GEOMETRIC STRESS CONCENTRATION (GSC) This mechanism can act on a surface when, for example, one contacting part is shorter axially than the other (common with cam-follower joints and roller bearings). The ends of the shorter roller create linecontact stress concentration in the mating roller as shown in Figure 12-25 a, and pitting or spalling will likely occur at that location. This is one reason for using crowned rollers, which have a large crown radius of curvature in the yz plane in addition to their roller radius in the xz plane. If the contact load is predictable, the crown radius can be sized to provide a more uniform stress distribution across the axial length of the contact area due to the deflections of the rollers, as shown in Figure 12-25 b . However, at lighter loads, there will be reduced contact area and thus higher stresses at the center, and at higher-than-design loads the stress concentrations at the ends will return. A partial crown can be used as shown in Figure 12-25 c, but may cause some stress concentration at the transition from straight to crown. Reusner[25] has shown that a logarithmic curve on the crown, as shown in Figure 12-25 d ,will give a more uniform stress distribution under varied load levels.

POINT-SURFACE ORIGIN (PSO) This phenomenon is described by Way and discussed above. Littman et al.[20] consider PSO to be more a manner of crack propagation than crack initiation and suggest that an inclusion at or near the surface may be responsible for starting the crack. Handling nicks or dents can also provide a crack nucleus on the surface. Once present, and if pointing in the right direction to capture oil, the crack rapidly propagates to failure. Once spalling starts, the debris can create new nicks to serve as additional crack sites.

PEELING This refers to a situation in which the fatigue cracks are at shallow depth and extend over a large area such that the surface “peels” away from the substrate. Rough surfaces exacerbate peeling if the surface asperities are larger than the lubricant film thickness.

SUBCASE FATIGUE Also called case crushing , this occurs only on case-hardened parts and is more likely if the case is so thin that the subsurface stresses extend into the softer, weaker core material. The fatigue crack starts below the case and eventually causes the case to either collapse into the failed subsurface material or break out in pits or spalls.

Whatever the detailed cause of the start of a crack, once started the outcome is predictable. So, the designer needs to take all possible precautions to improve the part’s resistance to pitting as well as to all other wear modes. The summary section to this chapter will attempt to set some guidelines to this end.

12.17 SURFACE FATIGUE STRENGTH

Repeated, time-varying loads tend to fail parts at lower stress levels than the material can stand in static load applications. The concept of surface fatigue strength is similar to that of bending- and axial-fatigue strength[2] except for one main difference. While steels and a few other materials loaded in bending or axial fatigue show an endurance limit, no materials show an equivalent property when loaded in surface fatigue. Thus, we should expect that our machine, though carefully designed to be safe against all other forms of failure, will eventually succumb to surface fatigue if so loaded for enough cycles.

Morrison[26] and Cram[27] report separately on an experimental study of the surfacefatigue strength of materials done at USM Corp. from 1932 to 1956.

FIGURE 12-25

Stress concentrations beneath variously shaped rollers

Four wear-testing machines were operated 24 hours per day for 24 years to gather surface fatigue strength data on cast iron, steel, bronze, aluminum, and nonmetallic materials. Their tests included rollers in pure rolling as well as rolling plus varying percentages of sliding. Most of their roll/slide data are done at 9% sliding, since that simulates the average conditions on spur and helical gear teeth. The percent sliding figure is defined as the relative sliding velocity between the rollers or gear teeth divided by the pitch-line velocity of the interface.

Previous sections have shown the complexity of the stress state that exists in the surface and subsurface regions of the contact zones of mating cylinders, spheres, or other bodies. The discussion of crack initiation mechanisms above indicates that the location of an incipient crack is quite unpredictable, given the random distribution of inclusions in the material. Therefore it is more difficult to accurately predict the condition of stress at an expected point of failure in a contact zone than was the case in designing a cantilever beam, for example. This dilemma is resolved by using one, easily calculated contact-zone stress as a reference value to compare to material strengths. The one chosen is the largest negative (compressive) principal contact stress. In a pure rolling case, its magnitude will be equal to the applied maximum contact pressure Pmax . But it will be greater than that value if sliding is present.

To develop allowable surface fatigue strengths, the material is typically run under controlled loading conditions (i.e., controlled pmax ) and the number of cycles to failure recorded and reported along with other loading factors such as percent sliding, lubrication, body geometry, etc. This “virtual strength” can be compared to the peak magnitude of compressive stress in other applications having similar loading factors. Thus the reported surface fatigue strength has only an indirect relationship to the actual stresses that may have been present in the test piece and in your similarly loaded part, since the Hertzian stress equations are only valid for static loading.

The expression for the normal, compressive Hertzian static stress in cylindrical contact is found by combining equations 12.14b (p. 359) and 12.17a (p. 360):

Substitute the expression for a from equation 12.15b (p. 360), square both sides, and simplify:

Rearrange to solve for the load F ,

and collect terms in a constant K ,

where

This factor K is termed an experimental load factor and is used to determine the safe endurance load F at a specified number of cycles or the number of cycles that can be expected before failure occurs at a given load.