基于加工模型的大重合度齿轮时变啮合刚度计算

Calculation of Time-Varying Mesh Stiffness with High Contact Ratio Gear Based on Machining Model

针对大重合度齿轮实际加工齿廓的过渡曲线、齿顶修缘、齿厚均与理想齿廓有所不同,对其啮合时变刚度计算方法进行了研究,建立了凸角修缘类型滚刀参数方程,依据齿轮啮合原理,推导剃(磨)齿前滚刀参数方程以及剃(磨)齿后齿轮齿廓的参数方程,结合现有计算大重合度齿轮时变啮合刚度的能量法,设计了改进势能法模型.根据齿廓参数方程编制了大重合度齿轮模拟软件,基于有限元软件计算出齿轮时变啮合刚度.将改进势能法模型与有限元法模型求解出来的结果进行对比,得出改进势能法模型的计算结果与有限元分析结果有较好的一致性,证明了所提出的改进势能法模型具有有效性.利用改进势能法模型研究了齿厚、过渡曲线、齿顶修缘对单齿啮合刚度最大值以及时变啮合刚度均值的影响.结果表明:齿厚对单齿啮合刚度最大值以及时变啮合刚度均值影响较大;过渡曲线部分主要的影响参数--凸角凸出部分径向高度、凸角径向高度、滚刀齿顶圆弧的半径对单齿啮合刚度最大值以及时变啮合刚度均值影响较小;齿顶修缘参数中的加工滚刀的修缘高和修缘角对单齿啮合刚度最大值的影响较小,但是对齿轮啮合刚度均值影响较大.

Focusing on the differences in the transition curve,top trimming,and tooth thickness between a gear with a high contact ratio and the ideal profile,a method of calculating time-varying stiffness was studied.Referring to existing literature,a parameter equation for a flange-type hob was established.According to the meshing principle of a gear,the parameter equation of the hob before shaving(grinding)teeth and the parameter equation of the gear profile after shaving(grinding)teeth were deduced.Combining the existing energy method for calculating the timevarying meshing stiffness of a gear with a high contact ratio,an improved potential energy method model system was designed and developed.Based on the parameter equation of the tooth profile,the simulation software for high contact ratio gears was developed,and the time-varying meshing stiffness of the gear was calculated using finite element software.By comparing the results of the improved potential energy method model system with those of the finite element method model,the conclusion was reached that the results from the proposed method were in good agreement with those of the finite element analysis results,which proved the effectiveness of the proposed method.The effects of tooth thickness,transition curve,and tip trimming on the maximum meshing stiffness and mean meshing stiffness of a single tooth were systematically studied using the improved potential energy method model.The results show that tooth thickness has considerable influence on the maximum meshing stiffness of single tooth and the mean meshing stiffness of time-varying meshing.The main parameters of the transition curve are the radial height of the convex corner that protrudes,the radial height of the convex angle,and the radius of the top arc of the hob,which have little influence on the maximum meshing stiffness of a single tooth and the mean meshing stiffness of timevarying meshing.In the top-trimming parameters,the trimming height and trimming angle of the machined hob have less influence on the maximum meshing stiffness of a single tooth,but have considerable influence on the mean meshing stiffness of the gear.The research results can provide a theoretical basis for dynamic analysis of spur gears with large coincidence based on the actual processing model.