Koshulyan A. Evaluation of residual stresses in railroad wheels by stochastic modeling

The thesis is devoted to the problem of assessing the conformity of residual stresses in the rims of new railroad wheels if stress measurement is performed using an ultrasonic method. Based on handling the measurements of 89 wheels with a Debbie device, it was found that residual stresses could be considered as random variables with their own probability properties. As the result of the full-scale experiments, a general form of the stochastic model for the sequences of stress measurements on a wheel rim was proposed. This model includes the following three latent variables: a random constant component, the sequence of correlated stress fluctuations and the random error of the stress measurement. The constant component is treated as an informative parameter for assessing the conformity of the residual stress in a wheel rim. The autoregressive model of finite stationary random sequences on the unit circle was proposed. The use of this model for describing the fluctuations of residuals stresses allows taking into account a correlation between the sequence terms of stress measurements, their coordinate uncertainty and their closure on a wheel rim. The rules for detecting outliers were obtained based on the finite-difference model of the random errors. The model of stress fluctuations and the model of the random errors allowed obtaining the equations for calculating the uncertainty of the estimate of the constant component for various number of measurement points on a wheel rim. A sufficient number of measurement points for calculating the estimate of the constant component was recommended on the results of the stochastic modeling. The models of probability density functions that are necessary for conformity assessment were obtained on the base of the proposed stochastic model of residual stresses. Optimal criteria for computing acceptance limits were obtained for the case of measurement uncertainty and unknown global risks of a producer and a consumer. The equations for calculating the approximate acceptance limits were provided. On the results of the research, the recommendations on assessing the conformity of the residual stress in a wheel rim were proposed.