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Science Update

##### in Vol. 8 - November Issue - Year 2007

##### Shot Peening Improves Load Capacity Of Gear

Figure 1: Trend of residual stresses versus depth in two cases for Ni Cr steel: case hardened, case hardened followed by shot peening (Institut f

Figure 2: Measurement of residual stresses on a gear with X Ray diffractometer (Labs, Department of Mechanical Engineering, Politecnico di Milano, Italy)

Figure 3: Trend of principal stresses at toot root, force applied at the Highest Single Contact Point (FEM calculation from Department of Mechanical Engineering, Politecnico di Milano, Italy)

Figure 4: Bending fatigue tests of gear teeth performed with a resonance pulsator (Labs, Department of Mechanical Engineering, Politecnico di Milano, Italy)

Figure 5: Comparison of fatigue resistance and fatigue limit (bending), case hardened gears, module m = 5 mm; no shot peening (lower curve), shot peening at different intensities [5].

Figure 6

Figure 7

Figure 8

Figure 9

Shot peening is widely used to improve fatigue strength of heavily loaded components like springs, shafts and crankshafts. Also when applied to gears, shot peening proved to be very effective, and it can be used to significantly improve gear performances.

**Introduction**

The ever increasing demand for highly loaded gear power transmission, that comes from the trend to use power transmission systems with improved performances together with lightness and reduced volumes, lead engineers to look for new design solutions, able to overcome the ones traditionally used and known as reliable ones. In other words, it is necessary to use gears with smaller dimensions and to load them with higher torque and power, that is to say that it is necessary to increase the ratio power/mass (volume) of the system.

This is possible if we apply a so called “design by analysis” procedure. This means that we should have an accurate knowledge of the effective applied loads and of the mechanical characteristics of the materials, we should use accurate analysis methods (like Finite Elements), and we should be able to finely determine the effect of surface treatments used to improve both fatigue and contact fatigue strength of gears. This approach leads to smaller safety coefficients.

One of the treatments most widely used to improve the mechanical characteristics of the materials is shot peening [1, 2], that can be successfully applied also to steel gears, especially to those that were previously surface hardened by means of some surface thermal treatment (most of time carburizing). Shot peened gears are commonly used in some particular field of application, where the first objective of the engineers is to reduce weight (aerospace, race cars,..). But it does not mean that shot peening cannot be used also in industrial application. In this case the extra cost for shot peening application can be balanced by the increment of the performances that can be obtained.

**The effects of shot peening on materials and components**

Shot peening is a well known surface mechanical treatment and it has been used for many decades to improve the fatigue strength of steel components, previously surface hardened too (carburized, nitrided ore induction hardened). Typical applications of shot peening are helical springs, but this treatment is widely used for a great variety of mechanical components, generally cyclically loaded.

Shot peening consists of shooting the surface of a component with spheres of small diameter (0.1mm-1.5 mm). The energy of the impact of the shot flow must be sufficient to induce plastic deformation of a thin layer of material. The result is a surface with modified roughness and hardness and, what is more important, with a residual stress field that is compressive in the sub-surface layer of material, whose depth depends on the treatment parameters and on the treated material (until 0.2-0.3mm from the surface). The effectiveness of shot peening is mainly related not to the surface value of the residual stresses but to the residual stress trend under the surface: deeper layers subjected to compressive residual stresses lead to more relevant results.

In Figure 1 the in-depth trend of residual stresses due to shot peening and to carburizing is shown the different results in terms of residual stresses are evident. The magnitude of residual stresses is some hundred MPa, and it depends on the treatment parameters (shot dimension and material,shot velocity, coverage) and on the treated material. Values like -300/-500 MPa are usual [3]; the value of the residual stresses decrease by moving far from the surface until they can be neglected.

The residual stress field is self-equilibrated and can be appreciated only in a thin sub-surface layer of material. It does not generate macroscopical deformation if the thickness of the treated component is large enough. If the peened component is loaded with forces that originate tensile stresses, these latter sum to the residual ones: in this way it is possible to reduce the maximum value of the effective stress. On the contrary, if the applied stresses are compressive, the maximum effective compressive stress will increase. But it is well known that, concerning fatigue strength and its damage mechanism (crack initiation on or under the surface and rack propagation), having fatigue cycles with compressive mean stress induces the possibility of increasing the amplitude of the cycle with respect to cases of null or tensile mean stress. This is the role played by residual stresses, that gives important advantages in terms of increased applied loads or, if the load remains the same, in terms of the life of the peened component.

