并车螺旋锥齿轮传动动力学参数二维域界结构分析

Two-dimensional domain structure of dynamical parameters of combining spiral gear transmission

构建了并车螺旋锥齿轮传动含间隙非线性动力学模型,采用变步长Gill数值法对振动方程进行了求解。将胞映射法引入齿轮动力学全局性态域界分析中,获得了动力学参数二维域界解结构。分别考虑了系统在齿侧间隙、综合误差、时变刚度以及阻尼比等参数域界结构中的稳态特性,借助相图、Lyapunov指数(LE)、Poincaré截面、快速傅里叶频谱分析(FFT)等手段研究了齿轮系统在多参数域共同激励下的动态分岔行为,验证了胞映射法在齿轮动力学参数域设计中的准确性。结果表明:当阻尼比ξ∈[0.025,0.225]时,在间隙和综合误差激励下系统均通过倍周期分岔进入混沌;较大阻尼比有助于系统处于稳态周期域中;时变啮合刚度激励下,系统在周期域和混沌域之间发生跃迁,域界附近参数的微小波动将导致吸引子进入另一吸引域中。

The nonlinear dynamical model including piecewise backlash was created for combining spiral gear train,the governing equations of motion was solved by employing variant-step Gill＇s numerical algorithm.The cell-mapping technique was put forward to investigate the two dimensional basins of dynamic parameters.Parametric excitations covering the backlash,transmission error,time-varying mesh stiffness and damping ratio,were considered in basin planes in terms of steady solutions.The dynamical bifurcation behavior under the excitation of various parameters was performed by means of the phase portrait,Lyapunov exponent （LE）,Poincar section and fast Fourier transform （FFT）.It is validated that Cell-mapping approach is effective in gear dynamic parameter design.The result shows that the system leads to chaos via period-doubling cascades under the backlash and transmission error while large damping ratio within the range ξ∈ [0.025,0.225] is beneficial to periodic states of the system.Under the excitation of time-varying mesh stiffness,significant transition between periodic response and chaotic motion was exhibited,small changes nearby parametric domain boundary guided the attracter into another basin of attraction.