IEEE TRANSACTIONS ON MAGNETICS, VOL. 50, NO. 2, FEBRUARY 2014 7019704 Quasi-Zero Torque Pulsation of Surface Permanent Magnet Synchronous Motor for Ship Gyro Stabilizer by Pole/Slot Number and Air-Gap Designs Sun-Kwon Lee 1,2 , Gyu-Hong Kang 1 , Jin Hur 2 , and Byoung-Woo Kim 2 1 Korea Marine Equipment Research Institute, Busan 1631-10, Korea 2 Department of Electrical Engineering, University of Ulsan, Ulsan 680-749, Korea This paper deals with the reduction of torque pulsation including torque ripple and cogging torque in surface PM brushless ac motors. The fractional combination and air-gap shape design by shaping the PM and stator core are studied to reduce torque pulsation. Torque ripple reduction is achieved by adjusting the magnetic flux density in air-gap contour by cutting magnet outer shape. Quasi-zero torque pulsation in this paper means the ripple ratio to average torque <0.5%. The magnetic field and torque characteristics are analyzed by 2-D finite element analysis and prototype to validate is manufactured and measured. Index Terms—Finite element analysis, permanent magnet, SPMSM, torque pulsation. I. I NTRODUCTION M ARINE applications have strict limits on vibrations and interference for electromagnetic comparability, and so high efficiency and low vibrations are key requirements [1]. The reduction of vibration is a very important design issue for ship gyro stabilizers to operate reliably due to their heavy mass flywheel. PM machines with a fractional number of slots per pole and a concentrated winding have shorter end windings and lower overall length and yet have high efficiency, torque, and power density [1]–[3]. Furthermore, fractional slot machines have extremely low cogging torque without the need for design features such as skew [2]. Torque ripple caused by rotor field and stator current is affected by harmonic components of radial flux density. The cogging torque is generated from the interaction between the air-gap flux density distribution and stator slotting. The torque pulsation reduction can be achieved by minimizing torque ripple and cogging torque [3]. Thus, many previous studies [1]–[11] dealt with torque pulsation reduction approaches of PM machines. Hur et al. [4] proposed a third harmonic elimination method to reduce cogging torque. The analytical approach was introduced to calculate the cogging torque of an interior permanent magnet (IPM) motor [5]. Some researchers [6]–[9], studied the torque pulsation reduction of IPM machines and PM assisted reluc- tance machine including optimization problems. Kwon [10] studied the sinusoidal PM shape to the axial direction to obtain sinusoidal back EMF and low torque pulsation. The sensitivity of harmonics caused by manufacturing tolerance is also studied [11]. In this paper, torque pulsation reduction is introduced by poles/slots combination and air-gap structure design using magnet shapes and stator core structure. The torque ripple Manuscript received June 29, 2013; revised August 12, 2013; accepted September 24, 2013. Date of current version February 21, 2014. Corresponding author: G.-H. Kang (e-mail: kang@komeri.re.kr). 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.2013.2284004 Fig. 1. Designed and analysis models. (a) 8p12s model. (b) 10p12s model1. (c) 10p12s model2. (d) Magnet shape difference between 10p12s model1 and model2. TABLE I SPECIFICATIONS OF ANALYZED MODELS reduction principle by adjusting air-gap magnetic flux density distribution is also discussed. The flux density on the air-gap contor is investigated to compare the relationship between torque pulsation and air-gap flux density in detail. Close to torque pulsation is achieved compared with the average generated torque. 2-D finite element analysis using Maxwell is used to calculate the magnetic field of the designed motor. II. ANALYSIS MODEL DESCRIPTIONS Fig. 1 shows the cross sections of the analyzed models. An identical stator with 12 slots concentrated windings is employed for each model. The detailed descriptions of ana- lyzed models are listed in Table I. The differences between 0018-9464 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.