Modeling and Simulation of Normal and Damage Vibration Signatures of Idealized Gears

A physics-based first principles approach is adopted in this study to simulate vibration signatures from an idealized gear such as a thin spur gear under plane dynamic stresses induced by an impulsive rotation. The governing equations of velocity—stress are solved using a finite-difference formulation in generalized curvilinear coordinates and a fully characteristic set of boundary conditions based on the theory of hyperbolic systems. The vibration signatures are thus directly obtained in the time domain. A second-order accurate in time and space, time-staggered leapfrog scheme, is used to integrate the time-dependent partial differential equations. Normal as well as damage signatures are obtained and compared; normal signatures correspond to uniform material properties of the gear, and damage signatures correspond to one of the gear teeth being made less rigid in a certain fashion so as to mimic a damage such as due to impact-induced pitting, deformation or incipient crack formation. It is observed that significant deviations from the normal signature occur in amplitude due to this seeded damage. Using this approach, baseline or reference vibration signatures can be obtained for any structural subsystem to aid in its health monitoring.