多档位行星变速传动系统动力学参数优化修改
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摘要
针对多档位行星变速传动系统因为参数选取不当致使多个档位存在扭转共振的问题,提出以系统固有频率对参数相对灵敏度为约束条件,采用相对初始参数变化率最小的动态优化目标函数和动态约束边界的多步遗传优化算法,对系统进行了多档位动力学参数优化修改。对采用不同优化步长情况下以基于相对初始参数最优和基于单步最优为目标函数进行了对比研究,并对行星传动系统固有频率对参数灵敏度用于传动系统多档位和单个档位参数优化修改的特点进行了分析。结果表明:以相对初始参数最优的多步遗传优化算法可以获得相比以单步最优的多步遗传优化算法更好的优化结果;行星变速传动系统单个档位固有频率对参数的灵敏度不能直接作为多个档位同时进行参数优化修改的参考。参数优化修改后系统所有档位在工作转速范围内都不会发生扭振共振,可为多档位行星变速传动系统设计提供一定的指导。
To prevent torsional resonance of multi-gears of a multi-speed planetary transmission system because of improper choose of parameters,dynamic optimization and modification of the parameters for the system were conducted by using the multi-step genetic algorithm which adopts relative sensitivity of natural frequencies. Minimization parameter change rate relative to its initial value was taken as the dynamic objective function and dynamic constraint boundary.Based on the comparison of the initial parameters and the single-step optimization as the objective function, the characteristic of natural frequencies to parameters of planetary transmission system applied to multi-gears and single-gear was analyzed. The result indicates that better optimization result can be achieved in the multi-step genetic algorithm by optimizing the change rate of parameters relative to its initial value compared with optimizing every step. The natural frequencies of single-gear planetary transmission system can not be used as guidance of multi-gears system directly.Resonance will not happen at the range of working speed of the system after optimization and modification of parameters.This work provides guidance for the design of planetary transmissions.
To prevent torsional resonance of multi-gears of a multi-speed planetary transmission system because of improper choose of parameters,dynamic optimization and modification of the parameters for the system were conducted by using the multi-step genetic algorithm which adopts relative sensitivity of natural frequencies. Minimization parameter change rate relative to its initial value was taken as the dynamic objective function and dynamic constraint boundary.Based on the comparison of the initial parameters and the single-step optimization as the objective function, the characteristic of natural frequencies to parameters of planetary transmission system applied to multi-gears and single-gear was analyzed. The result indicates that better optimization result can be achieved in the multi-step genetic algorithm by optimizing the change rate of parameters relative to its initial value compared with optimizing every step. The natural frequencies of single-gear planetary transmission system can not be used as guidance of multi-gears system directly.Resonance will not happen at the range of working speed of the system after optimization and modification of parameters.This work provides guidance for the design of planetary transmissions.
引文
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[13]QU Z Q,SELVAM R.Hybrid expansion method for frequency responses and their sensitivities,Part II:viscously damped systems[J].Journal of Sound and Vibration,2000,238(3):369-388.
[14]王东华,刘占生,窦唯.基于混合遗传算法的转子系统优化设计[J].振动与冲击,2009,28(5):87-91.WANG Donghua,LIU Zhansheng,DOU Wei.Rotor dynamics optimization based on a hybrid genetic algorithm[J].Journal of Vibration and Shock,2009,28(5):87-91.
[15]钟一谔,何衍宗,王正,等.转子动力学[M].北京:清华大学出版社,1987:95-97.
[16]CHEN S,QIU Z,SONG D.A new method for computing the upper and lower bounds on frequecies of structures with interval parameters[J].Mechanics Research Communications,1995,21(6):583-592.
[2]GUO Y,PARKER R G.Sensitivity of general compound planetary gear natural frequencies and vibration modes to model parameters[J].Journal of Vibration and Acoustics,2010,132(1):011006.
[3]刘辉,项昌乐,郑慕侨.车辆动力传动系固有特性灵敏度分析及动力学修改[J].汽车工程,2003,25(6):591-594.LIU Hui,XIANG Changle,ZHENG Muqiao.Sensitivity analysis and dynamic modification of natural characteristic in vehicle powertrain[J].Automotive Engineering,2003,25(6):591-594.
[4]XIANG C L,HUANG Y,LIU H.Response sensitivity and the assessment of nonlinear vibration using a nonlinear lateraltorsional coupling model of vehicle transmission system[J].Journal of Vibration&Acoustics,2015,137(3):031013-11.
[5]LIN J,PARKER R G.Sensitivity of planetary gear natural frequencies and vibration modes to model parameters[J].Journal of Sound and Vibration,1999,228(1):109-128.
[6]齐寅明,龚宪生,张干清,等.盾构刀盘驱动三级行星齿轮系统固有特性及灵敏度分析[J].振动与冲击,2013,32(15):14-19.QI Yinming,GONG Xiansheng,ZHANG Ganqing,et al.Natural characteristics and sensitivity analysis of a 3-stageplanetary gears train used in shield machine cutter driver[J].Journal of Vibration and Shock,2013,32(15):14-19.
[7]黄毅,刘辉,项昌乐,等.车辆传动系统非线性平移扭转耦合振动响应灵敏度研究[J].振动与冲击,2014,33(23):92-99.HUANG Yi,LIU Hui,XIANG Changle,et al.Response sensitivity of nonlinear translation-torsional vibration coupled model of a vehicle transmission system[J].Journal of Vibration and Shock,2014,33(23):92-99.
[8]刘辉,蔡仲昌,曹华夏,等.车辆动力传动系统扭转强迫振动响应灵敏度研究[J].兵工学报,2011,32(8):939-944.LIU Hui,CAI Zhongchang,CAO Huaxia,et al.Sensitivity analysis of forced torsional vibration on vehicle powertrain[J].Acta Armamentarii,2011,32(8):939-944.
[9]项昌乐,廉晓辉,周连景.针对实际传动系统的灵敏度分析与动力学修改[J].中国机械工程,2006,17(3):325-328.XIANG Changle,LIAN Xiaohui,ZHOU Lianjing.Sensitivity analysis and dynamic modification based on the physics model of vehicular powertrain[J].China Mechanical Engineering,2006,17(3):325-328.
[10]张代胜,王浩.基于灵敏度分析的汽车动力传动系扭振特性优化[J].中国机械工程,2013,24(5):685-689.ZHANG Daisheng,WANG Hao.Optimization of vehicle drivetrain torsional vibration characteristics based on sensitivity analysis[J].China Mechanical Engineering,2013,24(5):685-689.
[11]渐开线圆柱齿轮承载能力计算方法:GB/T 3480—1997[S].北京:国家技术监督局,1997.
[12]QU Z Q.Hybrid expansion method for frequency responses and their sensitivities,Part I:undamped systems[J].Journal of Sound and Vibration,2000,231(1):175-193.
[13]QU Z Q,SELVAM R.Hybrid expansion method for frequency responses and their sensitivities,Part II:viscously damped systems[J].Journal of Sound and Vibration,2000,238(3):369-388.
[14]王东华,刘占生,窦唯.基于混合遗传算法的转子系统优化设计[J].振动与冲击,2009,28(5):87-91.WANG Donghua,LIU Zhansheng,DOU Wei.Rotor dynamics optimization based on a hybrid genetic algorithm[J].Journal of Vibration and Shock,2009,28(5):87-91.
[15]钟一谔,何衍宗,王正,等.转子动力学[M].北京:清华大学出版社,1987:95-97.
[16]CHEN S,QIU Z,SONG D.A new method for computing the upper and lower bounds on frequecies of structures with interval parameters[J].Mechanics Research Communications,1995,21(6):583-592.