考虑齿顶修形和时变中心距的渐开线直齿轮振动特性研究
|
摘要
针对渐开线直齿轮,考虑时变中心距推导了动态啮合角、动态间隙的解析表达式,考虑时变转速、时变中心距和齿顶修形,并采用解析方法得到了齿轮的动态啮合刚度,在此基础上建立了齿轮啮合模型。考虑几何偏心、齿向偏载力矩和陀螺力矩,建立了单级齿轮传动系统10自由度横-扭-摆耦合非线性动力学模型。将非线性动力学模型和齿轮啮合模型进行耦合计算,对比分析了转速和扭矩对不同修形齿轮振动特性的影响。结果表明:当转速超过某临界值,短修形齿轮的振动载荷大于无修形齿轮,而长修形齿轮不存在临界转速;随着扭矩的增加,无修形齿轮的啮合力峰峰值呈线性比例增加,短修形齿轮和长修形齿轮的啮合力峰峰值近似呈先减小后增大的趋势变化,说明在某扭矩下修形齿轮的振动载荷最小,且长修形对应的扭矩大于短修形;短修形和长修形齿轮均存在临界扭矩,当扭矩小于该临界值时,修形齿轮的振动载荷大于无修形齿轮,且长修形对应临界扭矩小于短修形。
For spur gears,the analytic formulas of dynamic pressure angle and backlash are derived with considering the timevarying center distance.Taking into account the time-varying rotational speed,time-varying center distance and tip relief,we calculated the dynamic mesh stiffness with the analytic method.Thus,the gear mesh dynamic model is established.In consideration of the geometry eccentricity,gyroscopic effect and load distribution factor along the tooth width,a 10-DOF lateral-torsional-rocking coupled nonlinear dynamic model of a spur gear system was established.The nonlinear dynamic model and the gear mesh dynamic model are coupled.Comparison analysis on the vibration characteristic with different speeds and torques are carried out.The results show that when the speed exceeds certain value,the dynamic load for the short tip relief are bigger than the non-modification gear,while the long tip relief do not have critical speed.With the increase of the torque,the variation trend of the dynamic load will increase proportionally for the non-modification gear,while increase at first and then decrease for the long and short tip relief,and so an optimal amount of torque exists to acheive a minimum dynamic load factor.There exist critical torques for both long and short tip relief such that when the torque is smaller than these critical value,the dynamic load of modification gear are bigger than the non-modification gear,and the value for the long tip relief are bigger than the short tip relief.
For spur gears,the analytic formulas of dynamic pressure angle and backlash are derived with considering the timevarying center distance.Taking into account the time-varying rotational speed,time-varying center distance and tip relief,we calculated the dynamic mesh stiffness with the analytic method.Thus,the gear mesh dynamic model is established.In consideration of the geometry eccentricity,gyroscopic effect and load distribution factor along the tooth width,a 10-DOF lateral-torsional-rocking coupled nonlinear dynamic model of a spur gear system was established.The nonlinear dynamic model and the gear mesh dynamic model are coupled.Comparison analysis on the vibration characteristic with different speeds and torques are carried out.The results show that when the speed exceeds certain value,the dynamic load for the short tip relief are bigger than the non-modification gear,while the long tip relief do not have critical speed.With the increase of the torque,the variation trend of the dynamic load will increase proportionally for the non-modification gear,while increase at first and then decrease for the long and short tip relief,and so an optimal amount of torque exists to acheive a minimum dynamic load factor.There exist critical torques for both long and short tip relief such that when the torque is smaller than these critical value,the dynamic load of modification gear are bigger than the non-modification gear,and the value for the long tip relief are bigger than the short tip relief.
引文
[1]李润方,王建军.齿轮系统动力学[M].北京:科学出版社,1996.LI Runfang,WANG Jianjun.Gear System Dynamics[M].Beijing:Science Press,1996.
[2]李明,孙涛,胡海岩.齿轮传动转子-轴承系统动力学的研究进展[J].振动工程学报,2002,15(3):249-256.Li Ming,Sun Tao,Hu Haiyan.Review on dynamics of geared rotor-bearing systems[J].Journal of Vibration Engineering,2002,15(3):249-256.
[3]Wang J,Li R,Peng X.Survey of nonlinear vibration of gear transmission systems[J].ASME,2003,56(3):309-329.
[4]Kahraman A,Blankenship G.Experiments on nonlinear dynamic behavior of an oscillator with clearance and periodically time-varying parameters[J].Journal of Applied Mechanics,1997,64:217-226.
