Applications and Estimate Comparisons of Bezgin–Kolukırık Equations for Dynamic Impact Forces Because of Wheel Flats with Numerical Analysis Estimates and Instrumented Track Measurements

Abstract

Bezgin–Kolukırık equations (K’B3 and K'B3,H) are the last group of seven analytical equations based on the Bezgin Method. The method is based on the law of conservation of energy, rules of kinematics and a new concept, impact reduction factor, that describes the development of dynamic impact forces because of track and wheel roughness. K'B3 and K’B3,H estimate dynamic impact force factors because of wheel flats. K'B3,H includes the effect of Hertzian contact deformation on dynamic impact force factors. The proposed equations require up to six parameters to yield estimates. These parameters are: wheel diameter, wheel flat length, train speed, static wheel force transferred to the rail based on the tributary mass of the wheel, equivalent system stiffness of railway track and rolling stock, and length of Hertzian contact interface between wheel and rail. These equations empower users with the ability to estimate the highest values of the dynamic impact force factors because of wheel flats by manual calculations that yield realistic estimates comparable with estimates from advanced numerical methods and measurements obtained from instrumented test tracks. This paper presents the proposed Bezgin–Kolukırık equations followed by their application on hypothetical track and rolling stock conditions presenting a wide range of values for track and rolling stock stiffness, static wheel force, wheel diameters, train speed and wheel flat lengths. Estimates from the proposed equations are compared with the estimates of advanced numerical methods and experimental measurements from two previous papers.