Factors Influencing the Tooth Root Load Capacity

The load capacity of a gear describes the load limit up to which a gear can be operated without damage and is understood as the strength of the gear material against mechanical load (Refs. 21–23). The load capacity is determined by the selected gear material and the manufacturing processes used, including the process parameters (Refs. 4,5,10,24). A significant influence on the load capacity is the choice of the material and heat treatment combination, as this has a decisive influence on the material properties of a gear (Refs. 4,14,23).

The mean stress sensitivity is one of these material properties and describes the relationship between the fatigue limit stress amplitude and the mean stress present (Ref. 25). In general, the stress amplitude that can be withstood decreases as the mean stress increases (Ref. 25). In addition, surface-hardened components are more sensitive to mean stress in the tensile range than non-surface-hardened components (Refs. 25,26). Nevertheless, gears are usually surface hardened to provide a hard and high-strength surface that can withstand the tangential stresses in the tooth root area and the high pressures in the tooth contact area (Refs. 18,27). Inside the tooth, on the other hand, high ductility is required to withstand the load due to bending stresses and possible impacts (Refs. 18,27). Due to these requirements, case-hardened and nitrided steels are used for gears in many applications (Refs. 17,18).

Another material property is the notch sensitivity, which describes the property of a material to be sensitive to local stress increases due to changes in the shape of the component (Ref. 25). In this context, shape changes are any shapes with high local curvature ratios, such as undercuts in notches or the tooth root of gears (Refs. 14,18,25). Components with such shape changes, if they are made of a material with high notch sensitivity, have a lower load capacity than geometrically identical components made of a material with lower notch sensitivity (Ref. 25). Furthermore, notch effects can also be caused by the structure and condition of the component surface and lead to local stress increases (Refs. 17,18,27). The surface of a gear is determined by the final machining operation and depends on the selected process chain (Ref. 17). For non-ground tooth roots, the surface finish is already defined by the soft machining and the subsequent heat treatment (Refs. 17,18). Feed marks and enveloping cut deviations from soft machining can affect the tooth bending strength negatively due to the notch effect and promote crack initiation on the component surface (Refs. 17,18).

In shot peened gears, the location of crack initiation moves from the surface to the interior of the component due to the high compressive residual stresses near the surface (Refs. 10,28). Crack initiation usually occurs there due to the local stress increase at flaws, i.e., defects in the basic structure, such as non-metallic inclusions (Refs. 10,28). With continued loading, the crack initiation phase then transitions to the crack growth phase, ultimately leading to damage and failure of the application (Ref. 28). Typically, sub-surface damage only occurs at higher numbers of load cycles, in the so-called very-high cycle fatigue (VHCF) and ultra-high cycle fatigue (UHCF) range (Refs. 10,28). Therefore, high-purity steels are used in applications with high load cycles, such as in aircraft engines and rolling bearings, to reduce the number of defects and thus the possibility of crack initiation (Ref. 5).