Multi-Objective Optimization of Modified Cycloidal-Toothed Gerotor Pumps by Genetic Algorithm

Abstract

Cycloidal-toothed gerotors are formed by the combination of epicycloid and a hypocyloid arcs that use the pitch circles as their base circles. They are a common profile type used in industry likely because they can be generated by simple parametric equations. One of the problems with the cycloidal-toothed profile type is that the radius of curvature of both the inner and outer gear are zero when the gears contact at the pitch point which can lead to high contact stress. A gear generation algorithm has been developed that modifies the hypocycloid tooth form to eliminate contact in regions with very low radii of curvature that is yet to be described in scientific literature. Seven performance metrics are developed to evaluate size, flow ripple, adhesive wear, contact stress, radial gap leakage, lateral gap leakage, and inlet throttling that are used as objective functions in a multi-objective optimization. The pump geometry is optimized by applying the NSGA-II algorithm with a population size of 1000 for 500 generations to produce a pareto front, and the results are compared to two cycloidal-toothed gerotors used in the automotive industry. Two designs were found that significantly reduce the contact stress in the profiles while giving the same performance in the other six objective functions in comparison to the profiles used in industry. Another two designs are found that can significantly reduce several objective functions if the size of the pump can be increased slightly.