基于实验的数值反演的滚动轮胎稳态温度场的有限元分析

根据轮胎温度场的单向解耦分析思想,形成了一个基于ABAQUS程序的轮胎稳态温度场的分析方法,单向解耦过程分为变形、损耗、热传导三个分析过程。变形分析中,采用了平衡态的超弹性材料模型;损耗分析中,依据变形分析获得的应力应变场,结合材料粘性损耗特性来获得损耗能量;热传导分析中,依据实测的轮胎胎侧温度场,提出了一种基于实验的数值反演方法来确定胎侧的对流热边界条件。由于轮胎胎侧的形状和结构细节,其对流热边界不同于旋转平圆盘的对流热边界,本文的数值反演方法避免了实测胎侧对流热交换系数的困难。     

Theoretical and experimental analysis of the contact between a solid-rubber tire and a chassis dynamometer

We consider the problem of modeling the test where a solid-rubber tire runs on a chassis dynamometer for determining the tire rolling resistance characteristics.We state the problem of free steady-state rolling of the tire along the test drum with the energy scattering in the rubber in the course of cyclic deformation taken into account. The viscoelastic behavior of the rubber is described by the Bergströ m–Boyce model whose numerical parameters are experimentally determined from the results of compression tests with specimens. The finite element method is used to obtain the solution of the three-dimensional viscoelasticity problem. To estimate the adequacy of the constructed model, we compare the numerical results with the results obtained in the solid-rubber tire tests on the Hasbach stand from the values of the rolling resistance forces for various loads on the tire.     

Numerical simulation of friction stir butt welding process for AA5083-H18 sheets

Thermo-mechanical simulation of the friction stir butt welding (FSBW) process was performed for AA5083-H18 sheets, utilizing a commercial finite volume method (FVM) code, STAR-CCM+, which is based on the Eulerian formulation. Distributions of temperature and strain rate histories were calculated under the steady state condition and simulated temperature distributions (profiles and peak values) were compared with experiments. It was found that including proper thermal boundary condition for the backing plate (anvil) is critical for accurate simulation results. Based on the simulation, thermal and deformation histories of material elements were also calculated, useful to predict material characteristics of the weld such as hardness or grain size, and possibly for the susceptibility of weld to abnormal grain growth (AGG) after post-weld heat treatment.     

On the constitutive modeling of coupled thermomechanical phase-change problems

This paper deals with a thermodynamically consistent numerical formulation for coupled thermoplastic problems including phase-change phenomena and frictional contact. The final goal is to get an accurate, efficient and robust numerical model, able for the numerical simulation of industrial solidification processes. Some of the current issues addressed in the paper are the following. A fractional step method arising from an operator split of the governing differential equations has been used to solve the nonlinear coupled system of equations, leading to a staggered product formula solution algorithm. Nonlinear stability issues are discussed and isentropic and isothermal operator splits are formulated. Within the isentropic split, a strong operator split design constraint is introduced, by requiring that the elastic and plastic entropy, as well as the phase-change induced elastic entropy due to the latent heat, remain fixed in the mechanical problem. The formulation of the model has been consistently derived within a thermodynamic framework. All the material properties have been considered to be temperature dependent. The constitutive behavior has been defined by a thermoviscous/elastoplastic free energy function, including a thermal multiphase change contribution. Plastic response has been modeled by a J2 temperature dependent model, including plastic hardening and thermal softening. The constitutive model proposed accounts for a continuous transition between the initial liquid state, the intermediate mushy state and the final solid state taking place in a solidification process. In particular, a pure viscous deviatoric model has been used at the initial fluid-like state. A thermomecanical contact model, including a frictional hardening and temperature dependent coupled potential, is derived within a fully consistent thermodinamical theory. The numerical model has been implemented into the computational finite element code COMET developed by the authors. Numerical simulations of solidification processes show the good performance of the computational model developed.     