[5]Kang M,Kahraman A.Measurement of vibratory motions of gears supported by compliant shafts[J].Mechanical Systems and Signal Processing,2012,29:391-403.
[6]Kahraman A,Singh R.Nonlinear dynamics of gearrotor bearing system with multi-backlash[J].Journal of Sound and Vibration,1991,144:469-506.
[7]Lassaad W,Tahar F,Mohamed H.Nonlinear dynamics of a two-stage gear system with mesh stiffness fluctuation,bearing flexibility and backlash[J].Mechanism and Machine Theory,2009,44:1058-1069.
[8]Li S,Kahraman A.A tribo-dynamic model of a spur gear pair[J].Journal of Sound and Vibration,2013,332:4963-4978.
[9]Chen Z,Shao Y,LIM T.Nonlinear dynamic simulation of gear response under the idling condition[J].International Journal of Automotive Technology,2012,13:541-552.
[10]Kim W,Yoo H,Chung J.Dynamic analysis for a pair of spur gears with translational motion due to bearing deformation[J].Journal of Sound and Vibration,2010,329:4409-4421.
[11]Woohyung K,Lee J,Chung J.Dynamic analysis for a planetary gear with time varying pressure angles and contact ratios[J].Journal of Sound and Vibration,2012,331:883-901.
[12]Chen S,Tang J,Luo C,et al.Nonlinear dynamic characteristics of geared rotor bearing systems with dynamic backlash and friction[J].Mechanism and Machine Theory,2011,46:466-478.
[13]Fernandez A,Iglesias M,De-Juan A,et al.Gear transmission dynamic:Effects of tooth profile deviations and support flexibility[J].Applied Acoustics,2014,77:138-149.
[14]王成,刘辉,项昌乐.波动扭矩下渐开线直齿轮传动齿廓修形研究[J].振动与冲击,2014,12(24):1-8.WANG Cheng,LIU Hui,XIANG Chang-le.Influences of profile modification on dynamic characteristics of involute spur gears under a fluctuating torque[J].Journal of Vibration and Shock,2014,12(24):1-8.
[15]张慧博,田健,周峻,等.多间隙耦合齿轮转子系统动力学与试验研究[J].机械工程学报,2017,39(2):1-9.ZHANG Huibo,TIAN Jian,ZHOU Jun,et al.Dynamic and experimental investigation of gear-rotor system with multiple clearances coupled[J].Journal of Mechanical Engineering,2017,39(2):1-9.
[16]Lin H,Oswald F,Townsend D.Dynamic loading of spur gears with linear or parabolic tooth profile modifications[J].Mechanism and Machine Theory,1994,29:1113-1129.
[17]Liu G,Parker R.Dynamic modeling and analysis of tooth profile modification for multimesh gear vibration[J].Journal of Mechanical Design,2008,130:1-13.
[18]Cheon J,Parker R.Analytical investigation of tooth profile modification effects on planetary gear dynamics[J].Mechanism and Machine Theory,2013,70:298-319.
[19]Marcello F,Farhad S,Gabrieie B,et al.Dynamic optimization of spur gears[J].Mechanism and Machine Theory,2011,46:544-557.
[20]陈思雨,唐进元,王志伟,等.修形对齿轮系统动力学特性的影响规律[J].机械工程学报,2014,50(7):39-45.CHEN Siyu,TANG Jinyuan,WANG Zhiwei,et al.Effect of midificaton on dynamic characteristics of gear transmissions systen[J].Journal of Mechanical Engineering,2014,50(7):39-45.
[21]马辉,逢旭,宋溶泽,等.考虑齿顶修缘的齿轮-转子系统振动响应分析[J].机械工程学报,2014,50(7):39-45.MA Hui,PANG Xu,SONG Rongze,et al.Vibration response analysis of a geared rotor system considering the tip relief[J].Journal of Mechanical Engineering,2014,50(7):39-45.
[22]杨玉良,魏静,赖育彬,等.考虑齿顶修缘的斜齿轮传动振动响应分析[J].重庆大学学报,2017,40(1):31-40.YANG Yuliang,WEI Jing,LAI Yubing,et al.Vibration response analysis of helical gear transmission considering the tip relief[J].Journal of Chongqing University,2017,40(1):31-40.
[23]Liu H,Zhang C,Xiang C,et al.Tooth profile modification based on lateral-torsional-rocking coupled nonlinear dynamic model of gear system[J].Mechanism and Machine Theory,2016,105:606-619.
