3594 IEEE TRANSACTIONS ON MAGNETICS, VOL. 47, NO. 10, OCTOBER 2011 Hysteresis Effects of Laminated Steel Materials on Detent Torque in Permanent Magnet Motors Y. B. Li , Shuangxia Niu , S. L. Ho , Yanhai Li , and W. N. Fu Department of Electrical Engineering, The Hong Kong Polytechnic University, Hunghom, Kowloon, Hong Kong Management School, 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. I. INTRODUCTION D ETENT TORQUE, or drag torque, is an important pa- rameter 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]. Fric- tional torque is usually attributed to mechanical assembly is- sues, 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. 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 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 de- sign 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 Manuscript received February 20, 2011 ; accepted May 09, 2011. Date of current version September 23, 2011. Corresponding author: S. Niu (e-mail: eesxniu@polyu.edu.hk). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMAG.2011.2155633 Fig. 1. Detent torque including cogging torque and frictional torque. 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 me- chanical considerations, hysteresis effect of the steel materials is also a contributor to the detent torque. In this paper, the hys- teresis effects on detent torque are described; and an improved interpolating method, which takes into account the four-quad- rant 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. II. PHYSICAL DESCRIPTION Fig. 2 shows a typical hysteresis loop of ferro-magnetic ma- terials. Usually, the magnetizing curve, oa, is used in finite el- ement 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 tooth will be mag- netized as illustrated at point 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 0018-9464/$26.00 © 2011 IEEE