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Research Papers: Contact Mechanics

Method for Calculating Normal Pressure Distribution of High Resolution and Large Contact Area

[+] Author and Article Information
C. Brecher

Laboratory of Machine Tools and
Production Engineering,
RWTH Aachen,
Steinbachstraße 19,
Aachen D-52074, Germany
e-mail: C.Brecher@wzl.rwth-aachen.de

D. Renkens

Laboratory of Machine Tools and
Production Engineering,
RWTH Aachen,
Steinbachstraße 19,
Aachen D-52074, Germany
e-mail: D.Renkens@wzl.rwth-aachen.de

C. Löpenhaus

Laboratory of Machine Tools and
Production Engineering,
RWTH Aachen,
Steinbachstraße 19,
Aachen D-52074, Germany
e-mail: C.Loepenhaus@wzl.rwth-aachen.de

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received February 19, 2015; final manuscript received June 15, 2015; published online September 7, 2015. Assoc. Editor: Dong Zhu.

J. Tribol 138(1), 011402 (Sep 07, 2015) (9 pages) Paper No: TRIB-15-1059; doi: 10.1115/1.4031164 History: Received February 19, 2015; Revised June 15, 2015

The exact calculation of contact stresses below the surface is the basis for optimizing load capacity of heavily loaded rolling–sliding contacts. The level of stress is significantly influenced by the normal pressure distribution within the contact area, which occurs as a result of the transferred normal force and the contact geometry. In this paper, a new method for high resolution pressure calculation of large contact areas is presented. By this, measured surface topography can be taken into account. The basis of the calculation method is the half-space theory according to Boussinesq/Love. Instead of regular grids, optimized meshing strategies are applied to influence the calculation efforts for large contact areas. Two objectives are pursued with the targeted meshing strategy: on the one hand, the necessary resolution for measured surface structures can be realized; while on the other hand, the total number of elements is reduced by a coarse grid in the surrounding areas. In this way, rolling–sliding contacts with large contact areas become computable with conventional simulation computers. Using the newly developed “method of combined solutions,” the overall result is finally composed by the combination of section of separate solutions, which are calculated by consecutively shifting the finely meshed segment over the entire contact area. The vital advancement in this procedure is the introduction of irregular grids, through which the cross influences are not neglected and fully regarded for every separate calculation. The presented methodology is verified stepwise in comparison to the Hertzian theory. The influence of irregular grids on the calculation quality is examined in particular. Finally, the calculation approach is applied to a real disk-on-disk rolling contact based on measured surface topography.

