Axisymmetric FEA of temperature in a pad/disc brake system at temperature-dependent coefficients of friction and wear

Robust braking results in heat generation whose effects may have considerable impact on the parameters of the process such as wear rate and coefficient of friction. Fluctuations of the latter disagree with essential operational and braking requirements. Finite element analysis (FEA) of a single braking process for axisymmetric heat conduction problem of friction in a pad/disc brake system in the present article was carried out. Two materials of the pad FC-16L (retinax A) and FMC-11 (metal ceramic) and one material of the disc ChNMKh (cast iron) were analysed. Experimental dependencies of the coefficient of friction and wear rate on the temperature under specified contact pressures for these two friction pairs were approximated and applied to FE contact model. The temperature and wear evolutions on the contact surface of the pad/disc brake system obtained for constant and temperature-dependent abovementioned coefficients were confronted and compared. Mutual correlations of the obtained results with the studied materials were discussed.     

3D FE model of frictional heating and wear with a mutual influence of the sliding velocity and temperature in a disc brake

Numerical simulation of frictional heating in a disc brake of a typical passenger vehicle based on the equation of motion and the boundary-value problem of heat conduction was carried out. An influence of temperature-dependent coefficient of friction on the sliding velocity, braking time, braking distance and the thermomechanical wear was studied. Two materials of the pad combined with the cast-iron brake disc were examined. The dependencies of the coefficient of friction and wear rate on the temperature and contact pressure were derived from experimental measurements and implemented to the computational model of the brake. Comparisons of temperature for validation purposes calculated using the contact model developed in this study were made with the model introducing an approach based on the heat partition adopted from other studies.     

Finite Element Analysis of Heat Partition in a Pad/Disc Brake System

The heat partition ratio is an important input parameter in simulation carried out by the finite element method (FEM) of the transient temperature fields in such elements as brakes, a pad, and a disc. Therefore, the aim of this article is to study the influence of nine various (experimental and theoretical) formulas for heat partition ratio on temperature in a pad/disc tribosystem. The real dimensions, operating conditions, and thermophysical properties of materials of two different disc brake systems were adopted for the finite element analysis. The evolutions of the temperature on the contact surface of the pad, obtained for different heat partition ratios, are compared with corresponding experimental data. The results revealed a significant influence of heat partition ratio on the evolution of pad maximal temperature, whereas the disc contact temperature was reasonably stable and coincided with most cases under consideration.     

Determination of the maximum temperature at single braking from the FE solution of heat dynamics of friction and wear system of equations

A system of equations of heat dynamics of friction and wear (HDFW) for a pad–disc tribosystem during a single braking has been formulated. It takes into account the coefficient of friction dependent on the maximum temperature, which is the sum of the mean temperature of the nominal contact region (the macro contact) and the flash temperature on the real contact area (the micro contact), temperature-dependent properties of materials and wear. Numerical solution of the initial problem of motion and the nonlinear boundary-value heat conduction problem was obtained. Computations were performed using the axisymmetric FE contact model for the metal ceramic pad and the cast-iron disc.     

Three-dimensional FE model for calculation of temperature of a thermosensitive disc

An effect of variations of the temperature-dependent thermophysical properties of materials of a pad and a disc on the temperature generated due to friction was studied. A three-dimensional boundary-value problem of heat conduction of the disc heated locally within the contact area by the moving with the constant deceleration heat flux and the intensity proportional to the specific capacity of friction was formulated. An issue was solved numerically using the finite element method (FEM). The experimental dependences curves of the thermal conductivity and the thermal diffusivity on the temperature ranging from 20 to 500 °C indispensable for the calculations were approximated using Chichinadze's methodology. The comparative analysis of temperature values on the contact surface of the disc obtained with and without influence of temperature dependence of the four different pad and the same quantity of the disc materials was carried out. It was demonstrated that apparent temperature differences arose for each friction couple combining temperature-dependent and constant properties of materials, however, the largest observed discrepancy (13.7%) occurred for the disc made of aluminium alloy series Al MMC. Other disc materials i.e. iron alloy series FCD50, cast iron ChNMKh and steel EI-696 revealed relatively equal temperature differences of order of 6.4%. Furthermore incorporated in the formula for the heat partition temperature variability of the thermophysical properties of materials affected the resulting contact temperature of the disc for friction couple combined exclusively with the titanium pad VT-14 (3.1%).     

