IEEE TRANSACTIONS ON MAGNETICS, VOL. 38, NO. 2, MARCH 2002 1293 Analysis of Torque Ripple in a BDCM H. Zeroug, B. Boukais, and H. Sahraoui Abstract—In this paper, torque and torque ripple in a brushless direct-current motor drive are assessed. First, the cogging torque is determined using finite-element method. The torque ripple is then calculated for the motor drive with the controller. The simu- lation model allows a comparison between the motor design and the motor drive performance with respect to torque ripple. The analysis shows that although the machine is designed considering minimum cogging torque, the commutation process remains a major source of torque ripple. Its effect leads to a substantial ripple torque. Therefore, minimization techniques by controlling the excitation should be considered to improve motor dynamic performances. The simulation results are confirmed through experimental results. Index Terms—Drives, permanent magnet, torque, torque ripple. NOMENCLATURE emf Electromotive force. mmf Magnetomotive force. Advance angle. Phase back emf. Self inductance. Mutual inductance. Phase current. DC voltage supply. Peak value of the emf harmonic of order. Angular velocity. Mechanical velocity. Harmonic order. Electromagnetic torque. Load torque. Phase resistance. EMF phase harmonic. Maximum harmonic order. I. INTRODUCTION P ERMANENT magnet (PM) machines with trapezoidal back emf have been widely used due to their simplicity in their control. These machines inherently have three types of torque ripple associated with them [1]. 1) The cogging torque due to the interaction of the magnet and the stator tooth. Manuscript received July 5, 2001. H. Zeroug is with the Department of Electrical Engineering, University of Sciences and Technology Houari-Boumedien, 16111, Algiers, Algeria (e-mail: zeroughoucine@hotmail.com). B. Boukais is with the Department of Electrical Engineering, University of Moloud-Mammeri, 15200, Tizi-Ouzou, Algeria (e-mail: Bboukais@hot- mail.com). H. Sahraoui is with the Department of Electrical Engineering, National Polytechnic School, El-Harrach, 16200, Algiers, Algeria (e-mail: houri- asahraoui@hotmail.com). Publisher Item Identifier S 0018-9464(02)01143-3. Fig. 1. Structure of the BDCM. 2) The reluctance torque resulting from the interaction of the stator magnetomotive forces (mmf’s) with the angular variation of the rotor magnetic reluctance. 3) The ripple due to the commutation of current from one phase to the other. The achievement of smooth torque production in permanent- magnet alternating-current machine drives is a demanding ob- jective that requires painstaking attention to every aspect of ma- chine and controller design. This operation requires the deter- mination of the cogging torque and the commutation torque in order to proceed with further optimization either from the de- sign or the controller aspects. Some careful design leads to low cogging torque. However, the commutation can generate a sub- stantial ripple that has to taken into account to achieve a high performance drive [1], [2]. In this paper, a brushless direct-current motor (BDCM) per- formances with trapezoidal back emf, are examined, with a par- ticular attention to cogging torque. These were determined using finite-element method (FEM). Further, in order to assess the commutation torque ripple, analytical approach in the time do- main that combines both the machine and the inverter circuit was used. The results obtained are compared to those produced experimentally for the static and quasistatic conditions, so that the approach can validated and allows a comprehensive investi- gation into the torque and its ripple more accurately. II. ELECTROMAGNETIC CHARACTERISTICS Fig. 1 shows a section of the motor. The motor uses a PM made from Samarium cobalt material mounted at the surface of the rotor and a conventional three phase star connected wind- ings, with a floating neutral point on the stator nonconnected. The machine has an outer diameter of 86 mm and a stator length of 40 mm. The air gap is about 1.5 mm. The rating of the ma- chine is 750 W. Details of the machine are given in Table I. 0018-9464/02$17.00 © 2002 IEEE