The numerical estimation of thermal contact resistance in contacting surfaces

American Journal of Applied Sciences, Nov, 2008 by M.H. Shojaefard, K. Goudarzi

INTRODUCTION

The energy expended to plastically deform materials in manufacturing processes such as metal-forming processes is converted almost entirely into heat. This energy increases the temperature of the formed component and the tools while some of it is dissipated to the environment. The heat transfer to the component and tools has an effect on the accuracy of the formed component. Consequently, heat transfer from the work-material to the tool and the environment is of increasing interest to researchers and engineers participating in the manufacturing of high-precision components.

As a result of manufacturing processes, real surfaces have roughness and surface curvature. The real contact occurs only over microscopic contacts, which are typically only a few percent of the apparent contact area. Because of the surface curvature of contacting bodies, the macro-contact area is formed, the area where micro-contacts are distributed randomly. The heat flow must pass through the macro-contact and then micro-contacts to transfer from one surface to another. This phenomenon leads to a relatively high temperature drop across the interface. Also, the thermal contact resistance is a complex interdisciplinary problem, which includes geometrical, mechanical and thermal analyses. Analytical, experimental and numerical models have been developed to predict TCR since the 1930's. These models are applicable only to the limiting cases and none of them covers the general non-conforming rough contact (1).

The reliability of analytical approaches depends on the accuracy of the material properties and the physical parameters that influence heat transfer between surfaces. The last refers to values for specific heat, thermal contact resistance and coefficient of thermal expansion of both the component and the tool materials; whilst a further consideration is the allocation of a value for thermal contact resistance, since this determines the thermal balance in the component/tool/ environment system (1).

Thermal contact resistance, [R.sub.c], is defined as follows (2):

[R.sub.c] = [[[DELTA]T]/q](1)

where, [DELTA]T is the temperature difference at the contacting surfaces and q, heat flux, defined as:

q[d/[dA]]([dQ]/[dt])(2)

It is recognized that thermal contact resistance is a function of several parameters, the dominant ones being the type of contacting materials, the macro-and micro-geometry of the contacting surfaces, the temperature, the interfacial pressure, the type of lubricant or contaminant and its thickness. Further, the variation of the interfacial pressure with time has a significant influence on the thermal contact resistance. Until now, several different thermodynamic models have been used to compute the thermal contact resistance (3), (4).

Measurements of the thermal contact resistance have been carried out while heat transfer was either in steady-state or transient condition experiments were conducted using devices that contained two specimens or two tools with a specimen sandwiched between them. These experiments were followed by an assessment of the thermal contact resistance while the test specimen was deformed plastically; a further development involved the integration of thermocouples in the specimen. In the simplest case of steady-state heat transfer, the thermal contact resistance may be determined using . 1. The thermal contact resistance is assumed to be the value that provides the best match between simulation and experimental results. A new method is used based on the solution of an inverse problem. The sequential inverse method has been used to determine the thermal contact resistance in metal forming processes. Review of publications (5-12) suggests that values of thermal contact resistance vary significantly, perhaps due to the fact that these were derived using different experimental approaches. Published results were derived from experiments of different configurations, such as different materials, surface preparation, pressure and temperature, thus disabling comparison. These tests were conducted using specimens similar to those used in previous research (5). Further, the variation of thermal contact resistance at pressures is shown trends which appeared to depend on the work material and experimental conditions.

It may be concluded that experiments used to determine thermal contact resistance include some errors. Results depend on the measuring devices used in the experiments and on the method of processing the experimental data.

Therefore, the objective of this study is to develop an analytical model for predicting TCR for the entire range of non-conforming contacts. Therefore, a new approach for deriving values of thermal contact resistance under differing interfacial conditions is presented, together with results on the dependence of TCR on pressure and contact type (similar or dissimilar contact). A clear advantage of this method is the ability to measure the thermal contact resistance under precisely controlled and continuously sustained conditions. The other advantage of the present method is that no a priori information is needed on the variation of the unknown quantities, since the solution automatically determines the functional form over the domain specified.