TRANSIENT ANALYSIS OF THERMOELASTIC CONTACT BEHAVIORS IN COMPOSITE MULTIDISK BRAKES

The transient analyses of the thermoelastic contact problem are performed for carbon–carbon composite multidisk brakes subject to mechanical and frictionally excited thermal loads. The finite element method, based on the coupled theory in which displacement and temperature fields are mutually affected, is applied for the numerical simulations. In the present study, to improve the accuracy of computations and stabilize the algorithm, the implicit transient scheme is used for the thermoelastic analysis. The law of action and reaction, Signorini's law of contact, Coulomb's law of friction, and Archard's law of wear are applied to be valid locally at each point for friction surfaces. The computation results are obtained for the antiskid brake conditions and presented for the transient evolution of contact pressure, temperature on each friction surface between the bodies, and thermoelastic deformations. It is also found that the high thermal stresses due to considerable temperature difference during the landing process occur in multidisk brakes.     

TRANSIENT THERMOELASTIC ANALYSIS OF DISK BRAKE USING THE FAST FOURIER TRANSFORM AND FINITE ELEMENT METHOD

This article introduces a finite element method that combines the fast Fourier transform technique and a conventional finite element method as a computational technique for investigating a thermomechanical problem. The conventional finite element formulation is very inefficient in the analysis of a three-dimensional disk brake model of a rotating axisymmetric disk subjected to a nonaxisymmetric transient heat flux condition due to frictional contact with asymmetric pads fixed in space. Because the proposed technique reduces the three-dimensional disk brake mathematics to two dimensions, is an extreme time saver, and costs less, we can solve the transient thermoelastic problem and the thermoelastic instability. As a result of the study we present some analyses on temperature distributions and displacement distributions in a disk brake system at a low speed and on the hot spots at a high speed above critical speed.     

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.     

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.     

PLANE CONTACT PROBLEM INVOLVING FRICTIONAL HEATING FOR A THERMOELASTIC WEDGE

This article is concerned with the sliding contact between a rigid thermoinsulated flatended punch and a thermoelastic wedge. The heat generation due to friction forces is taken into account. With help of the method of Mellin integral transforms the problem is reduced to the integral equation, which is solved numerically. The influence of the frictional heating on distributions of the contact pressure and generated temperature is presented in diagrams for different input parameters.     

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.     

TRANSIENT THERMOELASTIC ANALYSIS FOR TWO-DIMENSIONAL DISSIMILAR MATERIALS BY THE BOUNDARY ELEMENT METHOD

This article deals with the transient thermoelastic analysis for dissimilar materials under the plane strain condition. In the process of the boundary element formulation, the time-dependent fundamental solution for the transient heat conduction problem and the thermoelastic displacement potential for the transient thermal stress problem are introduced. Consequently, domain integrals are completely eliminated. The discretization based on the domain combination method for these boundary integral equations is implemented, and the transient temperature and stress fields are analyzed numerically. The transient temperature at the lateral surface and the transient thermal stress at the interface are investigated for the three categories that have been determined according to the characteristic equation expressed by Dundurs parameters.     

天然气水合物取样钻头及岩层温度场数值分析

为防止深海海底天然气水合物钻探取样过程中发生分解及钻头热磨损,运用摩擦学及传热学基本原理,以弹性库仑摩擦模型作为接触单元本构模型,建立具有刚柔接触的取样钻头和岩层摩擦生热及传热的瞬态动力学耦合数学模型,采用有限元方法进行计算分析.结果表明,钻头温度变化较大,岩层温度变化较小,且只在和钻头接触局部区域内较明显.不同钻速、摩擦系数以及侧壁压力下,钻头和岩层温度变化趋势不同.在实际钻探取样时,对应不同工况和地质条件,应合理选择钻井液循环速率及分布,选择合适钻速,防止取样失败.     

