Thermoelastic instability in planar solidification

A linear perturbation method is used to examine the stability of a unidirectional solidification problem in which a liquid, initially at the melting temperature, becomes solidified by heat transfer across a pressure-dependent thermal contact resistance to a plane mold. The contact pressure will be influenced by thermal distortion in response to the instantaneous temperature field in the solidified shell. The heat transfer and thermal stress problems are therefore coupled through the boundary conditions.

The temperature and stress fields are assumed to consist of a unidirectional component and a small spatially-sinusoidal perturbation which can vary with time. Analysis of the thermoelastic problem for the solidified shell leads to an ordinary differential equation relating the perturbation in heat flux at the mold/casting interface and the corresponding perturbation in contact pressure. A second equation relating the same two variables is obtained by linear perturbation of the relation for heat conduction across the thermal contact resistance. These are then reduced to a single equation which is solved numerically. The results show that a small initial perturbation will grow substantially during the solidification process if the thermal contact resistance is very sensitive to pressure.     

Convection of Heat in Short-Bearings and Face Seals

For a short bearing or face seal, the temperature is determined by a steady Couette flow component and a zero-average perturbation, or waviness. In terms of these component flows, convection along the film and conduction into the surfaces is derived, and conditions are determined under which convection significantly influences the circumferential distribution of heat flux into the solid surfaces. For a stationary sinusoidal wave on a bearing surface, the phase relationship between this displacement perturbation and the wall heat input is found. The result is primarily of interest in systems where frictional heating may excite the thermoelastic growth of surface waviness, and where weak perturbations on heating may excite thermoelastic instability.     

Finite‐element heat‐transfer analysis of a PEEK‐steel sliding pair in a pin‐on‐disc configuration

Finite‐element (FE) thermal models have been developed in order to study the temperature distribution in a sliding pair comprising a poly(ether ether ketone) (PEEK) pin and a steel disc in a pin‐on‐disc configuration. First, a moving heat source model for the disc was created. An alternative distributed heat source model was also produced in order to reduce computing time for the evaluation of the moving heat source model by some orders of magnitude. This latter model gave the same results as the moving heat source model, except for a small region just below the moving heat source. On the basis of the distributed heat source approach, a complete axisymmetric FE model for the disc side (taking the effect of thermal resistance between the assembled components into consideration) and a steady‐state quarter model for the pin were developed. Water cooling and air cooling of the steel shaft were also compared. It was found that air cooling allowed a higher temperature in the contact region of the two sliding partners. The experimental results obtained with thermocouples and a thermal camera showed good agreement with the model predictions.     

Thermoelastic contact involving a sharp corner

Asymptotic analysis is used to study the thermoelastic contact near a sharp corner. It is found that perfect contact involving no resistance to heat flow is always possible for relatively blunt corners for which the mechanically induced stress concentrations dominate. Otherwise perfect contact is possible only if heat flows into the material with the smaller distortivity. The corner separates if heat flows in the opposite direction.     

二维轴对称摩擦制动器瞬态热弹性失稳的研究

提出考虑摩擦层闸片厚度的影响,建立二维轴对称摩擦制动器热弹性失稳的数学模型。基于扰动分析法,推导摩擦副的温度场扰动以及不同热点分布模式下的热特征平衡方程。研究临界速度和扰动增长系数的变化规律。计算摩擦面瞬态名义温度随制动时间的变化关系。分析和比较不同摩擦副厚度比、热导率、弹性模量、比热容以及热膨胀系数对系统稳定性的影响。结果表明,当热点呈反对称分布时,系统发生热弹性失稳时所需的最低临界速度远低于对称分布模式,临界速度随扰动频率的增加呈先减小后增加的变化趋势。不同扰动频率对应的扰动增长系数随滑动速度近似呈线性增加,最低临界扰动频率对应的扰动增长系数最大。当扰动频率低于临界扰动值时,温度随扰动频率的增加而增加,反之,则降低。增加摩擦副的厚度、摩擦层闸片的热导率和比热容以及减小滑动层制动盘的热导率和热膨胀系数和摩擦层闸片的弹性模量均可以提高滑动摩擦系统的稳定性。     

Structure influence on the operating limit range and mixing performance of non-axisymmetric jet pump

