Hysteresis Effects of Laminated Steel Materials on Detent Torque in Permanent Magnet Motors

Transcription

1 Hysteresis Effects of Laminated Steel Materials on Detent Torque in Permanent Magnet Motors Y. B. Li 1, Shuangxia Niu 1, S. L. Ho 1, Yanhai Li 2 and W. N. Fu 1 1 Department of Electrical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong 2 Management School of Xi an Jiaotong University, Shanxi, China Hysteresis effects of laminated steel materials on the detent torque in permanent magnet (PM) motors are described physically. There are many methods to simulate hysteresis effects. However most studies only focus on loss calculation but not on other important issues. Based on field orientation interpolation method, four-quadrant hysteresis effects are taken into consideration in the proposed cogging torque computation. Simulation results using finite element analysis (FEA) show that laminated materials with high hysteresis effects give higher detent torque when compared to those with narrow hysteresis loops. Two brushed type PMDC motors, with a 4-pole, 22-slot configuration and with different laminated steel materials, are built, and their test data are used to validate the analysis. Index Terms detent torque, finite-element analysis, frictional torque, hysteresis effect, magnetic field, permanent magnet. D I. INTRODUCTION ETENT TORQUE, or drag torque, is an important parameter in permanent magnet (PM) motors, especially in a PM servo motor system. There are mainly two components in the detent torque of PM motors which are, namely, cogging torque and frictional torque, as shown in Fig. 1 [1-2]. Frictional torque is usually attributed to mechanical assembly issues, such as bearing resistance, coaxial tolerance, or carbon-brush friction for brush PM dc (PMDC) motors and so on; and frictional torque is commonly measured by its average value. Cogging torque is attributed to PM materials interacting with the stator s soft magnetic steel teeth to oppose rotor rotation in brushless PM motors or brushed PMDC motor. Generally the cogging torque varies with rotor position; and it is defined by its peak to peak (p-p) value which is labeled by the dashed line in Fig. 1 in which the effect due to frictional torque is excluded. Torque (mnm) electrical power steering (EPS) system, for example, the average values of its frictional torque and peak to peak (p-p) values of cogging torque are specified to be less than 30 mnm and 10 mnm, respectively [5-7]. There are many mature methods to minimize the cogging torque in PM motors by using proper design variables and skills, such as slot/pole ratio (S/P), dummy-slot, skewed rotor, and so on [8]. There are also many classical good designs which are commonly observed. For example, an S/P ratio with 12 slots/14 poles has been employed in brushless EPS motor; and the ratio with 22 slots/4 poles is used widely in brushed PMDC EPS system. As to the reduction of frictional torque, mechanical improvements are commonly used as the main solution. Cogging torque can be computed accurately in digital simulation by using finite element method (FEM) [9-10]. Further investigations however found that there are some obvious contributions on the detent torque due to the hysteresis effect of laminated steel, not simply on the p-p value of cogging torque; it also increases the frictional torque, i.e., apart from mechanical considerations, hysteresis effect of the steel materials is also a contributor to the detent torque. In this paper, the hysteresis effects on detent torque are described; and an improved interpolating method, which takes into account the four-quadrant hysteresis loop effects, is introduced in the computation of the detent torque. Simulation results with FEM agree well with the experimental data which are obtained from prototypes being built to validate the analysis. Fig. 1. Detent torque including cogging torque and frictional torque. In order to obtain accurate and smooth control of electrical motors, the detent torque is required to be as small as possible, especially in PM servo systems, including brush PMDC and brushless PMAC servo systems [3-4]. In a 350 W automobile II. PHYSICAL DESCRIPTION Fig. 2 shows a typical hysteresis loop of ferro-magnetic materials. Usually, the magnetizing curve, oa, is used in finite element analysis (FEA) simulation for performance calculation, and its results are relative accurate for steady state performance study. If the full hysteresis loop is considered, it can be shown that an additional force will appear. Physically, as one piece of charged magnet moves past a steel tooth, the

