New Methods for the Calculation of the Load Capacity of Bevel and Hypoid Gears Authors: C. Wirth, B.­R. Höhn, C. Braykoff


A failure mode called "flank breakage" is increasingly observed in different applications of cylindrical and bevel gears. These breakages typically start from the active flank approximately in the middle of the active tooth height and propagate to the tooth root of the unloaded flank side. Crack initiation can be localized below the surface in the region between case and core of surface hardened gears. This failure mode can neither be explained by the known mechanism of tooth root breakage nor by the mechanism of pitting. Even bevel gears in truck and bus applications are at the risk to suffer from subsurface fatigue, if the optimum utilization of the material should be achieved. In this case a balance between the flank breakage and pitting risk has to be found. The purpose of this paper is to describe a new material physically based calculation method to evaluate the risk of flank breakage versus the risk of pitting. The verification of this new method by experimental tests is exemplarily shown.
In cooperation with "ZG ­ Zahnräer und Getriebe GmbH" (ZG) "MAN truck and bus AG" (MTB) developed a new method for the calculation of the risks of flank failure by flank breakage and pitting. The calculation method has been adjusted and approved by experimental tests on powertrain test rigs of MAN. The ten different test gear variants had an outer diameter of de2 = 390 mm to 465 mm, a ratio i = 4,5 to 5,7 and a normal module of mmn = 6 mm to 8 mm. Also variants with the same main geometry but different Ease­Off designs were examined. All gear sets were tested under a defined load spectrum. Based on the research work at the FZG (Gear Research Center at the Technical University of Munich in Germany) of Oster, Hertter and Wirth a calculation method for bevel gears was established. The principle of the calculation model is the local comparison of the occurring stresses and the available strength values over the whole tooth volume. Therefore it is possible to evaluate the risk of initial cracks beyond the surface of the flank. Close to the surface cracks may grow and cause pitting ­ especially in the flank area with negative specific sliding. Cracks in the transient area between case and core lead to a high flank breakage risk.
First the local stresses and forces on the flank are determined by a loaded tooth contact analysis followed by the calculation of the maximum exposure (regarding yielding) and dynamic exposure (regarding fatigue) of the material inside the tooth. Thereby the stress components from the Hertzian contact, bending, thermal effects (flash temperature) and friction are considered. Furthermore the positive effect of residual compressive stresses and accordingly the disadvantageous effect of the residual tensile stresses can be implicated. Finite elements method investigations have been carried out in order to achieve a sufficient approximation of the residual stress distribution in the transverse tooth section. The strength values are locally considered, depending on the material depth and the position on the flank.
The recalculation of the test gears showed a good correlation between the occurred type of damage and the determined material exposure inside the tooth. The variants failed with flank breakage could be reliably distinguished from the variants failed by pitting by the new material­physical method. With this knowledge it is now possible to optimize the main geometry parameters of the gear set (e.g. number of teeth, spiral angle, pressure angle) as well as the micro geometry (Ease­Off) that influences the load distribution on the flank. Altogether this new method leads to an insured increase of the permissible material utilization and hence to smaller gear sizes while keeping the load capacity on a constant level.
ISBN: 1-978-61481-046-9 Pages: 21
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