Effect of Backup Ratio on crack propagation in the tooth foot of Spur Gear

Abstract

Gears are the main components of power transmission and are mostly responsible for gearbox failure. Therefore, the implementation of Fail-Safe design in the design process of Spur Gear is very much important, considering the different failures that occurs while gears are in service. Among all the other failures, the crack initiation and propagation that occurs in the tooth foot region of spur gear due to tensile stresses are the most critical one, since it can lead to catastrophic damage. The primary objective of this study is the follow the crack propagation path in spur gear using Extended Finite Element Method(XFEM) in ABAQUS. The prediction of crack propagation path is carried out considering the tooth behaviour in bending fatigue. The parametric model of Spur gear is modeled in CATIA considering Backup ratio (Ratio of Rim thickness to total tooth height) as reference and this sketch is imported in ABAQUS. Stress concentration study is carried out to found region of maximum tensile and compressive stresses, where crack is initiated to follow crack propagation. The tooth foot crack propagation is the function of stress intensity factors(SIF), so SIF are evaluated as a function of crack angle and crack length. Static and Dynamic analysis is carried out for considered backup ratios of gear geometry and critical and recommended backup ratio are found out to show, that the gear should have the minimum backup ratio equal to recommended backup ratio, so that crack propagates through the tooth and not through rim. Fatigue life is estimated as a function of backup ratio to understand the nature of change of fatigue life as the backup ratio increases.