[24]王成,刘辉,项昌乐.基于齿轮传动系统横-扭-摆耦合非线性动力学模型的齿廓修形优化设计[J].振动与冲击,2016,35(1):142-148.WANG Cheng,LIU Hui,XIANG Chang-le.Optimal profile modification for spur gear systems based on their lateral-torsional-rocking coupled nonlinear dynamic model[J].Journal of Vibration and Shock,2016,35(1):142-148.
[25]杨丽,佟操,陈闯,等.基于Kriging模型和遗传算法的齿轮修形减振优化[J].航空动力学报,2017,32(6):1412-1418.YANG Li,TONG Cao,CHEN Chuang,et al.Vibration Reduction optimization of gar modification based on kriging model and genetic algorithm[J].Journal of Aerospace Power,2017,32(6):1412-1418.
[26]Chen Z,Shao Y.Dynamic simulation of spur gear with tooth root crack propagating along tooth width and crack depth[J].Engineering Failure Analysis,2011,18:2149-2164.
[27]Chen Z,Shao Y.Mesh stiffness calculation of a spur gear pair with tooth profile modification and tooth root crack[J].Mechanism and Machine Theory,2013,62:63-74.
[28]王奇斌,张义民.齿向修形直齿轮系统动力学特性分析[J].振动工程学报,2016,29(1):61-67.Wang Qibin,Zhang Yimin.Dynamic characteristics analysis of a spur gear system with the lead crown relief[J].Journal of Vibration Engineering,2016,29(1):61-67.
[29]李永焯,丁康,何国林,等.齿轮系统振动响应信号调制边频带产生机理研究[J].机械工程学报,2018,54(5):105-112.LI Yongzhuo,DING Kang,HE Guolin,et al.Modulation sidebands of the vibration signal of gearbox[J].Journal of Mechanical Engineering,2018,54(5):105-112.
[2]李明,孙涛,胡海岩.齿轮传动转子-轴承系统动力学的研究进展[J].振动工程学报,2002,15(3):249-256.Li Ming,Sun Tao,Hu Haiyan.Review on dynamics of geared rotor-bearing systems[J].Journal of Vibration Engineering,2002,15(3):249-256.
[3]Wang J,Li R,Peng X.Survey of nonlinear vibration of gear transmission systems[J].ASME,2003,56(3):309-329.
[4]Kahraman A,Blankenship G.Experiments on nonlinear dynamic behavior of an oscillator with clearance and periodically time-varying parameters[J].Journal of Applied Mechanics,1997,64:217-226.
[5]Kang M,Kahraman A.Measurement of vibratory motions of gears supported by compliant shafts[J].Mechanical Systems and Signal Processing,2012,29:391-403.
[6]Kahraman A,Singh R.Nonlinear dynamics of gearrotor bearing system with multi-backlash[J].Journal of Sound and Vibration,1991,144:469-506.
[7]Lassaad W,Tahar F,Mohamed H.Nonlinear dynamics of a two-stage gear system with mesh stiffness fluctuation,bearing flexibility and backlash[J].Mechanism and Machine Theory,2009,44:1058-1069.
[8]Li S,Kahraman A.A tribo-dynamic model of a spur gear pair[J].Journal of Sound and Vibration,2013,332:4963-4978.
[9]Chen Z,Shao Y,LIM T.Nonlinear dynamic simulation of gear response under the idling condition[J].International Journal of Automotive Technology,2012,13:541-552.
[10]Kim W,Yoo H,Chung J.Dynamic analysis for a pair of spur gears with translational motion due to bearing deformation[J].Journal of Sound and Vibration,2010,329:4409-4421.
[11]Woohyung K,Lee J,Chung J.Dynamic analysis for a planetary gear with time varying pressure angles and contact ratios[J].Journal of Sound and Vibration,2012,331:883-901.
[12]Chen S,Tang J,Luo C,et al.Nonlinear dynamic characteristics of geared rotor bearing systems with dynamic backlash and friction[J].Mechanism and Machine Theory,2011,46:466-478.
[13]Fernandez A,Iglesias M,De-Juan A,et al.Gear transmission dynamic:Effects of tooth profile deviations and support flexibility[J].Applied Acoustics,2014,77:138-149.