TEC结构的三维非线性瞬态温度场分析

热电制冷器(TEC)以其体积小、作用速度快及无噪音等机械制冷无法替代的优点在航空航天和电子工业等领域得到了越来越广泛的应用。本文根据TEC的导热特点,推导了TEC结构稳态温度场的解析解,建立了其瞬态非线性温度场分析的微分方程。利用伽辽金法导出TEC结构热分析的有限元方程,对非线性热分析的有限元方程进行了求解,得到了TEC的稳态温度场和瞬态响应温度场。算例结果表明,本文提出的TEC结构热分析有限元模型具有较高的精度,能够有效地分析TEC的非线性瞬态温度场。     

Homogenization in finite thermoelasticity

A homogenization framework is developed for the finite thermoelasticity analysis of heterogeneous media. The approach is based on the appropriate identifications of the macroscopic density, internal energy, entropy and thermal dissipation. Thermodynamical consistency that ensures standard thermoelasticity relationships among various macroscopic quantities is enforced through the explicit enforcement of the macroscopic temperature for all evaluations of temperature dependent microscale functionals. This enforcement induces a theoretical split of the accompanying micromechanical boundary value problem into two phases where a mechanical phase imposes the macroscopic deformation and temperature on a test sample while a subsequent purely thermal phase on the resulting deformed configuration imposes the macroscopic temperature gradient. In addition to consistently recovering standard scale transition criteria within this framework, a supplementary dissipation criterion is proposed based on alternative identifications for the macroscopic temperature gradient and heat flux. In order to complete the macroscale implementation of the overall homogenization methodology, methods of determining the constitutive tangents associated with the primary macroscopic variables are discussed. Aspects of the developed framework are demonstrated by numerical investigations on model microstructures.     

Linear stability analysis for a thermoviscoplastic material under cyclic axial loading

Some mechanical properties exhibit a very strong dependence upon temperature; these evolutions can be properly analyzed by the steady state response in cyclic loading. To relate experimental conditions to thermomechanical characteristics, the existence and the stability of steady state solutions are studied for cylinders submitted to cyclic compression. The material, considered as rigid viscoplastic, is modeled by a non-Newtonian temperature dependent viscous law. Closed form solutions are obtained in the framework of a large deformation theory by neglecting thermal expansion and inertia effects. Steady state regime is analyzed. The stress versus strain rate response and the temperature distribution are established as functions of the geometry of the cylinder, the loading characteristics and the material parameters. The stability of steady state solutions is analyzed with use of a linear perturbation scheme.Received: 4 July 2002, Accepted: 5 August 2004, Published online: 24 February 2005PACS: 46.15.Ff, 83.60.St Correspondence to: F. Dinzart     

共线式热电发电机在侧面散热情况下的性能

热电材料是一种环境友好型功能材料,其可以实现热能与电能的相互转化,在热电发电、热电制冷中具有许多应用.传统的热电发电机为$\pi$型结构,要求热电腿的长度相等,在某些情况该结构不利于热电发电机的优化设计.热电发电机在高温工况下会引起强烈的热应力甚至应力集中,从而缩短了其工作寿命.另外,热电发电机的工作温度于环境温度,这样必然会有一部分热量散失到环境中,从而影响热电发电机的性能.针对该现象,本文建立了考虑散热的新型共线式热电发电机模型,该模型的热电腿可以独立进行优化,基于有限元方法,对考虑侧面散热的共线式热电发电机进行了仿真模拟,分析了其在狄利克雷边界条件下的热电性能和力学性能,得到了热电发电机的温度场、电势场、应力场,探究了不同强度的对流散热系数对热电发电机热电性能和力学性能的影响.结果表明,对流散热会降低热电发电机的能量转化效率,当对流换热系数达到~100W/(m$^{2}\cdot$\textcelsius) 时,效率为~0.0479,该值比绝热状态的转化效率0.066 7 低28%.对流散热使热电发电机侧面热损失增加,降低了热应力.在实际应用中,应合理优化设计隔热系统,提高能量的转化效率.      

Development of a two-dimensional model of a compliant non-pneumatic tire

An analytical model for a compliant non-pneumatic tire on frictionless, rigid ground is presented. The tire model consists of a thin flexible annular band and spokes that connect the band to a rigid hub. The annular band is modeled using curved beam theory that takes into account deformations due to bending, shearing and circumferential extension. The effect of the spokes, which are distributed continuously in the model and act as linear springs, is accounted for only in tension, which introduces a nonlinear response. The quasi-static, two-dimensional analysis focuses on how the contact patch, vertical tire stiffness and rolling resistance are affected by the stiffness properties of the band and the spokes. A Fourier series representation of the shear strain in the annular band and the complex modulus of the material were used to predict rolling resistance due to steady state rolling. From the analysis point of view, when the wheel is loaded at its hub, the following three distinct regions develop: (1) a support region where the hub hangs by the spokes from the upper part of the flexible band, (2) a free surface region where the spokes buckle and have no effect, and (3) a contact region where the flexible band is supported by the ground without the effect of the spokes. The angular bounds of these three regions are determined by the spoke angle and the contact angle, which are respectively the angle at which the spokes start to engage in tension and the angle that defines the edge of contact. Closed-form expressions of contact stress, stress-resultants and displacements at the centroids of the cross-sections of the flexible band are expressed in terms of these angles, which must be determined numerically. A thorough parametric analysis of quantities of interest for the tire is presented, which can be used to help support the optimal and rational design of compliant non-pneumatic tires. The model was validated by comparison with two computational models using the commercial finite element software ABAQUS and by experimental rolling resistance data.     

