Torque Modelling and Validation for a Spherical Motor with Stepped Permanent Magnets
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ORIGINAL ARTICLE
Torque Modelling and Validation for a Spherical Motor with Stepped Permanent Magnets Jingxiong He2 · Guoli Li1 · Rui Zhou2 · Qunjing Wang3 · Yuanzhong Qiao2 Received: 28 February 2020 / Revised: 9 April 2020 / Accepted: 14 September 2020 / Published online: 24 September 2020 © The Korean Institute of Electrical Engineers 2020
Abstract A spherical motor is an electromagnetic device with multi-degree-of-freedom motion. Three-dimensional (3-D) magnetic field analysis and torque analysis are needed for the design, optimization and control of the motor. Presently, these analyses are carried out by the finite-element method (FEM) with a large amount of calculation and time consumption. An analytical method (AM) can reduced the computational burden of the FEM without sacrifice of the accuracy. A stepped permanent magnet (PM) can obtain a large range of the magnetic field while effectively saving PM materials. However, its special structure causes difficulties in analytical modelling. This paper presents an AM for the 3-D magnetic field and torque of a permanent magnet spherical motor with stepped PMs. The analytical model of the 3-D magnetic field of the stepped PM is derived based on the loop current method, and the electromagnetic force of the stator coil is calculated based on the Lorentz force method. Thus the 3-D magnetic field and torque can be calculated efficiently with reasonable accuracy. The analytical model is verified by the FEM and experimental tests. The test results confirm the high accuracy of the developed model. Keywords Spherical motor · Stepped permanent magnet · Analytical model · Loop current method · Lorentz force method
1 Introduction Electrically driven actuators are wildly used in mechanical arms and other transmission devices [1, 2]. The traditional multi-degree-of-freedom (multi-DOF) transmission device * Guoli Li [email protected] Jingxiong He [email protected] Rui Zhou [email protected] Qunjing Wang [email protected] Yuanzhong Qiao [email protected] 1
National Engineering Laboratory of Energy‑Saving Motor and Control Technology, Anhui University, Hefei 230601, China
2
School of Electrical Engineering and Automation, Anhui University, Hefei 230601, China
3
Collaborative Innovation Centre of Industrial Energy‑Saving and Power Quality Control, Anhui University, Hefei 230601, China
consists of multiple single-degree-of-freedom (single-DOF) motors and the complex mechanical transmission [3]. They are effective but the three separate motors need coordinated control. Therefore, there are accumulative errors in implemental acting [4, 5]. Spherical motors have the advantages of simple and light structure, excellent dynamic response and high precision [6, 7]. They have attracted much attention across the world. In this paper, a permanent magnet spherical motor (PMSpM) is designed for a multi-DOF motion, and can be conveniently applied to multi-DOF transmission devices. Due to the three-dimensional (3-D) motion characteristics of the spherical motor, both magn
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