Although cavitation chocked jet pumps guarantee a steady and accurate liquid mixture, the existing pumps have the shortcomings of big energy loss and small cavitation working range. In the current study, aiming at enhancing the performance of the cavitation mixing devices, an innovative non-axisymmetric jet pump design is proposed. The cavitation characteristics and the mixing performance of the new design have been investigated by both computational simulation and experimental testing. Based on the results of computational fluid dynamics (CFD), it is found that the cavitation on the suction tube side is strengthened due to the turbulence caused by the abrupt change in the local flow channel structure, while the cavitation on the opposite side is weakened due to the gradual flow channel structure. Our experimental testing results prove that our new design can provide a steady mixing ratio as long as the non-axisymmetric vapor cloud steadily covers the suction tube outlet. Furthermore, geometric parameters (convergent angle, divergent angle, throat length and area ratio) of the device have been optimized through the orthogonal analysis. The critical pressure ratio of the optimized device ranges from 0.76 to 0.63 when the critical flow ratio is in the range of 0–10%, which indicates that the optimized device has much less energy loss and a wider working range than the current axisymmetric cavitating jet pumps. Through quantitative energy loss analysis, we have found that the cavitation maintenance corresponds to the greatest energy loss in the jet pumps, yet our non-axisymmetric structure design could effectively reduces energy loss. The current research reveals the physical mechanism on how a non-axisymmetric structure affects the cavitation characteristics as well as the performance of jet pumps.     

基于接触热阻的磨齿机电主轴热特性分析

大规格数控成形磨齿机高速电主轴系统在加工过程中产生大量热量,导致砂轮主轴产生相应热变形,影响加工精度。针对这一现象,提出了一种考虑接触热阻的瞬态热-结构耦合分析方法。该方法基于分形理论,利用W-M分形函数表征结合面接触状态,使用均方根测度法对分形参数进行识别。结合基体热阻和收缩热阻的影响计算结合面间总接触热阻,并计算热源发热量及各部件的对流换热系数,建立了综合考虑内部热源、边界条件和接触热阻的综合有限元模型,获得热误差仿真结果。分析电主轴温度及热变形在是否考虑接触热阻情况下变化差异。最后建立电主轴系统热误差测量试验平台,通过试验验证了该方法的准确性和可靠性。通过仿真得到温度及热位移量与实验值基本一致。     

玻璃润滑剂对TA15钛合金与K403镍基高温合金界面接触热阻的影响

为了给钛合金的模锻工艺制定提供理论依据,利用稳态法在自制的接触热阻测量装置上研究了玻璃润滑剂对TA15钛合金与模具用K403镍基高温合金界面接触热阻的影响。结果表明:在TA15和K403合金接触面间加入玻璃润滑剂可显著增大两者间的接触热阻;当界面平均温度不超过636℃,玻璃润滑剂厚度在0.06~0.96 mm范围内时,TA15与K403合金界面接触热阻与玻璃润滑剂厚度大致呈线性关系;TA15与K403合金的界面接触热阻随着温度的升高及压力的增大而减小。     

橡胶油封摩擦生热数值模拟与实验验证*

将橡胶油封使用中涉及的材料非线性、几何非线性和接触非线性考虑到轴对称有限元模型中,采用力场-温度场耦合的方法对油封与高速旋转轴之间的摩擦生热问题进行数值模拟,并与油封工装试验结果和红外成像仪测量的温度进行比较。模拟得到的油封摩擦扭矩和唇口温度与试验结果吻合很好,表明采用力场-温度场耦合方法可以预测油封的抱轴力和摩擦扭矩,以及稳态下的摩擦生热温度场,这为类似旋转密封件摩擦生热问题的仿真分析提供一种有效途径。     

Non-isothermal plane plastic flow of a thin layer compressed by flat rigid dies

An analysis of the plane rigid—plastic flow of a thin layer compressed by flat rigid dies coupled with the heat transfer in the die-layer system is considered. The numerical model of the thin layer compression includes non-homogeneous plastic dissipation rate, heat flux of the contact friction and thermal resistance of the die-layer interface boundary. The rigid—viscoplastic relation of the effective yield stress with accumulated plastic strain, effective strain rate and temperature is assumed for the layer. The effects of the contact friction, thermal resistance and the die velocity on the hot compression of the thin steel workpiece are investigated.     

