Study On The Derailment Mechanism Of The Vehicle Based On Swallowtail Catastrophe Theory

The derailment of train can cause huge losses to people’s lives and property. The derailment accidents are reported at home and abroad sometimes. With the continuous development of overload and high-speed railway, the safety running problem of the train appears more prominent. In recent decades the experts engaged in the study of railway have made great progress in derailment theory and test research. However the complexity of derailment problem and the difficulty of the study made the problem still not well solved. The studies have shown that there are some uncertainty and conservatism in the current criteria of derailment and can’t be effectively used for evaluation of train’s derailment. Therefore, it is necessary to seek more reasonable and effective evaluation method about the train’s derailment to guide the safe operation of the vehicle on the basis of recognition and analysis of the existing derailment evaluation standards and the catastrophe theory.The existing derailment evaluation standard and its defects are analyzed based on the introduction of the derailment research status at home and abroad. Based on the analysis of elementary catastrophe theory and the swallowtail catastrophe model, made the derailment coefficient, Angle of attack and overtime of the derailment coefficient as the control variables, the train’s running status as state variables, the swallowtail catastrophe model of the train’s derailment. The mutation form and area of the swallowtail catastrophe model are analyzed. The train’s mechanism of t derailment is described using the potential function of the model. The derailment critical section and derail area are concluded according to the bifurcation set of the swallowtail catastrophe model. The vehicle dynamics simulation model is established in the dynamics simulation software SIMPACK and the derailment coefficient and the attack angle of the train under different conditions is calculated. The distributions of the derailment coefficient, attack angle and the overtime of the derailment coefficient in bifurcation set of the swallowtail catastrophe model are given by data processing. Then the result of the qualitative analysis is verified. The index evaluation method of vehicle derailment mutation is raised based on Catastrophe Theory, the general mutation subordinate function values in different time are calculated using this method and the formula to quantify the control variable to analyze the train’s status. The swallowtail catastrophe model of single wheel is built combining the dynamics analysis model of single wheel and the reference coordinate system of wheel and rail.