Development of a Closed-Form Algorithm for Calculating Reliability and Fatigue Strength Indicators of a Stamp-Welded Bogie of a Freight Car

This article examines the problem of assessing the reliability of stamped-welded freight car bogie components based on fatigue strength criteria under operational loads. The theoretical framework utilizes the principles of the linear fatigue damage summation hypothesis, the power-law fatigue curve, the probabilistic description of the fatigue limit, and Rayleigh’s law for the distribution of dynamic stress amplitudes. An algorithm for calculating reliability indicators in a closed analytical form has been developed, enabling durability prediction at the design stage in the absence of complete information on the structural loading. The experimental part included strain gauge studies of the side frames and bolsters of freight car bogies, as well as fatigue bench tests of specimens under various cyclic load levels. Statistical processing of the test results was performed, determining the parameters of the fatigue curves, fatigue limits, and variation coefficients. It was established that the use of equivalent operational load amplitudes ensures a more accurate determination of the fatigue curve parameter and improves the reliability of the reliability assessment. A significant influence of the fatigue curve parameter on the estimated failure probability during the structural life cycle is demonstrated. The obtained results can be used in the design of advanced freight bogies and in improving regulatory methods for assessing the reliability of railcar structures. The scientific novelty of the study lies in the development of a closed-form algorithm for calculating reliability indicators and the substantiation of a method for processing fatigue test results, taking into account actual operating conditions. The article shows that when statistically processing the results of fatigue tests of the side frame, the transition from actual to equivalent load amplitudes leads to a change in the parameter of the power curve of fatigue (m) from 7.36 to 7.92. The average value of the endurance limit changes from 183.5 to 199.4 kN, the minimum value of the endurance limit—from 143.7 to 158.8 kN, and the coefficient of variation—from 0.1318 to 0.1237. It was also found that the difference in parameter (m) significantly affects the predicted reliability indicators: for the long service life under consideration, the estimated probability of failure was 2.0% and 1.1%, respectively; that is, it differed almost twofold.