Collapse mode transitions of thin tubes with wall thickness, end condition and shape eccentricity

Transition of deformation mode shapes of round aluminum tubes from axisymmetric concertina to non-axisymmetric diamond mode have been studied with varying tube wall thickness, boundary conditions and tube shape eccentricities. Quasi-static axial compression experiments were carried out on as received aluminum tubes and tubes with wall thickness eccentricity, incorporated by off center machining. Tubes were of D/t=29 and L/D=1.4. The numerical simulation of the collapse phenomenon has been undertaken using a static non-linear finite element analysis in ANSYS with a fine mesh discretization of the tube domain and small incremental displacements as load steps. Convergence studies for the finite element model with respect to load step size and mesh density have also been established. The numerical results are found to compare well with the experimental load compression and energy absorption responses both for the axisymmetric concertina and non-axisymmetric diamond collapse modes. Having validated the numerical model with experiments, it has been used to undertake a systematic study of the load–deformation characteristics, energy absorption response and collapse mode transition of the tubes in varying configurations of wall thickness, shape and inplane boundary condition eccentricities. Dependence of tube collapse characteristics and collapse mode transitions on such eccentricities have been discussed.     

Effect of Stefan number on thermoelastic instabilities in unidirectional solidification

During the casting process, thermoelastic distortion of the partially solidified material affects the contact pressure at the solid/mold interface, which in turn can affect the thermal contact resistance, thus coupling the heat transfer and thermomechanical problems. This coupled system has the potential for instability. In this paper, the effect of Stefan number on the stability of unidirectional solidification is investigated, under the simplifying assumption that the solidified material is linear elastic. The Stefan number is a measure of the influence of thermal capacity on the solution and previous analyses have generally been restricted to the case of zero Stefan number, corresponding to a solidifying material of zero thermal capacity.This generalization necessitates a numerical solution, which is here implemented using the finite difference method. However, since the growth of the perturbation is linear, the two-dimensional stability problem is reduced to two one-dimensional numerical problems which can be solved sequentially.The results show that, in all cases, an initial sinusoidal perturbation grows to a maximum amplitude in the solidification front and then decays, the maximum being reached when the mean solidified layer thickness is about half the wavelength of the perturbation.In general, increasing Stefan number has a stabilizing effect on the process. This effect is most noticeable in cases where the zero Stefan number approximation predicts substantial growth of an initial perturbation, e.g. where the thermal contact resistance is very sensitive to pressure.     

Thermal and thermomechanical effects in dry sliding

Whenever friction occurs in dry sliding of mechanical components, mechanical energy is transformed into heat through surface and volumetric processes in and around the real area of contact. This frictional heating, and the thermal and thermomechanical phenomena associated with it, can have a very important influence on the tribological behavior of the sliding components, especially at high sliding velocities. Significant developments in the study of these phenomena are reviewed in this paper. Among the topics reviewed are mechanisms of frictional heating and the distribution of heat during sliding friction, the measurement and analysis of surface and nearsurface temperatures resulting from frictional heating, thermal deformation around sliding contacts and the changes in contact geometry caused by thermal deformation and thermoelastic instability, and the thermomechanical stress distribution around the frictionally heated and thermally deformed contact spots. The paper concludes with a discussion of the influence of the thermal and thermomechanical contact phenomena on wear, thermocracking and other modes of failure of sliding mechanical components.     

Thermostressed state of a pad–disk tribosystem during single braking

The temperature and stress distributions in a disk under single braking have been studied. The finite-element method (FEM) has been used to obtain a numerical solution to the heat-conduction boundary problem for a steadily decelerated rotating disk heated in a local area of the working surface by a frictional heat flow. Given the temperature field, the finite-element method has been used to solve the corresponding quasistatic thermoelasticity boundary problem. The elastostatic boundary problem has been numerically solved separately for a disk loaded with distributed normal and shear stresses in the contact area. The complete field of stresses in the disk has been determined by adding up elastic and thermoelastic components. Numerical analysis has been performed for a cerametallic (FMC-11) pad—cast-iron (ChNMKh) disk friction couple.     

The thermoelastic Hertz problem with pressure dependent contact resistance

There is a considerable amount of experimental work establishing that the resistance to heat conduction between two solids in contact depends on the contact pressure, decreasing with increasing pressure. However, there are no solutions of thermoelastic contact problems taking into account this nonlinear behavior. In the present paper, we consider the thermoelastic Hertz contact problem and assume a contact resistance which is inversely proportional to pressure. The solution is compared with those assuming perfect or imperfect contact.     

