Local Stability of Balancing Speed of Train under Condition of Air Brake

In order to probe into the stability of train’s balancing speed under the condition of air brake,the relationship between its balancing speed and the monotonicity of the function of train unit resultant force was investigated.When the function of train unit resultant force is monotonously decreasing,the balancing speed is stable,otherwise it is instable.Therefore,under the condition of air brake the function of train unit resultant force is monotonously decreasing in some speed range,and the balancing speed is stable locally.The speed range in which the balancing speed is stable was calculated by using the dichotomy.To an empty freight train with an initial brake speed of 100 km/h equal to its limit running speed,drawn by an SS4 locomotive with medium phosphor cast iron brake shoes,its critical speed is 53.5 km/h.So when its running speed is between 53.5 and 100 km/h,the balancing speed is stable under the condition of air brake.