Analysis of transient average tool temperatures in face milling

The increased tool temperature has great effect on tool life, machining efficiency and even the quality of the products in face milling. The objectives of this study are to predict the transient average tool temperatures under different cutting conditions with fixed cutting velocity and metal removal rate, and investigate the evolution of tool temperature with cutting condition. Finite element simulations of orthogonal metal cutting are performed so as to predetermine the evolution process of the heat source on the tool rake face. An analytical model is proposed to calculate and analyze the tool temperatures under nine different cutting conditions. The results reveal that the minimum transient average tool temperature can be acquired by adopting suitable cutting condition. The proposed theoretical method provides insight into the complex evolution of tool temperatures. It also provides information for the search for the optimum cutting condition under which the longest tool life can be obtained.     

Estimation of heat flux imposed on the rake face of a cutting tool: A nonlinear,complex geometry inverse heat conduction case study

In this paper the sequential function specification method is used to estimate the transient heat flux imposed on the rake face of a cutting tool during the cutting operation with two different assumptions. In one of them the thermal conductivity is taken to be constant, and in the other one it varies with temperature. The cutting tool is modeled as a three dimensional object. The capabilities of the geometric modeling, mesh generation as well as solver of the commercial software ANSYS are utilized in order to reduce the time expended for modeling and direct heat conduction solution, in both linear and nonlinear problems. This way the inverse heat conduction algorithm employs ANSYS as a subprogram through the ANSYS Parametric Design Language (APDL). The stability as well as accuracy is compared for cases of linear and nonlinear heat conductions. The effect of nonlinearity, as well as different sensor locations is investigated in order to arrive at an optimal experimental procedure. Finally, a typical temperature data during the working condition are used to recover the heat flux at the cutting tool surface using linear as well as nonlinear solutions.     

Online Temperature Prediction Using a Branch Eigenmode Reduced Model Applied to Cutting Process

In this article, we propose a method to estimate the temperature field in the hottest zone of a cutting tool. Since temperature measurements are not possible in this zone, an inverse method using a branch modal reduction is implemented. The reduced model is used in an inverse problem to identify the heat flux density generated by the frictional forces. Knowing the interface heat flux, the direct problem is solved to compute the temperature field in the tool. The analysis of the results shows that this method enables supervision of the temperature field at the workpiece-tool contact area in real time.     

The BFGS method for estimating the interface temperature and convection coefficient in ultrasonic welding

An inverse heat transfer problem is investigated in the present study by the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method to predict the unknown time-dependent heat generation at the weld interface and convection heat transfer coefficient during an ultrasonic metal welding process based on the knowledge of temperature measurements taken on the horn. With known temperature data at some locations on the horn, the inverse solution was rapidly obtained by solving nonlinear direct problem, Central Finite Difference and Simple Step Method. The proposed method which did not need solving adjoint and sensitivity problem revealed the characteristics of high efficiency, lower iterations for a computational algorithm and high accuracy for estimating values even when measurement error was considered. Besides, a comparison of the BFGS method with some previous methods (i.e. CGM, SCGM) was established. These results show that an excellent estimation on interfacial heat generation (or temperature), as well as a convection heat transfer coefficient, can be simultaneously obtained in this study. The current methodology will provide a useful tool to optimize welding conditions in ultrasonic welding.     

Estimation of the Transient Heat Transfer Rate at the Boundary of an Electronic Chip Packaging

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to estimate the unknown time-dependent heat transfer rate at the electronic-packaging/heat-sink-assembly interface from the knowledge of temperature measurements taken within the packaging. The temperature data obtained from the direct problem are used to simulate the temperature measurements, and the effect of the errors in these measurements upon the precision of the estimated results is also considered. Results show that an excellent estimation on the time-dependent heat transfer rate can be obtained for the test case considered here.     

Improvement of the pulsed photothermal technique for the measurement of the convective heat transfer coefficient

<正>The present study concerns the measurement of the convective heat transfer coefficient on the solid-fluid interface by the pulsed photothermal method.This non-intrusive technique is apphed for the measurement of the local heat transfer coefficients in cooling of a rectangular slab that simulates an electronic component.The heat transfer coefficient is deduced from the evolution of the transient temperature induced by a sudden deposit of a luminous energy on the front face of the slab.In order to draw up the heat transfer cartography by a non-destructive tool, the infrared thermography has been used.Two inverse techniques for the identification of the heat transfer coefficient are presented here.The first one is based on the assumption that heat transfer coefficient remains constant during the pulsed experiment,and the second one considered it variable in space and time.The temporal and spatial evolutions are expressed as a constant heat transfer coefficient(h_0)multiplied by a function of time and space f(x,t).The function f is deduced from the resolution of the conjugated convection-conduction problem,by a control volume technique for the case of thermally thick sample.The results are given for different air velocities and deflection angles of the flow.     

Prediction of the Time-Varying Ledge Profile inside a High-Temperature Metallurgical Reactor with an Unscented Kalman Filter-Based Virtual Sensor

A non-intrusive inverse heat transfer procedure for predicting the two-dimensional time-varying profile of the protective phase-change ledge on the inside surface of the walls of a high-temperature metallurgical reactor is presented. The inverse method, used here as a virtual sensor, enables the on-line estimation of the position of the solid-liquid phase front using thermal sensors embedded in the reactor wall. The virtual sensor comprises a state observer coupled to a reduced model of the reactor. Results show that the virtual sensor that yields the best prediction comprises an unscented Kalman filter, a nonlinear state-space model of thereactor, and two heat flux sensors located at the wall/ledge interface.     