Transient Thermoelastic Analysis for a Functionally Graded Hollow Cylinder

This paper is concerned with the theoretical treatment of transient thermoelastic problem involving a functionally graded hollow cylinder due to uniform heat supply. The transient one-dimensional temperature is analyzed by the method of Laplace transformation. The thermal and thermoelastic constants of the hollow cylinder are expressed as power functions of the radial coordinate. We obtain the one-dimensional solution for the temperature change in a transient state, and thermoelastic response of a functionally graded hollow cylinder. Some numerical results for the temperature change, the displacement and the stress distributions are shown. Furthermore, the influence of the nonhomogeneity of the material upon the temperature change, displacement and stresses is investigated.     

THE IMPACT OF A THERMOELASTIC ROD AGAINST A HEATED BARRIER WITH ACCOUNT OF FINITE SPEED OF HEAT PROPAGATION

This paper examines the impact of a thin thermoelastic bar of finite length with a heat-insulated lateral surface against a heated massive barrier. The hyperbolic equation of heat conduction is used. During impact, thermoelastic waves propagate along the bar, and behind the wave fronts a solution is constructed in terms of ray series. The stresses, temperature, displacement velocity, and heat flux profiles are obtained. Also, the time-dependent contact stress and temperature and the contact time as a function of the temperature of wall heating, heat flow relaxation time, impact velocity, and coefficient of convective heat exchange from the wall to the rod are investigated.     

GROWTH INSTABILITY DURING PLANAR SOLIDIFICATION WITH A MOLD OF FINITE THERMAL CAPACITY

The temperature and the stress fields in the solidified layer and in the mold of finite thickness for a unidirectional casting process are investigated. Earlier solutions are extended to include the effect of the thermal capacity of the mold on the freezing front growth instability. A numerical solution is obtained for both the heat conduction and the residual stress problem. The results show that the perturbation in contact pressure tends asymptotically to a maximum value at larger times for the lower values of the thermal capacities of the mold materials. The magnitude of the contact pressure perturbation is decreased by the inclusion of the thermal capacity of the mold material, and this effect is enhanced for less distortive and thicker molds. The present article assumes that the thermal and mechanical problems are uncoupled along the casting mold interface. Despite this limitation, the results presented in this article indicate that a mold with a higher thermal capacity (or lower thermal diffusivity) might be less susceptible to thermoelastic instabilities associated with the contact pressure and its dependence on the thermal contact resistance at the casting mold interface.     

Modelling of heat transfer between two rollers in dry friction

An analysis of heat transfer between two rollers in dry friction is presented in this paper. The contact is peripheral and is assumed to be imperfect. The heat transfer at the interface is modelled by a thermal contact resistance. The heat flux is generated by dry friction at the interface. The two rollers are cooled by convection. A numerical model has been developed to determine the steady state temperature in rollers. Taking into account the transport phenomenon due to motion, the mesh is correlated with the velocity. The accuracy of the mesh is validated by comparison with an available analytical solution developed for a single roller in rotation. The thermal behaviour is analysed with respect to: (i) the velocity, (ii) the heat convection coefficient, and (iii) the thermal contact resistance. The evolutions of the temperature and the partition coefficient of frictional heat are presented and discussed.     

THERMOELASTICITY AND CONTACT

Thermoelastic deformations can have a significant effect on the contact between elastic bodies, particularly in cases where the thermal boundary conditions at the interface are influenced by the contact pressure. In the classical Hertzian problem, the size of the contact area depends on the magnitude and direction of heat flow between the bodies. Idealized thermal boundary conditions can lead to ill-posed steady-state problems, but this difficulty is resolved by assuming a pressure-dependent thermal contact resistance. Steady states of the system can be unstable even when they are unique, in which case the behavior is either oscillatory or involves the steady motion of a contact pressure wave along the interface. Analytical and numerical perturbation methods have been developed to investigate the stability problem. These results find applications in heat transfer processes involving solid-solid contact, including the solidification of castings. In brakes and clutches, the heat generated at the sliding interface causes thermal distortion leading to ''frictionally excited thermoelastic instability'' or ''TEI,'' in which contact becomes localized in ''hot spots'' at the interface. Recent results enable us to make good predictions of the conditions under which this occurs.     

