基于解析有限元的齿根裂纹时变啮合刚度计算方法

The Time-varying Mesh Stiffness Calculation for Gear Tooth Crack based on Analytical-finite Element Method

当齿轮发生故障时,时变啮合刚度的变化能够反映齿轮故障特征大小。因此,时变啮合刚度在齿轮传动过程中是一个重要的动力学参数。提出一种新的齿根裂纹啮合刚度计算方法,即解析有限元法(Analytical-finite element method, A-FM)。考虑到齿轮发生故障时,啮合刚度解析模型计算精度较低,将应力强度因子引入裂纹齿轮的啮合刚度计算过程。首先定义应力强度因子与啮合刚度之间的关系,通过建立齿轮接触模型计算裂纹尖端附近的应力强度因子,然后将计算结果替代解析模型中故障刚度部分。由于应力强度因子能够敏感地识别齿根裂纹的局部微小变化,故该方法相比于解析法具有更高的计算精度,相比于有限元法具备更快的计算效率。同时,建立6自由度动力学模型,通过对其振动响应进行分析,仿真结果验证了所提方法的可行性。

The time-varying meshing stiffness variation can reflect the size of gear fault feature when the gear fault occurs. Therefore, the time-varying meshing stiffness is an important dynamic parameter in the process of gear transmission. A novel tooth crack meshing stiffness calculation method namely analytical-finite element method (A-FM) is presented. Considering the calculation accuracy of the analytical model of the meshing stiffness is low when the gear fault occurs, the stress intensity factor is introduced into the calculation of the meshing stiffness of the cracked gear in this paper. First of all, define the relationship between the stress intensity factors and the meshing stiffness, calculate the stress intensity factor near the crack tip by means of establish the gear contact model, then replace the part of fault stiffness in the analytical model with calculation result. This method is more accurate compare with analytical method and more effective compare with finite element method due to the stress intensity factor is sensitive to small local changes in the tooth root crack. Simultaneously, the six-degree of freedom dynamic model is established. Through the analysis of vibration response, the simulation results verify the feasibility of the proposed method.