| Due to the compact structure and flexible multi-DOF motion mode,the spherical motor has broad application prospects in the field of robot arms and joints fields.As a typical 3D coupled electromagnetic mechanism,the calculation of the 3D air gap magnetic field torque of a spherical motor is now mainly based on the finite element method.However,despite the continuous improvement of computer capability,FEM calculation is still a kind of analysis method with a large amount of calculation,long calculation time and low results consistency.Therefore,using analytical or numerical algorithms instead of finite element calculations to establish accurate and fast magnetic field models to analyze the torque,velocity and motion trajectory of spherical motors has always been one of the most important contents of spherical motor research.This dissertation focuses on the structural design,the analysis models of magnetic field and electromagnetic torque,and optimal control of permanent magnet spherical motor.The main work and innovations are as follows:(1)A type of permanent magnet spherical motor with stator 24 coils distributed in two layers,16 rotor permanent magnets arranged into a single ring and 8 poles accordance with the Halbach regulation is designed.The no-load magnetic field and static torque characteristics of the motor are simulated by the finite element analysis software,and the applicability of the superposition theorem in the analysis of magnetic field and torque is verified.(2)Using the equivalent surface current to replace the magnet according to the ampere molecular circulation hypothesis,and derives the spatial magnetic field distribution expression of the rectangular permanent magnet.According to superposition theorem and using space coordinate transformation,a magnetic field 3D analytical model of Halbach array permanent magnet spherical motor is established.The magnetic density model is programmed.The finite element software simulations and the Gauss meter tests are used to measure the no-load air gap magnetic field of the rotor.The validity of the proposed magnetic field model is proved by comparing the results of calculation,simulation and experiment of 3D magnetic density on the observation line.(3)On the basis of the magnetic field analytical model,according to the magnetic densities and current components in three orthogonal directions,the Lorentz force torque of the energized stator coil is obtained by space integration.According to the force reaction relationship and the superposition theorem of force,the torque analytical model of spherical motor based on the magnetic density and Lorentz force double integral is established.In order to avoid the repeated integration operation,according to the spatial transformation of torque,the torque interpolation model of spherical motor based on torque map graph is established,which greatly reduces the calculation amount while ensuring the calculation accuracy.A 3-DOF position/torque test-bench is designed to verify the validity of the torque model.(4)On the basis of the proposed torque model,taking the 3-DOF output torques under specific posture as the optimization objectives and all the input currents of stator coils as the control variables,an inverse solution model of the optimal control of the permanent magnet spherical motor is established by using particle swarm optimization algorithm.The main parameters are analyzed and selected.By switching the fitness function that control the search direction of the algorithm,different models of power on strategy are designed according to the symmetrical characteristics of the motor structure.Under the premise of ensuring that the output torques are close enough to the targets torque,the total root mean square value of the driving currents and the number of energized coils are reduced,which make the output load and communication pressure of the driving circuit board are reduced. |
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