THERMOELASTIC TOPOLOGY OPTIMIZATION FOR PROBLEMS WITH VARYING TEMPERATURE FIELDS

Elastic structures that exist in a thermal environment usually experience complex steady-state or transient heat conduction, whereby operational temperatures and stresses may change with time, heat sources, and thermal or kinematic boundary conditions. This article proposes an evolutionary optimization procedure for topology design involving thermoelasticity in which finite element heat analysis, finite element thermoelastic analysis, and subsequently design modification are iteratively carried out. To achieve as efficacious a material usage as possible, the relative efficiency of an element is defined in terms of its thermal stress level. In this article, design cases with uniform temperature fields, nonuniform temperature fields subjected to single or multiple heat load cases, and transient temperature fields are studied. The examples presented show the capabilities of the proposed procedure to solve various thermoelastic problems under varying temperature fields.     

INVERSE TRANSIENT THERMOELASTIC PROBLEM FOR A COMPOSITE CIRCULAR DISK

The present article deals with the application of a piezoelectric material as a sensor of thermomechanical disturbance. We consider a composite circular disk constructed of a transversely isotropic layer onto which a piezoceramic layer of crystal class 6mm is perfectly bonded. An inverse transient thermoelastic problem is solved to determine the unknown transient heating temperature distribution on the surface of the transversely isotropic layer, when the distribution of the electric potential difference across the piezoceramic layer is known. A finite difference method with respect to the time variable is employed to solve this inverse problem. The thermoelastic fields in the transversely isotropic and piezoceramic layers are analyzed by means of a transversely isotropic potential function method and a piezothermoelastic potential function method, respectively. Numerical results are presented for the time variation of the inferred heating temperature distribution and the corresponding distributions of temperature, displacements, stresses, and electric displacements.     

Thermal rectification between two thermoelastic solids with a periodic array of rough zones at the interface

An analysis of the effective thermal contact resistance between two semi-infinite solids in the presence of a periodic array of rough zones at the interface is carried out on the basis of a solution of the corresponding thermoelastic contact problem. The effect of the roughness is modeled by localized thermal contact resistances varying inversely with the contact pressure. The contact problem is reduced to a nonlinear singular integrodifferential equation, and an iterative procedure is proposed for its solving. The results demonstrate that the periodic array of rough zones between two semi-infinite solids exhibits thermal rectification. It is also found that the effective temperature jump and the effective thermal contact resistance are nonlinear functions of a far field heat flux.     

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.     

Contact temperature and wear of composite friction elements during braking

The analytical model for the determination of contact temperature and wear on a working surface of friction brakes is presented. It is assumed that one of the friction element is composed of a periodic two-layered composite and the second element is a homogeneous half-space. In the frictional process, the wear coefficient is linearly dependent on the contact temperature. The influences of composite parameters as well as a parameter characterizing the changing of loading from zero to the nominal value on the distribution of contact temperature and wear during braking is considered.     

Integral transform approach for solving dynamic thermal vibrations in the elliptical disk

The present article is concerned with the determination of thermally induced transverse vibration of a uniform thin elliptical disk with elastic supports at both radial boundaries. The temperature field on the disk is considered to be a ramp-type prescribed on the top face while the bottom face is kept at zero temperature. In this study, integral transform technique is used to investigate the conductivity equation in an exact manner by the use of Mathieu functions and modified Mathieu functions. The thermal moment is derived on the basis of temperature distribution, and its stresses are derived based on the resultant bending moments per unit width. The numerical calculations of the distributions of the transient temperature and its associated thermoelastic results are performed, and the numerical results are shown in the figures.