Calculation of the Combined Torsional Mesh Stiffness of Spur Gears with Two- and Three-Dimensional Parametrical FE Models

Abstract

The torsional mesh stiffness is one of the most important characteristics of spur gears. This paper presents the development of detailed two- and three-dimensional finite element models which can be used to calculate the torsional mesh stiffness. Using the parametrical design language of the FE software ANSYS the models offer the possibility to generate various different pairs of spur gears and include an adaptive meshing algorithm for the contact zones. Due to the short computation times the 2D model is well suited to simulate a variety of different gear pairs in a short time period. The more complex 3D model features more options in terms of investigating tooth face modifications for further studies. The resulting values of the torsional stiffness can be used - for example - in multi body simulations of gearboxes. The results from the 2D FEA are used to derive a simple formula for the combined torsional stiffness of spur gears in mesh. The results presented are based on the individual stiffness of the three main components - body, teeth and contact. Hence, the introduced formula uses these three parts to determine the overall stiffness for a wide range of gears and gear ratio combinations. Finally, the results from both the two- and three-dimensional finite element model and the derived formula are compared and the results from the 3D model are checked against results obtained by analytical equations.