2 tooth will be magnetized as illustrated at point a in Fig. 2; the magnetized tooth tries to attract the magnet that has just past over it, and at the same time, it repels the one moving towards it. Furthermore, as another magnet piece with opposite field orientation moves towards it, an alternating magnetic field will try to recharge the magnetized tooth. In other words, the crystal orientation in the magnetized core has to be reversed. Due to hysteresis effects of the steel, the magnetic flux density B is non-zero when the magnetizing force H reaches zero at point b in Fig. 2. At point c when H = -H c, the flux density B is zero. Such pattern is repeated for the negative area in the 3 rd and 4 th quadrants. Therefore, the energy, corresponding to the area of the enclosed hysteresis loop bounded by the loop abcdefa in Fig. 2, will repel the moving magnet with opposite orientation towards it. The repelled force will bring an additional detent torque. Obviously, the value of this additional torque will depend on the loop area, or coercitive force, H c of the magnetic material. The bigger the loop area, or the higher coercitive force H c, the higher is the detent torque. For different steel materials, their hysteresis loops are different, and therefore the additional detent torque will vary. This phenomenon can be verified by numerical simulation. typical FEA calculation, because there are different B values corresponding to the same H value under different working conditions. Because there are very big mesh volumes in FEA, it requires very large memory size if all meshes are recorded. To simplify the simulation, field orientation interpolating (FOI) method is introduced as shown in Fig. 3. Based on the magnetic field orientation, the magnet position or field magnetizing direction before interpolation is recalled and the slope of the B-H variation can then be found. Based on the above laminated material model, the cogging torque of a typical brushed PMDC motor with a 4-pole, 22- slot configuration in automobile EPS application is computed. Fig. 4 shows the motor geometry and its flux distribution. Fig. 5 is the simulation results in one tooth width. For the sake of simple comparison, three curves are shown in Fig. 5, in which curve 1, labeled with dotted line, is obtained from conventional B-H curve without considering hysteresis effects; the other two curves have both taken steel hysteresis effects into account, but with different materials, namely 50H400 and 50H800 and their B-H curves are shown in logarithmic scale in Fig. 6. Fig. 2. Hysteresis loop of ferromagnetic material. III. FEM SIMULATIONS CONSIDERING OF HYSTERESIS EFFECT There are many literatures on hysteresis effect simulation, but most papers focus on the hysteresis loss calculation and there are very few papers discussing the hysteresis effects on detent torque and its related calculation method [11-13]. To include four-quadrant hysteresis effects in FEA computation, single input, multi-output (SIMO) of the material model will be used, and such format is different from the single input, single output (SISO) interpolating method in Fig. 3. Block diagram of the detent torque computation. From the simulation, one can find that by using conventional method, the average value of cogging torque is zero, due to the exclusion of the mechanical frictional torque. When taking hysteresis effects into consideration, the cogging

3 torque average value is shifted upward, i.e., its average value is not zero; and the shifting-up value will change according to the characteristics of the laminated material. From the simulation results, the hysteresis effect to the torque of 50H400 is shown to be around 7 mnm, and this is lower than that of using 50H800 which is 17 mnm. In other words, there is a relationship between the average torque and the area of hysteresis loop which obviously is dependent on its coercitive force, i.e, the bigger the area of hysteresis loop, or the higher the coercitive force of the laminated material, the higher is the detent torque. Therefore, in order to minimize the detent torque, higher grade laminated materials with low coercive force are preferred. Fig. 4. Motor geometry model. Rotor Position (degree) Fig. 5. Simulation of cogging torque with different materials. Fig. 6. Hysteresis loop for simulation. IV. PROTOTYPE TESTS To verify the above analysis, two brushed PMDC prototypes with a 4-pole, 22-slots configuration have been built. Fig. 7 shows one of the prototypes and the physical appearance of both motors are identical. Their main design parameters are listed in Table I. In the following discussion the motor labeled as Sample A is made of 50H400, while the motor labeled as Sample B is fabricated using 50H800. Apart from differences in laminated material, the other parameters for the two motors are the same. Fig. 8 shows the detent torque test rig. The detent torque test results of the two samples are shown in Fig. 9. In order to separate the detent torque which is caused by magnetizing force from the mechanical frictional torque, the drag torque curve without PM is shown in Fig. 10. It is shown that the detent torque with no hysteresis effect is 18 mnm. From Fig. 9 (a), the hysteresis effect with 50H400 is found as 25 mnm - 18 mnm = 7 mnm. From Fig. 9 (b), the hysteresis effect from 50H800 is also found to be 34 mnm - 18 mnm = 16 mnm. The simulation results agree well with the measured ones. From these test curves, one can find that apart from the mechanical effects on the frictional torque given in Fig. 10, the laminated material also plays some contributions on the detent torque, especially on the average shifting-up values. Table II lists some comparison items. It can be seen that for both samples, their cogging torque p-p values can both meet the specified requirement originally stipulated by the designer. However the frictional average torque of Sample B with 50H800 is higher and exceeds the specification, while the fictional torque of Sample A with 50H400 meets the requirement. Therefore, high grade materials can decrease the average detent torque, which coincides with simulation results and the conclusions from the above analysis. TABLE I MOTOR MAIN DESIGN PARAMETERS Item Value Unit Nominal voltage 12 V Rated torque 2 Nm Rated speed 1050 rpm Stator outer diameter 73 mm Stator inner diameter 58.6 mm Rotor outer diameter 56.6 mm Rotor inner diameter 10 mm

