大齿数裂纹直齿轮时变啮合刚度算法研究  

Research on the Time-varying Meshing Stiffness Algorithm of Spur Gears with Large Tooth Number Cracks

作　　者：焦为 徐可君 秦海勤 Jiao Wei;Xu Kejun;Qin Haiqin(Department of Aviation Mechanical Engineering and Management in Qingdao Branch,Naval Aviation University,Qingdao 266041,China)

机构地区：[1]海军航空大学航空机械工程与指挥系(青岛校区),山东青岛266041

出　　处：《机械传动》2023年第6期8-15,共8页Journal of Mechanical Transmission

基　　金：国家自然科学基金项目(11772089)。

摘　　要：针对齿数大于41的直齿轮,基于切齿几何和齿轮啮合原理,明确渐开线齿廓起点和渐开线与基圆交点的区别,引入过渡曲线参数方程,对基于能量法的时变啮合刚度计算公式进行改进,全面建立了不同裂纹水平的故障轮齿模型。在此基础上,以斜线作为有效齿厚削减限制线,使得裂纹轮齿模型更严格、考虑因素更全面。参考有限元法计算结果,分别讨论了模型修正、裂纹程度、有效齿厚削减限制线具体形式等因素对时变啮合刚度的影响。计算结果表明,未修正轮齿模型会导致大齿数裂纹齿轮时变啮合刚度计算结果偏小;啮合刚度降低程度随裂纹水平的增大而不断增加。根据裂纹水平给出了有效齿厚削减限制线的建模建议:当裂纹水平较低时,有效齿厚削减限制线宜采用直线;当裂纹水平较高时,采用直线会产生较大误差;采用斜线不仅便于计算,同时能够满足计算精度需求,具有更强的实用性。For spur gears with more than 41 teeth,based on the geometry of cutting teeth and the principle of gear meshing,the difference between the starting point of the involute profile and the intersection of the involute and the base circle is clarified,and the transition curve parameter equation is introduced to calculate the time-varying meshing stiffness based on the energy method.The formula has been improved,and the faulty gear tooth models with different crack degrees are comprehensively established.On this basis,the oblique line is used as the effective tooth thickness reduction limit line,which makes the crack tooth model stricter and the considerations more comprehensive.With reference to the calculation results of the finite element method,the effects of model correction,crack extent,and the specific form of the effective tooth thickness reduction limit line on the time-varying meshing stiffness are discussed respectively.The calculation results show that the uncorrected gear tooth model will lead to a small calculation result of the time-varying meshing stiffness of gears with large numbers of teeth;the reduction degree of meshing stiffness increases with the increase of the crack level.According to the degree of cracks,the modeling suggestion for the effective tooth thickness reduction limit line is given:when the crack level is low,the effective tooth thickness reduction limit line should be a straight line;when the crack level is high,using a straight line will cause significant errors.Using a diagonal line is not only convenient for calculation,but also can meet the requirements of calculation accuracy and has stronger practicability.

关 键 词：大齿数 齿根裂纹 不同裂纹程度 有效齿厚削减限制线 时变啮合刚度 

分 类 号：TH132.41[机械工程—机械制造及自动化]