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Journal of Tribology | Volume 135 | Issue 1 | research-article
Research Papers

Analysis of Micro-Elastohydrodynamic Lubrication and Prediction of Surface Fatigue Damage in Micropitting Tests on Helical Gears

[+] Author and Article Information
R. W. Snidle

e-mail: SnidleR@cf.ac.uk

K. J. Sharif

School of Engineering,
Cardiff University,
Cardiff, CF24 3AAUnited Kingdom

J. Zhang

Design Unit,
Newcastle University,
Newcastle, NE1 7RUUnited Kingdom

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received April 4, 2012; final manuscript received September 20, 2012; published online November 30, 2012. Assoc. Editor: Dong Zhu.

J. Tribol 135(1), 011501 (Nov 30, 2012) (9 pages) Paper No: TRIB-12-1045; doi: 10.1115/1.4007693 History: Received April 04, 2012; Revised September 20, 2012
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The paper describes results obtained from the micro-elastohydrodynamic lubrication (micro-EHL) modeling of the gear tooth contacts used in micropitting tests together with a contact fatigue and damage accumulation analysis of the surfaces involved. Tooth surface profiles were acquired from pairs of helical test gears and micro-EHL simulations were performed corresponding to surfaces that actually came into contact during the meshing cycle. Plane strain fatigue and damage accumulation analysis shows that the predicted damage is concentrated close to the tooth surfaces and this supports the view that micropitting arises from fatigue at the asperity contact level. A comparison of the micropitting performance of gears finish-ground by two alternative processes (generation-grinding and form-grinding) suggests that 3D “waviness” may be an important factor in explaining their different micropitting behavior.
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References

1
Hohn, B. R., Oster, P., and Emmert, S., 1996, “Micropitting in Case-Carburized Gears —FZG Micropitting Test,” International Conference on Gears, Dresden, Germany, VDI Berichte No. 1230, pp. 331–334.
2
Brimble, K., Atkins, I., Blencoe, K., Aylott, C., and Shaw, B. A., 2001, “A Comparison of Micropitting Performance of Identical Oils Using Standard FZG Test Gears and Helical Test Gears,” BGA Annual Congress, London, UK, pp. 44–50.
3
Chang, L., and Webster, M. N., 1991, “A Study of Elastohydrodynamic Lubrication of Rough Surfaces,” ASME J. Tribol., 113, pp. 110–115. [CrossRef]
4
Jiang, X., Hua, D. Y., Cheng, H. S., Ai, X., and Lee, S. C., 1999, “Mixed Elastohydrodynamic Lubrication Model With Asperity Contact,” ASME J. Tribol., 121, pp. 481–491. [CrossRef]
5
Zhao, J., Sadeghi, F., and Hoeprich, M. H., 2001, “Analysis of EHL Circular Contact Start Up—Part I: Mixed Contact Model With Pressure and Film Thickness Results,” ASME J. Tribol., 123, pp. 67–74. [CrossRef]
6
Hu, Y. Z., and Zhu, D., 2000, “Full Numerical Solution to the Mixed Lubrication in Point Contacts,” ASME J. Tribol., 122, pp. 1–9. [CrossRef]
7
Hughes, T. G., Elcoate, C. D., and Evans, H. P., 2000, “Coupled Solution of the Elastohydrodynamic Line Contact Problem Using a Differential Deflection Method,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 214, pp. 585–598. [CrossRef]
8
Elcoate, C. D., Evans, H. P., Hughes, T. G., and Snidle, R. W., 2001, “Transient Elastohydrodynamic Analysis of Rough Surfaces Using a Novel Coupled Differential Deflection Method,” Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol., 215, pp. 319–337. [CrossRef]
9
Holmes, M. J. A., Evans, H. P., and Snidle, R. W., 2005, “Analysis of Mixed Lubrication Effects in Simulated Gear Tooth Contacts,” ASME J. Tribol., 127, pp. 61–69. [CrossRef]
10
Zhang, J., and ShawB. A., 2011, “The Effect of Superfinishing on the Surface Fatigue of Case Carburised Gears,” Appl. Mech. Mater., 86, pp. 348–351. [CrossRef]
11
Oila, A., Shaw, B. A., Aylott, C. J., and Bull, S. J., 2005, “Martensite Decay in Micropitted Gears,” Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol., 219, pp. 77–83 [CrossRef].
12
Johnson, K. L., 1985, Contact Mechanics, Cambridge University Press, Cambridge, UK.
13
Qiao, H., Evans, H. P., and Snidle, R.W., 2008, “Comparison of Fatigue Model Results for Rough Surface Elastohydrodynamic Lubrication,” Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol., 222, pp. 381–393. [CrossRef]
14
Amzallag, C., Gerey, J. P., Robert, J. L., and Bahuaud, J., 1994, “Standardization of the Rainflow Counting Method for Fatigue Analysis,” Int. J. Fatigue, 16, pp. 287–293. [CrossRef]
15
Fatemi, A., and Socie, D. F., 1988, “A Critical Plane Approach to Multiaxial Fatigue Damage Including Out-of-Phase Loading,” Fatigue Fract. Eng. Mater. Struct., 11, pp. 149–165. [CrossRef]
16
Zahavi, E., and TorbiloV., 1996, Fatigue Design: Life Expectancy of Machine Parts, CRC, Boca Raton.
17
Dowling, N. E., 1998, Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue, Second ed., Prentice Hall, Englewood Cliffs, NJ.

