Bifurcation control and complex motion analysis of high-speed bogie based on active yaw damper

In order to ensure the hunting stability of high-speed trains and improve critical speed, a study on control of the bifurcation characteristics of vehicle system based on active yaw dampers was carried out. A simplified dynamics model containing the lateral/yaw motion of a rigid bogie and the lateral motion of the car body was established, and a nonlinear wheel-rail relationship was given by combining the measured wheel tread data at the end-worn stage. Active yaw dampers were connected in parallel on the basis of traditional passive suspension, and the Hopf bifurcation and complex motion of the vehicle system after bifurcation were analyzed based on the yaw motion control of bogie. Research results show that the Hopf bifurcation point can be delayed, and the critical speed of vehicle system can be directly increased from 247 km·h^-1 in passive state to 328 km·h^-1 through linear stiffness and damping control. The lateral wheelset displacement after bifurcation is not affected by linear stiffness control, increasing the hunting frequency from 5 Hz to 7 Hz, while the limit cycle amplitude and hunting frequency after bifurcation are effectively reduced via linear damping control. The critical speed is not changed by nonlinear stiffness and damping control, and quadratic control gain will cause the vehicle system to produce an unstable limit cycle. The amplitude of the limit cycle after bifurcation can be reduced through cubic control gain, of which the cubic stiffness control can increase the hunting frequency, while the cubic damping control can inhibit hunting frequency. Meanwhile, after Hopf bifurcation of the vehicle under traditional passive suspension, the system will go through the limit cycle motion into period doubling bifurcation and then lead to the chaotic state, whereas the linear control can maintain the stable single-cycle motion of the limit cycle after the supercritical Hopf bifurcation occurs at the speed of 386 km·h^-1, and its maximum Lyapunov exponent is always less than 0, which can effectively avoid the generation of complex chaotic motion of vehicle system, but the effect of nonlinear control is limited.