Research Papers: Applications

Evaluation of Contact Fatigue Life of a Wind Turbine Gear Pair Considering Residual Stress

[+] Author and Article Information
Heli Liu, Caichao Zhu, Haifeng He, Peitang Wei

State Key Laboratory of Mechanical
Chongqing University,
Chongqing 400030, China

Huaiju Liu

State Key Laboratory of Mechanical
Chongqing University,
Chongqing 400030, China
e-mail: huaijuliu@cqu.edu.cn

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received July 21, 2017; final manuscript received December 27, 2017; published online March 2, 2018. Assoc. Editor: Mihai Arghir.

J. Tribol 140(4), 041102 (Mar 02, 2018) (9 pages) Paper No: TRIB-17-1285; doi: 10.1115/1.4039164 History: Received July 21, 2017; Revised December 27, 2017

Contact fatigue is a main fatigue mode of gears such as those used in wind turbines, due to heavy duties occurring in engineering practice. The understanding of the gear contact fatigue should be based on the interaction between the local material strength and the stress state. Under the rolling–sliding motion, the multi-axial stress state makes the gear contact fatigue problem more complicated. A numerical contact model is proposed to evaluate the contact fatigue life of an intermediate parallel gear stage of a megawatt level wind turbine gearbox. The gear meshing theory is applied to calculate the geometry kinematics parameters of the gear pair. The gear contact is assumed as a plane strain contact problem without the consideration of the influence of the helical angle. The quasi-static tooth surface load distribution is assumed along the line of action. The elastic mechanics theory is used to calculate the elastic stress field generated by surface tractions. The discrete convolute, fast Fourier transformation method is applied to estimate the subsurface stresses distributions. In order to describe the time-varying multi-axial stress states during contact, the Matake, Findley, and Dang Van multi-axial fatigue criteria are used to calculate the critical planes and equivalent stresses. Both the statistic and the deterministic fatigue life models are applied by choosing the Lundberg–Palmgren (LP), Zaretsky models, respectively. The effect of the residual stress distribution on the contact fatigue initiation lives is discussed. In addition, the crack propagation lives are estimated by using the Paris theory.

