齿轮线接触与点接触理论与有限元分析

Theoretical Formula and Finite Element Analysis between Gear Pairs with Line Contact and Point Contact

由于制造误差、安装误差、支撑条件、齿轮承载变形等因素的影响,齿轮接触情况复杂且难以试验验证。齿轮接触按照初始接触条件通常分为线接触和点接触,承载后均为面接触:前者接触面为矩形,后者为椭圆形。线接触理论利用赫兹接触理论已经成熟,即采用两个圆柱体的线接触方式进行计算;点接触理论计算较为复杂,须考虑接触椭圆和其他非线性因素。用有限元方法分析渐开线及其修形齿轮的接触状态,计算实例表明,没有考虑安装误差的影响,线接触的仿真结果与赫兹接触理论相吻合,且接触状况明显好于点接触;当考虑安装误差的影响,二者接触应力均有上升,但线接触的接触状况明显恶化,接触应力急剧上升57倍以上,而点接触的接触应力上升不到1倍,说明齿轮线接触对安装误差的敏感性远大于齿轮点接触,极易造成齿轮的点蚀破坏。

The gear contact stress is very difficult to calculate and test owing to complexity of gear pairs contact condition by manufacturing error,assembly error,support conditions,deformation of loaded gear pairs,etc.The gear contact can be constituted of line contact and point contact in non-loaded condition,and will be change to surface contact in loaded condition.When the load is applied,the area of the contact is rectangular and ellipse respectively in line contact and point contact.The theory of line contact is perfect using Hertz contact to calculate two cylinders contact.However the theory of point contact is more complicated considering contact ellipse and other nonlinear factors,etc.The calculation examples of involute gear and the same parameter gear with modification are analyzed by finite element method.It shows that the simulation result of gear line contact is consistent with calculation result of Hertz contact theory without considering assembly error,and contact stress of line contact is less than the one of point contact.The contact stress of line contact and point contact will both rise if considering assembly error,but contact stress of line contact and point contact will rise rapidly to 57 times and less than twice respectively comparing with no assembly error.It shows that contact sensitivity of line contact is more sensitively than one of point contact,and it is reason that line contact gear will easily cause gear pitting destruction.