Gearbox Design via Mixed-integer Programming

Gearboxes are mechanical transmission systems that consist of multiple gear wheels and shafts. The transmission ratios of the gears are determined by the size and interconnection of these components. Gearboxes have to adhere to very strict requirements regarding weight, production costs, and available space. Moreover, the load cases as a result of motor-vehiclepairings are often not clear a priori. Therefore, automobile manufacturers are confronted with a multicriteria design problem under uncertainty. In this work, we present an approach on how to formulate the gearbox design problem as a mixed-integer nonlinear program. This enables us to compute provably globally optimal gearbox designs. We show how different degrees of freedom, input parameters and the numerical accuracy influence the computation time and the quality of solutions. Acknowledgement. The authors thank the German Research Foundation DFG for funding this research within the Collaborative Research Center SFB 805 “Control of Uncertainties in Load-Carrying Structures in Mechanical Engineering”.