精密钢球传动啮合法向力与弹性回差

doi:10.3901/JME.2016.09.042

摘要/Abstract

摘要： 针对精密钢球传动法向力的传统求解方法和弹性回差对传动性能的影响,在分析啮合副弹性回差产生机理的基础上,提出利用啮合点刚度系数精确求解法向力和弹性回差的方法。建立啮合副力学模型,利用啮合点刚度系数并通过力矩平衡方程分别推导出减速啮合副和等速啮合副的弹性转角和啮合点法向力公式,应用啮合副弹性转角分别推出减速啮合副弹性回差、等速啮合副弹性回差和传动机构弹性回差的计算公式,并分析机构参数对弹性回差的影响规律。研究结果表明,减速啮合副和等速啮合副啮合法向力可用统一公式表示,传动机构弹性回差曲线呈周期性波动,机构参数变化对弹性回差影响较明显,减速钢球数对弹性回差影响最大。研究结果为精密钢球传动的传动精密性和运动平稳性分析及机构设计提供理论依据。

关键词: 弹性回差, 刚度系数, 接触变形, 精密钢球传动, 啮合法向力

Abstract: In view of usual resolved method of the engagement normal force and influence of the elastic backlash on the transmission performance of the precision ball transmission, based on mechanism analysis of the engagement pairs elastic backlash, the method to be resolved exact calculation engagement normal force and elastic backlash of engagement pairs is proposed by rigidity coefficient. The mechanical model of the engagement pairs is established. The formulas of the elastic turn angel and engagement normal force of the reduction speed engagement pair and equi-speed engagement pair are respectively deduced by the engagement point stiffness coefficient and torque balance equation. The elastic backlash formulas of the reduction speed engagement pair , the equi-speed engagement pair and the transmission mechanism are respectively deduced with the engagement pair elastic turn angel. The influence of the mechanism parameters on the elastic backlash is analyzed. The results show that engagement normal forces of the reduction speed engagement pair and the equi-speed engagement pair are represented by the unified formula. The elastic backlash curve of the transmission mechanism is changed periodically. It is obvious that mechanism parameters change affects the elastic backlash. The most important factor affecting the elastic backlash is the reduction of the number of steel balls. The research result provides theoretical basis for analysis of transmission accuracy, rotation smoothness and mechanical design of the precision ball transmission.

Key words: contact deformation, elastic backlash, engagement normal force, precision ball transmission, rigidity coefficient

中图分类号:

TH132

安子军, 杨荣刚, 宜亚丽. 精密钢球传动啮合法向力与弹性回差[J]. 机械工程学报, 2016, 52(9): 42-48.

AN Zijun, YANG Ronggang, YI Yali. Engagement Normal Force and Elastic Backlash of Precision Ball Transmission[J]. Journal of Mechanical Engineering, 2016, 52(9): 42-48.

参考文献

[1] 王国彪,赖一楠,范大鹏,等. 新型精密传动机构设计与制造综述[J]. 中国机械工程,2010,21(16)：1891-1897.
WANG Guobiao,LAI Yinan,FAN Dapeng,et al. Summary of new type precision transmission design and manufacture[J]. China Mechanical Engineering,2010,21(16)：1891-1897.
[2] 寺田英嗣,牧野洋,今瀬憲司. サイクロイドボール減速機の基礎解析[J]. 精密工学会誌,1995,61(12)：1075-1079.
TERADA H,MAKINO H,IMASE K. Fundamental analysis of cycloid ball reducer[J]. JSPE,1995,61(12)：1075-1079.
[3] HIDETSUGU T. The development of gearless reducers with rolling balls[J]. Journal of Mechanical Science and Technology,2010,24(1)：189-195.
[4] 徐盛林,陈耿. 精密超精密定位技术及其应用[J]. 中国机械工程,1997,8(4)：73-75.
XU shenglin,CHEN Geng. Precision ultra-precision positioning technology and its applications[J]. China Mechanical Engineering,1997,8(4)：73-75.
[5] 安子军,曲志刚,王广欣. 基于模糊理论的摆线钢球行星传动接触模糊疲劳强度可靠性研究[J]. 中国机械工程,2002,13(23)：2010-2012.
AN Zijun,QU Zhigang,WANG Guangxin. Research on fatigue strength reliability for the cycloid ball planetary transmission based on fuzzy theory[J]. China Mechanical Engineering,2002,13(23)：2010-2012.
[6] 张鹏,安子军. 摆线钢球行星传动动力学建模与固有特性分析[J]. 中国机械工程,2014,25(2)：157-162.
ZHANG Peng,AN Zijun. Cycloid ball planetary dynamics modeling and analysis of the inherent characteristics[J]. China Mechanical Engineering,2014,25(2)：157-162.
[7] De MOERLOOZE K,AL-BENDER F,VAN BRUSSEL H. Modeling of the dynamic behavior of systems with rolling elements[J]. International Journal of Non-Linear Mechanics,2011,46(1)：222-233.
[8] 张鹏,安子军,杨作梅. 摆线钢球行星传动啮合副非线性力学性能研究[J]. 工程力学,2010,27(3)：186-192.
ZHANG Peng,AN Zijun,YANG Zuomei. Research on nonlinear mechanical properties for engagement pair of cycloid ball planetary transmission[J]. Engineering Mechanics,2010,27(3)：186-192.
[9] 西庆坤,朱俊平,赵曙光,等. 摆线钢球行星减速器误差的蒙特卡洛分析[J]. 西北农林科技大学学报,2008,36(7)：224-228.
XI Qingkun,ZHU Junping,ZHAO Shuguang,et al. Error analysis of cycloid ball planetary reducer based on the Monte Carlo[J]. Journal of Northwest Agriculture and Forestry University,2008,36(7)：224-228.
[10] GUAN Tianmin,SHI Xiaochun. Force analysis considering manufacture error of pin-hole-output mechanism in cycloid drive[J]. Chinese Journal of Mechanical Engineering,2002,15(2)：142-144.
[11] 徐辅仁. 对由轴弹性变形产生回差的研究[J]. 机械传动,2002(1)：22-24.
XU Furen. Research backlash elastic deformation generated by the shaft[J]. Journal of Mechanical Transmission,2002(1)：22-24.
[12] 周玉林,刘磊,高峰. 3自由度球面并联机构3-RRR静力全解[J]. 机械工程学报,2008,48(6)：169-176.
ZHOU Yulin,LIU Lei,GAO Feng. Static full-solution of spherical parallel mechanism 3-RRR with 3-DOF[J]. Chinese Journal of Mechanical Engineering,2008,48(6)：169-176.
[13] 潘存云,温熙森. 渐开线环形齿球齿轮传动原理与运动分析[J]. 机械工程学报. 2005,41(5)：1-9.
PAN Cunyun,WEN Xisen. Research on transmission principle and kinematic analysis for involute spherical gear[J]. Chinese Journal of Mechanical Engineering,2005,41(5)：1-9.
[14] HARRIS T A,KOTZALAS M N. Rolling bearing analysis[M]. 5th ed. Boca Raton：CRC Press Inc.,2006.
[15] ZHOU Changjiang,CHEN Siyu. Modeling and calculation of impact friction caused by corner contact in gear transmission[J]. Chinese Journal of Mechanical Engineering,2014,27(5)：958-964.
[16] 张然,武建勋. 圣维南原理的一般性能量衰减指标[J]. 工程力学,2008,25(3)：14-17,25.
ZHANG Ran,WU Jianxun. Common energy decay indices of saint-venant’s principle[J]. Engineering Mechanics,2008,25(3)：14-17,25.