少齿差星轮传动多目标优化及其强度仿真分析
|
摘要
少齿差星轮传动存在弹性啮合效应,其真实承载能力数倍于按传统齿轮设计理论所得的计算值。作者基于多齿弹性接触效应,以星轮核心单元啮合效率最大、体积最小以及内外齿轮等强度为优化目标,以齿轮基本参数为设计变量,建立了少齿差星轮传动多目标优化数学模型。优化结果表明:内外齿轮强度接近,啮合效率99.65%,结构体积下降29.3%。运用ANSYS Workbench对少齿差星轮进行静力学仿真,验证了多齿弹性接触效应载荷分配系数计算方法的正确性,同时得到轮齿的最大应力位置与理论计算一致、应力值误差均小于6%,满足工程精度要求,验证了多齿弹性啮合齿轮设计理论的正确性以及优化方案的合理性。
Due to the elastic meshing effect existed in planetary reducer with small tooth number difference,its real carrying capacity is many times greater than the calculation value obtained by the traditional gear design theory. Therefore,based on the elastic multi- tooth contact effect,taking the basic parameters of gear as design variables,and a multi- objective optimization model of small tooth difference planetary drive is established,while targeting on maximum efficiency as well as smallest volume and the internal and external gear equal strength of the core unit of the planet wheel. The optimization results show that the internal and external gear strength is close enough,and the meshing efficiency raised to 99. 65%,construction volume decreased by29. 3%. The ANSYS Workbench is applied for the statics simulation of the planetary reducer with small tooth difference. The correctness of the multi- tooth elastic contact load distribution calculation method is verified.The maximum stress position and value is consistent with the theoretical calculation results with the error less than 6. 0%,meeting the engineering accuracy requirements. The validity of the multi- tooth elastic meshing gear design theory and reasonableness of optimization scheme are verified.
Due to the elastic meshing effect existed in planetary reducer with small tooth number difference,its real carrying capacity is many times greater than the calculation value obtained by the traditional gear design theory. Therefore,based on the elastic multi- tooth contact effect,taking the basic parameters of gear as design variables,and a multi- objective optimization model of small tooth difference planetary drive is established,while targeting on maximum efficiency as well as smallest volume and the internal and external gear equal strength of the core unit of the planet wheel. The optimization results show that the internal and external gear strength is close enough,and the meshing efficiency raised to 99. 65%,construction volume decreased by29. 3%. The ANSYS Workbench is applied for the statics simulation of the planetary reducer with small tooth difference. The correctness of the multi- tooth elastic contact load distribution calculation method is verified.The maximum stress position and value is consistent with the theoretical calculation results with the error less than 6. 0%,meeting the engineering accuracy requirements. The validity of the multi- tooth elastic meshing gear design theory and reasonableness of optimization scheme are verified.
引文
[1]杨锡和.关于少齿差内啮合实际接触齿数及承载能力的研究[J].雷达与对抗,1990(1):11-19.
[2]刘丹,唐德威,邓宗全,等.少齿差齿轮传动承载能力分析及体积优化[J].机械设计与制造,2012(12):39-41.
[3]赵宁,杨杰.高重合度圆柱齿轮传动多目标优化设计[J].机械传动,2012,36(7):43-46.
[4]范元勋,王华坤.基于遗传算法的少齿差行星齿轮传动参数优化设计[J].机械设计与制造工程,2002,31(6):16-18.
[5]舒小龙,夏齐霄.少齿数差内啮合齿轮的强度计算[J].机械设计,2002,19(10):35-37.
[6]舒小龙.渐开线少齿差传动的轮齿载荷研究[J].北京联合大学学报(自然科学版),1991(2):44-52.
[7]陈立周.机械优化设计方法[M].北京:冶金工业出版社,1995:151-163.
[8]王家序,余波,李俊阳,等.孔销式少齿差行星减速器的多目标优化及动力学仿真分析[J].湖南大学学报(自然科学版),2013,40(12):50-54.
[9]龚纯,王正林.精通MATLAB最优化计算[M].北京:电子工业出版社,2009:175-206.
[10]LI S.Contact problem and numeric method of a planetary drive with small teeth number difference[J].Mechanism and Machine Theory,2008,43(9):1065-1086.
[11]陈万吉,胡志强.三维摩擦接触问题算法精度和收敛性研究[J].大连理工大学学报,2003,43(5):541-547.
[2]刘丹,唐德威,邓宗全,等.少齿差齿轮传动承载能力分析及体积优化[J].机械设计与制造,2012(12):39-41.
[3]赵宁,杨杰.高重合度圆柱齿轮传动多目标优化设计[J].机械传动,2012,36(7):43-46.
[4]范元勋,王华坤.基于遗传算法的少齿差行星齿轮传动参数优化设计[J].机械设计与制造工程,2002,31(6):16-18.
[5]舒小龙,夏齐霄.少齿数差内啮合齿轮的强度计算[J].机械设计,2002,19(10):35-37.
[6]舒小龙.渐开线少齿差传动的轮齿载荷研究[J].北京联合大学学报(自然科学版),1991(2):44-52.
[7]陈立周.机械优化设计方法[M].北京:冶金工业出版社,1995:151-163.
[8]王家序,余波,李俊阳,等.孔销式少齿差行星减速器的多目标优化及动力学仿真分析[J].湖南大学学报(自然科学版),2013,40(12):50-54.
[9]龚纯,王正林.精通MATLAB最优化计算[M].北京:电子工业出版社,2009:175-206.
[10]LI S.Contact problem and numeric method of a planetary drive with small teeth number difference[J].Mechanism and Machine Theory,2008,43(9):1065-1086.
[11]陈万吉,胡志强.三维摩擦接触问题算法精度和收敛性研究[J].大连理工大学学报,2003,43(5):541-547.