高速永磁同步电机转子瞬态温度场解析解

An Analytical Solution to the Transient Temperature Field in Rotors of High Speed Permanent Magnet Synchronous Motors

在转子的热设计中,很自然地有如下要求:在已知转子内热源的条件下,确定转子需要多大的对流换热系数以及相应气隙流体温度,使得转子局部最高温度不超过设计值。内热源已知的条件下,实验测量转子温度和气隙流体温度便可得到相应的对流换热系数。为解决高速永磁电机转子热设计问题,本文给出了转子温度场的解析解。首先将时变的且含内热源的传热方程无量纲化,然后利用傅里叶积分变换法求解,其中轴向分布不均的对流换热系数和气隙流体温度用等效的对流换热系数和等效气隙流体温度代替。通过与有限元计算结果对比,验证了该解析解的正确性。获得了一类高速永磁电机转子在各种散热因素作用下的稳态最高温度分布图,为转子的热设计提供了理论支持。

In the thermal design of the rotor, the appropriate convective heat-transfer coefficient and temperature of the main flow need to be determined to guarantee its local temperature not exceeding the design value, whereas the corresponding convective heat-transfer coefficient can be ascertained through the experimental measured temperature of the rotor and main flow, when the heat sources are known. This paper proposes the analytical solution to the thermal field of the rotor for the thermal design of the high speed permanent magnet （PM） rotors. First, dimensionless formulation of the transient heat conduction equation including interior heat source is derived, where the axially uniform convective heat-transfer coefficient and main flow temperature are equivalent to their mean values. Next, the Fourier integral transform method is used to solve the dimensionless equation. Finally, the analytical solution is verified by simulation. According to the analytical solution, a distribution of stead maximum temperature of a class of high speed PM rotors can be obtained under different heat dissipations and provides a theoretical support in the thermal design of the rotor.