双滚柱少齿差行星传动齿形综合与精度优化
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摘要
围绕精密机械装备对精密传动的需求,针对双滚柱少齿差行星传动进行齿形综合研究和精度优化设计.利用曲面单参数的包络方法建立中心轮和行星轮的共轭齿廓方程,对齿廓方程进行曲率分析,提出利用圆形滚柱作为行星轮齿的可行性.再根据齿廓曲率半径的极值确定出圆形滚柱行星轮齿的中心,建立圆形滚柱行星轮齿的齿形方程.为保证传动精度,建立双滚柱少齿差行星传动的齿形优化模型,采用粒子群优化算法,得到满足设计条件的齿形参数优化结果.对优化结果进行传动误差分析,验证双滚柱少齿差行星传动作为精密传动的可行性.
According to the requirement of precision transmission for the precision mechanical equipment, the tooth profile synthesis and the precision optimization of the double rollers planetary transmission with small tooth number difference is presented. Firstly, the conjugate tooth profile equations of the center gear and the planetary gear are established using the envelope theory for an one-parameter family of surface. Then, the curvature of the tooth profile equation is analyzed, and the circular rollers can be used as the planetary gear tooth as possible. The center of the circular roller planetary gear tooth is determined by the extremum of the tooth profile curvature radius, and the tooth profile equation of the circular roller planetary gear tooth is established. In order to ensure the transmission accuracy, the tooth profile optimization model is established, and the particle swarm optimization algorithm is used to get the optimization result of tooth profile parameters which satisfies the design conditions. Finally, the transmission error of the optimized result is analyzed, and the feasibility of the double rollers planetary transmission with small tooth difference is verified as a precision transmission.
According to the requirement of precision transmission for the precision mechanical equipment, the tooth profile synthesis and the precision optimization of the double rollers planetary transmission with small tooth number difference is presented. Firstly, the conjugate tooth profile equations of the center gear and the planetary gear are established using the envelope theory for an one-parameter family of surface. Then, the curvature of the tooth profile equation is analyzed, and the circular rollers can be used as the planetary gear tooth as possible. The center of the circular roller planetary gear tooth is determined by the extremum of the tooth profile curvature radius, and the tooth profile equation of the circular roller planetary gear tooth is established. In order to ensure the transmission accuracy, the tooth profile optimization model is established, and the particle swarm optimization algorithm is used to get the optimization result of tooth profile parameters which satisfies the design conditions. Finally, the transmission error of the optimized result is analyzed, and the feasibility of the double rollers planetary transmission with small tooth difference is verified as a precision transmission.
引文
[1] 村田精密股份有限公司.TSUNTIEN产品系列型录[Z-OL].(2004-09-10) [2018-06-17].http://www.tsuntien.com.tw.
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[6] 刘景亚,王蜀生.双滚柱少齿差行星传动设计及传动误差分析[J].机械传动,2015,39(12):95-99.
[7] HWANG Y W,HSIEH C F.Determination of surface singularities of a cycloidal gear drive with inner meshing[J].Mathematical and Computer Modelling,2007,45:340-354.
[8] 吴素珍,何卫东.RV针摆传动齿面接触强度非线性分析[J].郑州大学学报,2015,36(4):100-104.
[9] 齿轮手册委员会.齿轮手册[M].北京:机械工业出版社,2004:795-796.
[10] 余胜威.Matlab优化算法案例分析与运用[M].北京:清华大学出版社,2014:199-226.
[11] 姚文席.摆线针轮行星减速器传动误差分析[J].机械传动,1998,22(4):14-18.
[12] 黄斌.渐开线少齿差行星减速器传动误差研究[D].湘潭:湘潭大学,2015.
[2] LAI T S.Design and machining of the epicycloid planet of cycloid drive[J].Int J Adv Manuf Tech,2006,28:665-670.
[3] LAI T S.Geometric design of roller drives with cylindrical meshing elements[J].Mech Mach Theory,2005,40:55-67.
[4] 陈兵奎,房婷婷.摆线针轮行星传动共轭啮合原理[J].中国科学,2008,38(1):148-160.
[5] TSUKADA T,TAKASU I,ANNO Y,et al.An optimum design of planetary reduction gear using rollers as gear teeth[J].Bulletin of the JSME,1980,23(183):1530-1535.
[6] 刘景亚,王蜀生.双滚柱少齿差行星传动设计及传动误差分析[J].机械传动,2015,39(12):95-99.
[7] HWANG Y W,HSIEH C F.Determination of surface singularities of a cycloidal gear drive with inner meshing[J].Mathematical and Computer Modelling,2007,45:340-354.
[8] 吴素珍,何卫东.RV针摆传动齿面接触强度非线性分析[J].郑州大学学报,2015,36(4):100-104.
[9] 齿轮手册委员会.齿轮手册[M].北京:机械工业出版社,2004:795-796.
[10] 余胜威.Matlab优化算法案例分析与运用[M].北京:清华大学出版社,2014:199-226.
[11] 姚文席.摆线针轮行星减速器传动误差分析[J].机械传动,1998,22(4):14-18.
[12] 黄斌.渐开线少齿差行星减速器传动误差研究[D].湘潭:湘潭大学,2015.