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References

Hertz, H. , 1882, “ Über die Berührung Fester Elastischer Körper,” Crelle’s J., 92, pp. 156–171.
Boussinesq, J. , 1885, Application des Potentiels à l'étude de l'équilibre et du Mouvement des Solides Élastiques, Gauthier-Villars, Paris.
Love, A. E. H. , 1929, “ The Stress Produced in a Semi-Infinite Solid by Pressure on Part of the Boundary,” Philos. Trans. R. Soc. London, Ser. A, 228(659–669), pp. 377–420. [CrossRef]
Brandt, A. , and Lubrecht, A. , 1990, “ Multilevel Matrix Multiplication and Fast Solution of Integral Equations,” J. Comput. Phys., 90(2), pp. 348–370. [CrossRef]
Venner, C. H. , and Lubrecht, A. A. , 2000, Multilevel Methods in Lubrication, Elsevier, New York/Amsterdam.
Ju, Y. , and Farris, T. , 1996, “ Spectral Analysis of Two-Dimensional Contact Problems,” ASME J. Tribol., 118(2), pp. 320–328. [CrossRef]
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]
Hartnett, M. , 1979, “ The Analysis of Contact Stresses in Rolling Element Bearings,” ASME J. Lubr. Technol., 101(1), pp. 105–109. [CrossRef]
Wang, F. S. , Block, J. M. , Chen, W. W. , Martini, A. , Zhou, K. , Keer, L. M. , and Wang, Q. J. , 2009, “ A Multilevel Model for Elastic–Plastic Contact Between a Sphere and a Flat Rough Surface,” ASME J. Tribol., 131(2), p. 021409. [CrossRef]
Lubrecht, A. A. , and Ioannides, E. , 1991, “ A Fast Solution of the Dry Contact Problem and the Associated Sub-Surface Stress Field Using Multilevel Techniques,” ASME J. Tribol., 113(1), pp. 128–133. [CrossRef]
Xiong, S. , Lin, C. , Wang, Y. , Liu, W. K. , and Wang, Q. J. , 2010, “ An Efficient Elastic Displacement Analysis Procedure for Simulating Transient Conformal-Contact Elastohydrodynamic Lubrication Systems,” ASME J. Tribol., 132(2), p. 021502. [CrossRef]
Brunetiere, N. , and Wang, Q. , 2014, “ Large-Scale Simulation of Fluid Flows for Lubrication of Rough Surfaces,” ASME J. Tribol., 136(1), p. 011701. [CrossRef]
Redlich, A. , 2002, Simulation von Punktkontakten unter Mischreibungsbedingungen. Fortschritte in der Maschinenkonstruktion, Shaker, Aachen, Germany.
Yu, C. , Wang, Z. , Sun, F. , Lu, S. , Keer, L. M. , and Wang, Q. J. , 2013, “ A Deterministic Semi-Analytical Model for the Contact of a Wafer and a Rough Bi-Layer Pad in CMP,” ECS J. Solid State Sci. Technol., 9(2), pp. 368–374. [CrossRef]
Bartel, D. , 2001, “ Berechnung von Festkörper- und Mischreibung bei Metallpaarungen,” Ph.D. dissertation, University of Magdeburg, Magdeburg, Germany.
Allwood, J. , 2005, “ Survey and Performance Assessment of Solution Methods for Elastic Rough Contact Problems,” ASME J. Tribol., 127(1), pp. 10–23. [CrossRef]
Bartel, D. , 2010, Simulation von Tribosystemen: Grundlagen und Anwendungen, Vieweg + Teubner, Wiesbaden, Germany.
Becker, A. , 1990, “ Numerische Berechnung des Kontaktes beliebig gekrümmter Körper unter besonderer Berücksichtigung der Einflußgrößen des Rad-Schiene-Systems,” Ph.D. dissertation, University of Bochum, Bochum, Germany.
Bartel, D. , Bobach, L. , Illner, T. , and Deters, L. , 2012, “ Simulating Transient Wear Characteristics of Journal Bearings Subjected to Mixed Friction,” Proc. Inst. Mech. Eng., Part J, 226(12), pp. 1095–1108. [CrossRef]
Bobach, L. , Beilicke, R. , Bartel, D. , and Deters, L. , 2012, “ Thermal Elastohydrodynamic Simulation of Involute Spur Gears Incorporating Mixed Friction,” Tribol. Int., 48, pp. 191–206. [CrossRef]
Chiu, Y. , and Hartnett, M. , 1983, “ A Numerical Solution for Layered Solid Contact Problems With Application to Bearings,” ASME J. Lubr. Technol., 105(4), pp. 585–590. [CrossRef]
Bugiel, C. , 2009, Tribologisches Verhalten und Tragfähigkeit PVD-beschichteter Getriebe-Zahnflanken, Apprimus-Verl., Aachen, Germany.
Hurasky-Schönwerth, O. , 2004, Einsatzverhalten von PVD-Beschichtungen und Biologisch Schnell Abbaubaren Synthetischen Estern im Tribologischen System des Zahnflankenkontaktes, Shaker, Aachen, Germany.
Shannon, C. , 1949, “ Communication in the Presence of Noise,” Proc. IRE, 37(1), pp. 10–21. [CrossRef]

Figures

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Fig. 1

Contact model and discretization of elastic half-space theory

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Fig. 2

Application and limits of half-space theory by Boussinesq/Love

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Fig. 3

Meshing strategies for elastic half-space theory: (a) regular square grid, (b) irregular grid, and (c) optimized grid

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Fig. 4

Calculation approach for the method of combined solutions

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Fig. 5

Flowchart of the method of combined solutions

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Fig. 6

Scheme of coordinate transformation with meshed half-space

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Fig. 8

Local pressure deviation for different meshing strategies

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Fig. 9

Verification results for the method of combined solutions

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Fig. 10

Efficiency and computability analysis of the method of combined solutions

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Fig. 11

Disk-on-disk contact geometry and measurement procedure

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Fig. 12

Calculation examples of simulated disk-on-disk contact

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