ABSTRACT
An analytical model to find the temperature field that has been developed for friction systems consists of a strip and semi-space. The strip is made of a two-component functionally graded material (FGM) with an exponentially changing coefficient of thermal conductivity. In contrast, the material of the semi-space is homogeneous. An appropriate boundary-value problem of heat conduction with constant specific friction power was formulated and solved using the Laplace integral transform method. The model takes into consideration the imperfect thermal friction contact between the strip and the semi-space, and also the convective cooling on the exposed surface of the strip. The appropriate asymptotic solutions to this problem for low and high values of Fourier number were obtained. It is shown how the determined exact solution can be generalized using Duhamel's formula for the case of a linearly reduction in time-specific friction power (a braking process with constant deceleration). Numerical analysis for selected materials of the friction pair was carried out in terms of examining the mutual impact on the temperature of the two Biot numbers, characterizing the intensity of the thermal contact conductivity and convective heat exchange on the exposed surface of the strip. The obtained results can be used to predict the temperature of friction systems containing elements made of FGM. In particular, such systems include modern disc braking systems.
ABSTRACT
An exact solution of the boundary-value problem of heat conduction was obtained with consideration of heat generation due to friction and convective cooling for the strip/semi-space system. Analytical solutions to this problem are known for the case with both friction elements made of homogeneous materials or a composite layer with a micro-periodic structure. However, in this study, the strip is made of a two-component functionally gradient material (FGM). In addition, the exact, asymptotic solutions were also determined at small and large values of the Fourier number. By means of Duhamel's theorem, it was shown that the developed solution for a constant friction power allows to obtain appropriate solutions with a changing time profile of this value during heating. Numerical analysis in dimensionless form was carried out for the FGM (ZrO2-Ti-6Al-4V) strip in combination with the cast iron semi-space. The influence of the convective cooling intensity (Biot number) on the temperature field in the considered friction system was investigated. The developed mathematical model allows for a quick estimation of the maximum temperature of systems, in which one of the elements (FGM strip) is heated on the friction surface and cooled by convection on the free surface.
ABSTRACT
A mathematical model of heat generation due to friction in a disc-pad braking system was developed with consideration of a thermal barrier coating (TBC) on the friction surface of the disc. The coating was made of functionally graded material (FGM). The three-element geometrical scheme of the system consisted of two homogeneous half-spaces (pad and disc) and a functionally graded coating (FGC) deposited on the friction surface of the disc. It was assumed that the frictional heat generated on the coating-pad contact surface was absorbed to the insides of friction elements along the normal to this surface. Thermal contact of friction between the coating and the pad as well as the heat contact between the coating and the substrate were perfect. On the basis of such assumptions, the thermal friction problem was formulated, and its exact solution was obtained for constant and linearly descending specific friction power over time. For the first case, the asymptotic solutions for small and large values of time were also found. A numerical analysis was performed on an example of the system containing a metal ceramic (FMC-11) pad, sliding on the surface of a FGC (ZrO2-Ti-6Al-4V) applied on a cast iron (ChNMKh) disc. It was established that the application of a TBC made of FGM on the surface of a disc could effectively reduce the level of temperature achieved during braking.
ABSTRACT
A mathematical model for determining the temperature distribution in the system consisting of a coating deposited on the surface of substrate was proposed. The foundation material is homogeneous, while the coating is made of a functionally gradient material (FGM) with thermal conductivity increasing exponentially along the thickness. Heating processes of the outer surface of the coating were considered with a constant and linearly decreasing in time intensity of the heat flux. Such thermal loads are common in thermal problems of friction, particularly regarding frictional heating during braking. An exact (in quadrature) solution of the corresponding boundary-value problems of parabolic heat conduction was obtained. Asymptotic solutions to these problems were also found for small and large values of the Fourier number. Calculations were performed for a coating made of two-component FGM ZrO2-Ti-6Al-4V, applied on a cast iron substrate. In order to explain the effect of FGM on temperature, corresponding analysis was carried out for the coating made of a homogeneous (ZrO2) material.
ABSTRACT
The object of study is the temperature of a braking system, operating in repetitive short-term (RST) mode. One element of the considered friction pair is made of a functionally gradient material (FGM), and the other of a homogeneous material. To determine the temperature on the friction surfaces of both elements, the previously obtained, exact solution of the boundary value problem of heat conduction was adopted, with account of the heat generation due to the friction. A calculation scheme was proposed that takes into consideration thermal sensitivity of materials and variations of the friction coefficient under the influence of temperature. Calculations were performed for two-component FGM (ZrO2-Ti-6Al-4V) in combination with gray cast iron (ChNMKh). It was found that for selected friction pair materials, consideration of their thermal sensitivity reduces the time of braking and the value of temperature achieved on the friction surfaces. At the same time, the whole process was characterized by a good stability of braking with a slight decrease in efficiency in each subsequent cycle.
