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Research Papers

# Thermo-Mechanical Model for Moving Layered Rough Surface Contacts

[+] Author and Article Information

Tribology Group, Imperial College, London, SW7 2BX, United Kingdom

E. Ioannides

Tribology Group, Imperial College, London, SW7 2BX, United Kingdom; SKF ERC, 3430 DT, Nieuwegein, The Netherlands

We are grateful to one of the reviewers for a useful discussion of the potential effects of setting the temperature rise at infinite distance away from the contact to zero. The solution for temperature field as presented here is used for both the moving and the stationary body (relative to the contact). This boundary condition imposes a situation, which can be rather unrealistic in real engineering problems, particularly when the stationary body is considered. For a stationary body, the temperature rise does not tend to zero even far away from the heated region. However, this boundary condition is used in other thermomechanical models (see, for example, Vick et al. (8)) and it can be considered suitable in a model that serves as a general tool for investigating the relative influence of various contact parameters on thermomechanical behavior of the contact, rather than providing a solution to a specific engineering problem. If one’s aim is to deal with a particular engineering application as realistically as possible it would be necessary to impose boundary conditions appropriate to that situation, which is beyond the scope of the current paper. It should also be noted that the remote boundary conditions can influence the effective heat partitioning in the contact (heat partitioning is discussed later in the paper). Some insight into this can be gained by setting the bulk temperature (which also includes the temperature at “infinity”) of the two bodies to be different. This is possible with the current model since, as explained above, the Boundary Condition 9 only sets the temperature rise to zero at infinity. This modifies the heat partition so that the body with higher bulk temperature now absorbs less heat than if the two bulk temperatures were equal. It would be interesting to study these effects further and the authors would hope to be able to report on this matter at a later stage. (Please note that the results presented in this paper were all calculated assuming that the bulk temperature of the two bodies is zero.)

We are thankful to one of the reviewers for pointing out that it would be useful to establish how much of the observed thermomechanical influences are due to the effects on macrocontact scale and how much due to asperity effects. Equivalent analyses to that presented in Figs.  56 were carried out for the contact of two smooth bodies. Under certain conditions similar effects to those in Figs.  56 are observed in that the pressure distribution becomes skewed toward the trailing edge of the contact since the thermal growth here is larger. The observed differences are not as pronounced as in the rough cases, however. Nevertheless, it can be said that the thermomechanical influences discussed above are partly due to effects on the asperity scale and partly to those on the overall macrocontact scale. How significant each contribution is, would depend on the particular surface roughness structure studied. Figure 7, discussed later in the paper, for example, clearly indicates the important influence of the roughness structure on the predicted contact temperature rise and it is to be expected that a particular roughness structure would have similarly important effects on the phenomena discussed here. In order to give a full answer to this question a type of parametric study with a large number of rough surfaces would have to be carried out and it is hoped that such results may be presented in the future.

J. Tribol 130(1), 011016 (Jan 18, 2008) (15 pages) doi:10.1115/1.2805440 History: Received April 05, 2006; Revised July 29, 2007; Published January 18, 2008

## Abstract

A numerical model designed to simulate a moving line contact of two rough layered bodies is presented. Fourier transforms are used to obtain fundamental solutions to relevant differential equations and then these solutions are used as kernel functions in a numerical scheme designed to provide a full thermomechanical solution for real layered contacts. The model assumes steady state heat transfer and predicts contact pressures and deformations, contact temperature rise, and resulting thermal stresses. The heat division between the contacting components is fully accounted for, as are the interactions between the mechanical and thermal displacements. Some results are presented to illustrate the potential importance of a full thermomechanical analysis as compared to a purely mechanical one as well as to demonstrate the influence of coating properties and surface roughness structure on the contact temperatures.

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## Figures

Figure 1

An illustration of rough layered contact that is simulated by the present model. The double arrows at the points of contact represent local heat inputs, q.

Figure 2

An illustration of the moving band heat source problem on a layered body as used to obtain the fundamental solution of the current model. Two sets of coordinates are considered. x1′, x2′ are fixed to the half-space (material reference frame), while x1, x2 are fixed to the moving heat source (the convective reference frame).

Figure 3

A flowchart showing the basic steps of the simulation algorithm

Figure 4

Comparison of the predicted dimensionless temperatures calculated with the numerical model (points) with those calculated using Jaeger’s classical moving heat source theory (lines) for a band heat source of width 2l and strength q at different Peclet numbers (L=Vl∕2κ).

Figure 5

Contact pressure distribution, deformed profiles, and temperature rise for a steel cylinder in contact with a coated rough half-space. Analysis excludes the effects of thermal displacement. The predicted temperatures are shown for information only. Contact conditions:μ=0.5, h=5μm, α1=48K−1×10−6, α2=12K−1×10−6, P0=0.6GPa, load=0.1N∕μm, Rcyl=10mm, V=1.4232m∕s, real contact area (real contact length along x axis) =151.72μm, all other material properties are those of steel, i.e., E=207GPa, ν=0.3, k=45W∕mK, ρ=7835kg∕m3, c=460J∕kgK; surface parameters:rms=0.0651μm, β*=15.54μm.

Figure 6

Contact pressure distribution, deformed profiles, and temperature rise for a steel cylinder in contact with a coated rough half-space. Analysis includes the effects of thermal displacements and the mechanical-thermal interactions. All contact conditions are identical to those in Fig. 5. Predicted real contact area (real contact length along the x axis) =136.5μm.

Figure 7

Temperature rise and pressure distributions for various sinusoidal surfaces (a) wavelength=15.7μm, amplitude=1μm (RMS=0.707μm, β*=2.937μm), (b) wavelength=125.7μm, amplitude=1μm (rms=0.707μm, β*=23.5μm), (c) wavelength=125.7μm, amplitude=1∕3μm (rms=0.2357μm, β*=23.5μm). All results at same loading conditions and same Peclet number and both bodies are homogenous and same material: k=45W∕mK, c=460J∕kgK, ρ=7835kg∕m3, E=207GPa, υ=0.3, α=12K−1×10−6, Hertz max pressure=1GPa, Hertz semiwidth=175.5μm, smooth surface temperature rise 116.85K.

Figure 8

Variation of heat partition fraction, alpha (proportion of heat entering the body which is moving relative to the contact) across the contact for a selected rough surface contact. Contact pressure distribution, deformed profiles, and temperature rise are also shown. Overall heat partition fraction is 0.93. Contact conditions:μ=0.1, h=5μm, k1=90W∕mK, k2=k3=45W∕mK, P0=1GPa, load=0.275N∕μm, Rcyl=10mm, V=0.25m∕s, real contact area (length along x axis) =100μm, all other material properties are those of steel, i.e., E=207GPa, ν=0.3, α=12K−1×10−6, ρ=7835kg∕m3, c=460J∕kgK.

Figure 9

The ratio of maximum surface temperature rise with coating present (Tc) to that without the coating (Twc) versus the product of dimensionless coating thickness (h∕l) and coating Peclet number (Vl∕2κ1) for a set of ratios b1∕b2 where b=kρc, for a contact of a smooth cylinder on a smooth layered surface. k2∕k3=1.

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