This paper on "An Efficient FE Fracture Mechanics Technique for Fatigue Design of Gears" was presented at the NAFEMS World Congress on The Evolution of Product Simulation From Established Methods to Virtual Testing & Prototyping - 24-28 April 2001, The Grand Hotel, Lake Como, Italy.

Abstract

Life prediction is a key feature in the economical design of gears and other heavy-duty components. To reduce costs, it is desirable to economise on the quality of steel, the degree of surface treatment, and the amount of experimental validation, subject to the constraints of warranty commitments, process variability, and possible regional variations in the duty cycle.
Computer simulation of gear tooth fatigue provides a means to generate sets of applied stress vs. life (S-N) curves, reflecting (e.g.) different levels of shot-peen treatment or steel defect size. These synthetic S-N curves expedite the process of gear design or modification, provided they can be established accurately with modest computing effort. For accuracy, it is necessary to model realistic microscopic steel defects using a true fracture mechanics approach, such as the alternating finite element method (AFEM).
AFEM is an efficient crack superposition method which is ideally suited to precise fatigue crack growth modeling. Starting with a routine finite element (FE) analysis of the complicated gear tooth geometry, the method introduces user-specified defects by superimposing special singular crack stress functions on the FE stresses. Stress functions are a particularly accurate means of modeling surface treatment stresses and computing crack stress intensity factors (SIF) for the governing fatigue growth law. Furthermore, the cracks are not meshed, and are grown easily in fatigue by changing their stress function coordinates. A concise iterative technique guarantees crack stress equilibrium on component surfaces.
By eliminating crack meshing, AFEM facilitates the investigation of surface and subsurface defects, multiple interacting defects, and probabilistic studies of defect size and location. The technique is illustrated by application to forged spur gears.