THERMOELASTO-PLASTIC STRESSES AND THERMAL DISTORTIONS IN A BRAKE DRUM

Most analyses of thermal stresses generated in a brake drum are studies within either an elastic or a plastic region with constant yield strength. As a matter of fact, however, a severe brake application will create a thermal environment on the friction surface with an excessively high surface temperature. At a high temperature, the degradation of yield strength of a drum material may become significant and an important factor to be taken into account in the analysis. This article deals with the thermoelasto-plastic stresses and the thermal distortions produced in a brake drum during a severe braking condition, taking account of the temperature dependence of the yield strength of a drum material. It is found that high compressive thermoelastoplastic stresses are created during a brake application but eventually residual tensile stresses are developed in the vicinity of the rubbing surface in the course of cooling. These residual tensile stresses are strongly presumed to be one of the significant factors causing the heat crack in a brake drum. In addition, the thermal distortions of the drum suggest a loss of the contact area between the drum fictional surface and the brake shoe linings during braking.     

A thermomechanical model for the analysis of disc brake using the finite element method in frictional contact

Abstract

In this work, a numerical simulation of the transient thermal analysis and the static structural one was performed here sequentially, with the coupled thermo-structural method using the ANSYS software. Numerical procedure of calculation relies on important steps such that the CFD thermal analysis has been well illustrated in 3D, showing the effects of heat distribution over the brake disc. This CFD analysis helped in the calculation of the values of the thermal coefficients (h) that have been exploited in the 3D transient evolution of the brake disc temperatures. Three different brake disc materials were selected in this simulation and comparative analysis of the results was conducted in order, to derive the one with the best thermal behavior. Finally, the resolution of the coupled thermomechanical model allows to visualize other important results of this research such as; the deformations, and the equivalent stresses of Von Mises of the disc, as well as the contact pressure of the brake pads. Following our analysis and results we draw from it, we derive several conclusions. The choice makes it possible to deliver the best brake rotor so as to ensure and guarantee the good braking performance of the vehicles.     

Temperature in the railway disc brake at a repetitive short-term mode of braking

The finite element (FE) model to determine the transient temperature field in the ventilated disc brake of the traction diesel multiple unit (DMU) has been proposed. The advantage of the developed numerical model is the representation of mutual motion of the stationary pad and the rotating disc, by a heat source of arbitrary shape moving over the stationary disc. Computations were carried out for the pad and the disc separately introducing the heat partition ratio. Both the single and the multiple modes of braking were examined. The calculated distributions in contact temperature were compared with the corresponding results obtained from analytical solutions of the boundary-value thermal problem of friction, and with experimental data determined by the method of thermocouples. It was demonstrated that the calculated mean temperature on the friction surfaces of the brake components and the bulk temperature of the disc during multiple brake application agree well with the corresponding results, obtained by methods mentioned above.     

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.     

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.     

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.     

Temperature and thermal stresses in a pad/disc during braking

A two-element model of braking process for a tribosystem consisting of the pad (the strip) sliding with the time-dependent velocity (braking at uniform retardation) on a surface of the disc (the semi-space) is studied. The dependences of temperature and thermal stresses on the boundary conditions on upper surface of the ceramic–metal strip were investigated. It was proved that there is a possibility of applying the obtained results to modelling of a thermal cracking of the frictional elements during braking.     

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.     

列车制动技术的研究与展望

概述了列车常用的几种制动方式,分析了其工作原理、特点和应用场合。针对应用最广泛的闸瓦制动方式和盘形制动方式,重点阐述了提升其制动性能的方法及应用。通过分析闸瓦工作状况对列车行车安全的影响,讨论了闸瓦自动检测技术的重要性和研究现状。最后对列车制动技术的发展做了展望。     

Fatigue Analysis of Railway Wheels Under Combined Thermal and Mechanical Loads

Nowadays, the railway vehicles are widely used in many countries as one of the most important transportation systems. Nucleation and growth of fatigue cracks in railway wheels stem from different factors such as wheel-rail rolling contact, thermal loads between wheel-rail and wheel-brake block created in braking process, presence of structural defects in wheel material, and so forth. Also, increasing speed and axle loads of wheels aggravates these factors. These cracks can reduce wheel life and even in severe cases derailment may occur. Therefore, the thermo-mechanical fatigue problem of wheels is a very important issue as is doing an accurate mechanical and thermal analysis of the investigation and estimation of fatigue life of wheels, and also, the prediction of crack behavior under thermo-mechanical loads is necessary. In this article, stress fields created by combined thermal and mechanical loads in railway wheels is investigated. Thermal stresses are usually created as a result of frictional heating produced by applying brake shoes on the wheel tread and also as a result of the occurrence of slip between wheel and rail at the braking stage. The obtained results confirm the important effects of thermal loads on stress fields and fatigue life of wheels. In this article, thermal loads are determined by modeling the contact of the rail-wheel and two brake blocks and by identifying heat partition factors and friction coefficient between these components. One of the other advantages of the presented work is modeling of wheel rotation, while in many of the similar investigations either this rolling is not modeled or its effect is simplified as translating pressure distribution along the rail-wheel contact region. The use of a 3D FE analysis for determination of rail-wheel contact pressure instead of Hertz contact theory is also noteworthy.     

