裂纹齿轮啮合刚度的劣化特性

Degradation Characteristics of Meshing Stiffness of Spur Gears with Root Crack

基于轮齿的变截面阶梯悬臂梁假设,综合考虑轮齿弯曲、基础变形、接触变形等因素,首先,建立了健康齿轮时变刚度的计算模型,利用解析法与有限元仿真对比研究,获得了健康齿轮啮合刚度的分布曲线;然后,基于线弹性断裂力学前提下的齿根裂纹扩展路径,建立了包含不同尺度裂纹的有限元模型;最后,针对不同长度的裂纹齿轮,计算获得了1.5个啮合周期内的刚度曲线,从而建立了裂纹尺寸与刚度劣化特性的影响关系。通过对比单、双齿不同啮合区内的劣化规律,表明单齿啮合区由于单齿承载,其劣化程度明显高于双齿啮合区。此外,啮入阶段与啮出阶段的双齿啮合区劣化特性也存在一定差异。

One of the main defects that influences the lifetime of a gear are cracks.The phenomenon induced by crack initiation and propagation is the continuous degradation of meshing stiffness,which will determine the response feature of the entire gear transmission system.Based on the assumption that the gear tooth is simplified as a variable cross-section cantilever beam,a time-varying meshing stiffness calculation model is established,in which the tooth bending,basis deformation and contact deformation are all included.The meshing stiffness curve of the healthy gear is obtained with comparative analysis between the above analytical model and FEM simulation.Furthermore,on the basis of a tooth root crack propagation prediction from the linear elastic fracture mechanics theory,the FEM models of gear tooth with cracks of different lengths are found.The stiffness calculation within one and a half meshing periods for each model is completed,and the relationship between crack size and stiffness degradation trend is established.The comparison between degradation trends in different meshing regions shows that the degree of degradation in a single tooth meshing area is much higher than that in a double teeth meshing region.In addition,there is some difference between the double teeth meshing areas.