The Static Transmission Error of Cracked Spur Gear Teeth Using FEA

Abstract

Abstract This paper considers a Finite Element Model which is used to predict the torsional mesh stiffness and static transmission error of a pair of spur gears in mesh. The model involves the use of 2D plain strain elements, coupled with contact elements at the points of contact between the meshing teeth. A simple strategy of how to determine an appropriate value of the penalty parameter of the contact elements (gap element) is also presented. When gears are unloaded, a pinion and gear with perfect involute profiles, should theoretically run with zero transmission error. However, when gears with involute profiles are loaded, the individual torsional mesh stiffness of each gear changes throughout the mesh cycle, causing variations in angular rotation of the gear body and subsequent transmission error. The theoretical changes in the torsional mesh stiffness throughout the mesh cycle are developed using finite element analysis and related to the static transmission error. A 5mm through thickness tooth crack is also modelled, and the comparison of the torsional mesh stiffness and static transmission error with and without the tooth crack is discussed.