电机三维温度场的有限公式法计算技术

Calculation Technology of Finite Formulation Method for 3D Motor Temperature Field

有限公式法是一种类似有限积分技术的新型数值计算方法,其应用及理论研究仍在完善中。基于有限公式法下温度场代数场控制方程及其三维离散格式,该文对通用化程序编制中的对流散热边界条件简化处理、基于单元分析的模块化程序设计、计算数据前后处理等问题做了相关工作。讨论了有限公式法在三维复杂求解域问题中适用性与计算性能,并从数值计算角度验证了线性插值下有限公式法具有二阶计算精度。最后,结合3台不同结构、冷却方式的永磁电机三维温度场分析来说明有限公式法在复杂求解域问题上计算的准确性。就文中仿真算例而言,在相同网格、求解自由度以及求解迭代算法下,有限公式法比有限元法节约计算时间在12%~71.5%,两者计算占用内存基本一致。

Finite formulation method （FFM） is a new kind of numerical method similar to finite integration technology （FIT）. Its application and theoretical research is still in progress. Based on the temperature field algebraic equations and 3D discrete format of FFM, the simplified programming of convection boundary conditions, modular programming on the basis of element analysis and technology of pre-and post-processing were presented. The applicability and computational performance of FFM on 3D complex structure were also discussed, and a second order accuracy was verified under the linear interpolation with numerical computation methods. Finally, the solution accuracy of FFM on complex models was verified by analyzing the 3D temperature fields of 3 permanent magnet synchronous motors with different structures and cooling conditions. According to the computation results, when the mesh, degrees of freedom and iterative algorithm are identical, both FFM and FEM use about the same amount of memory, but FFM can save computing time by 12% to 71.5%.