Research Papers

Experimentally Calibrated Abrasive Sliding Wear Model: Demonstrations for Rotary and Linear Wear Systems

[+] Author and Article Information
Xiu Jia, Tomas Grejtak, Brandon Krick

Department of Mechanical Engineering
and Mechanics,
Lehigh University,
Bethlehem, PA 18015

Natasha Vermaak

Department of Mechanical Engineering
and Mechanics,
Lehigh University,
Bethlehem, PA 18015
e-mail: xij214@lehigh.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received August 10, 2018; final manuscript received September 12, 2018; published online October 1, 2018. Assoc. Editor: Junlan Wang.

J. Appl. Mech 85(12), 121011 (Oct 01, 2018) (9 pages) Paper No: JAM-18-1471; doi: 10.1115/1.4041470 History: Received August 10, 2018; Revised September 12, 2018

Considerable effort has been made to model, predict, and mitigate wear as it has significant global impact on the environment, economy, and energy consumption. This work proposes generalized foundation-based wear models and a simulation procedure for single material and multimaterial composites subject to rotary or linear abrasive sliding wear. For the first time, experimental calibration of foundation parameters and asymmetry effects are included. An iterative wear simulation procedure is outlined that considers implicit boundary conditions to better reflect the response of the whole sample and counter-body system compared to existing models. Key features such as surface profile, corresponding contact pressure evolution, and material loss can be predicted. For calibration and validation, both rotary and linear wear tests are conducted on purpose-built tribometers. In particular, an experimental calibration procedure for foundation parameters is developed based on a Levenberg–Marquardt optimization algorithm. This procedure is valid for specific counter-body and wear systems using experimentally measured steady-state worn surface profiles. The calibrated foundation model is validated by a set of rotary wear tests on different bimaterial composite samples. The established efficient and accurate wear simulation framework is well suited for future design and optimization purposes.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Holmberg, K. , and Erdemir, A. , 2017, “ Influence of Tribology on Global Energy Consumption, Costs and Emissions,” Friction, 5(3), pp. 263–284. [CrossRef]
Meng, H. , and Ludema, K. , 1995, “ Wear Models and Predictive Equations: Their Form and Content,” Wear, 181, pp. 443–457. [CrossRef]
Williams, J. A. A. , 1999, “ Wear Modelling: Analytical, Computational and Mapping: A Continuum Mechanics Approach,” Wear, 225–229, pp. 1–17. [CrossRef]
Dorini, F. A. , and Sampaio, R. , 2012, “ Some Results on the Random Wear Coefficient of the Archard Model,” ASME J. Appl. Mech., 79(5), p. 051008. [CrossRef]
da Silva, C. R. Á. , Pintaude, G. , Al-Qureshi, H. A. , and Krajnc, M. A. , 2010, “ An Application of Mean Square Calculus to Sliding Wear,” ASME J. Appl. Mech., 77(2), p. 021013. [CrossRef]
Maekawa, K. , and Itoh, A. , 1995, “ Friction and Tool Wear in Nano-Scale Machining—A Molecular Dynamics Approach,” Wear, 188(1–2), pp. 115–122. [CrossRef]
Fang, L. , Cen, Q. , Sun, K. , Liu, W. , Zhang, X. , and Huang, Z. , 2005, “ Fem Computation of Groove Ridge and Monte Carlo Simulation in Two-Body Abrasive Wear,” Wear, 258(1–4), pp. 265–274. [CrossRef]
Argatov, I. , 2011, “ Asymptotic Modeling of Reciprocating Sliding Wear With Application to Local Interwire Contact,” Wear, 271(7–8), pp. 1147–1155. [CrossRef]
Argatov, I. , and Tato, W. , 2012, “ Asymptotic Modeling of Reciprocating Sliding Wear–Comparison With Finite-Element Simulations,” Eur. J. Mech. A, 34, pp. 1–11. [CrossRef]
Mamalis, A. , Vortselas, A. , and Panagopoulos, C. , 2013, “ Analytical and Numerical Wear Modeling of Metallic Interfaces: A Statistical Asperity Approach,” Tribol. Trans., 56(1), pp. 121–129. [CrossRef]
Hockenhull, B. , Kopalinsky, E. , and Oxley, P. , 1993, “ Predicting Wear for Metal Surfaces in Sliding Contact Using a Low-Cycle Fatigue Wear Model,” ASME J. Appl. Mech., 60(1), pp. 85–92. [CrossRef]
Tan, L. , Gao, D. , Zhou, J. , Liu, Y. , and Wang, Z. , 2018, “ Casing Wear Prediction Model Based on Drill String Whirling Motion in Extended-Reach Drilling,” Arabian J. Sci. Eng. (epub).
Tan, L. , Gao, D. , and Zhou, J. , 2018, “ A Prediction Model of Casing Wear in Extended-Reach Drilling With Buckled Drillstring,” ASME J. Appl. Mech., 85(2), p. 021001. [CrossRef]
Zhang, L. , and Tanaka, H. , 1997, “ Towards a Deeper Understanding of Wear and Friction on the Atomic Scale—A Molecular Dynamics Analysis,” Wear, 211(1), pp. 44–53. [CrossRef]
Jang, I. , Burris, D. L. , Dickrell, P. L. , Barry, P. R. , Santos, C. , Perry, S. S. , Phillpot, S. R. , Sinnott, S. B. , and Sawyer, W. G. , 2007, “ Sliding Orientation Effects on the Tribological Properties of Polytetrafluoroethylene,” J. Appl. Phys., 102(12), p. 123509. [CrossRef]
Dong, Y. , Li, Q. , and Martini, A. , 2013, “ Molecular Dynamics Simulation of Atomic Friction: A Review and Guide,” J. Vac. Sci. Technol. A, 31(3), p. 030801. [CrossRef]
