History of Bending Fatigue, Part IV

When analyzing gear tooth bending fatigue, keep in mind that the influence of frequency on the gears cannot be underestimated and natural frequencies should be avoided all together.


The influence of frequency for monotonic or reversing load applications should not be underestimated. Natural frequencies must clearly be avoided. In single tooth fatigue tests (as seen in Figure 1), the oscillation load is usually located at the high point of single tooth contact. Frequency of the input wave is such that, depending on material, the bending area will not overheat by hysteretic damping. Damping action is generated by the dissipation of energy stored by the oscillation waveform. If the energy cannot adequately dissipate before the next load input, it continues to build to the point where excess energy can only be released thermally. This condition can detrimentally affect the results. This is especially true with plastics, where strain rates are greatly impacted by temperature. In fact, if enough oscillation energy is not dissipated in a plastic gear mesh, the flank temperature can continue to build within the material, thermally expanding until the material melts or catastrophically fails.

Another frequency issue that is particularly critical in plastic gearing is the specific sliding ratio. Since gear teeth come into contact and exit mesh with a varying rate of sliding to rolling, the mesh frequency determines how critical the sliding ratio is to the performance of the gear train. In an actual gear mesh, the higher the speed, the more the sliding ratio matters. Tooth sliding, combined with deflective oscillations of the teeth coming in and out of load, results in additional hysteretic energy. If that energy is not able to dissipate adequately in a gearbox, the lubricant can cook, friction goes up, scoring begins, and mechanical strength of the material could drop. It is recommended that the technologist critically monitor accelerated experiments to determine if frequency reduction or cooling is required to dispel excess energy.

Stress Concentrations —Notch Effects
Notch effects are one of, if not the most significant factors in many fatigue designs. In the 1860s, August Wöhler introduced the S-N concept and fatigue limits. Affectionately known as the “father of systematic fatigue testing,” Wöhler understood that sharp corners create stress risers, and should be eliminated by smoothing the notch transitions. R.E. Peterson’s later extensive published work on stress concentration factors verified and validated the effect that various notch concentrations have on the strength of materials. Since notches and stress concentrations cannot be avoided in machine design, one must consider the attributes that determine notch sensitivity to the flow of stress.

These attributes include:
a) How stress flows under resultant load conditions
b) Stress gradients and how the stress flow is imposed around geometric risers
c) Mean stress effects and the impact of residual stresses on notch sensitivity
d) The influence of localized yielding in the material microstructure
e) Nucleation and crack propagation in macro and micro elements
f) The alleviation of notch effects by design

A crack that nucleates from a stress concentration will usually propagate to failure, but can sometimes be arrested once it passes through the riser. But crack growth, once started in a high-stress gear fillet, rim areas, or a critical rotating shaft section, will almost always dominate the fatigue life of the component. Cracks will also form during fatigue from surface irregularities including deep machining grooves, grinding burns, assembly scoring, voids, discontinuities, and porosity in the case of castings or material inclusions. In any design, the technologist should first carefully evaluate the modes of load-inducing stresses in a component and determine the potential venues of failure at critical notch-sensitive geometry. It is paramount to know where the critical stress concentrations exist in a part. The result may be that only a surrogate stress concentration and an accelerated test is necessary to determine the critical fatigue life and risk associated with a specific design. This is especially advantageous when actual machine components are intricate, expensive to manufacture, and can’t be justified for full-scale testing. Figure 2

Residual Stresses
Whenever possible, the material and manufacturing processes should avoid inducing tensile mean stress in the component. To improve fatigue resistance in critical areas, an induction of compressive mean stress can be integrated into the material. This is residual stress such that the intentional stress resides in the part permanently. Once the component is subjected to fatigue-causing tensile stress, a negative residual compressive stress will cancel the tensile stress to the degree that these two entities oppose each other. Residual stresses will either improve or destroy components subjected to cyclic load spectrums. Their effect can hardly be overestimated.
There are four main categories of producing residual stresses into fatigue-related geometry — mechanical, thermal, plating, and machining.

