Thermodynamics of Shape Memory Alloy Wire: Modeling, Experiments, and Application

A thermomechanical model for a shape memory alloy (SMA) wire under uniaxial loading is implemented in a finite element framework, and simulation results are compared with mechanical and infrared experimental data. The constitutive model is a one–dimensional strain-gradient continuum model of an SMA wire element, including two internal field variables, possible unstable mechanical behavior, and the relevant thermomechanical couplings resulting from latent heat effects. The model is calibrated to recent and new experiments of typical commercially available polycrystalline NiTi wire. The shape memory effect and pseudoelastic behaviors are demonstrated numerically as a function of applied displacement rate and environmental parameters, and the results compare favorably to experimental data. The model is then used to simulate a simple SMA actuator device, and its performance is assessed for different thermal boundary conditions.     

Transient heat conduction in two-dimensional functionally graded hollow cylinder with finite length

In this paper a thick hollow cylinder with finite length made of two dimensional functionally graded material (2D-FGM) subjected to transient thermal boundary conditions is considered. The volume fraction distribution of materials, geometry and thermal boundary conditions are assumed to be axisymmetric but not uniform along the axial direction. The finite element method with graded material properties within each element is used to model the structure and the Crank–Nicolson finite difference method is implemented to solve time dependent equations of the heat transfer problem. Two-dimensional heat conduction in the cylinder is considered and variation of temperature with time as well as temperature distribution through the cylinder are investigated. Effects of variation of material distribution in two radial and axial directions on the temperature distribution and time response are studied. The achieved results show that using two-dimensional FGM leads to a more flexible design so that transient temperature, maximum amplitude and uniformity of temperature distributions can be modified to achieve required specifications by selecting a suitable material distribution profile in two directions.     

An analytic model for transient heat conduction in bi-layered structures with flexible serpentine heaters

Uniform heating of complex surfaces, especially non-developable surfaces, is a crucial problem that traditional rigid heaters cannot solve. Inspired by flexible electronic devices, a novel design for the stretchable heating film is proposed with the flexible serpentine wire embedded in the soft polymer film, which can be attached to non-developable surfaces conformally. It provides a new way for the stretchable heaters to realize uniform heating of complex surfaces. However, the thermal field of flexible serpentine heaters(FSHs) depends on the configurations of the embedded serpentine heating wire, which requires accurate theoretical prediction of real-time temperature distribution. Therefore,the analytical model for the transient heat conduction in FSHs is solved by the separation of variables method and validated by the finite element analysis(FEA) in this paper. Based on this model, the effects of the geometric parameters, such as the radius and the length of the serpentine heaters, on the thermal uniformity are systematically investigated. This study can help to design and fabricate flexible heaters with uniform heating in the future.     

Experimental study of the temperature field generated during orthogonal machining of an aluminum alloy

During the machining of metals, plastic deformation and friction lead to the generation of heat in the workpiece, which results in thermomechanically coupled deformation. Recently, several numerical models of this highly coupled process have been produced in response to increased interest in high speed machining. It is important to characterize the thermal field in the cutting zone in order to completely verify these models of high speed machining and to direct further advancement in this area. In this work, HgCdTe infrared detectors are used to experimentally measure the temperature distribution at the surface of a workpiece during orthogonal cutting. From these temperature measurements, the heat generated in the primary shear zone and the friction zone can be examined and characterized. A modified Hopkinson bar technique has been developed to perform orthogonal machining at speeds ranging from 10 to 100 m/s. In the present work, a cutting velocity of 15 m/s is employed in all the tests in order to demonstrate the capability of the apparatus and characterize thermal fields during low speed machining. Temperature fields are obtained during the orthogonal cutting of aluminum as a function of depth of cut. It is seen that depth of cut can vary both the maximum temperature as well as the distribution of the temperature field in the aluminum workpiece. the maximum temperature increased with depth of cut (238°C for 1.5 mm cut, 207°C for 1.0 mm cut and 138°C for 0.5 mm cut) and the temperature field extended further beneath the cut surface with decreasing depth of cut.     

