Finite element modeling of spur gearing fractures

Abstract

A new numerical procedure of solution has been developed for the study of stress singularities in gear teeth fractures incorporating kinematic rotations and varying contact conditions. The parametric description of both the geometry and the operation by means of global design variables, and the approximation of elastic deformations by the finite element method enables the development of a computational design procedure which simulates the operation of spur gear drives. Considering the members of the drive as individual subdomains which can elastically deform and rotate, the engagement of operating surfaces at successive points enables the simulation of conjugate action. In the presence of cracks, the behavior of stress singularities is approximated by quarter point elements and the stress intensity factors are evaluated through displacement formulas. This generalized formulation efficiently approximates the load sharing and thus permits evaluation of the dynamic stress intensity factors along the path of contact, for any crack appearing in spur gear drives. Numerical results are presented and discussed for some important gear fractures. This method seems to be a powerful tool for computational procedures in the design of gear drives incorporating fracture defects.