Figures

Grahic Jump Location
Fig. 9

Typical raw profilometer trace of the gear tooth showing the tooth tip location on the right (origin of the x-coordinate)

+Typical raw profilometer trace of the gear tooth showing the tooth tip location on the right (origin of the x-coordinate)
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Typical raw profilometer trace of the gear tooth showing the tooth tip location on the right (origin of the x-coordinate)
Grahic Jump Location
Fig. 10

Illustration of contact between gears at s = +9.4 mm; z is the pitch point

+Illustration of contact between gears at s = +9.4 mm; z is the pitch point
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Illustration of contact between gears at s = +9.4 mm; z is the pitch point
Grahic Jump Location
Fig. 11

Typical tooth profile from the wheel of test A corresponding to s = −5.0 mm

+Typical tooth profile from the wheel of test A corresponding to s = −5.0 mm
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Typical tooth profile from the wheel of test A corresponding to s = −5.0 mm
Grahic Jump Location
Fig. 8

Illustration (to scale) showing the setup for measurement of the tooth profile. Here, AB is the datum line of the profilometer, which is tangential to the tooth at the working pitch point z and x is the distance along the profile measured from the tooth tip.

+Illustration (to scale) showing the setup for measurement of the tooth profile. Here, AB is the datum line of the profilometer, which is tangential to the tooth at the working pitch point z and x is the distance along the profile measured from the tooth tip.
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Illustration (to scale) showing the setup for measurement of the tooth profile. Here, AB is the datum line of the profilometer, which is tangential to the tooth at the working pitch point z and x is the distance along the profile measured from the tooth tip.
Grahic Jump Location
Fig. 7

Helical test gear with illustration of the position of surface profiles

+Helical test gear with illustration of the position of surface profiles
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Helical test gear with illustration of the position of surface profiles
Grahic Jump Location
Fig. 6

Graph showing the average gear profile deviation versus the running cycles. It shows the progression of cumulative micropitting damage on gears ground by the generation and form grinding processes during two stepwise micropitting tests under the same operating conditions. The final load stage corresponds to a pinion torque of 4 kN m.

+Graph showing the average gear profile deviation versus the running cycles. It shows the progression of cumulative micropitting damage on gears ground by the generation and form grinding processes during two stepwise micropitting tests under the same operating conditions. The final load stage corresponds to a pinion torque of 4 kN m.
View Large  |  Save Figure  |  Download Slide (.ppt)
Graph showing the average gear profile deviation versus the running cycles. It shows the progression of cumulative micropitting damage on gears ground by the generation and form grinding processes during two stepwise micropitting tests under the same operating conditions. The final load stage corresponds to a pinion torque of 4 kN m.
Grahic Jump Location
Fig. 5

Three-dimensional representation of the surfaces produced by the two types of finish grinding processes: (a) generation-ground, and (b) form-ground

+Three-dimensional representation of the surfaces produced by the two types of finish grinding processes: (a) generation-ground, and (b) form-ground
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Three-dimensional representation of the surfaces produced by the two types of finish grinding processes: (a) generation-ground, and (b) form-ground
Grahic Jump Location
Fig. 4

The 160 mm helical gear test rigs with a close-up view of exposed test gears (inset)

+The 160 mm helical gear test rigs with a close-up view of exposed test gears (inset)
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The 160 mm helical gear test rigs with a close-up view of exposed test gears (inset)
Grahic Jump Location
Fig. 3

Sections through micropits showing the characteristic direction of cracks in the dedendum (left) and addendum (right) of the same tooth on the driven gear. Arrows above the surface indicate the direction of rolling over the contact (R), and the direction of the sliding traction (S) acting on the tooth.

+Sections through micropits showing the characteristic direction of cracks in the dedendum (left) and addendum (right) of the same tooth on the driven gear. Arrows above the surface indicate the direction of rolling over the contact (R), and the direction of the sliding traction (S) acting on the tooth.
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Sections through micropits showing the characteristic direction of cracks in the dedendum (left) and addendum (right) of the same tooth on the driven gear. Arrows above the surface indicate the direction of rolling over the contact (R), and the direction of the sliding traction (S) acting on the tooth.
Grahic Jump Location
Fig. 2

Sections through micropits showing crack growth

+Sections through micropits showing crack growth
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Sections through micropits showing crack growth
Grahic Jump Location
Fig. 1

Micropitting predominantly in the dedendum region of a helical test gear tooth

+Micropitting predominantly in the dedendum region of a helical test gear tooth
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Micropitting predominantly in the dedendum region of a helical test gear tooth
Grahic Jump Location
Fig. 12

Pressure profile (lower curve) and deflected surface profiles (upper curves) at a particular timestep during the micro-EHL simulation. The operating condition corresponds to gear set B; s = +5.0 mm. The dashed line shows the corresponding Hertzian pressure with a maximum value of 1.0 GPa. The Hertzian contact dimension is a = 0.247 mm.

