修形直齿锥齿轮副加载接触分析方法研究  

Loading contact analysis method of modified straight bevel gears

作　　者：杜建霞 包广清 DU Jian-xia;BAO Guang-qing(College of Mechanical Engineering,Gansu Institute of Mechanical&Electrical Engineering,Tianshui 741001,China;School of Electrical Engineering and Information,Southwest Petroleum University,Chengdu 610500,China)

机构地区：[1]甘肃机电职业技术学院机械工程学院,甘肃天水741001 [2]西南石油大学电气信息学院,四川成都610500

出　　处：《机电工程》2023年第7期1008-1016,共9页Journal of Mechanical & Electrical Engineering

基　　金：国家自然科学基金资助项目(51967012)。

摘　　要：针对修形直齿锥齿轮副的接触特征及接触形态计算方面存在的问题,提出了一种修形直齿锥齿轮副加载接触分析方法,对修形直齿锥齿轮副啮合特征计算过程进行了系统的阐述。首先,根据球面渐开线展成原理,生成了标准的直齿锥齿轮齿面,并根据齿根圆与球形渐开线相切的原理,构建了齿底倒圆的数学模型;然后,采用二元二次多项式对齿面进行了修形,并得到了相应的齿面离散点,在此基础上,应用样条曲面构造方法,重构了修形齿面方程;接着,依据齿轮啮合原理,进行了齿面接触分析(TCA),获得了瞬时共轭接触点以及整个啮合周期的啮合迹线;最后,应用赫兹接触修正模型,计算了受载状态下的接触椭圆、椭圆长短轴、最大接触应力以及应力分布,对共轭接触直齿锥齿轮副进行了加载接触分析。研究结果表明:与有限元计算结果相比,采用加载接触特性计算方法,两者接触迹线和接触椭圆等啮合特征相符,接触力和最大接触应力误差在1%和2%以内;对比结果表明,加载接触特性计算方法能够准确地对修形直齿锥齿轮副进行加载接触分析。Aiming at the calculation of the contact characteristics and contact forms of the modified straight bevel gear pair,a loaded contact analysis method for the modified straight bevel gear pair was proposed.The calculation process of meshing characteristics of modified straight bevel gear pair was systematically expounded.Firstly,the standard tooth surface of straight bevel gear was generated based on the principle of spherical involute spreading,and the mathematical model of tooth root fillet was constructed according to the principle of tangential tooth root circle and spherical involute.Then,combining with binary quadratic polynomial,the tooth surface was modified and the corresponding discrete points were obtained.On this basis,the modified tooth surface equation was reconstructed by using spline surface construction method.After that,according to the principle of gear meshing,the tooth contact analysis was further completed,and the instantaneous conjugate contact points and the meshing traces of the whole meshing period were obtained.At last,the contact ellipse,the major and minor axes,maximum contact stress and stress distribution under load were calculated by using Hertz contact correction model,and the loading contact analysis of conjugate contact straight bevel gears was completed.The research results show that,comparing with the results of finite element,under the condition of using the calculation method of loading contact characteristics,the meshing characteristics such as contact trace and contact ellipse are consistent,and the errors of contact force and maximum contact stress are within 1%and 2%.The comparison results show that the loading contact of modified straight bevel gears can be accurately analyzed by the proposed method.

关 键 词：齿轮传动 齿面接触分析 加载接触分析 齿轮啮合原理 赫兹接触修正模型 接触特征 

分 类 号：TH132.41[机械工程—机械制造及自动化]