Xoptimization of HCR gearing geometry using generalized particle swarm optimization algorithm

Abstract

Special kind of basic involute profile of non-standard gearing is called high contact ratio (HCR) gearing, when the contact ratio is higher and there are always at least two pairs of teeth in contact (εα ≥ 2) and where unit addendum height is not equal one like for standard gearing, so the tooth height is increased and it is bigger than one ha* > 1. When HCR gearing is used, it is not necessary to achieve a greater gear load capacity, but nevertheless there is a greater risk of interference due to a greater height of tooth. Advantage of the HCR gearing is also a higher resistance (load distribution is shared on the more pairs of teeth at the same time) and lower relative noise level of gearing, which can be significantly reduced by using integer HCR factor εα. HCR profiles are more complicated than standard involute profiles, they have greater predisposition for occurring interference, pointed tip thickness, but also undercut of teeth during the production (primary production interference). Due to increased addendum height, there is larger possibility of occurring some interference or pointed tooth tip. Therefore it should prevent these errors and check if all equation and constraints are satisfied. The given method of finding optimal solutions for h*a1, h*a2 and x1 uses Generalized Particle Swarm Optimization Algorithm and MATLAB as a program for optimization. This GPS optimization is a very fast and reliable method.