基于分形齿面粗糙度的双渐开线齿轮时变啮合刚度研究  

Fractal Model of Double Involute Gears Time-Varying Meshing Stiffness Considering Friction Factors

作　　者：陈亮 樊智敏[1] 尹兆明 曲伟 张耘瑞 CHEN Liang;FAN Zhimin;YIN Zhaoming;QU Wei;ZHANG Yunrui(College of Electromechanical Engineering,Qingdao University of Science&Technology,Shandong Qingdao 266061,China)

机构地区：[1]青岛科技大学机电工程学院,山东青岛266061

出　　处：《摩擦学学报》2023年第4期358-367,共10页Tribology

基　　金：国家自然科学基金项目(52075279)资助.

摘　　要：为更精确求解双渐开线齿轮时变啮合刚度并考虑齿面形貌的影响,将每一啮合时刻下齿轮接触线“分段”,每段接触线上的接触等效为圆柱体接触,并基于M-B分形理论与赫兹接触理论,建立考虑分形齿面粗糙度的双渐开线齿轮时变啮合刚度模型.通过齿轮啮合刚度分形模型、有限元模型与ISO 6336-1:2006(E)结果对比分析,验证了所建分形模型的合理性.分析了摩擦系数、齿轮材料的特性参数、分形维数以及粗糙度幅值等对双渐开线齿轮时变啮合刚度的影响,结果表明:同载荷条件下,啮合刚度随摩擦系数的减小而提高,摩擦系数小到一定范围时,其改变对啮合刚度影响较小;分形维数与齿轮材料特性参数增加,可以提高啮合刚度;减小粗糙度幅值可以提高啮合刚度,分形维数不同对啮合刚度的影响程度不同.该研究为结合齿面形貌的齿轮摩擦动力学分析提供一定理论基础.Most conventional time-varying gear mesh stiffness calculations do not take into account the effect of tooth profile on the time-varying gear mesh stiffness.Due to the machining characteristics of gears,there is usually a certain amount of roughness on the tooth surface,similar to the distribution of many micro-convexities on the tooth surface.This tooth surface profile is characterised by a random distribution of micro-convexities in a small area,but a selfsimilar distribution over the whole range.In order to solve more accurately for the time-varying mesh stiffness of double involute gears,this paper takes into account the microscopic morphology and friction of the tooth surfaces and combines a pair of inverse stepped tapered roller contact models to“segment”the gear contact line at each moment of engagement,with the contact on each segment being equivalent to a cylindrical contact.And based on M-B fractal theory and Hertzian contact theory,a time-varying meshing stiffness model for double involute gears considering fractal tooth surface roughness is developed.Analysis of the effect of tooth profile parameters and friction factors on the timevarying meshing stiffness of gears.By comparing the results of the gear mesh stiffness fractal model,finite element model and ISO 6336-1:2006(E),the calculation results of the fractal model proposed in this paper are closer to the ISO calculation results,and the error between them is within 9.4%,which verifies the reasonableness of the proposed fractal model.The effects of friction factor,gear material characteristics,fractal dimension and roughness amplitude on the time-varying mesh stiffness of double involute gears were analysed using Matlab software based on the proposed fractal model of double involute gear time-varying mesh stiffness.The results showed that under the same load conditions,the increase in the friction factor leaded to an increase in the critical area for the elastic-plastic deformation of the microconvex body on the tooth surface,i.e.an increase in

关 键 词：双渐开线齿轮 时变啮合刚度 摩擦 M-B分形理论 有限元法 

分 类 号：TH117.1[机械工程—机械设计及理论] TH132.4