Calculation of sub-surface-initiated fatigue fractures in gears

Power-transmitting gears are typically heat-treated, most often case-hardened, to improve the fatigue strength and therefore to ensure higher fatigue life. The heat treatment causes higher hardness in the surface area as well as compressive residual stresses in the hardened layer. The near-surface compressive residual stresses are compensated by tensile stresses in higher depths of the gear volume. Pitting and tooth root breakage are the most common failure modes of gears, which are well researched and are also addressed in ISO 6336 [14]. The assessment of these failure modes provides the basis for the dimensioning of gears in the design phase. However, subsurfaceinitiated failures, like tooth flank fracture (TFF), can also appear at loads below the allowable level of loading for pitting and tooth root bending. TFF is a fatigue damage with crack initiation in the region of the transition between compressive and tensile residual stresses and usually leads to a total loss of drive. The existing calculation models for fatigue strength of gears with regard to TFF consider residual stresses differently. The base of the investigated calculation models is a local comparison of the occurring stresses and the strength value in the gear volume. The outcome of the calculation model from Oster [26] is highly influenced by the residual stress state. However, the material-physical model by Hertter [10] is more tolerant to slightly varying residual stresses. Further approaches such as Weber [34] and Konowalcyk [18] are based on the ideas of Oster and Hertter. The verification of the models is complicated due to the lack of residual stress measurements in larger depths under the gear flank surface. For example, residual stress measurement by Xray diffraction is only possible up to depths of approximately one millimeter. Therefore, tensile residual stresses in the inner tooth volume are considered zero in the common residual stresses calculation of Lang [19] and are not considered i