Also treatments like carburizing and nitirding induce compressive residual stresses, but generally they are low and vanish soon under the surface, while the ones due to shot peening (if done well) are effective for a deeper layer of material.

Residual stress measurement can be done by using different methods, both destructive and non-destructive. Among these latter, X-ray diffraction gives accurate results [4]. It can be used also for in-depth measurements but, in this case, it is necessary to remove the surface layer of material by some non invasive method, like electro-polishing, to prevent the residual stress filed being altered by the action of a mechanical tool. In Figure 2a measurement on a gear tooth is shown.

The knowledge of in-depth trends of residual stresses leads to understanding of the greater effectiveness of shot peening for notched components, like at the gear tooth root. In fact, in this case there is a strong stress gradient and the in-depth applied stress strongly reduces just where the compressive residual stress is maximum. Shot peening can be usefully applied also to gears. Its application is now confined to high-tech applications, like aerospace, helicopters or race cars, where it is fundamental to the development of light systems, while it is not adequately considered in other industrial fields due to its cost.

But a more accurate knowledge of the largely positive effect of shot peening on the mechanical behaviour of gears can lead to considering shot peening in new fields of application.

**Increasing fatigue performance of gears**

Shot peening on the active flank of gear teeth and on the tooth root surfaces is known to increase single tooth bending fatigue strength and contact fatigue strength and in general the overall performance of gears. However, the actual performance gain is quite difficult to assess, because many parameters play a role in controlling the effectiveness of the shot peening treatment. The most important factors affecting the results of shot peening are: material characteristics; type of surface hardening (case hardening, nitriding, etc.); amount and in-depth profile shape of residual stresses; shot peening intensity; type, shape and dimensions of shots; and other.

In literature, it is difficult to find reference test results that could be directly employed in a new design. In fact, transferring results would imply that shot peening parameters are the same, or at least quite similar, which is not always the case. Moreover, the companies that have achieved considerable experience and success in using shot-peening as a means of increasing component performance, are not likely to publicize the details about their know-how.

Hereafter, some test results produced in well established research centres or by renowned companies are shown. Even with caution, they might be generalized and applied to different cases with an adequate degree of reliability.

*Increasing tooth bending fatigue strength*

The state of stress at the root of gear teeth is shown in Figure 3: stress gradients at the fillet can be very high and usually the maximum stress is located quite near to the 30° tangent to the tooth axes at the tooth root, which is the most relevant position according to the calculation method of ISO standard. Since every given tooth goes from unloaded condition to fully loaded condition, the material in its most critical position experiences a fatigue type of loading. In the most common case, a zero-to-maximum pulsating loading is observed, while for the teeth of an intermediate wheel in a gear train, an alternating type of loading is also possible.

A compressive stress left by shot-peening in the very thin surface layer at the critical position has the beneficial effect to lower the peak (tensile) stress due to the applied load. The overall effect is to increase the fatigue strength and, consequently, the fatigue limit but, in order to fully assess the beneficial effect of shot-peening on gear fatigue strength, fatigue tests need to be carried out by single tooth bending in a fatigue testing machine, like that shown in Figure 4. Fatigue test results shown in Figure 5, obtained by researchers at the Institut für Werkstoffkunde of the Technical Universiy of Karlsruhe, Germany, show a significant increase of the fatigue strength for case hardened 16MnCr5 steel gears [5]. The amount of increase of the fatigue strength mainly depends on the shot-peening intensity. By increasing the peening intensity, the fatigue limit can be improved from +22% to +40% when compared to un-peened gears. This can mainly be ascribed to the beneficial effect of compressive residual stress generated by shot-peening. Even though the surface residual stresses of the case hardened material is not significantly different from that of case hardened and shot-peened condition, in the case of shot-peened material the extension and effectiveness of compressive residual stress is quite different in these two cases. In fact, in the case-hardened material, compressive residual stresses vanish at a distance from the free surface of some 10 microns in depth. On the contrary, in the case of case hardening followed by shot-peening, the compressive residual stresses have an effective depth of some hundreds of microns. These differences are sufficient alone to justify the superior fatigue performance of shot-peened gears (see Figure 1).

