多间隙齿轮副系统非线性动力学特性分析
|
摘要
齿侧间隙和支承间隙对齿轮系统非线性动力学特性有重要的影响。首先,建立了齿轮副系统多间隙非线性动力学模型。模型中考虑了时变啮合刚度、静态传动误差、齿侧间隙与支承间隙等因素。然后,对系统方程进行量纲一化。最后,利用数值积分方法对方程进行求解,分析了系统在不同载荷条件下随齿侧间隙、支承间隙与阻尼变化的分岔特性。结果表明:在轻载条件下,系统随齿侧间隙的变化表现出丰富的运动状态,包括单周期、倍周期与混沌运动,而在重载条件下,系统的动力学特性未发生变化,仅振幅增大。同样地,系统的运动状态在重载条件下不随支承间隙的变化而改变;然而,在轻载条件下,当支承间隙增大时,系统处于不同的运动形式。研究结果为齿轮系统参数选取与优化提供理论依据。
The gear backlash and bearing clearance have a significant influence on the nonlinear dynamics of gear system.Firstly,a nonlinear dynamic model of gear pair system with multi-clearance is established,considering comprehensively time-varying meshing stiffness,static transmission error,gear backlash and bearing clearance.Then,the dimensionless dynamic equations are derived.Finally,the equations are solved by using numerical integration method.And the bifurcation features of the system are analyzed with different parameters including gear backlash,bearing clearance and damping coefficient under different loaded conditions.The results show that when gear backlash changes,the system undergoes rich motion forms consisting of period-one,period-doubling and chaos under lightly loaded condition.However,the dynamic characteristic of the system is not changed under heavily loaded condition,while only the vibration amplitude changes.Similarly,the motion state of gear system does not change when bearing clearance increases under heavily loaded condition,whereas the system will enter into complex motion states under lightly loaded condition with the change of bearing clearance.The research results provide certain guiding role for reasonably choosing and optimizing backlash value of gear system.
The gear backlash and bearing clearance have a significant influence on the nonlinear dynamics of gear system.Firstly,a nonlinear dynamic model of gear pair system with multi-clearance is established,considering comprehensively time-varying meshing stiffness,static transmission error,gear backlash and bearing clearance.Then,the dimensionless dynamic equations are derived.Finally,the equations are solved by using numerical integration method.And the bifurcation features of the system are analyzed with different parameters including gear backlash,bearing clearance and damping coefficient under different loaded conditions.The results show that when gear backlash changes,the system undergoes rich motion forms consisting of period-one,period-doubling and chaos under lightly loaded condition.However,the dynamic characteristic of the system is not changed under heavily loaded condition,while only the vibration amplitude changes.Similarly,the motion state of gear system does not change when bearing clearance increases under heavily loaded condition,whereas the system will enter into complex motion states under lightly loaded condition with the change of bearing clearance.The research results provide certain guiding role for reasonably choosing and optimizing backlash value of gear system.
引文
[1]李润方,王建军.齿轮系统动力学——振动、冲击、噪声[M].北京:科学出版社,1997.LI Runfang,WANG Jianjun.Gear system dynamics—Vibration,shock,noise[M].Beijing:Science Press,1997.
[2]KAHRAMAN A,SINGH R.Non-linear dynamics of a geared rotor-bearing system with multiple clearances[J].Journal of Sound and Vibration,1991,144(3):469-506.
[3]KIM W,Hong H Y,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(21):4409-4421.
[4]王三民,沈允文,董海军.多间隙耦合非线性动力系统的分叉与混沌[J].西北工业大学学报,2003,21(2):191-194.WANG Sanmin,SHEN Yunwen,DONG Haijun.Bifurcation and chaos in a nonlinear dynamic with multiple clearances and time-varying stiffness[J].Journal of Northwestern Polytechnic University,2003,21(2):191-194.
[5]杨富春,周晓军,胡宏伟.两级齿轮减速器非线性振动特性研究[J].浙江大学学报:工学版,2009(7):1243-1248.YANG Fuchun,ZHOU Xiaojun,HU Hongwei.Nonlinear vibration characteristics of two-stage gear reducer[J].Journal of Zhejiang University:Engineering Science,2009(7):1243-1248.
