Adaptive finite element solution for the heat conduction with a moving heat source

We have demonstrated that some of the parabolic type problems encountered in such branches of engineering as heat conductions with a moving source can be analyzed successfully by means of the finite element method. Adapted mesh generation technique is implemented for solving heat transfer involving a moving heat source so that small elements can be used in areas of large time rates of change of temperature. It has been adjusted to steep gradients of the solution with respect to the relatively large time interval. A program has been developed for the case of two-dimensional triangular elements, and algorithm is possessed a number of usual advantages that made solutions very divergent. Numerical results have shown that the adaptive gridding scheme is effective in localizing oscillations due to the sharp gradients or discontinuities in the solution. Furthermore, the numerical results near the region of moving source from the present method are under and over estimated the solution of traditional finite element method by almost 3% respectively. The several examples are given to illustrate the validity and practicality of the method. The results of various sample solutions are evaluated and discussed.     

An analytical solution to heat conduction with a moving heat source

This paper deals with an analytical solution to heat conduction in the medium subjected to a moving heat source. It evaluates the temperature distribution around a rectangular shape source moving at a constant speed along the axis of a bar. The transient temperature field from a moving heat source was analyzed using a Fourier series procedure. The most interesting result of the theory, is the derivation of a single formula capable of predicting the cooling time and cooling rate with a fairly good accuracy for ranges of temperature. Because of the passage of the heat source, the rise of temperature produced at a given near the source, tends to rapidly become constant. Several sample problems are discussed and illustrated, and comparisons with numerical approaches where these can also be used made. The results show that these solutions are in good agreement with the numerical results.     

Numerical solution for temperature and flow fields in crossflow moving bed heat exchanger

The steady state solution of flow and temperature distributions in the crossflow moving bed heat exchanger using granular materials was obtained numerically. The effectiveness of crossflow moving bed was compared with that of crossflow heat exchanger with both fluids unmixed. The effect of bed geometry and solid particle size on the performance of moving bed was investigated. Also, the effect of thermal capacities of gas and solid particle and the gas flowrate was studied. The design data to estimate the heat exchanger performance of moving bed are given from the results of calculation in this study.     

Residual stresses due to a moving heat source

An analytical model based on finite element method is presented for determination of the residual stresses of thermal and mechanical origin due to surface grinding process. The temperature field within the workpiece is determined as the quasi-steady state temperature distribution due to the moving heat source. An iterative procedure is employed for evaluation of the step-by-step movement of the temperature field and the force, in order to simulate the movement of the grinding wheel over the workpiece. Computation of the elastic-plastic stress history culminates in the residual stress state of the workpiece. Influence of the magnitude of mechanical force, the rate of heat input and the speed of movement of workpiece on the residual stress distribution, are discussed.     

Detailed modelling of a moving heat source using multigrid methods

The actual contact between solid surfaces is generally rough and time dependent. This roughness can only be correctly described using a 3D model. Moreover, severe thermo-mechanical loading induces high stress and temperature gradients within a thin subsurface layer. Even higher gradients are obtained in the case of surface coatings. Consequently, the problem is strongly multiscale: from contact to coating to roughness, the characteristic dimensions range from millimeter to nanometer.A straightforward discretization of this multiscale problem would exceed the memory and CPU capabilities of current computers. The aim of this work is to propose a more efficient numerical model able to deal with this multiscale problem: using 10⁹ points and 10³ timesteps.This paper traces the history of the numerical solutions of the heat equation from the pioneering work of Carslaw and Jaeger, to the current era.The proposed model is based on multigrid techniques within a finite difference frame work. Localized refinement is implemented to optimize memory and computing time costs. The numerical performance of the solver is presented through a comparison with analytical results using different types of boundary conditions. A multisource contact is studied as a first approximation to real asperity interaction.     

基于ANSYS的磨削热分析中移动热源加载技巧

介绍利用ANSYS进行磨削热分析时移动热源的加载方法,阐述当磨削面为曲面时移动热源的加载技巧,对曲面(如齿轮)磨削过程热状态研究具有指导意义.     

Thermal modeling of the metal cutting process — Part III: temperature rise distribution due to the combined effects of shear plane heat source and the tool–chip interface frictional heat source

