Modeling of Fatigue/Creep in Polymer Cage of Large Size Bearing

Abstract:

A single pocket cage is the SKF product, which is used in Large Size Bearings for wind industry. The function of a bearing cage is to hold, guide and separate rolling elements, and differently from the conventional cage, the current one consists of segments, which eases the bearing assembly and reduces its weight. The long life challenge (25 years!) requires considering fatigue, and since the single pocket cage is made of PEEK polymer, it is also susceptible to creep (in near room temperature), which enhances fatigue damage. The current work proposes the numerical model capturing non-linear viscoelasticity of PEEK. The mechanical behavior of this material is identified in uniaxial tension test and is modeled in Finite Elements (FE) by means of the Parallel Rheological Framework (this numerical tool has been recently implemented in the commercial software ABAQUS). The current FE model enables to apply cyclic loading, simulating the material response of cage when it operates in running bearing. By applying sub-modeling technique only a small domain is modeled which improves the computational time efficiency. The sub-model domain corresponds to the cage region, where the stress is high resulting to the material yielding, fatigue/creep degradation (due to inelastic cyclic deformation) and initiation of fatigue crack. The FE results were combined with the test data, in attempt to relate the numerically predicted damage to the cage life. The development of irreversible deformation during cyclic loading, shakedown analysis and the stress volume effect, are the main focuses of the current work.

• Periodical: Advances in Science and Technology (Volume 158)
• Pages: 3-18
• DOI: https://doi.org/10.4028/p-lMJa4I
• Online since: January 2025
• Authors: Yuri Kadin*, Gerrit Jan Dop, Richard Schaake, Gijs de Kort, Marcus Boehm
• Keywords: Bearing Cage, Creep, Fatigue, Fibers Reinforced Polymer, Finite Elements, Large Size Bearing, Nonlinear Viscoelasticity, PEEK, Shakedown, Sub-Modeling

References

[1] G. E. Morales-Espejel, A. Gabelli, The progression of surface rolling contact fatigue damage of rolling bearing, Evolution – SKF business & technology magazine (2015) https://evolution.skf.com/the-progression-of-surface-rolling-contact-fatigue-damage-of-rolling-bearings/

DOI: 10.1080/10402004.2014.983251

[2] A.V. Olver. The mechanism of rolling contact fatigue: an update, Proc. IMechE, 219, Part J, J. Eng. Tribol. (2005) 313–331.

[3] G.E. Morales-Espejel, A. Gabelli, The progression of surface rolling contact fatigue damage of rolling bearings with artificial dents, Tribol. Transactions, 58 (2015) 418–431.

DOI: 10.1080/10402004.2014.983251

[4] M.H. Nazir, Z.A. Khan, A. Saeed, Experimental analysis and modelling of C-crack propagation in silicon nitride ball bearing element under rolling contact fatigue, Tribol. Int., 126 (2018) 386-401.

DOI: 10.1016/j.triboint.2018.04.030

[5] Y. Kadin, C. Vieillard, J. Wensing, A. Theerthan, Finite Elements modelling and assessment of ceramic rollers with edge cracks, Proc. Struct. Integrity, 57 (2024) 236–249.

DOI: 10.1016/j.prostr.2024.03.026

[6] Q. Chen, S. Jiang, D. Duan, Fracture analysis and working stress calculation of bearing cage used in charging pump in a nuclear power plant, Metals, 13-1380 (2023) 1-14.

DOI: 10.3390/met13081380

[7] A.M. Alshoaibi, Y.A. Fageehi, A comparative analysis of 3D software for modeling fatigue crack growth: a review, Appl. Sci., 14-1848 (2024) 2-20.

DOI: 10.3390/app14051848

[8] C. Guster, G. Pinter, A. Mösenbacher, W. Eichlseder, Evaluation of a simulation process for fatigue life calculation of short fibre reinforced plastic components, Proc. Eng., 10 (2011) 2104–2109.

DOI: 10.1016/j.proeng.2011.04.348

[9] A. Vencl, V. Gašić, B. Stojanović, Fault tree analysis of most common rolling bearing tribological failures, IOP Conf. Ser.: Mater. Sci. Eng., 174-012048 (2017) 1-10.

DOI: 10.1088/1757-899x/174/1/012048

[10] N. Nosrati, A. Zabett, S. Sahebian, Stress dependency of creep response for glass/epoxy composite at nonlinear and linear viscoelastic behaviour, Int. J. Polymer Sci. (Hindawi), Article ID 9733138 (2022) 1-11.

DOI: 10.1155/2022/9733138

[11] L. Pastukhov, Long-term Performance of Fibre-reinforced Thermoplastics, PhD Thesis, TU Eindhoven, the Netherlands, 2019.

[12] Y. Kadin, R. Schaake, Modeling viscoelasticity and cyclic creep of PEEK by parallel rheological framework (PRF), European J. Mech. - A/Solids 104 (2023) 105216.

DOI: 10.1016/j.euromechsol.2023.105216

[13] T.B. Van Erp, C.T. Reynolds, T. Peijs, J.A.W., Van Dommelen, L.E. Govaert, Prediction of yield and long-term failure of oriented polypropylene: kinetics and anisotropy, J. Polymer Sci.: Part B: Polymer Phys., 47 (2009) 2026-2035.

DOI: 10.1002/polb.21801

[14] E. Parodi, Structure Properties Relations for Polyamide 6, PhD Thesis, TU Eindhoven, the Netherlands, 2017.

[15] ABAQUS/Standard User's Manual.

[16] P.H. Foss, H.C. Tseng, J. Snawerdt, Y.J. Chang, W.H. Yang, C.H. Hsu, Prediction of fiber orientation distribution in injection molded parts using Moldex3D simulation, Polymer Composites, 35 (2014) 671–680.

