旋转向量减速器纯扭转模型固有频率和灵敏度分析
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摘要
为得到影响旋转向量减速器的固有特性和动态性能的关键因素,建立了减速器的纯扭转动力学模型,求解了系统在无阻尼条件下的固有频率和模态振型,并对半正定系统进行了坐标变换和无量纲化,得到了转换后系统的固有频率和各部件的动态响应曲线,以及在输入转速为10r/min、输出负载为30N·m工况下的系统传动误差曲线和对应频谱图。研究了固有频率相对于多种系统参数的灵敏度,得到转动惯量参数比刚度参数对系统固有频率影响更显著的结论。最后,搭建了减速器动力性能综合检测实验平台,实测了系统传动误差和对应频谱图,理论和试验的结合为旋转向量减速器研究和发展提供了一定的理论基础。
A pure torsional dynamic model was established for the study of inherent characteristics and dynamic performance of rotate vector reducer system.The natural frequencies and mode shapes of the model were obtained under no damping condition.The coordinate transformation method was used to eliminate the rigid body freedom of the system and the dimensionless method was used to get the same magnitude of parameters.After calculation,the natural frequencies and dynamic performance curves of the transformed system were obtained.In particular,under the condition of input angular velocity10 r/min and output load 30 N·m,the system transmission error curve and corresponding spectrum were obtained.Then,the sensitivity of the natural frequencies to system parameters was studied.Results show that the influence of inertia parameters on the natural frequencies are more significant than that of stiffness parameters.Finally,a test platform of RV reducer dynamic performance was built,and the real-time transmission error curve and corresponding spectrogram of a RV-40 E were obtained.The combination of theoretical and experimental results provides a theoretical basis for the research and development of RV reducers.
A pure torsional dynamic model was established for the study of inherent characteristics and dynamic performance of rotate vector reducer system.The natural frequencies and mode shapes of the model were obtained under no damping condition.The coordinate transformation method was used to eliminate the rigid body freedom of the system and the dimensionless method was used to get the same magnitude of parameters.After calculation,the natural frequencies and dynamic performance curves of the transformed system were obtained.In particular,under the condition of input angular velocity10 r/min and output load 30 N·m,the system transmission error curve and corresponding spectrum were obtained.Then,the sensitivity of the natural frequencies to system parameters was studied.Results show that the influence of inertia parameters on the natural frequencies are more significant than that of stiffness parameters.Finally,a test platform of RV reducer dynamic performance was built,and the real-time transmission error curve and corresponding spectrogram of a RV-40 E were obtained.The combination of theoretical and experimental results provides a theoretical basis for the research and development of RV reducers.
引文
[1]Ishida T,Wang H,Hidaka T,et al.Rotational transmission error of K-H-V planetary gears with cycloid gear(2nd report,effects of manufacturing and assembly error)[J].JSME International Journal:Serises C,1994,60(578):278-285.
[2]Hidaka T,Wang H,Ishida T,et al.Rotational transmission of K-H-V plantary gears with cycloid gear(1st report,analytical method of the rotational transmission error)[J].JSME International Journal:Serises C,1994,60(570):645-653.
[3]张大卫,王刚,黄田,等.RV减速机动力学建模与结构参数分析[J].机械工程学报,2001,37(1):69-73.Zhang Da-wei,Wang Gang,Huang Tian,et al.Dynamic formulation of RV reducer and analsis of structural parameters[J].Chinese Journal of Mechanical Engineering,2001,37(1):69-73.
[4]杨玉虎,朱临宇,陈振宇,等.RV减速器扭转刚度特性分析[J].天津大学学报:自然科学与工程技术版,2015,48(2):111-117.Yang Yu-hu,Zhu Lin-yu,Chen Zhen-yu,et al.Characteristic analysis of torsional stiffness of RV reducer[J].Journal of Tianjin University(Science Technology),2015,48(2):111-117.
[5]Chen Chuan,Yang Yu-hu.Structural characteristics of rotate vector reducer free vibration[J].Shock and Vibration,2017(1):4214-4370.
[6]韩林山,沈允文,董海军,等.2K-V型传动装置动态传动精度理论研究[J].机械工程学报,2007,43(6):81-86.Han Lin-shan,Shen Yun-wen,Dong Hai-jun,et al.Theoretical research on dynamic transmission accuracy for 2K-V type drive[J].Chinese Journal of Mechanical Engineering,2007,43(6):81-86.
[7]Han Lin-shan,Guo Fei.Global sensitivity analysis of transmission accuracy for RV-type cycloid-pin drive[J].Journal of Mechanical Science and Technology,2016,30(3):1225-1231.
[8]刘柏希,王文军,聂松辉.RV减速器扭转振动的固有特性及灵敏度分析[J].中国机械工程,2016,27(3):322-327.Liu Bai-xi,Wang Wen-jun,Nie Song-hui.Analysis of natural characteristic and sensitivtiy for torsional vibration of RV reducer[J].China Mechanical Engineering,2016,27(3):322-327.
[9]陈忠敏,侯力,段阳,等.新型摆线针轮行星减速器传动系统的振动[J].吉林大学学报:工学版,2018,48(1):174-185.Chen Zhong-min,Hou Li,Duan Yang,et al.Vibration characteristics analysis of the new pin-cycloid speed reducer[J].Journal of Jilin University(Engineering and Technology Edition),2018,48(1):174-185.
