Formulation for an optimal design problem of spur gear drive and its global optimization

In this article, an optimal design problem of spur gear drive with a fixed load factor is formulated as a nonlinear optimization model. Three methods are presented to find the globally optimal design scheme on the structure of the spur gear pair. By suitable variable transformation, the constructed model is first converted into a linear program with mixed variables. By developing an algorithm of global optimization for solving a binary linear programming with mixed variables, all global optimal solutions are found for the original design problem. Taking into account the modification of the contact ratio factors, a specific global optimization method is provided to optimize the design of spur gear drive with soft tooth flank in a continuous variable space. On the basis of enumeration of the discrete variables and utilization of the monotonicity in the optimal model, another global optimization method is designed to search for the global optimal solutions in the mixed variable space, which does not depend upon whether the modification of contact ratio factor exists or not. Case studies are employed to demonstrate the validity and practicability of the constructed model and the proposed methods.