Temperature in thermally nonlinear pad–disk brake system

The influence of the thermal sensitivity of pad and disk materials on temperature at braking is under investigation. A mathematical model of process of frictional heating in a pad–disk brake system, which takes into account the temperature-sensitive materials, is proposed. The basic element of this model is the thermal problem of friction—a one-dimensional boundary-value heat conduction problem with temperature-dependent thermal conductivity and specific heat. Contrary to the prior studies of authors, where a simple nonlinearity was considered, in this article the arbitrary nonlinearity of the thermophysical properties of materials is studied. The solution of a nonlinear boundary-value heat conduction problem is obtained by the method of successive approximations. The numerical analysis of temperature is executed for some materials of a pad and a disk with and without taking into account their thermal sensitivity.     

Investigation of the temperature field induced in the process of friction of a composite pad and a homogeneous disc

The analytical model for the determination of transient temperature field and heat fluxes in friction elements of brakes (pad/disc) is presented. It is assumed that one friction element is composed of a multi-layer composite strip, and the second element is a homogeneous semi-space. The solution to a non-stationary thermal problem of friction is obtained for a tribosystem with heat generation on a surface of contact and convective heat exchange with an environment on outer surface of a strip. The influences of composite parameters, for example, reinforcement fraction in the cross-section of periodic cells and the ratio of the conductivities of matrix and fibers, on the maximal temperature are studied.     

Accounting changes of pressure in time in one-dimensional modeling the process of friction heating of disc brake

The analytical solution to a thermal problem of friction during braking, which simulates the process of frictional heating in the disc/pad/caliper tribosystem, has been obtained. It is assumed that the pressure during braking is time-dependent, and the heat transfer takes place through a contact surface of the pad and the disc. The influence of duration of increase in pressure from zero (in the initial moment of time of braking) to nominal value (at the stop) and an amplitude of the pressure fluctuations on the temperature have been studied.     

Influence of the pressure fluctuations on the temperature in pad/disc tribosystem

The influence of the duration of increase in pressure from zero (at the initial moment of time) to nominal value (at the moment of a stop) on the temperature for a friction pair metal–ceramic pad/cast iron disc is studied. Fluctuations of pressure are taken into account, too. The analytical solution to a thermal problem of friction during braking is obtained for a plane-parallel strip/semi-space tribosystem with a time-dependence friction power and the heat transfer through a contact surface.     

3D investigation of thermal stresses in a locomotive ventilated brake disc based on a conjugate thermo-fluid coupling boundary conditions

The frictional heat generated during braking application can cause several negative effects on the brake system such as brake fade, premature wear, thermal cracks and disk thickness variation. It is then important to determine with precision, the temperature field and thermal stresses of the brake disc. In this study, thermal stress analyses on a ventilated locomotive wheel-mounted brake disc R920K with a three-dimensional model for two cases (the first case considers braking to a standstill; the second case considers braking on a hill and maintaining a constant speed) were investigated. The rate of braking heat generation is calculated using the assumption of uniform pressure distribution at the contact area. Then, thermal stress analyses for each case were performed. Finally, we have found that the maximum thermal stresses occur in the case with an emergency braking in the beginning of the braking process.     

