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以六轴机车系统为研究对象,采用Vermeulen-Johnson蠕滑理论和一分段线性函数分别计算轮轨滚动接触蠕滑力和轮缘力,研究了机车系统运行于理想平直轨道上的蛇形运动分岔问题。将基于切向量进行预测、牛顿迭代进行校正、可逐步求解整个系统解分支曲线的延续算法应用于机车系统的Hopf分岔及周期解的追踪和求解。计算结果表明:车辆系统在速度达到53.700m.s-1时,从稳定的定常解分岔出一不稳定的周期解,该周期解在速度降到50.855m.s-1时又恢复了稳定,在此过程中出现的亚临界Hopf分岔会引起系统摆振幅值出现突跳与迟滞现象;在低速及高速情况下的一些速度区间,机车系统都有可能出现多种摆振形式共存的非线性动力学现象。
Taking the six-axis locomotive system as the research object, the rolling contact creep force and wheel rim force of wheel-rail rolling contact were calculated by using the Vermeulen-Johnson creep theory and a piecewise linear function respectively. The serpentine shape of the locomotive running on the ideal straight orbit Movement bifurcation problem. Based on the tangent vector and the Newton iteration, the continuation algorithm of the whole system solution branching curve can be used to solve the Hopf bifurcation and the periodic solution of locomotive system. The calculation results show that the vehicle system bifurcates an unstable periodic solution from the steady stationary solution when the velocity reaches 53.700ms-1, and the periodic solution returns to stable when the velocity drops to 50.855ms-1 The subcritical Hopf bifurcation will cause sudden jump and hysteresis in the amplitude of the system. In some speed ranges at low speed and high speed, the locomotive system may have a variety of nonlinear dynamic phenomena of shimmy coexistence .