*Increasing contact fatigue (pitting) strength*Fatigue damage due to friction contact between mating gear flanks under lubricated conditions is known as pitting. The formation of contact "pits" on the surface of gear teeth is due to the high contact stresses that arise at the surface and in the subsurface layer under contact of up to a depth of few hundreds microns [6]. The simplest model makes use of the hertzian contact stress theory, where friction and lubrication are neglected and real contact is idealised and modelled as two equivalent cylinders in contact, as shown in Figure 6. Since contact loading on a given gear tooth is cyclic, the cyclic contact stresses are likely to cause fatigue damage. In Figure 7 the typical “pit” damage on a gear tooth surface as observed by SEM at high magnification is shown. It can be clearly observed a propagating fatigue crack emanating from the pit damage. Moreover, it must be observed that contact stresses are tensile: by inducing a compressive stress state by shot-peening or other surface treatments not only do maximum stresses have a reduced influence but also cracks that may propagate from microstructural defects in the materials have a slower crack growth rate or, in some cases, their propagation can be stopped altogether.

The usual way to quantify the increase of loading capacity of gears with respect to contact fatigue is done by experimental tests of contact fatigue with special gear testing rigs, where other competing phenomena are left out: for instance, damage caused by scuffing cannot be classified as a contact fatigue problem and thus scuffing service conditions must be avoided in the tests.

Contact fatigue tests on gears are conducted by employing special power re-circulating rigs like the FZG rig or similar: even if the results of such tests are of paramount importance for designers, they are quite time consuming and they call for a high accuracy in test results analysis.

Alternatively, if reduction of testing associated costs is an issue, roller-follower contact fatigue tests can be carried out but, since the friction condition of real gears cannot be reproduced in such tests (only constant sliding speed can be achieved in roller tests), test results obtained in roller contact fatigue test rigs are more difficult to transfer to real gears. If gear performance needs to be accurately assessed, power re-circulating test rig results are to be preferred over other competing test techniques.

In Figure 8 results of a contact fatigue test conducted in a power re-circulating test rig by researchers of the Mitsubishi Motor Corporation, Japan, are presented in a Wöhler diagram [7]. These tests have been performed on cylindrical gears, made of a Cr-Mo steel grade, with a modulus m=3 mm, with shaving after case-hardening, with and without shot-peening final treatment. In this case, un-peened gears have a surface hardness of 752 HV and residual stress, measured by X-ray diffraction, is ?res=-270 MPa. After shot-peening, surface hardness is 835 HV and surface residual stress is ?res=-330 MPa. From comparison of contact fatigue limits, without and with shot-peening, an increase of loading capacity of gears of about 35% is observed. It should be observed that increase of loading capacity cannot be justified by the increase of surface hardness and only dedicated tests do permit to appreciate the increase of material fatigue resistance. As a comparison, the same research group made rolling fatigue tests on rollers, with the same type of materials and surface treatment but the increase of fatigue strength by shot-peening was only 15%. This could demonstrate that rolling fatigue tests can underestimate the beneficial effect of shot-peening on real gears. An increase of contact fatigue strength (resistance to pitting damage) of 30% has been observed by other research groups in tests conducted in power recirculating test rigs on case hardened gears. The advantage of this type of tests is that they permit the reproduction in controlled conditions of service loading experienced by gears in vehicle transmissions [8].

Similar tests have been performed at NASA Glenn Research Center in Cleveland, OH, with a special power re-circulating test rig designed for high rotational speeds, typical of aerospace transmissions. Comparison tests conducted on superclean case hardened steel gears which have been shot-peened with different Almen intensity, ranging from 7-9 A up to 15-17 A, show an increase of contact fatigue strength of 115% (the fatigue strength is more than doubled). These results are not uncommon provided that extremely high quality steel grade is employed: in fact these materials can get a consistent benefit from higher shot-peening intensity. For more conventional gear materials (case hardening steels) the increase of contact fatigue strength due to shot-peening is about 60% (maximum). Even if test results obtained by high speed power recirculating test rigs could be difficult to transfer to different service conditions (f.i.: lower speed, different materials, etc.), they demonstrate that gear loading capacity can be greatly improved by shot-peening [9].