THERMAL-STRESS PROBLEMS IN INDUSTRY. 2: TRANSIENT THERMAL STRESSES IN A DISK BRAKE

A general solution is given for the transient thermal stresses in a disk brake caused by constant heat generation on both plane surfaces. The solution rigorously meets the traction-free boundary condition on both the lateral and plane surfaces of the disk. Numerical results for the stress fields are given.     

Thermal stress analysis of eccentric tube receiver using concentrated solar radiation

In the parabolic trough concentrator with tube receiver system, the heat transfer fluid flowing through the tube receiver can induce high thermal stress and deflection. In this study, the eccentric tube receiver is introduced with the aim to reduce the thermal stresses of tube receiver. The ray-thermal-structural sequential coupled numerical analyses are adopted to obtain the concentrated heat flux distributions, temperature distributions and thermal stress fields of both the eccentric and concentric tube receivers. During the sequential coupled numerical analyses, the concentrated heat flux distribution on the bottom half periphery of tube receiver is obtained by Monte-Carlo ray tracing method, and the fitting function method is introduced for the calculated heat flux distribution transformation from the Monte-Carlo ray tracing model to the CFD analysis model. The temperature distributions and thermal stress fields are obtained by the CFD and FEA analyses, respectively. The effects of eccentricity and oriented angle variation on the thermal stresses of eccentric tube receiver are also investigated. It is recommended to adopt the eccentric tube receiver with optimum eccentricity and 90° oriented angle as tube receiver for the parabolic trough concentrator system to reduce the thermal stresses.     

Dynamic thermal behavior of a brake system

A mathematical model is presented to describe the thermal behavior of a brake system that consists of shoe and drum. The model is solved analytically using Green's function method for any type of the stopping braking action. In terms of the obtained solutions, the transient temperature distribution of the brake is described. The thermal behavior is investigated for three specified braking actions that are the impulse, unit step and trigonometric stopping actions.     

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.     

On-line heat flux identification from a rotating disk at variable speed

This paper presents the Branch Eigenmodes Reduction Method (BERM) applied to the identification of a heat flux in an advection–diffusion model, with time dependent parameters. The treated application is a 2D disc brake whose velocity and thermal solicitations are time dependent. One of the method’s strength lies in its ability to greatly reduce the dimension of the numerical problem, while maintaining a satisfying precision on the entire computation domain. In the considered case, the inverse problem difficulties come from the transport phenomena which requires the use of very small time steps for its numerical resolution. In order comply with the on-line identification objective, a filtering technique is used.     

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.     

Conductive heat transfer across a bolted automotive joint and the influence of interface conditioning

As part of commercial vehicle disc brake heat dissipation research, thermal contact resistance (TCR) across a bolted joint is analysed. Studies include new and slightly corroded interface surfaces. Measurements show that corrosion approximately doubles TCR, decreasing conductive heat dissipation, leading to higher brake temperatures. To reduce TCR, two methods of interface conditioning are investigated. The application of thermal conductance paste and the use of a thin aluminium gasket at the interface have similar effects, reducing TCR by over 80%. The paper deals with the methodology of measuring TCR and defining its relationship with the change of interface pressure, temperature and interface conditioning. This approach ensures results of a generic nature applicable to a variety of bolted joints.     

Thermal Residual Stresses in One-Directional Functionally Graded Plates Subjected to In-Plane Heat Flux

This study carries out the transient thermal residual stress analyses of functionally graded clamped plates for different in-plane material compositions and in-plane heat fluxes. The heat conduction and Navier equations representing the two-dimensional thermoelastic problem were discretized using the finite-difference method, and the set of linear equations were solved using the pseudo singular value method. Both in-plane temperature distributions and the heat transfer period were affected considerably by the compositional gradient. The type of in-plane heat flux had a minor effect on the temperature profile, but on the heat transfer period. The high stress levels appeared in the ceramic-rich regions. The normal and equivalent stresses exhibited a sharp change in the plates with ceramic-rich as well as metal-rich compositions, and the concentrated on a narrow ceramic layer. A smooth stress variation was achieved through the graded region with a balanced composition of ceramic and metal-phases, and the stress discontinuities disappeared. The in-plane shear stress was negligible. The equivalent stress exhibited a linear temporal variation for both constant and sinusoidal heat fluxes, but a nonlinear variation for the exponential heat flux. In case the heat flux is applied along the metal edge (metal-to-ceramic plate) instead of the ceramic edge, the displacement and stress components exhibited similar distributions to those of a ceramic-to-metal plate but in the opposite direction. As a result, the distribution of in-plane material composition affects only normal stress distributions, whereas the peak stress levels occur in the ceramic-rich regions. Since the normal stresses concentrate along a narrow ceramic layer for ceramic-rich or metal-rich compositions, a balanced in-plane material composition distribution of ceramic and metal would be useful to avoid probable local ceramic fracture or damage.     

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.