Optimisation of Railway Polynomial Transition Curves with Different Number of Terms

This paper presents the results of research of influence of degree and number of polynomial terms of railway transition curves (TCs) on their dynamical properties. The research performed for needs of this work are planned numeric tests. The search for the proper shape means the evaluation of the curve properties based on chosen dynamical quantity and generation of such shape with the use of mathematically understood optimisation methods. For the needs of this work advanced vehicle model, dynamical track-vehicle and vehicle-passenger interactions as well as optimisation methods were exploited. The subject of the analysis are odd degree polynomial transition curves of the 5th, 7th, 9th and 11th degree. For each degree of the polynomial a range of acceptable number of polynomial terms was determined. One dynamical quantity - minimum of integral of vehicle body lateral acceleration - being the results of simulation of railway vehicle advanced model is exploited in the determination of quality function (QF).