多级齿轮传动系统关键参数对响应的影响分析

Effect of Key Parameters on the Dynamic Performance of the Multi-mesh Gear Systems

为了研究数控刀架中动力齿轮传动系统运行的平稳状况,建立了考虑时变刚度、齿侧间隙的多级齿轮系统非线性动力学模型,并对方程组进行无量纲化处理。对时变啮合刚度进行了较精确的求解,并考虑了变位系数对刚度值的影响。将齿侧间隙引起的分段位移函数等效简化成一个含双曲正切的表达式,避免了迭代过程中的判断问题。采用4阶Runge-Kutta法对方程进行Matlab编程求解,分析了刚度展开项波动幅值、载荷力矩以及侧隙对响应的影响。通过分析可知:较小的刚度展开项波动幅值对系统的平稳性有利;重载下的系统发生跳跃现象的临界转速变大,而工作转速通常低于临界转速,从而提高了运转的平稳性;侧隙较小时易产生双边冲击,产生较大噪音。

A nonlinear dynamic model and relative dimensionless equations focusing on time-varying stiffness and backlash are developed to study the steady state of the dynamic gear drive system of the computer numerical control(CNC)turret.The time-varying stiffness is obtained,considering the effect of the modification coefficient on stiffness values.The piecewise displacement functions caused by the backlash are simplified into an expression containing a hyperbolic tangent to avoid the complex judging in the iterative process.The equations are solved by employing the fourth-order Runge-Kutta method in Matlab programming.The influence of the alternating mesh stiffness amplitudes,transmitted static torque and backlash are investigated.Results show that smaller amplitudes of harmonic stiffness benefit the system′s stability.Stability is also improved under heavy loads,since working speed is smaller than critical speed,which increases due to the jumping phenomenon.Double-sided impact occurs more easily with small backlash and leads to noise.