ABSTRACT
The article presents finite element models of the 2xBgu type tread brake for the simulation of extended repeated frictional heating carried out on a full-scale inertia dynamometer. The numerical calculations were conducted for the brake blocks made of two organic composite materials newly developed specifically for this study. The transient temperature changes obtained from the 2D axisymmetric and 3D finite element analyses and experimental data agreed well during continuous process of about 1200 s. Simulation of such a long period of braking sequence required introducing simplifications in the boundary conditions in the contact area, convection cooling, arrangement of the model (2D axisymmetric, 3D). The focus was laid on representation of variation of the coefficient of friction and the temperature dependence of the properties of the friction materials during braking. The carried out research indicates limitations in the finite element analysis and directions of necessary improvements in modelling as well as measurements with the use of embedded thermocouples.
ABSTRACT
A one-dimensional thermal problem of friction was formulated, taking into account the contact pressure increase at the beginning of the process. The obtained solution to this problem allows for the quick calculation of the transient temperature distribution in a railway brake disc during single braking application. In order to validate the developed model, the experimental tests were performed for two friction pairs consisting of the cast iron brake disc and pads comprising two composite materials. Theoretical results were compared with the data measured by thermocouples embedded in the brake disc during the full-size dynamometer tests. The maximum temperature values found based on the analytical solution are convergent with the corresponding empirical data. The consistency of the results obtained for two friction couples demonstrates the usefulness of the proposed computational model.
ABSTRACT
The basic function of friction clutches is to transfer the torque in the conditions of its smooth engagement without vibrations. Hard working conditions under high thermal and mechanical loads, leading to high temperature in the contact area, intense wear, and instability of the coefficient of friction impose restrictive criteria in the design of friction materials. In this paper, the results of experimental research of the effect of ceramic and intermetallic additives to the copper-based material of the friction disc of the clutch on the thermophysical and frictional properties were presented. Next, these properties were incorporated in the proposed contact 3D numerical model of the clutch to carry out computer simulations of the heating process and subsequent cooling. Based on the obtained experimental data and transient temperature changes of the friction and steel discs, the relations between the powder additives, thermophysical properties of the five friction materials, and coefficients of friction, wear, and temperature reached were discussed. Among these, it was found that when working with the lubrication, the largest values of the coefficient of friction 0.068 and wear 13.5 µm km-1 were reached when using the 3 wt.% SiC additive.
ABSTRACT
The theoretical scheme for determining the heat partition ratio (HPR) in a friction couple made of functionally graded materials (FGMs) was proposed. As a result, the formula for the calculation of the HPR was found, which depends on the thermal properties and the parameters of the material's gradient. In specific cases of these parameters, the known formulas for estimating the HPR for homogeneous materials were obtained. Calculations were carried out for the friction couple consisting of the following two-component FGMs: Al2O3-Cu (first body) and ZrO2-Ti-6Al-4V (second body), under the conditions corresponding to a single braking with a constant deceleration. It was established that the vast majority (almost 90%) of heat that was generated by friction was absorbed by the first body in the selected couple. The possibilities of using the obtained results were discussed herein.
ABSTRACT
An analytical model was developed to determine the temperature of friction coupling, in which one element was made of a functionally graded material (FGM) and the other was homogeneous. First, for such a system, the boundary-value problem of heat conduction was formulated with consideration of the heat generation due to friction. Then, using the Laplace integral transform, an exact solution to this problem was obtained for uniform sliding, and braking with constant deceleration. A numerical analysis was performed for the selected friction pair consisting of the FGM (zircon dioxide + titanium alloy) and cast iron. It was established that the use of elements made of a FGM consisting of ZrO2 and Ti-6Al-4V can significantly reduce the maximum temperature achieved in the friction system.
ABSTRACT
The model of the frictional heating process during single braking to determine the temperature of the functionally graded friction elements with an account of the thermal sensitivity of materials was proposed. The basis of this model is the exact solution of the one-dimensional thermal problem of friction during braking with constant deceleration. The formulas approximating the experimental data of the temperature dependencies of properties of the functionally graded materials (FGMs) were involved in the model to improve the accuracy of the achieved results. A comparative analysis was performed for data obtained for temperature-dependent FGMs and the corresponding data, calculated without consideration of thermal sensitivity. The results revealed that the assumption of thermal stability of FGMs during braking may cause a significant overestimation of temperature of the friction pair elements.