Mechanical Induction of Residual Stress
Some of these methods include elastic yielding, shot peening, glass peening, rolling, cold working burnishing, coining, grinding, high-frequency impact, and laser peening. Glass peening is used more for surface finish enhancements than producing significant residual stress in metals. Laser peening is a mechanical surface enhancement process and, surprisingly, not a thermal one. The process creates residual compressive stresses deep within part surfaces — typically five to ten times deeper than conventional metal shot peening. A pulsed laser beam produces high-energy shock waves penetrating the material. The shockwave mechanics are responsible for inducing cold working into the microstructure and enhancing high-cycle fatigue life. On the other hand, shot peening aims high-velocity steel shot at the critical part section to produce a dimpled compressive layer at the surface and to a depth determined by the intensity of the peening. Inducing beneficial residual stresses in critical sections of high-strength materials is significant to fatigue life in order for component to utilize the majority of its greater mechanical strength. It would not make sense to specify an exotic alloy only to realize that a lack of localized yielding benefits — typical for a high strength material — would produce low cycles due to notch effects.

Thermal Induction of Residual Stress
These methods include heat treatments of all kinds — carburizing, nitriding, induction hardening, flame hardening, casting, and forging. The residual stress produced by these processes can be helpful or detrimental. These treatments leave the surface in compression relative to the inner core material. Surface compression in shafting and gear fillets can be very favorable in terms of wear, abrasion resistance, and bending fatigue life. However, whenever there is a distinct layer of hardening phase transformation relative to the core material, delaminating of the structure can occur in some circumstances as well as subsurface cracking in high-cycle applications. Subsurface cracking can be troublesome because there is no visual surface indication until the propagation reaches critical mass. Figure 3

Plating and Fatigue
Be warned: some plating scenarios can be extremely detrimental to fatigue life. Plating of machine components is generally done for corrosion protection, aesthetics, or a hard and smooth surface finish such as that used in pneumatic, hydraulic, and oil-sealing applications. Chrome-plating is also used to increase wear resistance or build up worn parts for further service. However, chromium- and nickel-plating — often used in machine components — have significant drawbacks. During the electroplating process, hydrogen can be integrated into the base metal causing “hydrogen embrittlement,”which if not dealt with will result in a significant reduction in strength. This is a particularly vexing problem for fasteners. Typically, this effect is counter-measured by heating the component to 400°C and driving out the hydrogen. This will also relieve some of the residual stresses.

Independent of hydrogen embrittlement: electroplating with chromium or nickel-plating on its own contributes to significant reduction in the fatigue strength of the material. However, softer plated materials such as cadmium, zinc, tin lead, or copper have a greatly lessened affect on fatigue resistance. One way to reverse the trend is by adding favorable residual stress the component surface or critical notch areas to counter the loss. Figure 4

Machining operations such as hobbing, skiving, grinding, shaping, milling, and turning can significantly impact the fatigue resistance of a component in three ways: thermally; by surface roughness; and by residual stresses (cold working). Overheating of the material during metal removal can change some of the phase transformations of the microstructure. High feed rates can cause plastic deformation of the grain boundaries and elastic working of the surface during metal removal. This situation becomes more profound when tools dull and greater machining pressures are needed to maintain production speeds. High-production speeds and feeds can also cause scalloping or deep grooving, depending on the process. Depending on how the machining process is optimized, the surface treatment by machining can be either beneficial or detrimental to fatigue life.