二阶非定常多宗量热传导反问题的正则解

引入Bregman距离函数及其加权函数作为正则项，应用Tikhonov正则 化方法，对二阶非定常多宗量热传导反问题进行求解. 利用测量信息和计算信息构造最小二 乘函数，将多宗量反演识别问题转化为一个优化问题. 空间上采用8节点等参元进行离散， 时域上采用时域精细算法进行离散，建立了二阶非定常多宗量热传导问题的有限元正/反演数 值模型. 该模型不仅考虑了非均质和参数分布的影响，而且也便于正反演问题的敏度分析， 可对导热系数和边界条件等宗量进行有效的单一和组合识别. 给出了相关的数值验证，对信 息测量误差以及不同正则项的计算效率作了探讨. 数值结果表明，该方法能够对二阶非定常 多宗量热传导反问题进行有效的求解，并具有较高的计算精度.     

Super element approach to cable passing through multiple pulleys

A parametric super element model for cable passing through multiple pulleys is presented in this study for the static analysis of structures. The amounts of cable passages over pulleys are introduced as additional degrees-of-freedoms in the finite element model and the relationship between cable tensions at the two sides of each pulley is imposed based on the friction law or empirical data. The proposed finite element model is firstly verified by a simple pulley cable system and then applied to the analysis of real complex engineering structures. The verification results satisfy the static equilibrium and deformation compatibility conditions of the structural system and basic engineering principles. With the application of the proposed super element model, the global deformation and stress distribution for structures with multiple-pulley cable systems can be effectively and accurately computed. Numerical results for structural analysis show that the effect of friction of pulleys on the cable tensions is significant and the friction-free and fixed models both give unrealistic and incorrect results in cable tensions in some cases.     

Thermo-Mechanical Model and Thermal Analysis of Hollow Cylinder Planetary Roller Screw Mechanism

Planetary roller screw mechanism (PRSM) is widely used for rapid and precise motion translation from rotary into linear motion due to its high stiffness and high position accuracy. However, a high speed PRSM drive system naturally generates significant amount of frictional heat at the contact interfaces, which causes thermal deformation and thermal error and reduces motion accuracy. Preload is usually applied to remove the axial backlash of the PRSM for achieving high accuracy and great stiffness. However, more frictional heat is produced by such preload. On the other hand, larger numbers of angular contact bearings are needed to support the heavy axial load. The friction heat generated in support bearings has also to be investigated. In order to estimate the thermal distribution and thermal error of the hollow cylinder PRSM, a thermo-mechanical model based on finite element method (FEM) is developed, where heat generation from the two main sources of the PRSM, the parameters calculation of heat transfer coefficient and other thermal boundary conditions were studied. The presented model is proven capable of investigating temperature distribution, thermal error, and cooling performances of coolants of the PRSM system.     

Analysis of turbulent heat transfer from sinusoidal profile finned dissipators

 In the present work the effectiveness of thermal dissipators cooled by a fluid in turbulent flow is studied by varying the fins spacing and shape. The profile of the fin is described by a sinusoidal function depending on two parameters that define its amplitude and number of oscillations. The velocity distribution in the fluid, and the temperature distribution in the dissipator and in the fluid are determined with the help of a finite element method. The model allows to study the variations of the heat transfer coefficient due to the fluid dynamic conditions imposed by the fin profile. Lastly, a combination of geometrical parameters is proposed, which yields the best dissipator performance under particular conditions. Received on 29 June 2000     

开式热沉内冷刀具的设计及其导热性能分析

车削加工温度对工件的表面加工质量和刀具的使用寿命具有重要影响. 设计了一种开式热沉内冷刀具,计算了在实际加工工艺参数下刀具受到的切削力和前刀面上的热流密度,分析了刀具的结构强度;建立了刀具热-流-固耦合温度场模型,探讨了热稳态条件下刀具的温度场分布,以及刀片冷却液流道内热沉数量对刀具导热性能的影响规律,比较了在相同热源条件下开式热沉内冷刀具与其他内冷刀具的导热性能. 结果表明:对于刀片材料为硬质合金YT5的刀具,在热流密度为10 W/mm2的条件下,内置6个热沉的设计方案可获得最佳冷却效果,刀具的最高切削温度控制为187.1 ℃;与其他内冷刀具相比,开式热沉内冷刀具的最高切削温度降低了12.1 ℃.      

