基于ABAQUS的渐开线斜齿圆柱齿轮传动误差研究
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摘要
为了研究渐开线斜齿圆柱齿轮的传动误差,提出了渐开线斜齿轮的扭转振动模型。研究了渐开线斜齿圆柱齿轮的静态和动态传动误差,分析了不同载荷下动态传动误差曲线的变化规律,并与静态传动误差进行了对比分析。研究表明,载荷越大,静、动态传动误差的绝对值越大,但动态传动误差的峰值差并不是单纯地递增或递减,而是呈凹线型分布,存在一个最小值;静态传动误差曲线的波动较平稳,动态传动误差曲线在剧烈波动后快速趋于平稳。同时还研究了材料阻尼对动态传动误差的影响,研究表明:材料的临界阻尼越小,渐开线斜齿圆柱齿轮传动越不平稳。
The present paper comes up with torsional vibration model of involute helical gear in order to study the transmission error of involute helical cylindrical gear. It finished the analysis about transmission error of involute helical gear both in the static and the dynamic, at the same time, it showed the laws of dynamic transmission error curve under different loads, which would be compared with the laws of static transmission error curve. The research showed that the greater the load, the larger the absolute value of transmission error, however, the peak difference of dynamic transmission error is not a linear distribution for there exists a minimum, namely, the concave distribution; The results proved that the fluctuation of the static transmission error curve is steady and smooth and dynamic transmission error curve will tend to steady state after severe fluctuating. Meanwhile, it showed the impact of damping material on dynamic transmission error: the smaller value of the material critical damping, the more unstable involute helical tooth cylindrical gear.
The present paper comes up with torsional vibration model of involute helical gear in order to study the transmission error of involute helical cylindrical gear. It finished the analysis about transmission error of involute helical gear both in the static and the dynamic, at the same time, it showed the laws of dynamic transmission error curve under different loads, which would be compared with the laws of static transmission error curve. The research showed that the greater the load, the larger the absolute value of transmission error, however, the peak difference of dynamic transmission error is not a linear distribution for there exists a minimum, namely, the concave distribution; The results proved that the fluctuation of the static transmission error curve is steady and smooth and dynamic transmission error curve will tend to steady state after severe fluctuating. Meanwhile, it showed the impact of damping material on dynamic transmission error: the smaller value of the material critical damping, the more unstable involute helical tooth cylindrical gear.
引文
[1]何泽银.齿轮系统传动误差耦合分析与振动噪声优化研究[D].重庆:重庆大学,2015.He Zeyin.Transmission error Analysis and Optimization Research on Vibration and Noise of Gear System[D].Chong Qing,China:Chongqing University,2015.
[2]刘红彬,史永生,张磊.基于多体动力学的转炉扭振仿真研究[J].系统仿真学报,2015,27(7):1652-1657.Liu Hongbin,Shi Yongsheng,Zhang Lei.Simulation of Converter Torsional Vibration Based on Multi-body Dynamics[J].Journal of System Simulation(S1004-731X),2015,27(7):1652-1657.
[3]胡俊华,段礼祥,高广民.基于ADAMS的齿轮传动误差动力学仿真研究[J].制造业自动化,2016,38(4):112-114.Hu junhua,Duan Lixiang,Gao Guangmin.Dynamics simulation of gear transmission error based on ADAMS[J].Manufacturing Automation,2016,38(4):112-114.
[4]汪中厚,王杰,马鹏程.真实齿面的螺旋锥齿轮动传动误差研究[J].振动与冲击,2014,33(15):138-143.Wang zhonghou,Wang Jie,Ma Pengcheng.Dynamic transmission error analysis of spiral bevel gears with actual tooth surfaces[J].Journal of bibration and shock,2014,33(15):138-143.
[5]Jungho Park,Jong Moon Ha,Hyunseok Oh,et al.Model-based fault diagnosis of a planetary gear:a novel approach using transmission error[J].IEEE Transactions on Reliability(S0018-9529),2016,65(4):1830-1841.
[6]汪中厚,王杰,王巧玲.基于有限元法的螺旋锥齿轮传动误差研究[J].振动与冲击,2014,33(14):165-170.Wang zhonghou,Wang Jie,Wang Qiaoling.Transmission error of spiral bevel gear based on finite element method[J].Journal of Vibration and Shock,2014,33(14):165-170.
