The Effect of Functionally Graded Materials on Temperature during Frictional Heating: Under Uniform Sliding

Abstract

The mathematical model of heating process for a friction system made of functionally graded materials (FGMs) was proposed. For this purpose, the boundary-value problem of heat conduction was formulated for two semi-spaces under uniform sliding taking into consideration heating due to friction. Assuming an exponential change in thermal conductivities of the materials, the exact, as well as asymptotic (for small values of time), solutions to this problem were obtained. A numerical analysis was performed for two elements made of ZrO2–Ti-6Al-4V and Al3O2–TiC composites. The influence of the gradient parameters of both materials on the evolution and spatial distributions of the temperature were investigated. The temperatures of the elements made of FGMs were compared with the temperatures found for the homogeneous ceramic materials.

The Effect of Functionally Graded Materials on Temperature during Frictional Heating at Single Braking

“…The presented results are the continuation of an investigation from a previous article of the authors [ 17 ], in which, in the dimensionless form, a comparative, qualitative analysis was performed in order to study the influence of gradient of FGMs on the temperature during frictional heating under uniform sliding. However, in this paper the mathematical model was derived to determine the temperature field in a disc–pad system during single braking.…”

“…In the case of a uniform slip with a constant specific power of friction , , the solution to the problem in Equations (11)–(16) can be written in the following form [ 17 ]: where …”

“…From Equation (2), the braking time with constant deceleration was found and, next, the stop time This allowed determining from Equation (50) the effective depths of heat penetration and , as well as the value of the scaling parameter . According to the methodology, described in detail in [ 17 ], the dimensionless parameters of the material gradient were also established as and .…”

“…We note that a more comprehensive review of the literature on thermoelastic contact problems with frictional heating for functionally graded materials was provided in our previous article [ 17 ]. This article is a continuation of the research cycle started in [ 17 ], in which the case of the uniform sliding of an FGM tribosystem was considered.…”

“…We note that a more comprehensive review of the literature on thermoelastic contact problems with frictional heating for functionally graded materials was provided in our previous article [ 17 ]. This article is a continuation of the research cycle started in [ 17 ], in which the case of the uniform sliding of an FGM tribosystem was considered. The present article concerns the transient thermal problem of friction during braking, which takes into account the time-dependent specific friction power due to the exponential increase in contact pressure.…”