Investigation of asymmetric gear tooth bending stress formulation

Download
2018
Orak, Mahir Gökhan
An asymmetric gear has different pressure angle and base radius for the drive and coast side tooth flanks. A standard is not available to determine the bending stresses of external and internal asymmetric spur gears, although there are international standards to determine the bending stresses of external and internal symmetric spur gears. The main objective of this thesis is to determine the bending stresses of the external and internal asymmetric spur gears. The tooth thickness of a gear tooth at the critical bending stress section is summation of both drive and coast side tooth thicknesses. These thicknesses are not same for an asymmetric gear tooth contrary to a symmetric gear tooth. Then, the bending stress of an asymmetric gear tooth cannot be calculated same with a symmetric gear tooth. Therefore, the bending stresses of external and internal asymmetric spur gears shall be formulated. In this thesis, ISO B methodology is modified to determine both external and internal asymmetric spur gear bending stresses. In this method, although the drive side tangent angle at the critical section is equal to 30° and 60° for external and internal asymmetric spur gears, respectively, the coast side tangent angles at their critical sections are calculated by using the kinematics of the generations of the gear coast vi side root fillets. In this thesis, the analytical results of the modified ISO method are verified by FEA works. In order to do FEA works and determine the critical bending stress sections, detailed geometry studies of both of external and internal asymmetric spur gears are carried out. In these studies, an asymmetric rack-cutter and pinion type shaper cutter are used to generate the external and internal asymmetric spur gears, respectively. For the external asymmetric spur gears, the calculated bending stress decreases with an increase in drive side pressure angle. This enables to enhance the bending strength of the gear tooth. The maximum bending stress calculated in analytical method is %5 lower than FEA results for low number of teeth and that increases to %10 for high number of teeth. For the internal asymmetric spur gears, the calculated bending stress decreases with an increase in drive side pressure angle only for low coast side pressure angle smaller than 20°. The bending stresses of the modified ISO method are about % 5 different than the results of the FEA for drive and coast side pressure angles larger than 20°, but the percentage difference increases to % 15 for low drive and coast side pressure angles smaller than 20° (for example for 16°). As a result, the modified ISO methods for external and internal asymmetric spur gears give as accurate results as the standard ISO methods for external and internal symmetric spur gears.
Citation Formats
M. G. Orak, “Investigation of asymmetric gear tooth bending stress formulation,” M.S. - Master of Science, Middle East Technical University, 2018.