Influence of thermal sensitivity of the materials on temperature and thermal stresses of the brake disc with thermal barrier coating

The time-dependent frictional heating of a disc with applied thermal barrier coating (TBC) on its working surface was investigated. To determine the temperature fields in the coating and the disc a one-dimensional friction heat problem during braking was formulated, with taking into account the dependence of thermal properties of materials from temperature. A model was adopted for materials with a simple non-linearity, i.e. materials whose thermal conductivity and specific heat are temperature dependent, and their ratio – thermal diffusivity is constant. The linearization of the corresponding boundary-value heat conduction problem was made by the Kirchhoff transformation and the linearizing multipliers method. A numerical-analytical solution to the obtained problem was found by Laplace transform method. Knowing the temperature distributions, quasi-static thermal stresses in the strip (TBC) with taking into account change in temperature mechanical properties, were determined. The distribution of temperature and thermal stresses in the strip made from ZrO₂ deposited on the UNS G51400 steel disc, was investigated.     

Experimental Study and Thermal Analysis on the Buckling of Friction Components in Multi-Disc Clutch

A full-scale multi-disc clutch test bench was set up and some sliding experiments were conducted to investigate the temperature evolution processes in low and high lubrication regimes. Friction discs with single friction lining were used and arranged back-to-back in order to preserve possible evidences of buckling. Temperatures were measured with thermocouples from four different radii on the mid-plane of the separator disc. Two different kinds of temperature variation processes with obvious critical points of cone shape buckling were obtained. These temperatures can be divided into three effective stages that represent different deformation status of the discs in these experiments. The temperature fields in the contacting separator disc and friction disc were studied through a transient heat conduction model, and the results show that the temperatures measured by the thermocouples from the separator disc can represent the average temperatures in both of the separator disc and friction disc for a long sliding time. By comparing the computational critical moments of the friction components with the experimental results, the capability of the curved beam model for predicting the critical moments of cone buckling was validated.     

Influence of thermal sensitivity of the pad and disk materials on the temperature during braking

The transient frictional heating of pad–disk tribosystem at single braking is under consideration. To determine the average friction surface temperature, the one-dimensional thermal problem of friction at braking has been formulated. The linear dependence of the thermophysical properties of the disk and pad materials on the temperature has been taken into account. Model of materials with a simple nonlinearity has been adopted, i.e. materials in which coefficients of heat conduction and specific heat depend on the temperature, and their ratio – coefficient of thermal diffusivity – is constant. Linearization of the corresponding boundary-value heat conduction problem by the Kirchhoff transformation and linearizing parameter method has been performed. The numerical–analytical solution to the problem has been found by using the integral Laplace transform and the Newton–Raphson methods. The influence of the thermosensitive materials of titanium pad, sliding over the surface of the disk made of steel, aluminum alloy or gray cast iron, on the temperature has been studied.     

The thermal problem of friction during braking for a three-element tribosystem with a composite pad

The analytical solution to a thermal problem of friction during braking with constant retardation for a three-element system (a foundation/strip/semi-space) is obtained. The solution allows to find the evolution and distribution of transient temperature in the caliper/pad/disk tribosystem. Unlike known solutions for three-element tribosystem, this one is obtained on the assumption that material of the pad (strip) is the periodic composite. The every unit cell of the composite contains four sub-cells with rectangular cross-section and with different thermo-physical properties. It is assumed, that intensity of the heat generation on the contact surface is equal to power of friction and through this surface the heat transfer takes place. The influence of the geometrical dimensions and thermo-physical properties of composite sub-cells on the maximum temperature in the system has been investigated.     

Measurements of brake disc surface temperature and emissivity by two-color pyrometry

A fiber optic two-color pyrometer was developed for brake disc surface temperature and emissivity measurements. The two-color pyrometer consists of a fluoride glass optical fiber, two HgCdTe detectors equipped with bandwidth filters and a data conditioning and acquisition device. The two-color pyrometer measures the brake disc temperature in the 200–800 °C range with a time resolution of 8 μs. The calibration formula for the signals obtained using a blackbody of known temperature is used to compute the true temperature. The uncertainty estimation for temperature and emissivity was obtained from the calibration results. Tests were carried out on known temperature target and a good correlation was found between results obtained with our two-color pyrometer and those obtained with a commercial two-color pyrometer. Hold braking and deceleration braking tests performed on a braking test bench enabled us to reach the brake disc surface temperature and emissivity during braking. Experimental results show a significant variation of emissivity during braking. Direct measurement of emissivity was carried out on the brake disc after braking and shows the emissivity dependence with the surface quality.     