轮胎胎面橡胶-冰面摩擦试验方法研究

基于一种新开发的轮胎胎面橡胶摩擦试验机,建立了轮胎和整车与冰面间的模拟摩擦试验手段,提出了在高滑移速度段的瞬时试验法和低滑移速度段的连续采样试验法;分别在不同滑移速度、压力、温度下针对轮胎胎面胶块与冰面进行了摩擦试验,并对试验结果进行了模型拟合和分析.结果表明:作为轮胎主要组成部分的橡胶表现出很特殊的摩擦特性,其并不符合库仑摩擦定律;橡胶轮胎的机械特性在很大程度上取决于橡胶的摩擦特性,在一些极限工况下尤其如此;相关的橡胶摩擦实验研究对轮胎力学特性的研究具有重要的参考价值.     

Comprehensive numerical analysis of a three-pass bead-in-slot weld and its critical validation using neutron and synchrotron diffraction residual stress measurements

The current paper presents a finite element simulation of the residual stress field associated with a three pass slot weld in an AISI 316LN austenitic stainless steel plate. The simulation is split into uncoupled thermal and mechanical analyses which enable a computationally less expensive solution. A dedicated welding heat source modelling tool is employed to calibrate the ellipsoidal Gaussian volumetric heat source by making use of extensive thermocouple measurements and metallographic analyses made during and after welding. The mechanical analysis employs the Lemaitre–Chaboche mixed hardening model. This captures the cyclic mechanical response which a material undergoes during the thermo-mechanical cycles imposed by the welding process. A close examination of the material behaviour at various locations in the sample during the welding process, clearly demonstrates the importance of defining the correct hardening and high temperature softening behaviour. The simulation is validated by two independent diffraction techniques. The well-established neutron diffraction technique and a very novel spiral slit X-ray synchrotron technique were used to measure the residual stress–strain field associated with the three-pass weld. The comparison between the model and the experiment reveals close agreement with no adjustable parameters and clearly validates the used modelling procedure.     

A thermomechanically coupled viscoelastic cohesive zone model at large deformation

A new viscoelastic cohesive zone model is formulated for large deformation conditions and within a fully coupled thermomechanical framework. The model is suitable for the simulation of a wide range of problems especially for polymeric materials. It can capture viscoelastic crack propagation as well as energy dissipation due to this process. Starting from the principles of thermodynamics, a 3D finite element formulation is derived for a fully coupled simultaneous solution of the thermal field and the deformation field. The viscoelastic model is constructed by extending an elastic exponential traction separation law using a simple rheology. The viscous part of the tractions is postulated to have the same characteristic length as the elastic part and that they are related by a single material parameter. A Newtonian dashpot is used to describe the evolution of the viscous separation. Furthermore, thermal effects are accounted for using temperature expressions in both the traction laws and the viscosity of the dashpot, and using a heat conduction law across the interface. The model is implemented within an implicit finite element code and the internal variable is calculated using an internal iteration. Different numerical examples are used to verify the model and a comparison with experimental data shows a satisfactory agreement.     

高导C/C材料在疏导式热防护中的应用探索

针对高超声速飞行器飞行时气动加热严重的问题，为了保证高升阻比外形，提出疏导式热防护结构，建立了一套内置高导C/C材料的疏导式热防护结构原理模型，通过数值模拟和电弧风洞的方法对疏导式热防护结构进行了分析，得到内置高导C/C材料的防热效果．数值模拟结果表明来流马赫数为8时，模型驻点温度下降了500度，柱面最低升高了380度，实现了热流从高温区到低温区的疏导，减弱了端头的热载荷，强化了端头的热防护能力．通过电弧风洞试验可以获得相似的结果，内置普通C/C材料表层抗氧化层出现严重烧蚀，而内置高导C/C材料基本不变，验证了数值模拟方法的准确性以及内置高导C/C材料疏导式热防护结构的有效性．     

Multi-scale framework for the thermo-viscoelastic analyses of polymer composites

This paper presents a multi-scale framework for analyzing coupled heat conduction and viscoelastic deformation of polymers reinforced with solid spherical particles. The viscoelastic and thermal properties of the polymer constituents are temperature dependent. A simplified micromechanical model for the particle reinforced composite is formulated to obtain the effective thermal properties and viscoelastic responses. The micromechanical model is implemented at material points within elements in the finite element (FE) analyses.     