This paper is Part III of a 3-part series on the Thermal Modeling of the Metal Cutting Process. In Part I (Komanduri, Hou, International Journal of Mechanical Sciences 2000;42(9):1715–1752), the temperature rise distribution in the workmaterial and the chip due to shear plane heat source alone was presented using modified Hahn's moving oblique band heat source solution with appropriate image sources for the shear plane (Hahn, Proceedings of the First US National Congress of Applied Mechanics 1951. p. 661–6). In Part II (Komanduri, Hou, International Journal of Mechanical Sciences 2000;43(1):57–88), the temperature rise distribution due to the frictional heat source at the tool–chip interface alone is considered using the modified Jaeger's moving-band (in the chip) and stationary rectangular (in the tool) heat source solutions (Jaeger, Proceedings of the Royal Society of New SouthWales, 1942;76:203–24; Carlsaw, Jaeger. Conduction of heat in solids, Oxford, UK: Oxford University Press, 1959) with appropriate image sources and non-uniform distribution of heat intensity. The matching of the temperature rise distribution at the tool–chip contact interface for a moving-band (chip) and a stationary rectangular heat source (tool) was accomplished using functional analysis technique, originally proposed by Chao and Trigger (Transactions of ASME 1955;75:1107–21). This paper (Part III) deals with the temperature rise distribution in metal cutting due to the combined effect of shear plane heat source in the primary shear zone and frictional heat source at the tool–chip interface. The basic approach is similar to that presented in Parts I and II. The model was applied to two cases of metal cutting, namely, conventional machining of steel with a carbide tool at high Peclet numbers (≈5–20) using data from Chao and Trigger (Transactions of ASME 1955;75:1107–21) and ultraprecision machining of aluminum using a single-crystal diamond at low Peclet numbers (≈0.5) using data from Ueda et al. (Annals of CIRP1998;47(1):41–4). The analytical results were found to be in good agreement with the experimental results, thus validating the model. Using relevant computer programs developed for the analytical solutions, the computation of the temperature rise distributions in the workmaterial, the chip, and the tool were found. The analytical method was found to be much easier, faster, and more accurate to use than the numerical methods used (e.g., Dutt, Brewer, International Journal of Production Research 1964;4:91–114; Tay, Stevenson, de Vahl Davis, Proceedings of the Institution of Mechanical Engineers (London) 1974;188:627). The analytical model also provides a better physical understanding of the thermal process in metal cutting.     

Effects of the heat source profiles on the thermal distribution for ultraprecision grinding

In order to investigate the thermal effects on the workpiece during ultraprecision grinding processes, an analytical thermal model is firstly developed. Based on the established model, both the steady-state and the transient temperature distributions are obtained and the effects of the grinding parameters on the temperature distribution are analyzed. Various heat source profiles are utilized to simulate diverse ultraprecision grinding conditions, and the effects of the parameters of the heat source on the temperature distribution are investigated. The developed thermal model and analysis results provide further insights of the temperature distributions for ultraprecision grinding processes.     

Mathematical modeling of moving heat source shape for submerged arc welding process

An attempt is made in this paper to find out the analytical solution of the thermal field induced in a semi-infinite body by a moving heat source with Gaussian distribution by selecting appropriate inside volume for submerged arc welding process. Three different types of heat source shapes in the form of oval, double ellipsoidal, and conical forms were considered and compared with the experimental result. The study shows that for heat input of submerged arc welding process, the best suitable heat source shape is in the form of an oval. The study also shows two alternate ways of predicting the size of the heat-affected zone.     

An isothermal temperature source with a large surface area using the metal-etched microwick-inserted vapor chamber heat spreader

For use of the thermal cycle of the biochemical fluid sample, the isothermal temperature source with a large surface area was designed, fabricated and its thermal characterization was experimentally evaluated. The comprehensive overview of the technology trend on the temperature control devices was detailed. The large surface area isothermal temperature source was realized by using the vapor chamber heat spreader. The cost-effectiveness and simple manufacturing process were achieved by using the metal-etched wick structure. The temperature distribution was quantitatively investigated by using IR temperature imaging system at equivalent temperatures to the PCR thermal cycle. The standard deviation was measured to be within 0.7°C for each temperature cycle. This concludes that the presented isothermal temperature source enables no temperature gradient inside bio-sample fluid. Furthormore it can be applied to the cooling of the electronic devices due to its slimness and low thermal spreading resistance.     

Analysis of temperature distributions in surface grinding with intermittent wheels

An analytical model was established to calculate the curve of temperature distributions in surface grinding with intermittent wheels. In order to predict the numbers of the pulses imposed on the fluctuating temperature profile, a new quantity, the dynamic number of wheel segments in the grinding zone, was defined. The temperatures at the grinding zone were measured by using a foil thermocouple. It is found that the new quantity, the dynamic number of wheel segments, can be used to accurately predict the pulses on the measured temperature curves in the grinding zone. Through matching the calculated temperature curves with the measured results, it is found that the temperature profile is greatly dependent on the wheel segment-engaging states even at identical grinding parameters. However, the wheel segment-engaging states have little influence on the values of peak and valley temperatures.     

