永磁无刷直流电机性能的影响因素的数学推导与仿真分析

Mathematical derivation and simulation analysis of factors affecting performance of permanent magnet Brushless DC motor

在理论上推导出电机性能的影响因素是科学设计电机的前提。为了在理论上推导出影响永磁无刷直流电机的电磁转矩和电磁效率的影响因素,并用虚拟仿真加以验证,按照电机学的粘性阻尼理论,结合电磁学基本原理推导了电磁转矩和电磁效率关于各设计变量的公式。通过公式可以发现,此类电机的电磁转矩和电磁效率可用多元函数来表达,两者的决定性因素是额定电压、平均半匝长系数、永磁体厚度、极数和气隙等设计参数,并且经过数学分析可以得到电磁转矩和效率关于各设计变量的变化趋势。为了进一步证实理论推导的正确性,ANSYS Electronics Desktop软件的RMxprt模块进行了此类电机性能影响因素的仿真分析,分析结果与理论研究基本一致。这些趋势可以为永磁无刷直流电机研发人员选取优化设计变量和调整变量的数值提供方向。

The premise of designing a motor in a scientific way is to derive the factors that influence the performance of the motor in theory.In an attempt to derive the factors that influence the electromagnetic torque and efficiency of a permanent magnetism Brushless Direct Current(BLDC)motor and verify the factors through virtual stimulation,this paper derives the formulas that associate designing variables with electromagnetic torque and efficiency based on the electro-mechanic viscous damping theory and other basic electromagnetism theories.It is concluded from the formulas that the electromagnetic torque and efficiency of the motor can be presented with a multivariate function.The determinate factors are designing parameters including rated voltage,coil half-turn length factor,and the depth,number of poles,and air gap of the permanent magnet.The tendency of designed variables associated with electromagnetic torque and efficiency is shown through mathematic analysis.In order to further verify the theory,the RMxprt module of ANSYS Electronics Desktop software is used to stimulate and analyze influencing factors of the motor performance,and the results conform to the theory.The tendency will provide references to permanent magnetic BLDC motor researchers in their selection of designing variables and adjustment of the variables.