DOI: 10.1002/pc.22710

[17] S.G. Advani, C.L. Tucker, The use of tensors to describe and predict fiber orientation in short fiber composites, J. Rheology, 31 (1987) 751-784.

DOI: 10.1122/1.549945

[18] A. Amiri-Rad, L.V. Pastukhov, L.E. Govaert, J.A.W. Van Dommelen, An anisotropic viscoelastic-viscoplastic model for short-fiber composites, Mech. Mater., 137 (2019) 103141.

DOI: 10.1016/j.mechmat.2019.103141

[19] R.B. Colby, Equivalent Plastic Strain for the Hill's Yield Criterion under General Three-dimensional Loading, BSc Thesis, Massachusetts Institute of Technology (MIT), MA, USA, 2013.

[20] S.W. Tsai, E. M. Wu, A general theory of strength for anisotropic materials, J. Composite Mater., 5 (1971) 58-80.

[21] P.V. Osswald, T.A. Osswald, A strength tensor based failure criterion with stress interactions, Polymer Composites, 39 (2018) 2826–2834.

DOI: 10.1002/pc.24275

[22] J.A. Williams, The influence of repeated loading, residual stresses and shakedown on the behaviour of tribological contacts, Tribol. Int., 38 (2005) 786–797.

DOI: 10.1016/j.triboint.2005.02.006

[23] M. Abdel-Karim, Shakedown of complex structures according to various hardening rules. Int. J. Pressure Vessels and Piping 82 (2005) 427-458.

DOI: 10.1016/j.ijpvp.2005.01.007

[24] J. Hodowany, G. Ravichandran, A.J. Rosakis, P. Rosakis, Partition of plastic work into heat and stored energy in metals, Experimental Mech., 40 (2000) 113–123.

DOI: 10.1007/bf02325036

[25] D.L. McDowell, F.P.E. Dunne, Microstructure-sensitive computational modeling of fatigue crack formation, Int. J. Fatigue, 32 (2010) 1521-1542.

DOI: 10.1016/j.ijfatigue.2010.01.003

[26] A. Launay, M.H. Maitournam, Y. Marco, I. Raoult, Multiaxial fatigue models for short glass fibre reinforced polyamide. Part II: fatigue life estimation, Int. J. Fatigue, 47 (2013) 390-406.

DOI: 10.1016/j.ijfatigue.2012.09.015

[27] S. Mortazavian, A. Fatemi, Fatigue behavior and modeling of short fiber reinforced polymer composites: A literature review, Int. J. Fatigue, 70 (2015) 297-321.

DOI: 10.1016/j.ijfatigue.2014.10.005

[28] H. Stadler, Effect of frequency, R-ratio and test specimen configuration on fatigue crack growth in PE pipe materials, Diploma Thesis, Institute for Materials Science and Testing of Plastics of the University of Leoben and Polymer Competence Center Leoben GmbH, Austria, 2006.

DOI: 10.24132/csrn.3301.92

[29] K. S. Saib, W. J. Evans, D. H. Isaac, The fatigue crack propagation behaviour of short carbon fibre reinforced PEEK composites, Fracture of Eng. Mater. Structures, Proceedings of the Joint FEFG/ICF Int. Conf. (1991) 215-220.

DOI: 10.1007/978-94-011-3650-1_30

[30] H. Liu, A. Ojha, Z. Li, C.C. Engler-Pinto Jr., X. Su, Q. Sun, H. Kang, W. Wen, H. Cui, Fatigue modeling for carbon/epoxy unidirectional composites under various stress ratios considering size effects, Int. J. Fatigue, 120 (2019) 184-200.

DOI: 10.1016/j.ijfatigue.2018.11.009

[31] M. Mejri, L. Toubal, J.C. Cuillière, V. François, Fatigue life and residual strength of a short- natural-fiber-reinforced plastic vs nylon, Composites Part B: Eng., 110 (2017) 429-441.

DOI: 10.1016/j.compositesb.2016.11.036

[32] M. De Monte, M. Quaresimin, P. Lazzarin, Modelling of fatigue strength data for a short fibre reinforced polyamide 6.6 based on local strain energy density, 16th Int. Conf. Composite Mater., Kyoto, Japan (2007).

[33] R. Sakin, I. Ay, Statistical analysis of bending fatigue life data using Weibull distribution in glass-fiber reinforced polyester composites, Mater. & Design, 29 (2008) 1170-1181.

DOI: 10.1016/j.matdes.2007.05.005

[34] M.C. Sobieraj, J.E. Murphy, J.G. Brinkman, S.M. Kurtz, C.M. Rimnac, Notched fatigue behavior of PEEK, Biomaterials, 31(35) (2010) 9156–9162.

DOI: 10.1016/j.biomaterials.2010.08.032

[35] S. Blachère, A. Gabelli, G.E. Morales-Espejel, Experimental conformity level for comparison between endurance tests and life calculation models, J. Bearing World, 6 (2021) 15-20.

[36] Y. Kadin, C. Vieillard, J. Wensing, A. Theerthan, M. Becchetti, Finite Elements modelling of edge imperfections in ceramic rollers for assessing the risk of fatigue failure, J. Bearing World, 7 (2022) 44-50.

DOI: 10.1016/j.prostr.2024.03.026

[37] A. Schönfeldt, Structural Analysis Routine for Construction Hoist Components - A Novel Method for Calculation and Testing of Mast Ties, Mechanical Engineering, master's level, Luleå University of Technology, Sweden, 2017.

[38] M. Wismans,  Multiaxial Failure of Short-fiber Reinforced Thermoplastics. PhD thesis. Eindhoven University of Technology, The Netherlands, 2023.