Numerical study of the plastic behaviour in tension of welds in high strength steels

The influence of the mismatch between material properties and constraint on the plastic deformation behaviour of the heat affected zone of welds in high strength steels is investigated in this study, using finite element simulations. An elastoplastic implicit three-dimensional finite element code (EPIM3D) was used in the analysis. The paper presents the mechanical model of the code and the methodology used for the numerical simulation of the tensile test of welded joints. Numerical results of the tensile test of welded samples with different hypothetical widths for the Heat Affected Zone and various material mismatch levels are shown. The analysis concerns the overall strength and ductility of the joint and in relation to the plastic behaviour of the heat affected zone. The influence of the yield stress, tensile strength and constraint on the stress and plastic strain distribution in the soft heat affected zone is also discussed.     

Natural convection heat transfer from a thin rectangular fin with a line source at the base — a finite difference solution

This paper presents an analysis of the problem of a thin fin of finite thermal conductivity, with an isothermal line source at the base, dissipating heat to the surrounding air by natural convection. The horizontal surface to which the fin is attached is adiabatic so that heat is dissipated only through the fin. The temperature and velocity distributions in the field, the temperature profile in the fin, local Nusselt numbers along the fin and the average heat transfer coefficient of the fin are obtained by solving the governing equations in the field and the heat transfer equation in the fin simultaneously, using an explicit unsteady Finite Difference formulation leading to the steady state result. Numerical experiments are performed to study the influence of parameters namely the fin height, temperature of the heating source and the fin material on the average heat transfer coefficient. Comparison is made with fins of infinite thermal conductivity and the vertical isothermal flat plate.     

轮轨滚动摩擦温升分析

利用有限元法,考虑轮轨间非稳态热传导、与环境的热对流以及热辐射的影响,建立了轮轨滚动接触热耦合计算模型来模拟轮轨滚滑摩擦温升;在模拟轮轨纯滑动条件下,计算分析了由磨损引起的滑动接触斑的尺寸增大对轮轨温度场的影响;在模拟轮轨接触斑部分滑动工况时,针对不同蠕滑率、摩擦系数以及轴重对轮轨温度场的影响进行了相应的计算分析.结果表明:接触斑材料的磨损速度只影响磨损过程中的温度场分布,其稳态温度场分布基本一致;热载荷随着纵向载荷、蠕滑率以及摩擦系数的增大而增大,进而影响轮轨滚动接触热疲劳.     

Numerical simulation and experimental investigation of the elastocaloric cooling effect in sputter-deposited TiNiCuCo thin films

The exploitation of the elastocaloric effect in superelastic shape memory alloys (SMA) for cooling applications shows a promising energy efficiency potential but requires a better understanding of the non-homogeneous martensitic phase transformation. Temperature profiles on sputter-deposited superelastic \({\mathrm {Ti_{55.2}Ni_{29.3}Cu_{12.7}Co_{2.8}}}\) shape memory alloy thin films show localized release and absorption of heat during phase transformation induced by tensile deformation with a strong rate dependence. In this paper, a model for the simulation of the thermo-mechanically coupled transformation behavior of superelastic SMA is proposed and its capability to reproduce the mechanical and thermal responses observed during experiments is shown. The procedure for experiment and simulation is designed such that a significant temperature change from the initial temperature is obtained to allow potential cooling applications. The simulation of non-local effects is enabled by the use of a model based on the one-dimensional Müller–Achenbach–Seelecke model, extended by 3D mechanisms such as lateral contraction and by non-local interaction, leading to localization effects. It is implemented into the finite element software COMSOL Multiphysics, and comparisons of numerical and experimental results show that the model is capable of reproducing the localized transformation behavior with the same strain rate dependency. Additionally to the thermal and the mechanical behavior, the quantitative prediction of cooling performance with the presented model is shown.