In this paper, a new type of interior composite-rotor bearingless permanent magnet synchronous motors (BPMSMs) with two layer permanent magnets (PMs) is proposed. In order to reduce the torque ripple of this kind of motors, the sizes of PMs are optimized. Moreover, the magnetic field analysis of the interior composite-rotor BPMSM with two layer PMs is carried out by the finite element method (FEM). The corresponding static electronic magnetic characteristics at no load, including magnetic field, PM flux linkage and inductance, are studied in detail. In addition, electromagnetic torque characteristics and suspension force characteristics are also investigated thoroughly. The results of the analysis and simulation lay a significant foundation for further research on the interior composite-rotor BPMSMs with two layer PMs.
 X. Sun, B. Su, L. Chen, Z. Yang, X. Xu, and Z. Shi, “Precise control of a four degree-of-freedom permanent magnet biased active magnetic bearing system in a magnetically suspended direct-driven spindle using neural network inverse scheme”, Mechanical Systems and Signal Processing 88, 36‒48 (2017).
 X. Sun, Z. Shi, L. Chen, and Z. Yang, “Internal model control for a bearingless permanent magnet synchronous motor based on inverse system method”, IEEE Transactions on Energy Conversion 31(4), 1539‒1548 (2016).
 X. Sun, L. Chen, H. Jiang, Z. Yang, J. Chen, and W. Zhang, “High-performance control for a bearingless permanent magnet synchronous motor using neural network inverse scheme plus internal model controllers”, IEEE Transactions on Industrial Electronics 63(6), 3479‒3488 (2016).
 X. Sun, B. Su, L. Chen, Z. Yang, J. Chen, and W. Zhang, “Nonlinear flux linkage modeling of a bearingless permanent magnet synchronous motor based on AW-LSSVM regression algorithm,” International Journal of Applied Electromagnetics and Mechanics 51(2), 151‒159 (2016).
 K. Raggl, B. Warberger, T. Nussbaumer, S. Burger, and J. Kolar, “Robust angle-sensorless control of a PMSM bearingless pump”, IEEE Transactions on industrial ececronics 56, 2076‒2085 (2009).
 W. Li, K.T. Chau, T.W. Ching, Y. Wang, M. Chen, “Design of a high-speed superconducting bearingless machine for flywheel energy storage systems”, IEEE Transactions on Applied Super-conductivity 25(3), 5700204 (2015).
 P. Bogusz, “A switched reluctance motor control method limiting the maximum dc source current in the low-speed range,” Bull. Pol. Ac.: Tech. 64(1), 197‒206 (2016).
 H. Wang, J. Liu, J. Bao, and B. Xue, “A novel bearingless switched reluctance motor with a biased permanent magnet”, IEEE Transactions on Industrial Electronics 61(12), 6947‒6955 (2014).
 X. Sun, L. Chen, Z. Yang, and H. Zhu, “Speed-sensorless vector control of a bearingless induction motor with artificial neural network inverse speed observer”, IEEE/ASME Transactions on Mechatronics 18(4), 1357‒1366 (2013).
 C.T. Kowalski, and M. Kaminski, “Rotor fault detector of the converter-fed induction motor based on RBF neural network”, Bull. Pol. Ac.: Tech. 62(1), 69‒76 (2014).
 X. Sun, L. Chen, Z. Yang, and H. Zhu, “Analysis of inductance characteristics for a bearingless permanent magnet synchronous motor”, Electrical Engineering 95(3), 277‒286 (2013).
 X. Sun, L. Chen and Z. Yang, “Overview of bearingless permanent-magnet synchronous motors”, IEEE Transactions on Industrial Electronics 60(12), 5528‒5538 (2013).
 K. Ahn, A.E. Bayrak, and P.Y. Papalambros, “Electric vehicle design optimization: Integration of a high-fidelity interior-permanent-magnet motor model”, IEEE Transactions on Vehicular Technology 64(9), 3870‒3877 (2015).
 A. Tessarolo, M. Mezzarobba, and R. Menis, “Modeling, analysis, and testing of a novel Spoke-Type interior permanent magnet motor with improved flux weakening capability”, IEEE Transactions on Magnetics 51(4), 1‒10 (2015).
 M. Mirzaei, S.E. Abdollahi, and H. Lesani, “A large linear interior permanent magnet motor for electromagnetic launcher”, IEEE Transactions on Plasma Science 39(6), 1566‒1570 (2011).
 S. Kim, J.-Y. Lee, Y.-K. Kim, J.-P. Hong, Y. Hur, and Y.-H. Jung, “Optimization for reduction of torque ripple in interior permanent magnet motor by using the taguchi method”, IEEE Transactions on Magnetics 41(5), 1796‒1799 (2005).
 J. Kwack, S. Min, and J. Hong, “Optimal stator design of interior permanent magnet motor to reduce torque ripple using the Level Set method”, IEEE Transactions on Magnetics 46(6), 2108‒2111 (2010).
 X. Sun, L. Chen, Z. Yang, H. Zhu, W. Zuo, and K. Shi, “Modeling of a bearingless permanent magnet synchronous motor considering rotor eccentricity and coupling relationship of windings,” Dian gong Ji shu Xue bao/Transactions of China Electrotechnical Society 28, 63‒73 (2013), [in Chinese].
 X. Cao, Z. Deng, G. Yang, Y. Yang, and X. Wang, “Mathematical model of bearingless switched reluctance motors based on Maxwell stress tensor method,” Zhongguo Dianji Gongcheng Xuebao/Proceedings of the Chinese Society of Electrical Engineering 29, 78‒83 (2009), [in Chinese].
 S. Berhausen and S. Paszek, “Use of the finite element method for parameter estimation of the circuit model of a high power synchronous generator”, Bull. Pol. Ac.: Tech. 63(3), 575‒582 (2015).
 X. Sun, S. Luo, L. Chen, R. Zhao, and Z. Yang, “Suspension force modeling and electromagnetic characteristics analysis of an interior bearingless permanent magnet synchronous motor”, Progress In Electromagnetics Research B. 69, 31‒45 (2016).