中文摘要：

针对齿轮接触表面层变曲率的特点，引入局部坐标系，构造出局部坐标下残余应力－应变场的分布状态，建立了齿轮连续啮合过程中安定状态残余应力的计算方法。该数值方法将弹塑性问题分解为弹性问题和特征应变决定的残余问题，并采用增量映射方法求解特征应变决定的残余问题，可直接得到齿轮安定状态下的接触残余应力。采用该数值方法分别计算了标准渐开线齿轮和齿顶修缘齿轮啮合过程中安定状态下残余应力的分布状态，并与有关试验结果相比较，验证了该数值方法的有效性。

英文摘要：

A model of gear contact has been established based on Hertz theory. Local coordinates are constructed on different meshing points because the curvature of gear profile is not constant, and then distributions of residual stresses and strains are constructed. A numerical approach for elastic-plastic analysis and shakedown is presented and its application to gear contact is demonstrated. The numerical approach consists of an operator split technique, which transforms the elastic-plastic problem into a purely elastic problem and a residual problem with prescribed eigenstrains. The eigenstrains are determined using an incremental projection method. The proposed method is applied to compute contact stresses and contact residual stresses of meshing gear teeth with standard and modified profile. The comparison with experimental results demonstrates the validity of the proposed method.