[14]王成,刘辉,项昌乐.波动扭矩下渐开线直齿轮传动齿廓修形研究[J].振动与冲击,2014,12(24):1-8.WANG Cheng,LIU Hui,XIANG Chang-le.Influences of profile modification on dynamic characteristics of involute spur gears under a fluctuating torque[J].Journal of Vibration and Shock,2014,12(24):1-8.
[15]张慧博,田健,周峻,等.多间隙耦合齿轮转子系统动力学与试验研究[J].机械工程学报,2017,39(2):1-9.ZHANG Huibo,TIAN Jian,ZHOU Jun,et al.Dynamic and experimental investigation of gear-rotor system with multiple clearances coupled[J].Journal of Mechanical Engineering,2017,39(2):1-9.
[16]Lin H,Oswald F,Townsend D.Dynamic loading of spur gears with linear or parabolic tooth profile modifications[J].Mechanism and Machine Theory,1994,29:1113-1129.
[17]Liu G,Parker R.Dynamic modeling and analysis of tooth profile modification for multimesh gear vibration[J].Journal of Mechanical Design,2008,130:1-13.
[18]Cheon J,Parker R.Analytical investigation of tooth profile modification effects on planetary gear dynamics[J].Mechanism and Machine Theory,2013,70:298-319.
[19]Marcello F,Farhad S,Gabrieie B,et al.Dynamic optimization of spur gears[J].Mechanism and Machine Theory,2011,46:544-557.
[20]陈思雨,唐进元,王志伟,等.修形对齿轮系统动力学特性的影响规律[J].机械工程学报,2014,50(7):39-45.CHEN Siyu,TANG Jinyuan,WANG Zhiwei,et al.Effect of midificaton on dynamic characteristics of gear transmissions systen[J].Journal of Mechanical Engineering,2014,50(7):39-45.
[21]马辉,逢旭,宋溶泽,等.考虑齿顶修缘的齿轮-转子系统振动响应分析[J].机械工程学报,2014,50(7):39-45.MA Hui,PANG Xu,SONG Rongze,et al.Vibration response analysis of a geared rotor system considering the tip relief[J].Journal of Mechanical Engineering,2014,50(7):39-45.
[22]杨玉良,魏静,赖育彬,等.考虑齿顶修缘的斜齿轮传动振动响应分析[J].重庆大学学报,2017,40(1):31-40.YANG Yuliang,WEI Jing,LAI Yubing,et al.Vibration response analysis of helical gear transmission considering the tip relief[J].Journal of Chongqing University,2017,40(1):31-40.
[23]Liu H,Zhang C,Xiang C,et al.Tooth profile modification based on lateral-torsional-rocking coupled nonlinear dynamic model of gear system[J].Mechanism and Machine Theory,2016,105:606-619.
[24]王成,刘辉,项昌乐.基于齿轮传动系统横-扭-摆耦合非线性动力学模型的齿廓修形优化设计[J].振动与冲击,2016,35(1):142-148.WANG Cheng,LIU Hui,XIANG Chang-le.Optimal profile modification for spur gear systems based on their lateral-torsional-rocking coupled nonlinear dynamic model[J].Journal of Vibration and Shock,2016,35(1):142-148.
[25]杨丽,佟操,陈闯,等.基于Kriging模型和遗传算法的齿轮修形减振优化[J].航空动力学报,2017,32(6):1412-1418.YANG Li,TONG Cao,CHEN Chuang,et al.Vibration Reduction optimization of gar modification based on kriging model and genetic algorithm[J].Journal of Aerospace Power,2017,32(6):1412-1418.
[26]Chen Z,Shao Y.Dynamic simulation of spur gear with tooth root crack propagating along tooth width and crack depth[J].Engineering Failure Analysis,2011,18:2149-2164.
[27]Chen Z,Shao Y.Mesh stiffness calculation of a spur gear pair with tooth profile modification and tooth root crack[J].Mechanism and Machine Theory,2013,62:63-74.
[28]王奇斌,张义民.齿向修形直齿轮系统动力学特性分析[J].振动工程学报,2016,29(1):61-67.Wang Qibin,Zhang Yimin.Dynamic characteristics analysis of a spur gear system with the lead crown relief[J].Journal of Vibration Engineering,2016,29(1):61-67.
[29]李永焯,丁康,何国林,等.齿轮系统振动响应信号调制边频带产生机理研究[J].机械工程学报,2018,54(5):105-112.LI Yongzhuo,DING Kang,HE Guolin,et al.Modulation sidebands of the vibration signal of gearbox[J].Journal of Mechanical Engineering,2018,54(5):105-112.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |