Gear Root Bending Strength: A Comparison Between Single Tooth Bending Fatigue Tests and Meshing Gears

Abstract

Gear tooth breakage due to bending fatigue is one of the most dangerous failure modes of gears. Therefore, the precise definition of tooth bending strength is of utmost importance in gear design. Single Tooth Bending Fatigue (STBF) tests are usually used to study this failure mode, since they allow to test gears, realized and finished with the actual industrial processes. Nevertheless, STBF tests do not reproduce exactly the loading conditions of meshing gears. The load is applied in a pre-determined position, while in meshing gears it moves along the active flank; all the teeth can be tested and have the same importance, while the actual strength of a meshing gear, practically, is strongly influenced by the strength of the weakest tooth of the gear. These differences have to be (and obviously are) taken into account when using the results of STBF tests to design gear sets. The aim of this paper is to investigate in detail the first aspect, i.e. the role of the differences between two tooth root stress histories. In particular, this paper presents a methodology based on high-cycle multi-axial fatigue criteria in order to translate STBF test data to the real working condition; residual stresses are also taken into account

Gear Root Bending Strength: A New Multiaxial Approach to Translate the Results of Single Tooth Bending Fatigue Tests to Meshing Gears

“…Specifically, in [73], the load carrying capacity of hypoid gears was determined through a method combining the Liu & Mahadevan fatigue criterion [67] and an FE approach. In [74,75], the Crossland fatigue criterion [54] was adopted to characterize the state of stress in spur gears. It is notable that while the Liu & Mahadevan fatigue criterion is based on the critical plane approach, the Crossland fatigue criterion is not.…”

Reliable Gear Design: Translation of the Results of Single Tooth Bending Fatigue Tests Through the Combination of Numerical Simulations and Fatigue Criteria

“…In addition, the force direction in STBF tests can be different from the one in the Outer Point of Single pair tooth Contact (OPSC) of RG and, therefore, a different share between pure bending and pure compressive stresses could be present. Moreover, in RG tests, the variable number of mating teeth pairs leads to an uneven force sharing [26]. Consequently, the stress time history at the tooth root is not sinusoidal as in the STBF tests [9], [11].…”

“…However, tests were conducted for a limited combination of materials and geometries and, therefore, new techniques to estimate for each specific combination of material and geometry have been developed. An advanced method is presented in [26], where the scholars have combined the Crossland fatigue criterion [27] with a numerical simulation of RG and the experimental results of STBF tests. In this case, the corrective factors have resulted equal to 0.82 and 0.84 for the two materials tested.…”

Bending Fatigue Behavior of 17-4 PH Gears Produced by Additive Manufacturing

“…While two teeth are tested at the same time, the friction between the teeth flanks and the anvils (used for applying the load), ensures that the forces acting on the gear-sample are automatically balanced and no additional supporting structures are required. On the other hand, this implies the existence of a stress ratio = 0 (the load varies between the maximum values and a fixed percentage of it, e.g., 10% → R = 0.1) to maintain the preload on the system [27][28][29].…”