A mathematical vibration model of the contact system is established during the closing process, considering the nonlinear insulating pull rod force and the contact force of the contact collision. The contacting rules and influencing parameters of the contact bounce are obtained by using MATLAB. The genetic algorithm is introduced to optimize the circuit breaker contact system. The results show that there are two obvious bounces during the closing process of the contact, and bounce rules are obtained. The vibration amplitude and period are determined by the contact quality, system damping and spring stiffness. After algorithm optimization, the closing time and the total bounce time are reduced to 37.90 ms and 0.901 ms. The maximum amplitude is reduced to 0.061 mm. The contact bounce time and maximum amplitude are reduced by 61.4% and 82.8%. Finally, the dynamic and characteristical tester of circuit breaker is used to conduct experiments, and the calculated results are compared with the measured results. They are highly consistent, which verifies the accuracy of the mathematical vibration model and theoretical calculations.

Aiming at the complex running state and instability state of rail car body under high-speed impact, a mathematical model of the collision force and overturning force of the car body is established by using the state space trajectory method of modern control theory. The program is written by Matlab language to solve the motion state of the rail car under high-speed impact, and then the change law of the motion state of the car body under different working conditions is obtained. The results show that the maximum nodding angle is related to the impact speed and the length-height ratio of the car body. The nodding angle increases with the increase of impact speed while decreases with the increase of length-height ratio. The turning radius of the rail is related to the turning angle. The limit instability state of the car body is affected by side-impact angle and varies with speed. The larger the speed, the smaller the allowable value. The stability of the car body motion state and the limit instability speed decrease with the decrease of the impact slope. With the increase of the impact slope, the stability of the car body motion state increases, and the limit instability speed increases.