基于分形理论的齿面形貌模拟方法研究

RESEARCH ON THE SIMULATION METHOD OF TOOTH SURFACE TOPOGRAPHY BASED ON THE FRACTAL THEORY

为了研究齿轮的齿面形貌对齿轮啮合的影响,引入分形理论,从而实现渐开线齿轮的齿面形貌模拟。通过分形理论中的W-M函数、渐开线方程和螺旋线方程,并运用Matlab编程对渐开线直齿轮和斜齿轮进行齿面模拟,观察仿真发现:随着分形维数的增加,齿面形貌由不规则波动向平整过渡,因此适当提高齿面维数有利于齿面质量的提高。研究为后续进一步研究齿轮啮合过程中的力学特性提供了前期理论基础。

In order to study the influences of gear engagement by tooth surface morphology, the fractal theory is introduced, thereby the goal of involute gear tooth surface topography simulation is achieved. Through using the W - M function of fractal theory, involute equation and helix equation, and combined with Matlab programming, to simulate the tooth surface of the involute spur gear and helical gear. The research shows that： with the increasing of fractal dimension, the tooth surface morphology transition from irregular volatility to smooth. Thus increasing the tooth surface dimension is beneficial to tlhe improvement of the quality of tooth surface. The research provides preliminary theoretical basis for further study on the mechanical characteristics of gear meshing process.