Calculation of the Equivalent Conicity Function of the Railway Wheelset Tread Profile at the Delta R Function with a Negative
Calculation of the Equivalent Conicity Function of the Railway Wheelset Tread Profile at the Delta R Function with a Negative

Summary/Abstract: The rail-wheel interface is fundamental to explain the dynamic running behaviour of a railway vehicle. It must therefore be understood and among the parameters by which it is characterised, the one called “equivalent conicity” plays an essential role since it allows the satisfactory appreciation of the wheel-rail contact on tangent track and on large-radius curves. By definition, the equivalent conicity is equal to the tangent of the cone angle tg e of a wheelset with coned wheels whose lateral movement has the same kinematic wavelength as the given wheelset. In order to be able to compare the results obtained by different railways, both as to the value of the equivalent conicity and as to the results where that parameter plays an important role, it is necessary for the equivalent conicity to be calculated according to the same principles. Methods, which determine ways of the calculation, are mentioned in the UIC leaflet, but it does not define either limits of accepted values of the equivalent conicity or the shape profiles, thanks to which the conicity could be reached. The equivalent conicity is calculated either by the application of the Klingel formula or with the help of the linear regression of the r function on the interval of the double amplitude of the wavelength of a periodical movement of the middle of a wheelset. The process of the calculation in the leaflet is determined for a standard case of the r function shape, which crosses the y-axis in one point in the graph of dependence of the r function on the lateral displacement. In practice there are cases when the r function crosses the y-axis in more than one point. The paper deals with the possibility of the calculation of the equivalent conicity with the help of the Klingel formula in the case when r function crosses the y-axis in three points. The leaflet describes such a case as a r function course with a negative slope. In this case not one, but three curves will be the results. Each of them will determine an equivalent conicity for another interval of validity (amplitude of oscillation of the middle of the wheelset). According to the initial conditions (amplitude of oscillation and position of the wheelset on the rail), the wheelset can have for some amplitudes two possible trajectories or none in the case of a negative conicity.

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