Research Papers: Contact Mechanics

Analysis of Steady-State Rolling Contact Problems in Nonlinear Viscoelastic Materials

[+] Author and Article Information
Alaa A. Abdelrahman

Department of Mechanical Design and
Production Engineering,
College of Engineering,
Zagazig University,
Zagazig 44511, Egypt
e-mail: alaaabouahmed@gmail.com

Ahmed G. El-Shafei, Fatin F. Mahmoud

Department of Mechanical Design and
Production Engineering,
College of Engineering,
Zagazig University,
Zagazig 44511, Egypt

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received July 21, 2014; final manuscript received February 1, 2015; published online April 15, 2015. Assoc. Editor: James R. Barber.

J. Tribol 137(3), 031402 (Jul 01, 2015) (10 pages) Paper No: TRIB-14-1183; doi: 10.1115/1.4029938 History: Received July 21, 2014; Revised February 01, 2015; Online April 15, 2015

A comprehensive numerical model is developed using Lagrangian finite element (FE) formulation for investigating the steady-state viscoelastic (VE) rolling contact response. Schapery's nonlinear viscoelastic (NVE) model is adopted to simulate the VE behavior. The model accounts for large displacements and rotations. A spatially dependent incremental form of the VE constitutive equations is derived. The dependence on the history of the strain rate is expressed in terms of the spatial variation of the strain. The Lagrange multiplier approach is employed. The classical Coulomb's friction law is used. The developed model is verified and its applicability is demonstrated.

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Fig. 1

Rolling contact of a cylinder over foundation

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Fig. 2

Representative divisions of the VE domain into FEs

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Fig. 3

Rolling of VE wheel on a flat rigid foundation

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Fig. 4

Contact pressure distributions for EL and LVE at full load intensity

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Fig. 5

Contact pressure distributions for the FE and Hertzian solution at different load fractions (F/Ft)

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Fig. 6

Frictionless contact pressure distributions for LVE and NVE responses

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Fig. 7

Frictional contact pressure distributions or LVE and NVE responses

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Fig. 8

Variation of Fcn with the vertical displacement for frictionless response

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Fig. 9

Variation of Fcn with the vertical displacement for frictional response

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Fig. 10

Tangential contact stress distributions for VE and NVE responses

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Fig. 11

Rolling of VE cylinder with rigid core over the internal surface of a hollow rigid cylinder

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Fig. 12

Contact pressure distributions for LVE and NVE responses

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Fig. 13

Variation of Fcn with the vertical displacement for LVE and NVE responses

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Fig. 14

Tangential contact stress distributions or LVE and NVE responses



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