Reliability Based Optimum Design of Gear Trains

Abstract

A reliability based approach is presented for the minimum mass design of gear trains. The gear train is idealized as a weakest link kinematic chain and the optimum design is sought for a specified value of the reliability of the gear train with respect to bending strength and surface wear resistance. The design parameters such as the power transmitted, the geometric dimensions, and the material properties are treated as normally distributed random variables. A linear combination of the mean value and standard deviations of the mass of the gear train is considered as the objective function while treating the mean values of the face widths of the gears as design variables. The reliability based optimization results are compared with those obtained by the deterministic procedure. The effects of variation of parameters like the reliability of the gear train and the coefficients of variation of the random variables are also studied. The minimum mass of the gear trains is found to increase as the specified value of the reliability is increased.