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Link, H. , Lacava, W. , Van Dam, J. , Mcniff, B. , Sheng, S. , Wallen, R. , Mcdade, M. , Lambert, S. , Butterfield, S. , and Oyague, F. , 2011, “Gearbox Reliability Collaborative Project Report: Findings From Phase 1 and Phase 2 Testing,” National Renewable Energy Laboratory (NREL), Golden, CO, Report No. NREL/TP-5000-51885.
Liu, H. , Mao, K. , Zhu, C. , Chen, S. , Xu, X. , and Liu, M. , 2013, “ Spur Gear Lubrication Analysis With Dynamic Loads,” Tribol. Trans., 56(1), pp. 41–48. [CrossRef]
Liu, H. , Mao, K. , Zhu, C. , and Xu, X. , 2012, “ Mixed Lubricated Line Contact Analysis for Spur Gears Using a Deterministic Model,” ASME J. Tribol., 134(2), p. 021501. [CrossRef]
Zhou, W. , Tang, J. , He, Y. , and Liao, D. , 2015, “ Associated Rules Between Microstructure Characterization Parameters and Contact Characteristic Parameters of Two Cylinders,” J. Central South Univ., 22(11), pp. 4228–4234. [CrossRef]
Liu, H. , Zhu, C. , Zhang, Y. , Wang, Z. , and Song, C. , 2016, “ Tribological Evaluation of a Coated Spur Gear Pair,” Tribol. Int., 99, pp. 117–126. [CrossRef]
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, 222(3), pp. 381–393. [CrossRef]
Paulson, N. R. , Golmohammadi, Z. , Walvekar, A. A. , Sadeghi, F. , and Mistry, K. , 2017, “ Rolling Contact Fatigue in Refurbished Case Carburized Bearings,” Tribol. Int., 115, pp. 348–364.
Walvekar, A. A. , and Sadeghi, F. , 2017, “ Rolling Contact Fatigue of Case Carburized Steels,” Int. J. Fatigue, 95, pp. 264–281. [CrossRef]
Paulson, N. R. , Sadeghi, F. , and Habchi, W. , 2017, “ A Coupled Finite Element EHL and Continuum Damage Mechanics Model for Rolling Contact Fatigue,” Tribol. Int., 107, pp. 173–183.
Li, S. , Kahraman, A. , and Klein, M. , 2012, “ A Fatigue Model for Spur Gear Contacts Operating Under Mixed Elastohydrodynamic Lubrication Conditions,” ASME J. Mech. Des., 134(4), p. 041007. [CrossRef]
Brandão, J. A. , Seabra, J. H. O. , and Castro, J. , 2010, “ Surface Initiated Tooth Flank Damage—Part I: Numerical Model,” Wear, 268(1–2), pp. 1–12. [CrossRef]
Zhu, D. , Wang, Q. J. , and Ren, N. , 2009, “ Pitting Life Prediction Based on a 3-D Line Contact Mixed EHL Analysis and Subsurface von Mises Stress Calculation,” Advanced Tribology, Springer, Berlin, pp. 178–179.
Hua, Q. , 2005, “Prediction of Contact Fatigue for the Rough Surface Elastohydrodynamic Lubrication Line Contact Problem Under Rolling and Sliding Conditions,” Ph.D. thesis, Cardiff University, Cardiff, Wales.
Sadeghi, F. , Jalalahmadi, B. , Slack, T. S. , Raje, N. , and Arakere, N. K. , 2009, “ A Review of Rolling Contact Fatigue,” ASME J. Tribol., 131(4), p. 041403.
Aid, A. , Bendouba, M. , Aminallah, L. , Amrouche, A. , Benseddiq, N. , and Benguediab, M. , 2012, “ An Equivalent Stress Process for Fatigue Life Estimation Under Multiaxial Loadings Based on a New Non Linear Damage Model,” Mater. Sci. Eng., A, 538(3), pp. 20–27. [CrossRef]
Mcdiarmid, D. L. , 1994, “ A Shear Stress Based Critical-Plane Criterion of Multiaxial Fatigue Failure for Design and Life Prediction,” Fatigue Fract. Eng. Mater. Struct., 17(12), pp. 1475–1484. [CrossRef]
Jalalahmadi, B. , Sadeghi, F. , and Bakolas, V. , 2011, “ Material Inclusion Factors for Lundberg-Palmgren–Based RCF Life Equations,” Tribol. Trans., 54(3), pp. 457–469. [CrossRef]
Agha, S. R. , 2000, “ Fatigue Performance of Superfinish Hard Turned Surfaces in Rolling Contact,” Wear, 244(1–2), pp. 52–59. [CrossRef]
Allison, B. D. , 2013, “Evolution of Mechanical Properties of M50 Bearing Steel Due to Rolling Contact Fatigue,” Ph.D. thesis, University of Florida, Gainesville, FL.
Jeon, H. B. , Song, T. H. , Huh, S. C. , and Park, W. J. , 2007, “ Evaluation on Fatigue Characteristics of Aluminum Alloys by Compressive Residual Stress,” International Conference on Physical and Numerical Simulation of Materials Processing, Zhengzhou, China, Oct. 23–27, pp. 2129–2137.
Shea, M. M. , 1980, “ Residual Stress and Microstructure in Quenched and Tempered and Hot Oil Quenched Carburized Gears,” J. Heat Treating, 1(4), pp. 29–36.
Moulik, P. N. , Yang, H. T. Y. , and Chandrasekar, S. , 2001, “ Simulation of Thermal Stresses Due to Grinding,” Int. J. Mech. Sci., 43(3), pp. 831–851. [CrossRef]
Pape, F. , Neubauer, T. , Maiß, O. , Denkena, B. , and Poll, G. , 2017, “ Influence of Residual Stresses Introduced by Manufacturing Processes on Bearing Endurance Time,” Tribol. Lett., 65(2), p. 70. [CrossRef]
Kim, J. , 2015, “Numerical Approach for Predicting Fatigue Crack Growth in Residual Stress Bearing Bodies,” Ph.D. thesis, University of California, Davis, CA.