AIR FLOW AND HEAT TRANSFER IN VENTILATED DISC BRAKE ROTORS WITH DIAMOND AND TEAR-DROP PILLARS

This study is part of an ongoing research project investigating the airflow and heat transfer of different disc brake rotors. This article reports on three geometries: straight radial vane (SRV) rotor; SRV rotor with rounded vanes (SRV-R); and a rotor with diamond and teardrop pillars (DTDP) instead of vanes. The total heat transfer from the SRV-R and DTDP passages is up to 20% greater than that for the SRV rotor. As much as 35% more heat is lost from the free side friction surface than the hub side friction surface. Flow development through the DTDP rotor passages is also noted.     

A numerical study of flow and heat transfer in internally finned rotating straight pipes and stationary curved pipes

In this article the effects of internal fins on laminar incompressible fluid flow and heat transfer inside rotating straight pipes and stationary curved pipes are numerically studied under hydrodynamically and thermally fully developed conditions. The fins are assumed to have negligible thickness with the same conditions as the pipe walls. Two cases, constant wall temperature and constant heat flux at the wall, are considered. First the accuracy of the numerical code written by a finite volume method based on SIMPLE algorithm is verified by the available data for the finless rotating straight pipes and stationary curved pipes, and then, the numerical results for those internally finned pipes are investigated in detail. The numerical results for different sizes and numbers of internal fins indicate that the flow and temperature field analogy between internally finned rotating straight pipes and stationary curved pipes still prevail. The effects of Dean number (K_L) versus friction factor, Nusselt number, and other non-dimensional parameters are studied in detail. From the numerical results obtained, an optimum fin height about 0.8 of pipe radius is determined for Dean numbers less than 100. At this optimum value, the heat transfer enhancement is maximum, and the heat transfer coefficient appears to be 6 times as that of corresponding finless pipes.     

Three-dimensional transient temperature field of brake shoe during hoist’s emergency braking

In order to exactly master the change rules of brake shoe’s temperature field during hoist’s emergency braking, the theoretical model of three-dimensional (3-D) transient temperature field was established according to the theory of heat conduction, the law of energy transformation and distribution, and the operating condition of mining hoist’s emergency braking. An analytic solution of temperature field was deduced by adopting integral-transform method. Furthermore, simulation experiments of temperature field were carried out and the variation regularities of temperature field and internal temperature gradient were obtained. At the same time, by simulating hoist’s emergency braking condition, the experiments for measuring brake shoe’s temperature were also conducted. It is found, by comparing simulation results with experimental data, that the 3-D transient temperature field model of brake shoe is valid and practical, and analytic solution solved by integral-transform method is correct.     

TRANSIENT THERMOELASTIC ANALYSIS OF DISK BRAKES IN FRICTIONAL CONTACT

The transient analysis of the thermoelastic contact problem of automotive disk brakes with frictional heat generation is performed using the finite element method. To analyze the thermoelastic phenomenon occurring in disk brakes, the coupled heat conduction and elastic equations are solved with contact problems. In the present work, the fully implicit transient scheme for the thermoelastic analysis is used to improve the accuracy of computations at every time step. The numerical simulation for the thermoelastic behavior of disk brakes is obtained in drag brake condition. The computational results are presented for the distributions of pressure and temperature on each friction surface between the contacting bodies. Also, the thermoelastic instability (TEI) phenomenon (the unstable growth of contact pressure and temperature) is investigated in the present study. The effects of the rotating speed of the disk on thermoelastic behaviors, such as the temperature distribution and contact ratio of the friction surfaces, are investigated.