渐开线曲率分析及其在齿轮啮合分析中的应用  

Analysis of Involute Curvature and Its Application to Gear Mesh Study

作　　者：庞志锋[1] 张春林[1] 赵自强[1] 曹东江[1] 

机构地区：[1]北京理工大学机械与车辆学院,北京100081

出　　处：《机械传动》2011年第3期1-3,共3页Journal of Mechanical Transmission

基　　金：某部预研项目资助(6130318);北京理工大学基础科研基金项目资助(3030012210935)

摘　　要：利用数学微分几何原理对渐开线曲线进行曲率分析,系统推导了渐开线上各点极径、压力角与曲率半径之间的定量关系,明确了渐开线曲率中心与基圆的对应关系,并定量计算了压力角与曲率半径沿渐开线齿廓曲线的分布状况。利用渐开线曲率分析的结论并结合高副低代的机构分析方法对齿轮啮合传动机构进行运动分析,得到了正确的传动比分析结果,验证了曲率分析过程的正确性和实用性,为齿轮齿廓啮合分析、齿形创新设计、齿廓修形加工新工艺开发提供了理论基础,对齿轮传动的创新研究和发展具有重要意义。With mathematical theory of differential geometry,the curvature of involute curve is scientifically researched.It is indicated that the involute curvature radius has quantitative relation with polar radius and pressure angle,and the involute curvature center has corresponding connection with base circle.The pressure angle and curvature radius are quantitatively calculated,and their distribution along the involute tooth profile curve are given.Based on the analysis of involute curvature,the method of substituting lower pair for higher pair is used to analyze gear tooth mesh mechanism.The analysis of transmission ratio accord with traditional theory about gear transmission.It poves that the analysis of involute curvature is correct and practical.Furthermore,the analysis of involute curvature has theoretical guidance meaning for deep research of gear mesh,innovative design of gear tooth profile and development of tooth profile modification machining technology,and it is significant for innovative research and development of gear transmission.

关 键 词：渐开线 曲率 齿轮传动 齿廓啮合 机构分析 

分 类 号：TH132.41[机械工程—机械制造及自动化]