基于分形理论及蒙特卡罗法的电主轴热特性分析

为了在设计阶段解决高速主轴在实际加工中因温升过高而突然失效问题,构建了主轴热-结构耦合有限元瞬态分析模型.提出了基于接触角迭代法的滚动轴承生热功率求解方法,利用电动机效率分析法求解其生热功率.引入分形理论与蒙特卡罗方法计算结合面间接触热导,有效避免了统计学方法的不准确性与实验法通用性不强的缺陷.由雷诺数判定冷却液流动状态,并依据努赛尔数计算出主轴不同部件的对流换热系数.将上述边界条件施加到有限元模型中,对主轴温度场与热变形进行仿真.结果表明,高速主轴热特性建模方法正确,并能准确预测主轴温度场分布和热变形.

Simulation of Thermal Behaviors of Motorized Spindle Based on Fractal Theory and Monte Carlo Method

Abstract： The finite element analysis thermal-structure model of a spindle was proposed at the design stage to avoid the sudden failure in actual machining caused by the high temperature rise in the spindle components. The calculation method of bearing heat power, which regarded the contact angle as the iterative variable, was proposed to avoid the disadvantages of the traditional Newton-Raphson algorithm when the bearing quasi static was analyzed, such as the poor convergence, slow convergence speed and low accuracy. The motor efficiency analysis method was applied to calculate the heat power of the built-in motor. To avoid the inaccuracy of the statistical methods and the poor generality of the experiment methods, the fractal theory and Monte Carlo method were utilized to calculate the thermal contact conductance between joint surfaces. Besides, the convective heat transfer coefficients of different components were calculated according to the Nusselt number. Furthermore, the spindle thermal deformation and temperature distribution were simulated by applying the above boundary conditions to the FEA model. The results show that the modeling approach of high-speed spindle thermal characteristics is correct and the FEA model can accurately predict the temperature distribution and thermal deformation.