Thermal modeling of the metal cutting process: Part I — Temperature rise distribution due to shear plane heat source

The model of an oblique band heat source moving in the direction of cutting, first introduced by Hahn (Proceedings of First U.S. National Congress of Applied Mechanics 1951. p. 661–6) for an infinite medium in 1951 and subsequently modified by Chao and Trigger (Transactions of ASME 1953;75:109–20) in 1953 for a semi-infinite medium, is extended in this investigation by including appropriate image heat sources. It is used for the determination of the temperature rise distribution in the chip and the work material near the shear plane caused by the main shear plane heat source in orthogonal machining of a continuous chip. A new approach is taken in that the analysis is made in two separate parts, namely, the workmaterial side and the chip side of the shear plane and then combined. The workmaterial (or the chip) is extended past the shear plane as an imaginary region for continuity to determine the temperature distribution in the workmaterial (or the chip) near the shear plane. The imaginary regions are the regions either of the workmaterial that was cut by the cutting tool prior to this instance and became the chip or will be cut by the cutting tool prior to becoming the chip. An appropriate image heat source with the same intensity as the shear plane heat source is considered for each case. The temperature distributions in the chip and the workmaterial were determined separately by this method and combined to obtain isotherms of the total temperature distribution (and not merely the average temperatures). It appears that the significance of Hahn's ingenious idea and his general solution have not been fully appreciated; instead, an approximate approach involving heat partition between the chip and the work was frequently used (Trigger and Chao. Transactions of ASME 1951;73:57–68; Loewen and Shaw. Transactions of ASME 1954;71:217–31; Leone. Transactions of ASME 1954;76:121–5; Nakayama. Bulletin of the Faculty of Engineering National University of Yokohama, Yokohama, Japan, 1956;21:1–5; Boothroyd. Proceedings of the Institution of Mechanical Engineers (Lon) 1963;177(29):789–810). It may be noted that in utilizing Hahn's modified solution, it is not necessary to make an explicit a priori assumption regarding partitioning of heat between the workmaterial and the chip, as was common in most prior work. Instead, this information is provided as part of the solution. The results obtained with the exact analysis were compared with other methods using the experimental data available in the literature to point out some of the discrepancies in the simplified models. It may be pointed out that these models assume the temperature rise at the chip–tool interface to be nearly uniform and equals the average temperature rise in this volume. A comparison of the calculated temperature rise by these methods with the exact analysis indicates that the differences can be quite significant (50% or higher). It is hoped that future researchers would recognize the significance and the versatility of the exact analysis in determining the temperature distribution in the shear zone in metal cutting.     

Selecting abrasive wheels for the plane grinding of airplane parts on the basis of surface roughness

The machinability of hardened Cr-Mr-Si and Cr-Mr-Si-Ni steels and the efficiency of traditional abrasive wheels are analyzed on the basis of parametric and nonparametric data. The applicability of the wheels is discussed.     

Free surface planar liquid jet impingement on a moving surface: interfacial flow and heat transfer characteristics

Journal of Mechanical Science and Technology - Understanding heat transfer characteristics of sheet metal is of practical importance in sheet metal rolling operation to ensure strength and quality...     

A study on large-area laser processing analysis in consideration of the moving heat source

This study proposed a way of reducing the time and memory required for analysis by adjusting the heat input area, to overcome the difficulties in analyzing large-area laser processing. An analytical model was manufactured using existing research results, and based on these results and the volume of the analysis, the efficiency of the new analysis method was verified. The new analysis method proposed in this study can be used as a simple analysis method utilizing a commercial analysis program for diverse areas, including the effect of temperature distribution on the material, the effect of temperature transfer on the mechanical structure, and thermal displacement prediction, in the thermal treatment after processing.     

Investigation of a 3-DOF micro-positioning table for surface grinding

A novel three degree of freedom numerically controlled micro-positioning table has been developed, optimized for applications such as improving the machining precision of precision grinders. The table consists of a moving platform, coupled to a base, three piezoelectric actuators and three capacitive sensors. An elastic structure with three notch-type flexure hinges both guides the platform and generates a preload for the piezoelectric actuators. The dimensions of the platform and flexure hinges and the position of flexure hinges are designed with the aid of finite element modeling to provide good stiffness with little bending deformation of the platform. The inverse model of the table is developed for numerical control. Experimental results are compared to the model predictions. The table has a natural frequency of 584 Hz, a resolution of 6 nm, an open loop control stiffness of 104 N/μm at the center of the moving platform and a closed loop control stiffness of 650 N/μm across the working area of the table.     

车用大尺寸软包锂离子电池在高低温升 工况下的生热率测定

提出了一种电动汽车用大尺寸软包锂离子电池的生热率测量方法——热补偿法,研究了电池生热率与工作电流、温度之间的曲线关系,其有效性得到了常规热流计法的验证,最后结合这两种方法研究了电池在高、低温升工况下的生热特性。研究结果表明,基于热补偿法的电池生热率平均测算偏差低于5.6%;电池的生热率随工作电流的增大而增大,二者呈二次非线性关系;电池在高温升工况下的生热率随放电深度呈先降后升趋势,形似U型曲线;电池在低温升工况下的平均生热率较其在高温升工况下高约13.7%。提出的热补偿法具有精度高、成本低、简便灵活等优势,研究成果可为大尺寸软包锂离子电池的热模型建立和热管理系统设计给予指导。