A Method for Analyzing Tooth Load Distribution and Contact Stress of a Thin Wall Spur Gear Using FEM and a Mathematical Programming Method.

A method for the analysis of load distribution and contact stress on tooth faces of a thin wall spur gear are proposed by combining a mathematical programming method with the three-dimensional finite element method (3D-FEM). A program that can be used to carry out tooth load calculation for a sophisticated gear structure with a personal computer is developed. The main procedures of the method are as follows: Firstly, the region on tooth faces surrounding the geometrical contact line which are fairly larger than the theoretical region calculated by the Hertzian's contact theory, is defined as a assumed contact face, secondly, reference points on the assumed contact face are taken on each gear, thirdly, influence coefficient on each reference point is calculated by 3D-FEM, lastly tooth load on each reference point is calculated by the mathematical programming method. The contact stress transformed from the tooth load is well agreed with the theoretical one for a thick gear. Furthermore, strains calculated on the compressive side of the tooth root of the thin wall gear are well agreed with the measured ones.