Comparison of isotropic hardening and kinematic hardening in thermoplasticity

A coupled thermo-mechanical problem is presented in this paper. The constitutive model is based on thermoplastic model for large strains where both kinematic and isotropic hardening are included. It is shown that a non-associated plasticity formulation enables thermodynamic consistent heat generation to be modeled, which can be fitted accurately to experimental data. In the numerical examples the effect of heat generation is investigated and both thermal softening and temperature-dependent thermal material parameters are considered. The constitutive model is formulated such that pure isotropic and pure kinematic hardening yield identical uniaxial mechanical response and mechanical dissipation. Thus, differences in response due to hardening during non-proportional loading can be studied. Thermally triggered necking is studied, as well as cyclic loading of Cook’s membrane. The numerical examples are solved using the finite element method, and the coupled problem that arises is solved using a staggered method where an isothermal split is adopted.     

基于特征正交分解的一类瞬态非线性热传导问题的新型快速分析方法

提出了一种基于特征正交分解(POD)和有限元法的瞬态非线性热传导问题的模型降阶快速分析方法, 建立了导热系数随温度变化的一类瞬态非线性热传导问题有限元格式的POD降阶模型. 在隐式时间推进方法的基础上有效结合单元预转换方法和多级线性化方法发展了一种加速求解瞬态非线性热传导降阶模型的新型计算方法,并通过二维和三维算例验证了该方法的准确性和高效性. 研究结果表明: (1)降阶模型解的均方根误差在经过初始时段轻微的脉动后稳定于0.01%以下, 而其计算效率比有限元全阶模型提高2$\sim $3个数量级, 并且自由度数量(DOFs)愈大提高的幅度也愈加显著; (2)新型算法解决了常规算法在计算非线性降阶模型时加速性能差的问题, 即使是在DOFs比较小的时候也能够明显提高计算效率; (3)常数边界条件下得到的POD模态可以用来建立相同求解域在各种复杂时变边界条件下的瞬态非线性热传导降阶模型, 并对其传热过程和温度场进行快速准确的分析与预测, 具有很好的工程应用价值.      

损伤因素对单层平面索网静力性能影响研究：有限元分析与试验验证

运用通用有限元软件ANSYS建立三维有限元模型,对横索与竖索连接节点失效、索预应力损失和锚固端失效这三种损伤因素的不同损伤工况下,单层平面索网结构的受力性能进行了非线性有限元分析,并与相应的试验结果进行了全面对比分析。结果表明：本文的有限元模型能够准确地分析计算上述三种损伤因素对单层平面索网结构受力性能的影响,包括结构...     

Optimization of heat transfer through finned dissipators cooled by laminar flow

In the present work, the problem of optimizing the shape and the spacing of the fins of a thermal dissipator cooled by a fluid in laminar flow is studied. For a particular finned conduit, the velocity and temperature distributions on the transversal section are determined with the help of a finite element model and a global heat transfer coefficient is calculated. A polynomial lateral profile is proposed for the fins and the geometry is optimized in order to make the heat transfer coefficient as high as possible with the smallest dimensions or the lowest hydraulic resistance to the flow. The optimum fin profile and spacing, obtained by means of a genetic algorithm, are finally shown for different situations. Increases of 45% are obtained in the heat transfer coefficient referring to the maximum values which can be obtained with rectangular fin profiles.     

基于数据驱动模型求解热传导反问题

热传导反问题求解在工程领域具有重要的应用价值.本文发展数据驱动模型识别了管道内壁几何形状和皮肤肿瘤生长参数等热传导反问题.在管道内壁几何形状识别问题中,首先采用随机生成模型结合有限元法求解热传导正问题,并采用有效导热系数转化的思想,建立机器学习模型,求解了测点温度与有效导热系数之间的抽象映射关系,进而实现管道内壁几何形...     

Thermal analysis of annular fins with temperature-dependent thermal properties

The thermal analysis of the annular rectangular profile fins with variable thermal properties is investigated by using the homotopy analysis method （HAM）. The thermal conductivity and heat transfer coefficient are assumed to vary with a linear and power-law function of temperature, respectively. The effects of the thermal-geometric fin parameter and the thermal conductivity parameter variations on the temperature distribution and fin efficiency are investigated for different heat transfer modes. Results from the HAM are compared with numerical results of the finite difference method （FDM）. It can be seen that the variation of dimensionless parameters has a significant effect on the temperature distribution and fin efficiency.     