Liu, S. , Wang, Q. , and Liu, G. , 2000, “ A Versatile Method of Discrete Convolution and FFT (DC-FFT) for Contact Analyses,” Wear, 243(1–2), pp. 101–111. [CrossRef]
Karolczuk, A. , and Macha, E. , 2005, “ A Review of Critical Plane Orientations in Multiaxial Fatigue Failure Criteria of Metallic Materials,” Int. J. Fract., 134(3–4), pp. 267–304. [CrossRef]
Ciavarella, M. , Monno, F. , and Demelio, G. , 2006, “ Maps for the Dang Van Fatigue Limit in Rolling Contact Fatigue,” Int. J. Fatigue, 28(8), pp. 852–863. [CrossRef]
Charkaluk, E. , Constantinescu, A. , Maïtournam, H. , and Van, K. D. , 2009, “ Revisiting the Dang Van Criterion,” Procedia Eng., 1(1), pp. 143–146. [CrossRef]
Cerullo, M. , 2014, “ Application of Dang Van Criterion to Rolling Contact Fatigue in Wind Turbine Roller Bearings,” Proc. Inst. Mech. Eng., Part C, 228(12), pp. 2079–2089. [CrossRef]
Harris, T. A. , and Yu, W. K. , 1999, “ Lundberg-Palmgren Fatigue Theory: Considerations of Failure Stress and Stressed Volume,” ASME J. Tribol., 121(1), pp. 85–89. [CrossRef]
Yan, X. L. , Wang, X. L. , and Zhang, Y. Y. , 2014, “ A Numerical Study of Fatigue Life in Non-Newtonian Thermal EHL Rolling–Sliding Contacts With Spinning,” Tribol. Int., 80, pp. 156–165. [CrossRef]
Zhu, D. , 2003, “ Effect of Surface Roughness on Mixed EHD Lubrication Characteristics,” Tribol. Trans., 46(1), pp. 44–48. [CrossRef]
Coy, J. J. , Townsend, D. P. , and Zaretsky, E. V. , 1975, “Analysis of Dynamic Capacity of Low-Contact-Ratio Spur Gears Using Lundberg-Palmgren Theory,” NASA Lewis Research Center; Cleveland, OH, Report No. NASA-TN-D-8029.
Glodež, S. , Winter, H. , and Stüwe, H. P. , 1997, “ A Fracture Mechanics Model for the Wear of Gear Flanks by Pitting,” Wear, 208(1–2), pp. 177–183. [CrossRef]
Glodež, S. , Flašker, J. , and Ren, Z. , 1997, “ A New Model for the Numerical Determination of Pitting Resistance of Gear Teeth Flanks,” Fatigue Fract. Eng. Mater. Struct., 20(1), pp. 71–83. [CrossRef]
Glodež, S. , Aberšek, B. , Flašker, J. , and Ren, Z. , 2004, “ Evaluation of the Service Life of Gears in Regard to Surface Pitting,” Eng. Fract. Mech., 71(4–6), pp. 429–438. [CrossRef]
Paris, P. C. , and Erdogan, F. , 1963, “ A Critical Analysis of Crack Propagation Laws,” ASME J. Basic Eng., 85(4), pp. 528–533. [CrossRef]
Kramberger, J. , Šraml, M. , Glodež, S. , Flašker, J. , and Potrč, I. , 2004, “ Computational Model for the Analysis of Bending Fatigue in Gears,” Comput. Struct., 82(23–26), pp. 2261–2269. [CrossRef]


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Fig. 1

Spalling of a wind turbine gear caused by contact fatigue

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Fig. 2

The simplified contact model

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Fig. 3

The calculation domain

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Fig. 4

Distributions of pH, bH and maximum Mises stress along the line of action

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Fig. 5

Distributions of σx, σz, τxz

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Fig. 6

Stress components distributions of pitch point at the depth of 0.5 bH

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Fig. 7

The critical plane and the multi-axial stresses

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Fig. 8

The critical planes of material nodes

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Fig. 9

Short crack propagation mechanism

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Fig. 10

Residual stress measurement of selected gear tooth

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Fig. 11

Two types of residual stress gradient curves and the actual residual stress data points

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Fig. 12

The FP along the direction of depth

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Fig. 13

The equivalent stress along the direction of depth

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Fig. 14

Predicted contact fatigue initiation SN curve of LP (left) and Zaretsky (right) models

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Fig. 15

The equivalent stresses under different residual stresses conditions

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Fig. 16

Predicted contact fatigue initiation SN curve with residual stress

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Fig. 17

Short (left) and long (right) crack propagation life



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