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

Abstract

A mathematical model for evaluation of the temperature mode of the disc–pad system during single braking is proposed. The model is based on the thermal problem of friction formulated for two semi-infinite bodies, compressed with pressure increasing over time while reducing the sliding velocity from the initial value to zero at the stop. The exact solution to this problem was obtained by means of Duhamel’s theorem. Validation of the solution was performed by achieving in special cases parameters of known solution to this problem with constant pressure and velocity (under uniform sliding). The results of the numerical calculations are presented for a selected friction pair, made of functionally graded materials with titanium alloy (disc) and aluminum alloy (pad) cores coated with ceramics graded toward friction surfaces. For the established values of the parameters such as the rise time in pressure and the FGM gradients, the ability to quickly obtain spatiotemporal temperature distributions in the disc and pad was presented. The influence of the variability of these parameters on the maximum temperature of the brake system was also investigated.

Influence of Thermal Sensitivity of Functionally Graded Materials on Temperature during Braking

“…The aim of this study was to investigate the influence of FGMs thermal sensitivity on the distribution of temperature in a disc brake system. This study is a continuation of our previous articles [ 11 , 18 ], which concern the transient thermal problem of friction under uniform sliding and during single braking with an exponential increase in the contact pressure. Due to the appearance of a high temperature level, there is a demand to improve the results by involving the variations of material properties dependent on the actual temperature, since the thermal sensitivity effect is particularly manifested in a high temperature range.…”

“…The key element of the proposed approach is the precise solution of the linear thermal problem of friction during braking with constant deceleration. In the case of FGMs, such a solution for the above-adopted scheme of two sliding semi-spaces for the specific friction power (8) and (9) can be written in the form [ 18 ]: where , are the real roots of the functional equation: —are the Bessel functions of the first kind of the k th order [ 22 ].…”

Temperature in the Friction Couple Consisting of Functionally Graded and Homogeneous Materials

“…On the other hand, the disc (body 2) is made of a homogeneous material (cast iron etc.). A more detailed description of the adopted model assumptions is presented in our previous articles [ 1 , 2 ].…”

“…Reviews of investigations on methods for establishing the temperature of systems containing friction elements made of functionally gradient materials (FGMs) can be found in previous articles [ 1 , 2 , 3 ]. In these studies, the methodology of determining the temperature in such friction couples under uniform sliding [ 1 ], during braking with time-dependent contact pressure [ 2 ], and considering the thermal sensitivity of component materials of FGMs was investigated [ 3 ]. The main factor in this methodology is an exact solution to the boundary–value heat conduction problem, taking into account the frictional heating of two semi-infinite bodies made of FGMs.…”

The Heat Partition Ratio during Braking in a Functionally Graded Friction Couple

“…where t s is the stop moment of heating. The evolution of the heat flux intensity (42) corresponds to the temporal profile of the specific friction power during braking with constant deceleration [39]. The corresponding dimensionless temperature rise of Θ * was searched based on Duhamel's theorem [40] as follows:…”