基于分形理论的双渐开线齿轮接触应力研究

综合考虑接触面粗糙度、材料特性等因素对齿轮接触应力的影响，基于分形理论和经典Hertz接触理论建立双渐开线齿轮分形接触模型. 该模型中，影响载荷和实际接触面积的主要因素包括分形维数、粗糙度幅值和材料特性参数. 理论分析表明:分形维数一定时，真实接触面积随着载荷的增大而增大；载荷一定时，接触面积随着粗糙度幅值的增大而减小；随着材料特性参数值的增加，在一定程度上加强了软材料轮齿承载能力，同时会使得微凸体由弹性变形到塑性变形的临界面积减小. 对比分形接触模型和有限元模型两种计算双渐开线齿轮轮齿接触应力方法，结果证明了分形接触模型计算双渐开线齿轮接触应力的有效性. 

Contact Stress of Double Involute Gear Based on Fractal Theory

Considering the influence of contact surface roughness, material characteristics and other factors on the contact stress of gears, the fractal contact model of double-involute gear was established which based on the fractal theory and the classical Hertz contact theory. In this model, the main factors influencing the load and the actual contact area consisted of fractal dimension, roughness amplitude and material characteristic parameters. Theoretical calculation showed that when the fractal dimension was constant, the real contact area increased with the increase of load. When the load was constant, the contact area decreasesd with the increase of roughness amplitude. With the increase of the material characteristic parameter value, the bearing capacity of the soft material wheel tooth was enhanced to some extent, while the critical area of the micro-convex body from elastic deformation to plastic deformation was reduced. Through the comparison of two methods including fractal contact model and finite element model for calculating tooth contact stress of double involute gear teeth, the results demonstrate the effectiveness of using fractal contact model to calculate contact stress of double involute gear.