+Pressure profile (lower curve) and deflected surface profiles (upper curves) at a particular timestep during the micro-EHL simulation. The operating condition corresponds to gear set B; s = +5.0 mm. The dashed line shows the corresponding Hertzian pressure with a maximum value of 1.0 GPa. The Hertzian contact dimension is a = 0.247 mm.
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Pressure profile (lower curve) and deflected surface profiles (upper curves) at a particular timestep during the micro-EHL simulation. The operating condition corresponds to gear set B; s = +5.0 mm. The dashed line shows the corresponding Hertzian pressure with a maximum value of 1.0 GPa. The Hertzian contact dimension is a = 0.247 mm.
Grahic Jump Location
Fig. 13

Contours of the subsurface damage (D) on the pinion tooth from gear set A at s = +5.0 mm (the pinion is the faster surface). The upper graph shows the corresponding section of the pinion surface profile. The Hertzian contact dimension is a = 0.247 mm.

+Contours of the subsurface damage (D) on the pinion tooth from gear set A at s = +5.0 mm (the pinion is the faster surface). The upper graph shows the corresponding section of the pinion surface profile. The Hertzian contact dimension is a = 0.247 mm.
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Contours of the subsurface damage (D) on the pinion tooth from gear set A at s = +5.0 mm (the pinion is the faster surface). The upper graph shows the corresponding section of the pinion surface profile. The Hertzian contact dimension is a = 0.247 mm.
Grahic Jump Location
Fig. 14

Contours of the subsurface damage (D) on the pinion tooth from gear set B at s = +5.0 mm (the pinion is the faster surface). The upper graph shows the corresponding section of the pinion surface profile. The Hertzian contact dimension is a = 0.247 mm.

+Contours of the subsurface damage (D) on the pinion tooth from gear set B at s = +5.0 mm (the pinion is the faster surface). The upper graph shows the corresponding section of the pinion surface profile. The Hertzian contact dimension is a = 0.247 mm.
View Large  |  Save Figure  |  Download Slide (.ppt)
Contours of the subsurface damage (D) on the pinion tooth from gear set B at s = +5.0 mm (the pinion is the faster surface). The upper graph shows the corresponding section of the pinion surface profile. The Hertzian contact dimension is a = 0.247 mm.
Grahic Jump Location
Fig. 15

Cumulative damage distribution for the pinion (slower surface) corresponding to s = −9.4 mm at a series of depths below the surface. The solid lines are for gear set A and the dashed lines are for gear set B.

+Cumulative damage distribution for the pinion (slower surface) corresponding to s = −9.4 mm at a series of depths below the surface. The solid lines are for gear set A and the dashed lines are for gear set B.
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Cumulative damage distribution for the pinion (slower surface) corresponding to s = −9.4 mm at a series of depths below the surface. The solid lines are for gear set A and the dashed lines are for gear set B.
Grahic Jump Location
Fig. 16

Cumulative damage distribution for the pinion (slower surface) corresponding to s = −5.0 mm at a series of depths below the surface. The solid lines are for gear set A and the dashed lines are for gear set B.

+Cumulative damage distribution for the pinion (slower surface) corresponding to s = −5.0 mm at a series of depths below the surface. The solid lines are for gear set A and the dashed lines are for gear set B.
View Large  |  Save Figure  |  Download Slide (.ppt)
Cumulative damage distribution for the pinion (slower surface) corresponding to s = −5.0 mm at a series of depths below the surface. The solid lines are for gear set A and the dashed lines are for gear set B.
Grahic Jump Location
Fig. 17

Cumulative damage distribution for the pinion (faster surface) corresponding to s = +5.0 mm at a series of depths below the surface. The solid lines are for gear set A and the dashed lines are for gear set B.

+Cumulative damage distribution for the pinion (faster surface) corresponding to s = +5.0 mm at a series of depths below the surface. The solid lines are for gear set A and the dashed lines are for gear set B.
View Large  |  Save Figure  |  Download Slide (.ppt)
Cumulative damage distribution for the pinion (faster surface) corresponding to s = +5.0 mm at a series of depths below the surface. The solid lines are for gear set A and the dashed lines are for gear set B.
Grahic Jump Location
Fig. 18

Cumulative damage distribution for the pinion (faster surface) corresponding to s = +9.4 mm at a series of depths below the surface. The solid lines are for gear set A and the dashed lines are for gear set B.

+Cumulative damage distribution for the pinion (faster surface) corresponding to s = +9.4 mm at a series of depths below the surface. The solid lines are for gear set A and the dashed lines are for gear set B.
View Large  |  Save Figure  |  Download Slide (.ppt)
Cumulative damage distribution for the pinion (faster surface) corresponding to s = +9.4 mm at a series of depths below the surface. The solid lines are for gear set A and the dashed lines are for gear set B.

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