ABSTRACT
This paper consists of two parts. The first one contains a description and methodology of the composite material used as friction material in clutches. Four variants of such material, differing in the type of carbon additive (the elemental graphite, pencil graphite and foundry coke powder of various fractions) were considered. Thermal conductivity, thermal diffusivity as well as the specific heat all materials were determined experimentally. On the inertial IM-58 stand, a simulation of the braking process of the friction pair consisting of a steel disc with friction material and a counterpart in the form of a homogeneous steel disc was carried out. On this basis, averaged coefficients of friction, unchanging in the entire sliding process, were found for the four friction pairs. The experimental data obtained in the first stage were used in the second stage to develop two (2D and 3D) numerical models of the friction heating process of the friction pairs under consideration. For four variants of the friction material, a comparative spatial-temporal temperature analysis was performed using both models. It was found that a simplified axisymmetric (2D) model can be used to estimate the maximum temperature with high accuracy. The lowest maximum temperature (115.6 °C) obtained for the same total friction work was achieved on the friction surface of the material with the addition of GP-1.
ABSTRACT
A new approach to numerical simulation using the finite element method (FEM) for the rotational motion of discs for railway vehicle disc brake systems was proposed. For this purpose, spatial models of transient heating due to the friction of such systems with solid and ventilated discs were developed. The performed calculations and the results obtained allowed justification of the possibility of simplifying the shape of the ventilated brake disc through elimination of ventilation channels. This contributes to a significant reduction in computational time, without compromising the accuracy of the results. The spatial and temporal temperature distributions in the ventilated and the solid disc of the same mass were analyzed. The share of energy dissipated due to convection and thermal radiation to the environment in relation to the total work done during a single braking was investigated. The maximum temperature values found as a result of computer simulations were consistent with the corresponding experimental results.
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.
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.
ABSTRACT
An algorithm to determine the maximum temperature of brake systems during repetitive short-term (RST) braking mode has been proposed. For this purpose, the intermittent mode of braking was given in the form of a few cyclic stages consisting of subsequent braking and acceleration processes. Based on the Chichinadze's hypothesis of temperature summation, the evolutions of the maximum temperature during each cycle were calculated as the sum of the mean temperature on the nominal contact surface of the friction pair elements and temperature attained on the real contact areas (flash temperature). In order to find the first component, the analytical solution to the one-dimensional thermal problem of friction for two semi-spaces taking into account frictional heat generation was adapted. To find the flash temperature, the solution to the problem for the semi-infinite rod sliding with variable velocity against a smooth surface was used. In both solutions, the temperature-dependent coefficient of friction and thermal sensitivity of materials were taken into account. Numerical calculations were carried out for disc and drum brake systems. The obtained temporal variations of sliding velocity, friction power and temperature were investigated on each stage of braking. It was found that the obtained results agree well with the corresponding data established by finite element and finite-difference methods.
ABSTRACT
An analytical model to determine temperature in a single brake disc of multi-disc system is proposed. The model considers the convective cooling on the lateral surfaces of the disc and structure of composite friction material. Calculations were carried out for a disc made of carbon friction composites material Termar-ADF. The influence of heat transfer with environment, length of bundles with fibers, and concentration of fibers in composite on the temperature of the disc was investigated during single braking with constant deceleration.
ABSTRACT
In this paper, a methodology for conducting a computer simulation of the frictional heating process of a multi-disc braking system is proposed. The single braking of a system of three identical discs made of carbon-carbon (C/C) carbon frictional composite material (CFCM) is considered. In order to determine the operational characteristics of the brake, a heat dynamics of friction (HDF) system of equations is formulated, which takes into account the contact pressure rise time, thermal sensitivity of the C/C material, the change in the coefficient of friction during braking, the parameters of the friction surface's microgeometry and the mutual influence of sliding velocity and temperature. A numerical solution using the finite element method (FEM) of the HDF system of equations allows us to determine changes in key braking process characteristics, such as work done, braking torque, friction coefficient, heat transfer coefficient, velocity and temperature. Finally, a comparative analysis of the results obtained for three different time profiles of the coefficient of friction is carried out.
ABSTRACT
A spatial computational model of a motor vehicle disc brake, based on the system of equations of heat dynamics of friction and wear (HDFW), was developed. The interrelations of temperature-dependent coefficient of friction and coefficient of intensity of wear through the contact temperature and vehicle velocity were taken into account. The solution of the system of equations of HDFW was obtained by the finite element method (FEM) for six different brake pad materials associated with the cast-iron disc during a single braking. Changes in the braking time, coefficient of friction, braking torque, vehicle velocity, mean temperature of the contact area of the pads with the disc and wear of the friction surfaces were determined. Then, the obtained calculation results were evaluated in terms of stabilization of the coefficient of friction (braking torque), as well as minimization of the maximum temperature, wear, braking time and pads mass. As a result, recommendations were given to select optimum brake pad material in combination with a cast-iron disc.