[10]刘景亚.二次包络少齿差行星齿轮传动啮合特性及动力学研究[D].重庆:重庆大学机械工程学院,2012.Liu Jing-ya.Study on meshing characteristics of the double-enveloping planetary gear drive with small tooth number difference and analysis of its dynamic behavior[D].Chongqing:College of Mechanical Engineering,Chongqing University,2012.
[11]韩清凯.机械振动系统的现代动态设计与分析[M].北京:科学出版社,2010.
[12]郑钰馨,奚鹰,李梦如,等.基于密切值法的RV减速器传动受力影响分析[J].中国工程机械学报,2017,15(2):153-157.Zheng Yu-xin,Xi Ying,Li Meng-ru,et al.Original error analysis on the second reduction part of RV reducer[J]. ChineseJournalofConstruction Machinery,2017,15(2):153-157.
[13]杨通强.斜齿行星传动动力学研究[D].天津:天津大学机械工程学院,2003.Yang Tong-qiang.A study on dynamics of helical planetary gear train[D].Tianjin:School of Mechanical Engineering,Tianjin University,2003.
[14]陶庆,孙文磊,周建星.考虑齿圈柔性的行星传动系统固有特性与灵敏度研究[J].西安交通大学学报,2015,49(3):113-120.Tao Qing,Sun Wen-lei,Zhou Jian-xing.Research on inherent characteristic and sensitivities of planetary gear transmission[J].Journal of Xi′an Jiaotong University,2015,49(3):113-120.
[2]Hidaka T,Wang H,Ishida T,et al.Rotational transmission of K-H-V plantary gears with cycloid gear(1st report,analytical method of the rotational transmission error)[J].JSME International Journal:Serises C,1994,60(570):645-653.
[3]张大卫,王刚,黄田,等.RV减速机动力学建模与结构参数分析[J].机械工程学报,2001,37(1):69-73.Zhang Da-wei,Wang Gang,Huang Tian,et al.Dynamic formulation of RV reducer and analsis of structural parameters[J].Chinese Journal of Mechanical Engineering,2001,37(1):69-73.
[4]杨玉虎,朱临宇,陈振宇,等.RV减速器扭转刚度特性分析[J].天津大学学报:自然科学与工程技术版,2015,48(2):111-117.Yang Yu-hu,Zhu Lin-yu,Chen Zhen-yu,et al.Characteristic analysis of torsional stiffness of RV reducer[J].Journal of Tianjin University(Science Technology),2015,48(2):111-117.
[5]Chen Chuan,Yang Yu-hu.Structural characteristics of rotate vector reducer free vibration[J].Shock and Vibration,2017(1):4214-4370.
[6]韩林山,沈允文,董海军,等.2K-V型传动装置动态传动精度理论研究[J].机械工程学报,2007,43(6):81-86.Han Lin-shan,Shen Yun-wen,Dong Hai-jun,et al.Theoretical research on dynamic transmission accuracy for 2K-V type drive[J].Chinese Journal of Mechanical Engineering,2007,43(6):81-86.
[7]Han Lin-shan,Guo Fei.Global sensitivity analysis of transmission accuracy for RV-type cycloid-pin drive[J].Journal of Mechanical Science and Technology,2016,30(3):1225-1231.
[8]刘柏希,王文军,聂松辉.RV减速器扭转振动的固有特性及灵敏度分析[J].中国机械工程,2016,27(3):322-327.Liu Bai-xi,Wang Wen-jun,Nie Song-hui.Analysis of natural characteristic and sensitivtiy for torsional vibration of RV reducer[J].China Mechanical Engineering,2016,27(3):322-327.
[9]陈忠敏,侯力,段阳,等.新型摆线针轮行星减速器传动系统的振动[J].吉林大学学报:工学版,2018,48(1):174-185.Chen Zhong-min,Hou Li,Duan Yang,et al.Vibration characteristics analysis of the new pin-cycloid speed reducer[J].Journal of Jilin University(Engineering and Technology Edition),2018,48(1):174-185.
[10]刘景亚.二次包络少齿差行星齿轮传动啮合特性及动力学研究[D].重庆:重庆大学机械工程学院,2012.Liu Jing-ya.Study on meshing characteristics of the double-enveloping planetary gear drive with small tooth number difference and analysis of its dynamic behavior[D].Chongqing:College of Mechanical Engineering,Chongqing University,2012.
[11]韩清凯.机械振动系统的现代动态设计与分析[M].北京:科学出版社,2010.
[12]郑钰馨,奚鹰,李梦如,等.基于密切值法的RV减速器传动受力影响分析[J].中国工程机械学报,2017,15(2):153-157.Zheng Yu-xin,Xi Ying,Li Meng-ru,et al.Original error analysis on the second reduction part of RV reducer[J]. ChineseJournalofConstruction Machinery,2017,15(2):153-157.
[13]杨通强.斜齿行星传动动力学研究[D].天津:天津大学机械工程学院,2003.Yang Tong-qiang.A study on dynamics of helical planetary gear train[D].Tianjin:School of Mechanical Engineering,Tianjin University,2003.
[14]陶庆,孙文磊,周建星.考虑齿圈柔性的行星传动系统固有特性与灵敏度研究[J].西安交通大学学报,2015,49(3):113-120.Tao Qing,Sun Wen-lei,Zhou Jian-xing.Research on inherent characteristic and sensitivities of planetary gear transmission[J].Journal of Xi′an Jiaotong University,2015,49(3):113-120.
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