Fang, L. , Liu, W. , Du, D. , Zhang, X. , and Xue, Q. , 2004, “ Predicting Three-Body Abrasive Wear Using Monte Carlo Methods,” Wear, 256(7–8), pp. 685–694. [CrossRef]
Podra, P. , and Andersson, S. , 1999, “ Simulating Sliding Wear With Finite Element Method,” Tribol. Int., 32(2), pp. 71–81. [CrossRef]
Hegadekatte, V. , Huber, N. , and Kraft, O. , 2004, “ Finite Element Based Simulation of Dry Sliding Wear,” Modell. Simul. Mater. Sci. Eng., 13(1), p. 57. [CrossRef]
Kim, N. H. , Won, D. , Burris, D. , Holtkamp, B. , Gessel, G. R. , Swanson, P. , and Sawyer, W. G. , 2005, “ Finite Element Analysis and Experiments of Metal/Metal Wear in Oscillatory Contacts,” Wear, 258(11–12), pp. 1787–1793. [CrossRef]
Mukras, S. , Kim, N. H. , Sawyer, W. G. , Jackson, D. B. , and Bergquist, L. W. , 2009, “ Numerical Integration Schemes and Parallel Computation for Wear Prediction Using Finite Element Method,” Wear, 266(7–8), pp. 822–831. [CrossRef]
Söderberg, A. , and Andersson, S. , 2009, “ Simulation of Wear and Contact Pressure Distribution at the Pad-to-Rotor Interface in a Disc Brake Using General Purpose Finite Element Analysis Software,” Wear, 267(12), pp. 2243–2251. [CrossRef]
Wu, J. S. S. , Lin, Y. T. , Lai, Y. L. , and Jar, P. Y. B. , 2017, “ A Finite Element Approach by Contact Transformation for the Prediction of Structural Wear,” ASME J. Tribol., 139(2), p. 021602. [CrossRef]
Arjmandi, M. , Ramezani, M. , Giordano, M. , and Schmid, S. , 2017, “ Finite Element Modelling of Sliding Wear in Three-Dimensional Woven Textiles,” Tribol. Int., 115, pp. 452–460. [CrossRef]
Woldman, M. , Van Der Heide, E. , Tinga, T. , and Masen, M. A. , 2017, “ A Finite Element Approach to Modeling Abrasive Wear Modes,” Tribol. Trans., 60(4), pp. 711–718. [CrossRef]
Schmidt, A. A. , Schmidt, T. , Grabherr, O. , and Bartel, D. , 2018, “ Transient Wear Simulation Based on Three-Dimensional Finite Element Analysis for a Dry Running Tilted Shaft-Bushing Bearing,” Wear, 408, pp. 171–179. [CrossRef]
Sierra Suarez, J. A. , and Higgs, C. F. , 2015, “ A Contact Mechanics Formulation for Predicting Dishing and Erosion CMP Defects in Integrated Circuits,” Tribol. Lett., 59(2), p. 121. [CrossRef]
Johnson, K. L. , 1987, Contact Mechanics, Cambridge University Press, Cambridge, UK.
Kerr, A. D. , 1964, “ Elastic and Viscoelastic Foundation Models,” ASME J. Appl. Mech., 31(3), pp. 491–498. [CrossRef]
Clastornik, J. , Eisenberger, M. , Yankelevsky, D. , and Adin, M. , 1986, “ Beams on Variable Winkler Elastic Foundation,” ASME J. Appl. Mech., 53(4), pp. 925–928. [CrossRef]
Nobili, A. , 2012, “ Variational Approach to Beams Resting on Two-Parameter Tensionless Elastic Foundations,” ASME J. Appl. Mech., 79(2), p. 021010. [CrossRef]
Põdra, P. , and Andersson, S. , 1997, “ Wear Simulation With the Winkler Surface Model,” Wear, 207(1–2), pp. 79–85. [CrossRef]
Telliskivi, T. , 2004, “ Simulation of Wear in a Rolling–Sliding Contact by a Semi-Winkler Model and the Archard's Wear Law,” Wear, 256(7–8), pp. 817–831. [CrossRef]
Sawyer, W. , 2004, “ Surface Shape and Contact Pressure Evolution in Two Component Surfaces: Application to Copper Chemical Mechanical Polishing,” Tribol. Lett., 17(2), pp. 139–145. [CrossRef]
Sidebottom, M. A. , Feppon, F. , Vermaak, N. , and Krick, B. A. , 2016, “ Modeling Wear of Multimaterial Composite Surfaces,” ASME J. Tribol., 138(4), p. 041605. [CrossRef]
Feppon, F. , Sidebottom, M. A. , Michailidis, G. , Krick, B. A. , and Vermaak, N. , 2016, “ Efficient Steady-State Computation for Wear of Multimaterial Composites,” ASME J. Tribol., 138(3), p. 031602. [CrossRef]
Jia, X. , Grejtak, T. , Krick, B. , and Vermaak, N. , 2017, “ Design of Composite Systems for Rotary Wear Applications,” Mater. Des., 134, pp. 281–292. [CrossRef]
Rowe, K. G. , Erickson, G. M. , Sawyer, W. G. , and Krick, B. A. , 2014, “ Evolution in Surfaces: Interaction of Topography With Contact Pressure During Wear of Composites Including Dinosaur Dentition,” Tribol. Lett., 54(3), pp. 249–255. [CrossRef]
Feppon, F. , Michailidis, G. , Sidebottom, M. , Allaire, G. , Krick, B. , and Vermaak, N. , 2017, “ Introducing a Level-Set Based Shape and Topology Optimization Method for the Wear of Composite Materials With Geometric Constraints,” Struct. Multidiscip. Optim., 55(2), pp. 547–568. [CrossRef]
Archard, J. , and Hirst, W. , 1956, “ The Wear of Metals Under Unlubricated Conditions,” Proc. R. Soc. London A, 236(1206), pp. 397–410. [CrossRef]
Kim, D. , Jackson, R. L. , and Green, I. , 2006, “ Experimental Investigation of Thermal and Hydrodynamic Effects on Radially Grooved Thrust Washer Bearings,” Tribol. Trans., 49(2), pp. 192–201. [CrossRef]
Yu, T. H. , and Sadeghi, F. , 2001, “ Groove Effects on Thrust Washer Lubrication,” ASME J. Tribol., 123(2), pp. 295–304. [CrossRef]
Fwa, T. , Shi, X. , and Tan, S. , 1996, “ Use of Pasternak Foundation Model in Concrete Pavement Analysis,” J. Transp. Eng., 122(4), pp. 323–328. [CrossRef]
Gavin, H. P. , 2017, “ The Levenberg-Marquardt Method for Nonlinear Least Squares Curve-Fitting Problems,” epub http://people.duke.edu/~hpgavin/ce281/lm.pdf.