温度循环应力剖面对QFP焊点热疲劳寿命的影响

采用统一型粘塑性Anand本构方程描述了QFP(四方扁平封装)焊点的粘塑性力学行为,利用有限元分析软件建立组装在印制电路板上QFP的有限元模型,通过研究焊点内部总应变范围的变化进而研究温度循环应力剖面各个参数对焊点热疲劳寿命的影响,为设计合理的温度循环应力剖面提供了理论依据。     

高温仪器化压入测试中热接触对位移测量漂移的影响

基于对室温压头和热试样接触后传热过程的分析, 重点研究热接触引起的压头基托热膨胀对高温仪器化压入测试中位移测量漂移的影响. 首先, 通过热传导理论分析, 获得热接触后基托内温度场分布的解析解, 进而研究基托热膨胀引起的位移测量漂移量; 然后, 建立有限元分析模型, 数值模拟高温仪器化压入过程, 验证理论模型的准确性. 研究发现, 压头与热试样接触面间的热传导性质显著影响基托内的温度场分布; 对于不同材料的试样, 接触面间传热性能不同, 基托的热膨胀量差异可以达到几个数量级. 研究结果有助于优化高温压入测试程序, 提高测试的可靠性.      

近场动力学与有限元方法耦合求解热传导问题

求解含裂纹等不连续问题一直是计算力学的重点研究课题之一,以偏微分方程为基础的连续介质力学方法处理不连续问题时面临很大的困难. 近场动力学方法是一种基于积分方程的非局部理论,在处理不连续问题时有很大的优越性. 本文提出了求解含裂纹热传导问题的一种新的近场动力学与有限元法的耦合方法. 结合近场动力学方法处理不连续问题的优势以及有限元方法计算效率高的优势,将求解区域划分为两个区域,近场动力学区域和有限元区域. 包含裂纹的区域采用近场动力学方法建模,其他区域采用有限元方法建模. 本文提出的耦合方案实施简单方便,近场动力学区域与有限元区域之间不需要设置重叠区域. 耦合方法通过近场动力学粒子与其域内所有粒子(包括近场动力学粒子和有限元节点)以非局部方式连接,有限元节点与其周围的所有粒子以有限元方式相互作用. 将有限元热传导矩阵和近场动力学粒子相互作用矩阵写入同一整体热传导矩阵中,并采用Guyan缩聚法进一步减小计算量. 分别采用连续介质力学方法和近场动力学方法对一维以及二维温度场算例进行模拟,结果表明,本文的耦合方法具有较高的计算精度和计算效率. 该耦合方案可以进一步拓展到热力耦合条件下含裂纹材料和结构的裂纹扩展问题.      

基于互补理论和扩展有限元法的摩擦接触裂纹应力强度因子计算

从虚功方程出发,结合扩展有限元离散技术与接触条件的非线性互补表述,建立了摩擦接触裂纹问题的扩展有限元非线性互补模型,将不等式接触条件转化为非线性互补类的非光滑方程组,并采用基于广义导数的非光滑阻尼牛顿法求解方程组,无需引入任何额外人工变量以及迭代求解。以含中心倾斜裂纹平板和边裂纹平板为例,运用相互作用积分法计算摩擦接触裂纹的应力强度因子,将其结果与理论解进行对比分析,该方法都能给出精确的计算结果;基于扩展有限元方法对单轴压缩作用下倾斜裂纹扩展过程进行了数值模拟,计算结果表明,受压裂纹数值结果与实验结果比较吻合,从而验证了本文方法的有效性与正确性。     

共轭梯度法求解非线性多宗量稳态传热反问题

应用共轭梯度法求解非线性多宗量稳态热传导反问题。采用八节点的等参单元在空间上进行离散,建立了便于敏度分析的非线性正演和反演的有限元模型,可直接求导进行敏度分析。给出了相关的数值验证,对测量误差及测点数目的影响作了初步探讨,结果表明,采用的算法能够对非线性稳态热传导中导热系数和边界条件联合反问题进行有效的求解,并具有较高精度。