基于分形理论的齿面法向接触阻尼计算模型

Model for calculating normal contact damping of tooth surface based on fractal theory

为了建立更为准确的微观尺度下齿面法向阻尼分形模型,以M-B模型为基础,利用存在摩擦时的弹塑性变形临界接触面积计算理论,并结合前期获得的两圆柱体接触面积分布公式,推导了考虑摩擦因素的齿面法向接触阻尼分形模型。通过MATLAB仿真,获得了模型中主要参数对分形接触模型影响的预测分析。结果表明:齿面法向接触阻尼在齿轮啮合过程中呈周期性变化,且随着法向载荷的增加而上升;摩擦系数与法向接触阻尼成正比关系;随着分形维数的增加,法向接触阻尼先下降后上升再下降;法向接触阻尼随着材料特性参数的变大而减小,随着粗糙度幅值参数的增加而下降;齿轮从初始啮合到结束啮合的过程中,法向接触阻尼由大变小;内接触的法向接触阻尼大于外接触。该模型的研究为后续进行齿轮动力学分析提供一定的理论参考。

In order to establish more accurate fractal contact model for analyzing gear normal damping in micro-scale, the fractal contact model for calculating Normal Contact Damping of Tooth Surface(NCDTS) with theconsideration of friction factors is established, which is on the basis of the M-B model, the theory of critical contact area of elastoplastic deformation with friction, and the equations of contact area distribution for cylinder surfaces. Through the prediction analysis of the model affected by the main parameters in the MATLAB, it is concluded that NCDTS changes periodically in the gear meshing process and rises with the increase of normal load. The friction coefficient is proportional to NCDTS, while along with the growth of fractal dimension, NCDTS declines firstly, and then goes up, and decreases finally. NCDTS reduces as the material characteristic parameter enlarges, and drops as the roughness amplitude parameter increases. From the initial state to the end state in the gear meshing, NCDTS varies from a big value to a small one. NCDTS of inner contact is bigger than that of outer contact. The research of the model helps to provide a definite theory conference for subsequent gear dynamics analysis.