同平面相交轴线齿轮的正反转啮合分析与稳定性评价  

Stability Evaluation and Forward-reverse Meshing Analysis of Line Gear with Intersection Axis of the Same Plane

作　　者：罗千杰 杨旭娟[1,2] 耿婷 丁江 Luo Qianjie;Yang Xujuan;Geng Ting;Ding Jiang(College of Mechanical Engineering,Guangxi University,Nanning 530004,China;Guangxi Key Lab of Manufacturing System and Advanced Manufacturing Technology,Nanning 530004,China;Department of Mechanical Engineering,Tsinghua University,Beijing 100084,China)

机构地区：[1]广西大学机械工程学院,广西南宁530004 [2]广西制造系统与先进制造技术重点实验室,广西南宁530004 [3]清华大学机械工程学院,北京100084

出　　处：《现代农业装备》2020年第3期29-37,共9页Modern Agricultural Equipment

基　　金：国家自然科学基金项目(51905113);广西自然科学基金项目(2017GXNSFBA198233);广西制造系统与先进制造技术重点实验室主任课题(16-380-12S002);2019年教育部中西部高等学校青年骨干教师国内访问学者项目。

摘　　要：线齿轮是一种基于空间曲线啮合的精密齿轮传动件,特别适用于微机电系统的设计。由于装配误差、尺寸误差等因素,加上线齿轮副在正反转时所受的推力方向不共线,导致线齿轮啮合的稳定性和传动精度受影响。本文以最常用的同平面相交轴线齿轮为例,在建立线齿轮数学曲面模型的基础上,分析线齿轮的啮合特性,计算线齿接触线的基本矢,求得线齿根部所受推力方向的偏差。对线齿轮进行反转分析,发现线齿轮反转时的空间曲线啮合方程与正转时不同,导致其线齿接触线方程和其推导出的主法矢与正转时均存在差异。应用Mathematica软件推导出线齿轮反转时的空间曲线啮合方程、线齿接触线方程以及啮合点处的基本矢,再利用主法矢的夹角评价该差异。最后,通过实例数据的代入计算,对分析和推导进行验证,为线齿轮啮合稳定性和传动精度提供评价方法与指标。With the development of modern technology,various micromechanics are emerging continuously in industry,agriculture,logistics and other aspects,and the transmission accuracy requirements applied in the micromechanics are synchronously improved.The line gear(LG)is a kind of precision gearing systems based on space curve meshing,which is especially suitable for the design of Micro-Electro-Mechanical System(MEMS).However,the meshing stability and the transmission accuracy of the LG pairs can be affected by the factors like assemble error,dimension error and different thrust directions during the forward and reverse rotation.In this paper,based on their mathematical mode,the meshing characteristics of the LG pairs are analyzed,their basic vector of contact line is calculated,and the deviation of thrust direction is obtained.The results show that the space curve meshing equation is different during forward and reverse rotation,which leaded to the line tooth contact line equation and that the principal normal vector are different between forward and reverse rotation.Then during reverse rotation through using Mathematica software to derive the space curve meshing equation,the line tooth contact line equation and the basic vector at the point of LG pair,so as to evaluate the difference through using the angle of principal normal vector Finally,through the substitution calculation of example data,the previous analysis and derivation can be verified,so as to provide the evaluation methods for ensuring the meshing stability and transmission accuracy of LG pair.

关 键 词：线齿轮副 相交轴 啮合稳定性 啮合方程 主法矢夹角 

分 类 号：V232.8[航空宇航科学与技术—航空宇航推进理论与工程]