含侧隙及时变刚度的多级齿轮非线性响应分析

Nonlinear Dynamic Analysis of Spur Gear Pairs with Gear Backlash and Time-varying Stiffness

对二级齿轮传动系统的物理模型进行简化,考虑啮合过程中的时变啮合刚度、齿轮动态综合误差以及齿侧间隙引起的非线性影响,建立二级齿轮传动系统的数学模型。给定齿轮的基本参数,确定动力学方程中的各个参数,对时变啮合刚度的求解采用了基于材料力学的Web能量法。对非线性方程组采用降阶后的四阶Runge-Kutta法,运用MatLAB进行数值仿真,对仿真得到的结果与理论分析进行对比。考虑到齿轮传动所引起的振动对整体系统的影响,分析系统的动态啮合力与系统转速的关系,确保系统在合理的转速下运行。

A simplified physical model of two stage gear system was given in the paper. Considering the nonlinear factors time-varying stiffness, gear composite error and gear backlash, we can get the mathematical model of the two stage gear system. The gears basic parameters were given to determine the parameters in the kinetic equation. Then using the Web energy method based on the material mechanics calculate the time-varying stiffness. The nonlinear equations were solved by the fourth order Runge-Kutta method based on the MatLAB. The result getting from the simulation should compare with the theoretical analysis. The vibration caused by the gear transmission will generate bad influence to the whole system.In order to ensure the system operation safety, it is necessary to figure out the relationship between the dynamic meshing force and system speed.