Design of Gerotor Gear Geometry by Multi-Objective Optimization

Andrew Robison, Purdue University

Abstract

Gerotor pumps are positive displacement pumps that are frequently used in low-pressure applications such as lubrication and charge pumps. They are characterized by their unique gearset that is an internal gearset with one tooth difference that has continuous contact throughout the entire rotation. Recent trends especially in the automotive industry suggest an increased demand for greater performance from these pumps, e.g. operating with higher pressure, higher speed, lower viscosity fluid, less noise emission, and greater energy efficiency. The shape of the gears is one of the most important aspects of a gerotor pump, as it determines the pump’s size and flow, affects its internal leakages, and influences its amount of wear. Although gerotors have been in operation for nearly 100 years, no design methodology has emerged in scientific literature that fully considers all the main performance aspects simultaneously and identifies the best designs. This problem is made more difficult, as gerotors can have an infinite number of different types of profiles. The main goals of this work are therefore to define a method to design gerotor gear geometry for several performance goals, identify the best designs for a given gear profile type, compare the best designs among the various profile types, and invent a new profile type that can offer improved performance over conventional designs. Gerotor profile generation is described in the beginning, first for the conventional epitrochoidal, hypotrochoidal, and standard cycloidal profile types. Then a description of how to generate gerotors from an arbitrary curve is given and applied to elliptical, generalized cycloidal, cosine, and asymmetric elliptical gerotors. The generalized cycloidal profile type is new to this work. Multi-objective optimization is used as the method to identify the best gear profiles for a given application considering seven performance metrics and ensuring a feasible gear profile. The seven performance goals to minimize are the radius of a pump for a given geometric displacement and face width, the kinematic flow ripple, the adhesive wear, the contact stress, the tooth tip leakage, the lateral gap leakage, and the mean displacement chamber inlet velocity. The conditions to generate feasible gerotor profiles without cusps or self-intersections are also given as constraints for the optimizations. Seven gerotor profiles were then optimized using a genetic algorithm to consider all the performance aspects. The design space for each profile type was thoroughly explored, and clear Pareto fronts were identified. The Pareto fronts from each profile type were then combined, and a new Pareto front was identified from the best designs of each profile type. No single profile type proves to be objectively better than the others, but the epitrochoidal, hypotrochoidal, elliptical, and generalized cycloidal profile types tend to produce the best designs. Two methods to select a design from the Pareto front that consider the relative importance of each performance goal were presented. The optimization strategy was then further validated by demonstrating significant possible performance improvement over state-of-the-art designs in industry and suggesting alternative designs to a specific gearset used in industry that were tested in simulation and experiment.

Degree

Ph.D.

Advisors

Vacca, Purdue University.

Subject Area

Mechanical engineering

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