**What standards say about shot peening of gears**

As a general rule, standards are conservative; that, perhaps, is not wrong. Consequently, standards don’t emphasize the effects of specific surface treatments as shot peening, whose beneficial effects are well known but cannot easily be generalised and quantified, because it is highly dependent on the way the treatment has been done. In particular, it’s difficult to quantify the beneficial effects concerning gear rating.

*AGMA standards*

The Standard ANSI/AGMA 2004-B89, January 1989, titled “Gear Materials and Heat Treatment Manual”, includes a paragraph dedicated to shot peening. The standard states that bending fatigue resistance can increase about 25% due to shot peening, and consequently this surface treatment can be utilised to upgrade existing gears. Concerning surface fatigue, the standard states that resistance can be improved; but states also that quantitative data to substantiate this condition is poor.

The well known ANSI/AGMA 2001-D4 Fundamental Rating Factors and Calculation Methods for Involute Spur and Helical Gear Teeth does’nt give a great importance to residual stresses; the standard only states that this kind of stresses, if properly induced (that is, if compressive), “should” increase the bending load limit of gears.

In other paragraphs of this standard, residual stresses obtained by different methods (nitriding, case-hardening) are mentioned. Finally, in the Appendix a paper of A. Datano e K. Namiki, 1992, is quoted, concerning the effects of shot peening on automotive gears; a Wöhler (S/N) diagram is reported, taken from this paper, that shows an improvement of bending fatigue resistance (or perhaps of fatigue limit) of about 30% (Figure 9).

The Information Sheet AGMA 938-A05 (Shot Peening of Gears) concerns only the shot peening process itself, and how it can be applied to gears; no quantitative data is given about the beneficial effects of this treatment.

*ISO Standards*

The ISO Standards too give little evidence and data concerning shot peening as a method to improve the fatigue resistance of gears; quantitative data is poor.

The ISO 6336-3 (1996) Calculation of load capacity of spur and helical gears, part 3, Calculation of tooth bending strength, states that the factor YRrelT, concerning surface roughness effects at tooth root, can have a different value for shot peened gears; but no data of this improvement is given.

The ISO 6336-3 del 1996 Calculation of load capacity of spur and helical gears, part 5, Strength and quality of materials, states that, in general, the allowable limits depend on residual stresses. In the tables that give the materials quality grades (ML, MQ, ME), it is stated that for specific materials, in agreement with the customer, a savage of existing gears can be obtained by shot peening.

The paragraph 6.7 is dedicated to shot peening, and some data on the beneficial effects is given. For case hardened gears the beneficial effects on bending fatigue are zero for ML grade, + 10% for MQ grade and +5% for ME grade. No details are given to support this data.

**References**

1. Marsh K.J. (Ed.) Shot peening: techniques and applications. EMAS, 1993.

2. V. Schulze. Modern Mechanical Surface Treatment. Wiley-VCH, 2004.

3. M. Guagliano, M. Guidetti, E. Riva, “Contact fatigue failure analysis of shot peened gears”, in “Engineering Failure Analysis”, Elsevier Science Ltd, Vol. 9, 2002, 147-158.

4. J. Lu., “Handbook of measurements of residual stresses”, Society for Experimental Mechanics SEM, 1996.

5. T. Hirsch, H. Wohlfahrt, E. Macherauch "Fatigue strength of case hardened and shot peened gears", Communication from the Institut fuer Werkstoffkunde I, Universitaet Karlsruhe, 1985.

6. Widmark M, Melander A., Effect of material, heat treatment, grinding and shot peening on contact fatigue life of carburised steels. Int J Fatigue 1999; 21:. 310-327.

7. S. Himasatsu, T. Kanazawa, T. Toyoda “Influence of the surface properties on the bending strength of shot peened carburized steel", Material Development Dept, Isuzu Motors Ltd, 1990.

8. Kobayashi M, Hasegawa K.”Effect of shot peening on the pitting fatigue strength of carburized gears”. Proceedings of the IV International Conference on Shot Peening, 1990, 465-476.

9. D. P. Townsend “Improvement in surface fatigue life of hardened gears by high-intensity shot peening", NASA Report, Lewis Research Center, 1992.

Dipartimento di Meccanica

Politecnico di Milano

Via La Masa, 34, 20156 MILANO (ITALY)

E-mail: mario.guagliano@polimi.it