# Structural reliability analysis of spiral bevel gear based on mixed uncertainty

In the reliability analysis of spiral bevel gear structure, there are inevitably uncertainties related to the external environment, material characteristics, geometric dimensions and loads, which lead to the variation or fluctuation of its performance, and then the reliability problem. Understanding, measuring and controlling the uncertain factors in the design process plays an important role in the reliability of spiral bevel gears. In practical engineering, due to the small sample capacity and insufficient experiment, we can only give the probability value of the uncertain variable falling within a certain interval length or only the interval value, which leads to the inaccurate and discontinuous information of the uncertain variable. Therefore, the traditional mechanical reliability modeling and analysis method based on probability theory will no longer be applicable.

In practical engineering problems, random and interval uncertain parameters exist at the same time. Scholars at home and abroad define the reliability analysis under the coexistence of multiple uncertain parameters as hybrid uncertain reliability analysis. It is pointed out that the failure probability can be characterized by a mixed reliability model, which considers both random variables and bounded uncertain variables. Combined with the definition of the shortest distance of structural reliability coefficient, the solution method of structural reliability with mixed uncertainty is given; Using the method of double-layer nested optimization, the probability reliability analysis is carried out in the outer layer and the interval analysis is carried out in the inner layer. The optimization problem of nested double loop is transformed into an approximate single loop minimization problem; Aiming at the reliability problem of structural system with random and interval information, a hybrid perturbation Monte Carlo (MC) method is proposed. Using Taylor expansion, matrix perturbation theory and random interval method, the upper and lower bounds of the mean value and variance of structural strain and stress are obtained by MC simulation. The upper and lower bounds of failure probability of structural units and systems are studied by first-order second moment reliability method and interval method Lower bound; A MC sampling method based on design points is studied. In this method, in order to make full use of the characteristics of design points in the standard normal space in probability reliability, the standard normal truncated distribution is used to replace the uniform distribution to process the interval information; A sampling simulation method is proposed by transforming interval variables and random variables into distribution function family.

In view of this, the n-dimensional limit state function is approximately transformed into a new two-dimensional function in polar coordinates, the polar probability density functions of random variables and interval variables are derived in polar coordinates space, and the failure probability interval is derived by integral method. The effectiveness of the method is verified by the reliability analysis case of spiral bevel gear structure of a comprehensive transmission device.

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