参数对分扭-并车齿轮传动系统动载和均载特性的影响
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摘要
为提高分扭-并车齿轮传动的动载稳定性,对直齿轮和人字齿轮构成的分扭-并车齿轮系统建立了考虑多间隙等激励因素的动力学模型。引入高斯消元技术使振动模型降为含9自由度的线性无关方程组;采用4阶Runge-Kutta法对量纲一方程组实施数值求解,分析了齿侧间隙、综合传动误差和时变啮合刚度等激励下的动载特性。结果表明,齿侧间隙在局部范围内存在动载加剧现象;动载系数激增至2. 705,综合传动误差激励下相同传动级上的均载特性基本一致;时变啮合刚度波动系数大于0. 25时,分扭级的动载波动较剧烈。研究结果对该类齿轮系统动载设计具有指导意义。
For the improvements of dynamical load stability of split torque-combine gear transmission,dynamical models of the system consisting of spur gears and herringbone gears is set up including excitations of multiple backlashes. The Gaussian elimination technique is introduced to deal with the elimination of extra rigid body displacements,ultimately,the dynamics equations are reduced to be 9 degrees of freedom. By applying the fourth order Runge-Kutta algorithm to solve the system dimensionless dynamical equations,dynamic load characteristic is analyzed under the excitations of backlash,general transmission error and timevarying mesh stiffness. The results show that dynamic load factor happens to jump to 2.705 under the backlash excitation,load sharing characteristic keeps very similar on the same stage when general transmission error varies,the dynamic characteristic vibrates severely on split torque gears while the perturbation factor of time-varying mesh stiffness is larger than 0.25,the investigation will provide a guidance for dynamic load design of this typical gear system.
For the improvements of dynamical load stability of split torque-combine gear transmission,dynamical models of the system consisting of spur gears and herringbone gears is set up including excitations of multiple backlashes. The Gaussian elimination technique is introduced to deal with the elimination of extra rigid body displacements,ultimately,the dynamics equations are reduced to be 9 degrees of freedom. By applying the fourth order Runge-Kutta algorithm to solve the system dimensionless dynamical equations,dynamic load characteristic is analyzed under the excitations of backlash,general transmission error and timevarying mesh stiffness. The results show that dynamic load factor happens to jump to 2.705 under the backlash excitation,load sharing characteristic keeps very similar on the same stage when general transmission error varies,the dynamic characteristic vibrates severely on split torque gears while the perturbation factor of time-varying mesh stiffness is larger than 0.25,the investigation will provide a guidance for dynamic load design of this typical gear system.
引文
[1]赵宁,王俊,付晨曦.齿轮分扭-并车传动系统设计与分析[J].机械设计与制造,2013(8):28-31.
[2]林何,王三民,董金城.多激励下某直升机传动系统动载特性[J].航空动力学报,2015,30(1):219-227.
[3]桂永方,朱如鹏,靳广虎,等.间隙非线性圆柱齿轮分流传动系统动力学与均载特性分析[J].振动与冲击,2014,33(18):177-184.
[4]王峰,方宗德,李声晋.重合度对人字齿轮非线性系统振动特性的影响分析[J].振动与冲击,2014(3):18-22.
[5]张婷,李育锡,王三民.功率二分支齿轮传动系统静态均载特性研究[J].机械传动,2012,36(3):14-16.
[6]杨振,王三民,范叶森.转矩分流式齿轮传动系统的非线性动力学特性[J].机械工程学报,2008,44(7):52-57.
[7]KAHRAMAN A,SINGH R.Non-linear dynamics of a geared rotorbearing system with multiple clearances[J].Journal of Sound and Vibration,1991,144(3):469-506.
[8]AL-SHYYAB A,KAHRAMAN A.Non-linear dynamic analysis of a multi-mesh gear train using multi-term harmonic balance method:sub-harmonic motions[J].Journal of Sound and Vibration,2005,284(1):151-172.
[2]林何,王三民,董金城.多激励下某直升机传动系统动载特性[J].航空动力学报,2015,30(1):219-227.
[3]桂永方,朱如鹏,靳广虎,等.间隙非线性圆柱齿轮分流传动系统动力学与均载特性分析[J].振动与冲击,2014,33(18):177-184.
[4]王峰,方宗德,李声晋.重合度对人字齿轮非线性系统振动特性的影响分析[J].振动与冲击,2014(3):18-22.
[5]张婷,李育锡,王三民.功率二分支齿轮传动系统静态均载特性研究[J].机械传动,2012,36(3):14-16.
[6]杨振,王三民,范叶森.转矩分流式齿轮传动系统的非线性动力学特性[J].机械工程学报,2008,44(7):52-57.
[7]KAHRAMAN A,SINGH R.Non-linear dynamics of a geared rotorbearing system with multiple clearances[J].Journal of Sound and Vibration,1991,144(3):469-506.
[8]AL-SHYYAB A,KAHRAMAN A.Non-linear dynamic analysis of a multi-mesh gear train using multi-term harmonic balance method:sub-harmonic motions[J].Journal of Sound and Vibration,2005,284(1):151-172.