The small load has fuzziness on the strengthening and damage of the component under the action of random fatigue load. This paper introduces the two-dimensional membership function in fuzzy mathematics to characterize the relationship between stress amplitude, mean value, and damage below the fatigue limit. An exponential function is used to describe the strengthening effect. Under the two-dimensional load spectrum, the influence of various levels on the component's life is comprehensively considered, and the fatigue life prediction model under random load is proposed. Through the small sample experiment of the car swing support rod, the relevant parameters of the model are obtained. The difference between the modified two-dimensional and the two-dimensional load spectrum is compared in fatigue life prediction results. The rules of membership function selection and parameter setting are summarized, and it makes the estimation of component load spectrum life more reasonable.

PurposeTo improve the accuracy of parameter prediction for small-sample data, considering the existence of error in samples, the error circle is introduced to analyze original samples.Design/methodology/approachThe influence of surface roughness on fatigue life is discussed. The error circle can treat the original samples and extend the single sample, which reduces the influence of the sample error.FindingsThe S-N curve obtained by the error circle method is more reliable; the S-N curve of the Bootstrap method is more reliable than that of the Maximum Likelihood Estimation (MLE) method.Originality/valueThe parameter distribution and characteristics are statistically obtained based on the surface roughness, surface roughness factor and intercept constant. The original sample is studied by an error circle and discussed using the Bootstrap and MLE methods to obtain corresponding S-N curves. It provides a more trustworthy basis for predicting the useful life of products.

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As one of the essential components of the braking system, the high-speed train brake disc is an integral part of ensuring the safety of the train. The main objective of this study is to conduct thermal analysis and reliable life prediction on brake discs. The research was conducted by developing a programmer spectrum of brake discs with high-speed train brake discs. According to the results of numerical analysis and the S-N curve of the material, the temperature distribution on the surface of the brake disc is determined, and the fatigue life of the brake disc is predicted. The comparison with the service life of the brake disc verifies the rationality of the calculation results. In addition, a fatigue damage probability model of brake discs is established based on the theory of fatigue cumulative damage. Through the relationship between the reliability of mechanical parts and the number of load cycles, the reliable life of the brake disc under different working conditions is predicted. This work establishes a method of reliable life analysis for brake discs of high-speed trains based on the load spectrum, which could analyze the life and reliability of brake discs more systematically.

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