角接触球轴承生热预测方法与灵敏度分析

通过拉丁超立方实验设计法获取角接触球轴承NSK-7015C的结构参数样本数据,采用Newton-Raphson法求解轴承变形几何协调方程、滚动体平衡方程和内圈平衡方程所构成的非线性方程组。应用Kriging和Monte Carlo相结合的方法(AK-MCS)构建样本数据与轴承生热的函数关系,在此基础之上使用全局灵敏度计算方法计算轴承结构参数对轴承生热的影响。研究结果表明:在相同轴承结构参数下,采用AK-MCS法预测的轴承生热与轴承拟静力学分析模型求得的结果差值均小于0.003 W,说明AK-MCS算法的预测结果具有较高的准确性；轴承生热对轴承滚动体直径变化反应最灵敏,轴承内、外圈沟道直径影响次之,轴承内、外圈沟道曲率半径影响最小,该研究能够为轴承结构参数的设计优化和加工精度的选择提供理论依据。 

Prediction method and sensitivity analysis of the heat generation for an angular contact ball bearing

Latin hypercube experimental design method was used to produce the sample data of structure parameters for the angular contact ball bearing NSK-7015C. The Newton-Raphson method was proposed for solving nonlinear equations composed of the equation of kinematic constraints, the ball equilibrium equations and the balance equations of the inner ring of the bearing. Then, the sample points corresponding the heat generation of the bearings were obtained. A combination method (active learning and Kriging-based Monte-Carlo simulation,AK-MCS) of the Kriging model and Monte Carlo was adopted to establish a function between sample points and the heat generation of the bearing. On this basis, a global sensitivity computational method was used to calculate the influence of structure parameters of the bearing on its heat generation. The results show that the differences between the prediction results of the heat generation for the bearing using AK-MCS method and the quasi-static analysis model of the bearing under the same structure parameters of the bearing are less than 0.003 W. This illustrates that the prediction results of the AK-MCS algorithm are highly accurate. The heat generation of the bearing is the most sensitive to the change of ball diameter,then the inner- and outer-ring raceway diameter take the second place, and the curvature radius of inner- and outer-ring raceway groove are the least. This research may bring forward the theoretical basis for the design optimization of structure parameters and selecting the machining accuracy of the bearing.