A multi-objective correction of machine settings considering loaded tooth contact performance in spiral bevel gears by nonlinear interval number optimization

A novel multi-objective correction of machine settings correlating to the loaded tooth contact performance is proposed by nonlinear interval optimization algorithm for spiral bevel gears. There are three items, namely, the maximum contact pressure, the maximum loaded transmission error and the contact ratio, are set to provide a comprehensive evaluation of the gear tooth contact performance. A universal machine setting correction is first applied to identify an initial set of machine settings only considering the ease-off. Then, a basic flowchart of multi-objective machine setting correction is established by the initial universal machine setting correction and the next proportional modification considering loaded tooth contact performance. Finally, multi-objective correction based on the nonlinear interval number algorithm is performed to obtain the high tooth contact performance. In this process, there are two major parts: i) the function of loaded tooth contact performance items with respect to machine setting and load is obtained by applying a polynomial interpolation fitting, and ii) the multi-objective correction is established based on nonlinear interval number optimization considering the uncertainty which only exists in constraints. A numerical instance is provided to verify the validity of the proposed multi-objective correction.