanent-magnet generator for mesoscale gas turbines, in Industry Applications Conference, 2005. Fourtieth IAS Annual Meeting. Conference Record of the 2005, 2005, vol. 1, pp. 253 260 Vol. 1. [4] F. Dubas, C. Espanet, and A. Miraoui, Design of a high-speed permanent magnet motor for the drive of a fuel cell air-compressor, in Vehicle Power and Propulsion, 2005 IEEE Conference, 2005, p. 8 pp. [5] M. R. Shah and A. M. EL-Refaie, Eddy-Current Loss Minimization in Conducting Sleeves of Surface PM Machine Rotors With Fractional-Slot Concentrated Armature Windings by Optimal Axial Segmentation and Copper Cladding, IEEE Transactions on Industry Applications, vol. 45, no. 2, pp. 720 728, Mar. 2009. [6] S. P. Timoshenko and J. N. Goodier, Theory of elasticity. McGraw-Hill Kogakusha, Ltd. 1970, ch. 4. [7] D. Eggers, S. Steentjes, and K. Hameyer, Advanced Iron-Loss Estimation for Nonlinear Material Behavior, IEEE Transactions on Magnetics, vol. 48, no. 11, pp. 3021 3024, Nov. 2012. [8] J. E. Vrancik, Prediction of windage power loss in alternators. 1968. [9] P.-D. Pfister and Y. Perriard, Very-High-Speed Slotless Permanent- Magnet Motors: Analytical Modeling, Optimization, Design, and Torque Measurement Methods, IEEE Transactions on Industrial Electronics, vol. 57, no. 1, pp. 296 303, Jan. 2010. [10] J. Saari, Thermal analysis of high-speed induction machines. Helsinki University of Technology, 1998.