Finite Element/Contact Mechanics Analysis of Spur Gear Pairs With Tooth Root Cracks

Abstract

This study analyzes the nonlinear static and dynamic response in spur gear pairs with tooth root crack damage. A finite element/contact mechanics (FE/CM) model is used that accurately captures the elastic deformations on the gear teeth due to kinematic motion, tooth and rim deformations, vibration, and localized increases in compliance due to a tooth root crack. The damage is modeled by releasing the connectivity of the finite element mesh at select nodes near a tooth crack. The sensitivity of the calculated static transmission errors and tooth mesh stiffnesses is determined for varying crack initial locations, final locations, and the path from the initial to final location. Gear tooth mesh stiffness is calculated for a wide range of tooth root crack lengths, including large cracks that extend through nearly all of the tooth. Mesh stiffnesses are meaningfully reduced due to tooth root crack damage. The dynamic response is calculated for cracks of varying length. Larger cracks result in increased peak dynamic transmission errors. For small tooth root cracks the spectrum of dynamic transmission error contains components near the natural frequency of the gear pair. The spectrum of dynamic transmission error has broadband frequency response for large tooth root cracks that extend further than one-half of the tooth’s thickness.