Technique of measurement of working rail profile curvature radius. Errors at indirect measurements

The article suggests a practical method of indirect curvature radius measurements of the working surface worn profile due to rail operation to create a conformal contact locomotive wheel tread with the rail. Conformal contact can provide an increase of the coefficient wheel-rail adhesion in the contact spot and lead to contact stress decrease due to an increase of the actual contact area of the interacting surfaces. The measured radius of curvature is used to restore the worn rail profile by of the rail surface grinding. It is established that in connection with the presence of random factors affecting on the surface of driving path at interaction of the locomotive wheel with the rail, random errors should be excluded from the obtained measurement results or the magnitude of the random components of errors should be estimated. At indirect measurements, it is not easy to find the best estimate of the true value of the measured size because of the unknown law of error distribution. On the basis of theoretical studies, the paper justifies a simplified formula for determination of the variance of the indirect measurement function of rail profile curvature radius according to the mathematical expectations and variances of the measured arguments. Simultaneous measurement of several arguments of the indirect measurement function leads to a correlation dependence of the arguments, that is taken into account in the proposed technique. Based on the measurement data, confidence intervals are constructed to estimate the mathematical expectation and the standard deviation of the radius of curvature of the rail. The question of choosing the number of measurements to achieve a specified accuracy of the curvature radius of the rail surface profile is considered.