Abstract:

There is often a mix of random and interval parameters in the design parameters and boundary conditions of spiral bevel gears. Because the measurement space and properties of the two types of uncertain variables are different， the traditional reliability modeling and analysis methods based on probability theory will no longer be applicable. Therefore， a second-order reliability analysis method for hybrid structural analysis with random and interval variables was presented. The limit state function is approximated at the most probable point（MPP） by using the second-order Taylor series expansion method. On this basis， the polar coordinates are introduced and the n-dimensional limit state function is approximately transformed into a new polar coordinate two-dimensional function. By using the gradient vector of the function instead of the failure domain centroid vector， the polar probability density functions of the random variables and the interval variables are derived in polar space. Based on the second-order moment reliability analysis method， the failure probability interval is deduced by the integration method. Finally， the validity of the proposed method is verified by a structural reliability analysis case for spiral bevel gears of a weapon's comprehensive transmission.

Key words: systems engineering, hybrid reliability analysis, second-order reliability method, harmonic reducer, spiral bevel gear