[7]唐进元,刘艳平.直齿面齿轮加载啮合有限元仿真分析[J].机械工程学报,2012,48(5):124-131.Tang Jinyuan,Liu Yanping.Loaded Meshing Simulation of Face-gear Drive with Spur Involute Pinion Based on Finite Element Analysis[J].Journal of Mechanical Engineering,2012,48(5):124-131.
[8]蒋进科,方宗德,苏进展.高阶传动误差斜齿轮修形设计与加工[J].哈尔滨工业大学学报,2014,46(9):43-49.Jiang Jinke,Fang Zongde,Su Jinzhan.Design and grinding for modified helical gears with a high-order transmission error[J].Journal of Harbin Institute of Technology,2014,46(9):43-49.
[9]张黎明,汪中厚.基于传动误差反馈的齿形设计方法[J].机械传动,2016,40(3):71-73.Zhang Liming,Wang Zhonghou.Design Method of Tooth Profile based on Transmission Error Feedback[J].Journal of Mechanical Transmission,2016,40(3):71-73.
[10]邵文,唐进元,李松.基于传动误差数据的齿轮误差检测方法与系统[J].测控技术,2011,30(11):91-95.Shao Wen,Tang Jinyuan,Li Song.Gear Errors Measuring Method and System Based on Transmission Error[J].Measurement&Control Technology,2011,30(11):91-95.
[11]王彦刚,崔彦平,李慧勇.基于传动误差检测法的早期齿轮磨损故障诊断[J].振动与冲击,2012,31(13):81-84.Wang Yangang,Cui Yanping,Li Huiyong.Fault diagnosis on incipient localized tooth wear of gear based on transmission error detection method[J].Journal of Vibration and Shock,2012,31(13):81-84.
[12]郭栋,石晓辉,施全.多级齿轮传动系统传动误差快速预测[J].四川大学学报,2012,44(3):224-228.Guo Dong,Shi Xiaohui,Shi Quan.Research on Fast Prediction of Multistage Gear Transmission Error[J].Journal of Sichuan University,2012,44(3):224-228.
[13]Lin Tengjiao,He Zeyin,Geng Feiyu,et al.Prediction and experimental study on structure and radiation noise of subway gearbox.Journal of Vibroengineering(S1392-8716),2013,15(4):1838-1846.
[14]汪中厚.准双曲面齿轮动态性能仿真[M].北京:科学出版社,2013.Wang Zhonghou.Simulation of hypoid gears dynamic performance[M].Beijing,China:Science Press,2013.
[15]毛君.机械振动学[M].北京:北京理工大学出版社,2016.Mao Jun.Mechanical vibration[M].Beijing,China:Beijing Institute of Technology Press,2016.
[16]蒋进科,方宗德,苏进展.基于承载传动误差幅值最小的斜齿轮齿面修形优化设计[J].航空动力学报,2013,28(7):1637-1643.Jiang Jinke,Fang Zongde,Su Jinzhan.Optimal design of modified helical gear tooth surfaces based on minimum amplitude of loaded transmission error[J].Journal of Aerospace Power,2013,28(7):1637-1643.
[17]邓效忠,徐爱军,张静.基于时标域频谱的齿轮传动误差分析与试验研究[J].机械工程学报,2014,50(1):85-90.Deng Xiaozhong,Xu Aijun,Zhang Jing.Analysis and Experimental Research on the Gear Transmission Error Based on Pulse Time Spectrum[J].Journal of Mechanical Engineering,2014,50(1):85-90.
[2]刘红彬,史永生,张磊.基于多体动力学的转炉扭振仿真研究[J].系统仿真学报,2015,27(7):1652-1657.Liu Hongbin,Shi Yongsheng,Zhang Lei.Simulation of Converter Torsional Vibration Based on Multi-body Dynamics[J].Journal of System Simulation(S1004-731X),2015,27(7):1652-1657.
[3]胡俊华,段礼祥,高广民.基于ADAMS的齿轮传动误差动力学仿真研究[J].制造业自动化,2016,38(4):112-114.Hu junhua,Duan Lixiang,Gao Guangmin.Dynamics simulation of gear transmission error based on ADAMS[J].Manufacturing Automation,2016,38(4):112-114.