4 Stack length 62 mm Pole number 4 - Magnet material TDK-6G - Magnet thickness 5.0 mm Slot number 22 - Fig. 8. Cogging torque test rig. Fig. 7. An EPS prototype. TABLE II DETENT TORQUE COMPARISON Item Specifications Sample A Sample B Friction torque < 25mNm 24 mnm 32.5 mnm Maximum value of < 30 mnm 28 mnm 37.5 mnm detent torque Cogging torque < 10 mnm 8 mnm 9.5 mnm V. CONCLUSIONS In this paper, the hysteresis effects on detent torque are discussed from basic physical observation, FEA simulation, as well as from experiment results. It can be found that: 1. Apart from mechanical issues, hysteresis effects of laminated materials also contribute to the value of detent torque. 2. Based on field orientation interpolation method, fourquadrant hysteresis effects are taken into consideration in cogging torque computation. 3. Samples have been built and tested, and test results have verified the FEA simulation results. 4. These conclusions are not only applicable to PMDC motors, they are also applicable to all brushless PM motors. Therefore, one can conclude that laminated steel materials with low coercitive force, which corresponds to high grade laminated materials, will give a slightly lower drag torque than those with high hysteresis effects. ACKNOWLEDGMENT This work was supported by the Research Grant Council of the Hong Kong SAR Government under projects PolyU 5176/09E and G-YX4B. VI. REFERENCES [1] G. Ombach and J. Junak, Design of PM brushless motor taking into account tolerances of mass production - six sigma design method, 42nd IAS Annual Meeting, pp , [2] J. J. Lee, S. O. Kwon, J. P. Hon1 and K. H. Ha, Cogging torque analysis of the PMSM for high performance electrical motor considering magnetic anisotropy of electrical steel, EV [3] G. Ombach, J. Junak and A. Ackva, Comparison of windings and rotors types of PM brushless motor for an electric power steering application, The 2006 International Conference on Electrical Machines and Systems, Nagasaki, Japan, Nov , 2006, [4] N. Bianchi, S. Bolognani, M. Dai Prè, M. Tomasini, L. Peretti and M. Zigliotto, The steering effect PM motor drives for automotive systems, IEEE Industry Applications Magazine, vol. 14, no. 2, pp , March- Apr [5] G. Ombach and J. Junak, Two rotors designs comparison of permanent magnet brushless synchronous motor for an electric power steering application, European Conference on Power Electronics and Applications, pp. 1-9, 2-5 Sept, [6] H. Eki, T. Teratani and T. Iwasaki, Power consumption and conversion of EPS systems, Power Conversion Conference, pp , 2-5 Apr, [7] A. Yoneda, T. Miyoshi and Y. Shimizu, Cogging torque target and design of motor for EPS, SAE International Conference, [8] N. Bianchi and S. Bolognani, Design techniques for reducing the cogging torque in surface-mounted PM motors, IEEE Trans.Ind. App., vol. 38, no. 5, pp , [9] W. N. Fu, P. Zhou, D. Lin, S. Stanton and Z. J. Cendes, Modeling of solid conductors in two-dimensional transient finite-element analysis and its application to electric machines, IEEE Trans. Magn., vol. 40, no. 2, pp , Mar [10] W. N. Fu and S. L. Ho, Enhanced nonlinear algorithm for the transient analysis of magnetic field and electric circuit coupled problems, IEEE Trans. Magn., vol. 45, no. 2, pp , Feb [11] M. Amde and M. Amir, A new hysteresis model for steel mmebers, Int. J. Numer. Meth. Engng. 45, pp , [12] F. Henrotte and K. Hameyer, A dynamic vector hysteresis model based on an energy approach, IEEE Trans. Magn., vol. 42, no. 4, pp , Apr [13] T. Nakata, N. Takahashi, K. Fujiwara and M. Nakano, Measurement of Magnetic Characteristics along Arbitrary Directions of Grain-Oriented

5 Silicon Steel Up to High Flux Densities, IEEE Trans. Magn., vol. 29, no. 6, Nov (a) (b) Fig. 9. Sample detent torque test curves. (a) 50H400. (b) 50H800. Fig. 10. Test curve without magnet.