Environmental Concerns
The effects of corrosion can be either the least- or single-most detrimental effect on fatigue life of any of the impending concerns. Corrosion effects are difficult to analytically predict. Counterbalancing the reduction of component fatigue life is generally done two ways. The first method involves peening, cold working, then zinc- or cadmium-plating for galvanic cathodic protection with sacrificial anodes. Chromium and nickel plating can increase corrosion protection, but these metals also cause unfavorable residual stresses as well as raise the potential for hydrogen embrittlement. The second way is to avoid galvanic corrosion all together by sealing, encapsulating, coating, or lubricant inclusion. Some components can be covered with rust preventative or grease to keep out the effects of external oxidation. In some cases, powder metal components can be oil-impregnated to beneficial effect. Figure 5

Fretting action can be mechanical or chemical. Mechanical fretting is often referred to as assisted fatigue cracking. By definition: “Fretting is a special wear process that occurs at the contact area between two materials under load and subject to minute relative motion by vibration or some other force.” One common example of wear and fatigue fretting is a gear shaft housed in a hollow bore connection. The inner shaft relative to the hollow bore is static. However, any eccentricity, bending, vibration, or relative movement of the shaft can cause friction such that, over time and under contact pressure, micro welding can occur between the contacting surfaces. With steel components, these tend to be very numerous and small, manifesting over time as the part surface disintegrates in reddish-brown powder. In extreme cases, contacting components can weld together and can only be separated by brute force. In bronze, with the breakdown of lubrication, welding can pluck out entire material grains, leaving the surface deeply pitted. In worm gearing, the phenomena of fatigue cracking, pitting, and fretting can occur simultaneously in the gear mesh. This would also suggest that temperatures in the fretting area can become high enough to melt and fuse portions of a micro-granular surface.

Resistance to fretting and pitting can be enhanced in three different ways. First, eliminate or reduce any potential sliding, vibrations, or movement actions between components. Secondly, a focused use of special lubricants and anti-seize compounds are helpful. These unique lubricants can significantly arrest fretting corrosion wear and cracking fatigue. The proper selection is application-dependent, but can be formulated to optimize life in specific applications. Anti-seize greases or pastes may include Cu, Ni, Pb, Al, Zn, ceramics, boron nitrides, molybdenum disulfide, or barium sulfate. Barium sulfate is a high-burning material and is insoluble in water. Its insolubility makes it non-toxic, and it is an excellent anti-seize component. Solutions of barium sulfate in water makes excellent mold release agents.

1. Structural Alloys Handbook, CINDAS/Purdue University, West LaFayette, IN, 1996.
2. Robert C. Juvinall, Fundamentals of Machine Component Design, John Wiley & Sons Inc, 1983.
3.  Walter D. Pilkey, Deborah F. Pilkey, Peterson’s Stress Concentration Factors, John Wiley & Sons Inc, 2008.
4. http://www.maintenancetechnology.com/2012/07/failure-analysis-of-machine-shafts/.
5. Curtis Wright Surface Technolgies: http://www.metalimprovement.com/metal_fatigue.php.
6. (Plating and Fatigue) http://www.scielo.br/scielo.php?pid=S1516-14392002000200002&script=sci_arttext.
7. Ataollah Javidi , Ulfried Rieger, Wilfried Eichlseder, “The Effect of Machining on the Surface Integrity and Fatigue Life,” International Journal of Fatigue, January 2008.
8. ASM Handbook, Volume 19: Fatigue and Fracture, ASM International, 1996; Page: 1057; ISBN: 978-0-87170-385-9
9. Ralph I Stephens, Ali Fatemi, Robert R. Stephens, Henry O. Fuchs, Metal Fatigue in Engineering, 2nd Edition, John Wiley & Sons Inc, 2001.
10. Julie A. Bannantine, Jess J. Comer, James L. Handrock, Fundamentals of Metal Fatigue Analysis, Prentice-Hall Inc, 1990.

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is a senior technical specialist in the development of gearing, drive motors, and power closure devices in the automotive industry. He currently serves on the AGMA Plastic and PM Gearing Committees. Eberle is a master six-sigma black belt and has authored many papers on gearing, measurement system analysis and process statistics. He can be reached at Fred_Eberle@hci.Hi-Lex.com.