[4]汪中厚,王杰,马鹏程.真实齿面的螺旋锥齿轮动传动误差研究[J].振动与冲击,2014,33(15):138-143.Wang zhonghou,Wang Jie,Ma Pengcheng.Dynamic transmission error analysis of spiral bevel gears with actual tooth surfaces[J].Journal of bibration and shock,2014,33(15):138-143.
[5]Jungho Park,Jong Moon Ha,Hyunseok Oh,et al.Model-based fault diagnosis of a planetary gear:a novel approach using transmission error[J].IEEE Transactions on Reliability(S0018-9529),2016,65(4):1830-1841.
[6]汪中厚,王杰,王巧玲.基于有限元法的螺旋锥齿轮传动误差研究[J].振动与冲击,2014,33(14):165-170.Wang zhonghou,Wang Jie,Wang Qiaoling.Transmission error of spiral bevel gear based on finite element method[J].Journal of Vibration and Shock,2014,33(14):165-170.
[7]唐进元,刘艳平.直齿面齿轮加载啮合有限元仿真分析[J].机械工程学报,2012,48(5):124-131.Tang Jinyuan,Liu Yanping.Loaded Meshing Simulation of Face-gear Drive with Spur Involute Pinion Based on Finite Element Analysis[J].Journal of Mechanical Engineering,2012,48(5):124-131.
[8]蒋进科,方宗德,苏进展.高阶传动误差斜齿轮修形设计与加工[J].哈尔滨工业大学学报,2014,46(9):43-49.Jiang Jinke,Fang Zongde,Su Jinzhan.Design and grinding for modified helical gears with a high-order transmission error[J].Journal of Harbin Institute of Technology,2014,46(9):43-49.
[9]张黎明,汪中厚.基于传动误差反馈的齿形设计方法[J].机械传动,2016,40(3):71-73.Zhang Liming,Wang Zhonghou.Design Method of Tooth Profile based on Transmission Error Feedback[J].Journal of Mechanical Transmission,2016,40(3):71-73.
[10]邵文,唐进元,李松.基于传动误差数据的齿轮误差检测方法与系统[J].测控技术,2011,30(11):91-95.Shao Wen,Tang Jinyuan,Li Song.Gear Errors Measuring Method and System Based on Transmission Error[J].Measurement&Control Technology,2011,30(11):91-95.
[11]王彦刚,崔彦平,李慧勇.基于传动误差检测法的早期齿轮磨损故障诊断[J].振动与冲击,2012,31(13):81-84.Wang Yangang,Cui Yanping,Li Huiyong.Fault diagnosis on incipient localized tooth wear of gear based on transmission error detection method[J].Journal of Vibration and Shock,2012,31(13):81-84.
[12]郭栋,石晓辉,施全.多级齿轮传动系统传动误差快速预测[J].四川大学学报,2012,44(3):224-228.Guo Dong,Shi Xiaohui,Shi Quan.Research on Fast Prediction of Multistage Gear Transmission Error[J].Journal of Sichuan University,2012,44(3):224-228.
[13]Lin Tengjiao,He Zeyin,Geng Feiyu,et al.Prediction and experimental study on structure and radiation noise of subway gearbox.Journal of Vibroengineering(S1392-8716),2013,15(4):1838-1846.
[14]汪中厚.准双曲面齿轮动态性能仿真[M].北京:科学出版社,2013.Wang Zhonghou.Simulation of hypoid gears dynamic performance[M].Beijing,China:Science Press,2013.
[15]毛君.机械振动学[M].北京:北京理工大学出版社,2016.Mao Jun.Mechanical vibration[M].Beijing,China:Beijing Institute of Technology Press,2016.
[16]蒋进科,方宗德,苏进展.基于承载传动误差幅值最小的斜齿轮齿面修形优化设计[J].航空动力学报,2013,28(7):1637-1643.Jiang Jinke,Fang Zongde,Su Jinzhan.Optimal design of modified helical gear tooth surfaces based on minimum amplitude of loaded transmission error[J].Journal of Aerospace Power,2013,28(7):1637-1643.
[17]邓效忠,徐爱军,张静.基于时标域频谱的齿轮传动误差分析与试验研究[J].机械工程学报,2014,50(1):85-90.Deng Xiaozhong,Xu Aijun,Zhang Jing.Analysis and Experimental Research on the Gear Transmission Error Based on Pulse Time Spectrum[J].Journal of Mechanical Engineering,2014,50(1):85-90.