Grahic Jump Location
Fig. 1

Schematics of the elastic Pasternak foundation model. (a) Indentation of worn sample into counter-body (elastic foundation). (b) Separate views of deformed counter-body and worn sample showing the contact region (Ωc), the noncontact region (Ωnc) on the deformed counter-body surface, and the worn sample surface region (D). (c) Graphical illustration of counter-body deformation (u), sample worn surface profile (z), and reference height (h).

Grahic Jump Location
Fig. 2

Illustration of rotary and linear wear systems. Rotary wear system: (a) top view, and (b) side view. Linear wear system: (c) top view and (d) side view.

Grahic Jump Location
Fig. 3

(a) Steady-state surface profile of a bimaterial composite system from Ref. [38] subject to linear abrasive sliding wear. (a-i) Numerical surface profile prediction from a symmetric Pasternak foundation-based linear wear model. (a-ii) Experimentally measured surface profile. (a-iii) Epoxy (dark color) and PEEK (light color) composite configuration. (b) Smoothed experimental surface profile from (a-ii) [38] shown in 3D [39]. Note the asymmetry in surface profile with respect to sliding and counter-sliding directions.

Grahic Jump Location
Fig. 4

Schematic of tribometers used for wear tests. (a) Rotary tribometer. (b) Linear reciprocating tribometer.

Grahic Jump Location
Fig. 5

Calibration procedure for foundation parameters

Grahic Jump Location
Fig. 6

Calibration of foundation parameters using experimental data and validation of numerical simulations. (a) Three composite samples (cases 1–3); the left image is half of the experimental sample and the right image is half of the numerical simulation domain. (b) Calibration of foundation parameters using case 1. (c) Validation of calibrated foundation parameters using cases 2 and 3. Note that experimental data are shown with solid lines and numerical results with dashed lines.

Grahic Jump Location
Fig. 7

Material removal histories of case 1–3: (a) Mass loss, (b) volume loss, and (c) errors of numerical predictions comparing experimental data

Grahic Jump Location
Fig. 8

Case study: sample surface profile evolutions at selected cycles using the experimentally calibrated proposed and previous [37] simulation procedures

Grahic Jump Location
Fig. 9

Case study for a linear wear system. (a) Composite sample under linear wear; the left image is half of the experimental sample and the right image is half of the numerical simulation domain. (b) Experimental steady-state surface profile. (c) Numerical steady-state surface profile. (d) Comparison of line-scans of experimental (solid lines) and numerical (dashed lines) steady-state surface profiles. Results for both sliding and counter-sliding directions are shown.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In