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Research Papers: Elastohydrodynamic Lubrication

Finite Element Modeling of Transient Thermomechanical Rolling Contact Featuring Mixed Control of the Rigid Body Motion

[+] Author and Article Information
Andreas Draganis

Department of Applied Mechanics,
CHARMEC,
Chalmers University of Technology,
Gothenburg SE-412 96, Sweden
e-mail: andreas.draganis@gmail.com

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received August 14, 2015; final manuscript received February 7, 2016; published online July 14, 2016. Assoc. Editor: Dong Zhu.

J. Tribol 139(1), 011503 (Jul 14, 2016) (17 pages) Paper No: TRIB-15-1296; doi: 10.1115/1.4033048 History: Received August 14, 2015; Revised February 07, 2016

A theoretical and computational framework for the analysis of fully transient, thermomechanically coupled, frictional rolling contact based on an arbitrary Lagrangian–Eulerian (ALE) kinematical description is presented. In particular, a computationally efficient methodology for mixed control between the ALE referential velocities and their corresponding driving forces is developed and discussed in depth. Numerical examples involving two-dimensional (2D) cylinder–plate rolling contact are presented, covering a range of transient, thermomechanically coupled rolling contact phenomena, taking place on a broad range of time scales. Here, particular points of emphasis include dynamical effects in the vicinity of the contact region and the time scales on which mechanical and thermal mechanisms operate.

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Figures

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Fig. 1

Illustration of configurations and maps relevant to the employed ALE description

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Fig. 2

A point on the slave surface and its projection on the master surface, along with relevant unit vectors

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Fig. 3

Resultants of external forces and moments acting on the cylinder

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Fig. 4

Employed FE mesh, with a zoomed-in view of the refined contact region

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Fig. 5

Schematic illustration of the thermomechanical model. A: applied mechanical load, B: cylinder hub (fixed in horizontal direction, fixed temperature), C: artificial plate domain ends (fixed temperature), and D: plate base (fixed in all displacement degrees-of-freedom).

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Fig. 6

Force–creepage curve for a series of stationary simulations, along with the analytical Carter–Hertz solution

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Fig. 7

Prescribed time-history of the creepage ξ

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Fig. 8

Frictional ratio Fxc/(μFyc) versus normalized time t̃ for the considered transient simulations (curves representing simulations 1–6 arranged from bottom to top), along with stationary/quasi-static (solid line with circle markers) and analytical (dashed curve) solutions. The vertical dashed line corresponds to t̃0 : the time at which ξ reaches its final value.

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Fig. 9

Contact stress distributions on the plate surface for three different values of t̃ and ξ: (a) t̃=0.17 (ξ = −2 × 10−4), (b) t̃=0.44 (ξ = −5 × 10−4), and (c) t̃=0.61 (ξ = −7 × 10−4). In each plot, the upper and lower set of curves represent normal and tangential contact stress distributions, respectively. The Carter–Hertz analytical solution, the stationary/quasi-static solution, and two transient solutions are included.

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Fig. 10

Excess temperature at the point of initial contact on the cylinder surface versus the normalized time t̃, for the considered set of transient simulations (curves representing simulations 1–6 arranged from bottom to top) and for a series of stationary/quasi-static simulations (solid line with circle markers)

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Fig. 11

Prescribed time-histories of the translational rolling velocity V¯ and the peripheral velocity −roω

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Fig. 12

Time-history of the creepage ξ as a result of the prescribed time-histories of V¯ and ω

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Fig. 13

Computed time-evolutions of horizontal forces: (a) simulation a and (b) simulation b

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Fig. 14

Computed time-evolutions of moments about the cylinder center: (a) simulation a and (b) simulation b

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Fig. 15

Temperature at the point of initial contact on the cylinder surface for simulations a and b

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Fig. 16

Time-histories of forces and moments: (a) prescribed time-history of the external horizontal force Fxext, and computed time-evolutions of the contact force Fxc and the total force Fxtot; (b) prescribed time-history of the external moment Mext, and computed time-evolutions of the contact moment Mc and the total moment Mtot

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Fig. 17

Computed time-evolutions of the translational rolling velocity V¯ and the peripheral velocity −roω. Note: the two curves coincide in the figure.

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Fig. 18

Computed time-evolution of the creepage

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Fig. 19

Time-evolution of the excess temperature at the point of initial contact: (a) cylinder and (b) plate

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Fig. 20

Time-evolution of the excess temperature at the point of initial contact: (a) cylinder and (b) plate

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Fig. 21

Time-evolution of the resultant normal force

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