[6]CHEN S Y,TANG J Y,LUO C W.Nonlinear dynamic characteristics of geared rotor bearing systems with dynamic backlash and friction[J].Mechanism and Machine Theory,2011,46(4):466-478.
[7]LIU J,WANG S J,ZHOU S H.Nonlinear behavior of a spur gear pair transmission system with backlash[J].Journal of Vibroengineering,2014,16(8):3922-3938.
[8]ZHOU S H,LIU J,LI C F.Nonlinear behavior of a spur gear pair transmission system with backlash[J].Journal of Vibroengineering,2014,16(8):3850-3861.
[9]FARSHIDIANFAR A,SAGHAFI A.Global bifurcation and chaos analysis in nonlinear vibration of spur gear systems[J].Nonlinear Dynamics,2014,75:783-806.
[10]盛冬平,朱如鹏,陆凤霞.多间隙弯扭耦合齿轮非线性振动的分岔特性研究[J].振动与冲击,2014,33(19):116-122.SHENG Dongping,ZHU Rupeng,LU Fengxia.Bifurcation characteristics of bending-torsional coupled nonlinear vibration with multi-clearanyce[J].Journal of Vibration and Shock,2014,33(19):116-122.
[11]GOU X F,ZHU L Y,CHEN D L.Bifurcation and chaos analysis of spur gear pair in two-parameter plane[J].Nonlinear Dynamics,2015,79(3):2225-2235.
[2]KAHRAMAN A,SINGH R.Non-linear dynamics of a geared rotor-bearing system with multiple clearances[J].Journal of Sound and Vibration,1991,144(3):469-506.
[3]KIM W,Hong H Y,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(21):4409-4421.
[4]王三民,沈允文,董海军.多间隙耦合非线性动力系统的分叉与混沌[J].西北工业大学学报,2003,21(2):191-194.WANG Sanmin,SHEN Yunwen,DONG Haijun.Bifurcation and chaos in a nonlinear dynamic with multiple clearances and time-varying stiffness[J].Journal of Northwestern Polytechnic University,2003,21(2):191-194.
[5]杨富春,周晓军,胡宏伟.两级齿轮减速器非线性振动特性研究[J].浙江大学学报:工学版,2009(7):1243-1248.YANG Fuchun,ZHOU Xiaojun,HU Hongwei.Nonlinear vibration characteristics of two-stage gear reducer[J].Journal of Zhejiang University:Engineering Science,2009(7):1243-1248.
[6]CHEN S Y,TANG J Y,LUO C W.Nonlinear dynamic characteristics of geared rotor bearing systems with dynamic backlash and friction[J].Mechanism and Machine Theory,2011,46(4):466-478.
[7]LIU J,WANG S J,ZHOU S H.Nonlinear behavior of a spur gear pair transmission system with backlash[J].Journal of Vibroengineering,2014,16(8):3922-3938.
[8]ZHOU S H,LIU J,LI C F.Nonlinear behavior of a spur gear pair transmission system with backlash[J].Journal of Vibroengineering,2014,16(8):3850-3861.
[9]FARSHIDIANFAR A,SAGHAFI A.Global bifurcation and chaos analysis in nonlinear vibration of spur gear systems[J].Nonlinear Dynamics,2014,75:783-806.
[10]盛冬平,朱如鹏,陆凤霞.多间隙弯扭耦合齿轮非线性振动的分岔特性研究[J].振动与冲击,2014,33(19):116-122.SHENG Dongping,ZHU Rupeng,LU Fengxia.Bifurcation characteristics of bending-torsional coupled nonlinear vibration with multi-clearanyce[J].Journal of Vibration and Shock,2014,33(19):116-122.
[11]GOU X F,ZHU L Y,CHEN D L.Bifurcation and chaos analysis of spur gear pair in two-parameter plane[J].Nonlinear Dynamics,2015,79(3):2225-2235.