Plastic buckling of circular tubes under axial compression—part II: Analysis

In the second part of this study, the evolution of uniform axisymmetric wrinkling in axially compressed cylinders is modeled using the principle of virtual work. A version of this formulation also allows localization of wrinkling. The model domain is assigned an initial axisymmetric imperfection of a chosen amplitude and the wavelength yielded by the first bifurcation check. The solution correctly simulates the growth of wrinkles and results in a limit load instability. The limit strain is influenced by the amplitude of the imperfection. Beyond the limit load, wrinkling tends to localize, eventually leading to local folding.The possibility of bifurcation of the axisymmetric solution to non-axisymmetric buckling modes is examined by using a dedicated bifurcation check. The bifurcation check was found to yield such buckling modes correctly. The evolution of such buckling modes is simulated by a separate non-axisymmetric model assigned imperfections with axisymmetric and nonaxisymmetric components. The domain analyzed is one characteristic wavelength long (2λ_C). Initially, compression activates mainly axisymmetric deformation. In the neighborhood of the bifurcation point, non-axisymmetric deformation starts to develop, eventually leading to a limit load instability. Experimental responses were simulated with accuracy by assigning appropriate values to the two imperfection amplitudes. Prediction of the limit strains for the whole range of diameter-to-thickness ratios (D/t) considered in the experiments was achieved by making the amplitude of the non-axisymmetric imperfection proportional to (D/t)²/m³ (m is the circumferential wavenumber). Matching all aspects of the experiments required inclusion of the anisotropy measured in the tubes tested through Hill's yield criterion in all models.     

Hydrodynamic plane and axisymmetric slip stagnation-point flow with thermal radiation and temperature jump

This work focuses on the steady boundary layer flow and heat transfer near the forward stagnation point of plane and axisymmetric sheet towards a stretching sheet with velocity slip and temperature jump. The resulting nonlinear partial differential equations are reduced to the system of nonlinear ordinary differential equations by means of similarity transformations. The analytical solutions for the velocity and temperature distributions are obtained for the various values of the ratio of free stream velocity and stretching velocity, velocity slip parameter, magnetic parameter, the suction parameter, temperature jump parameter, Prandtl number, the radiation parameter and dimensionality index parameter in the series forms with the help of homotopy analysis method. Convergence of the series is explicitly discussed. The flow and shear stresses depend heavily on the velocity slip parameter. The temperature gradient at the wall increases with velocity slip parameter, temperature jump factor and decreased thermal radiation.     

Pressure Distribution of a Multidisc Clutch Suffering Frictionally Induced Thermal Load

The transient thermal and thermoelastic analysis of an automotive multidisc clutch is performed to investigate the thermal deformation and the contact pressure distribution of the friction surfaces. An alternating finite volume method (FVM) and finite element method (FEM) for temperature distribution and contact pressure distribution, including the coupling between temperature, displacement, and contact pressure, is employed in MATLAB. A penalty function method is used to impose the constraints on the contact boundary. The computational results indicate that the contact pressure distributions on the surfaces near the pressure plate are more uniform than those near the opposite plate, and the nonuniformity is enlarged with the temperature rise. The contact pressure and temperature distributions on the two friction surfaces of the separate plate are dissimilar and asymmetric, which is in good agreement with the test results. The results further show that the contact pressure peaks diminish and the noncontact regions reduce due to the heat conduction and convection when the engagement ends.     

基于接触热阻的主轴热特性有限元分析

在考虑了轴承、主轴和箱体接触区域的接触热阻影响的基础上,利用大型有限元分析软件ANSYS对某型号机床的主轴系统进行了温度场建模,并综合分析了整个系统的热态特性.论述了热源和边界条件等因素的计算方法,考虑了以往建模时较少考虑的接触热阻因素,对模型在有、无热阻两种情况下进行了分析、对比.对比结果表明,接触热阻对系统的影响是显著的,对于精密机床的研究,建模时不应忽略这一重要因素.     

点焊熔核形成过程的有限元模型

介绍了模拟点焊熔核形成过程的轴对称电、热、力学有限元模型。提出了点焊过程导电、传热和力学行为之间耦合作用的模拟方法和接触电阻分析方法。模型中也考虑了焊机特性、随温度变化的材料性能以及各种边界冷却条件的影响。试验验证结果表明，数值模拟结果与实际吻合良好。该模型提供了一种有效的点焊过程理论分析手段。