Estimation of thermophysical properties of fouling using inverse problem and its impact on heat transfer efficiency

At high temperature, the circulation of fluid in heat exchangers provides a tendency for fouling accumulation to take place on the internal surface of tubes. In brief, the deposits on heat exchanger tubes are caused by the presence of inorganic salts, of small quantities of organic materials and products of corrosion in the water. From thermophysical point of view, the deposited fouling has harmful effects on the heat exchanger efficiency. Indeed, it increases the thermal resistance which can raise the energy consumption. This study shows an experimental and a theoretical process of estimation of thermophysical properties of the fouling deposited on a section of a heat exchanger and its effects on the heat transfer efficiency. The estimation method is based on the Gauss-Newton algorithm that minimizes the ordinary least squares function comparing a measured temperature and a theoretical one. The temperature response is measured on the rear face of a bi-layer system composed of a section of a heat exchanger and the fouling deposited on during and after a finite width pulse heat flux on its front face. The theoretical temperature, that is a function of the unknown thermophysical properties of the bi-layer system, is calculated by the resolution of the one-dimensional linear inverse conduction problem, and by the use of the quadrupole formalism.The results of the estimation procedure show, on the one hand the efficiency and the stability of the optimization algorithm to estimate the thermophysical properties of the fouling. On the other hand they underline the necessity of the maintenance of fluid circulating tubes at high temperature.     

An inverse problem to estimate relaxation parameter and order of fractionality in fractional single-phase-lag heat equation

In this paper, an inverse analysis is performed for simultaneous estimation of relaxation time and order of fractionality in fractional single-phase-lag heat equation. This fractional heat conduction equation is applied on two physical problems. In inverse procedure, solutions of a previously validated linear dual-phase-lag model on the physical problems under study have been used as the measured temperatures. The inverse fractional single-phase-lag heat conduction problem is solved using the nonlinear parameter estimation technique based on the Levenberg–Marquardt method. The results of the present study show that the Levenberg–Marquardt method can be successfully applied on the inverse fractional heat transfer problem. The solution procedures employed in the present study for direct and inverse problems have greatly increased the reliability and success of parameter estimation problem. In the present study, for the first time, relaxation time and fractionality of a non-homogeneous medium (i.e. processed meat) have been determined. Also, the results of this study show that the fractional single-phase-lag model can predict the same temperature distribution as the linear dual-phase-lag model for the problem under study. This latter result enables us to consider further generalization of the dual-phase-lag model to fractional dual-phase-lag models.     

Thermal Performance Prediction in the Air Gap of a Rotor-Stator Configuration: Effects of Numerical Models

This study is dedicated to a numerical investigation of convective heat transfer on the rotor surfaces of a rotor-stator configuration that is typically found in large hydro-generators. The computational fluid dynamics calculations with two turbulence modelling approaches are used to predict the flow structure and heat transfer in the air gap of the rotor-stator configuration. The steady state mixing plane approach is employed at the interface to couple the rotor and stator components. Results s...     

Experimental study of heat transfer in oscillating flow

This paper describes an experimental study of heat transfer in oscillating flow inside a cylindrical tube. Profiles of temperature are taken inside the wall and in the fluid from an instrumented test rig, in different conditions of oscillating flow. Profiles obtained allow the observation of the wall effect on heat transfer. A method using the inverse heat conduction principle allows the characterization of local heat transfers at the fluid-solid interface. Finally, a comparison between global and local approaches of heat transfer shows the difficulty of defining a dimensionless heat flux density to model local heat transfer in oscillating flow.     

Inverse methodology to determine mold set-point temperature in resin transfer molding process

This study consists of determining by inverse method the set-point temperature of the fluid flowing through heating plates in a Resin Transfer Molding (RTM) process tool so as to reach a predetermined thermal history in the composite part. Although the described methodology is applied in a specific mold in this paper, it remains general and may be transposed to a large scale of molding configuration. The considered mold is metallic and composed of several parts. Assembling these parts is not possible without introducing imperfect contacts that perturb heat transfer between them. The heat transfer at the interface is modeled by thermal contact resistances (TCR) whose values are unknown. In the case of metallic molds TCR are of the same order of magnitude than the equivalent thermal resistance of the mold. Therefore they cannot be neglected. The influence of these TCR is then a key-point on heat transfer since a bad knowledge of their values implies a wrong estimation of the temperature field. Then before being able to estimate the set-point of the temperature of the thermoregulated fluid, it is necessary in a first stage to evaluate the most influent TCR that are spatially and time dependent. Their determination is achieved by an optimization approach and carried out on a 2D transverse cut of the mold. Experimental temperature measurements in the mold are matched to the computed responses of the heat conduction model. A least square criterion is minimized by using the conjugate gradient algorithm. The gradient of the criterion is determined by solving a set of adjoint equations. After the identification of these parameters, the same optimization method is used to compute the mold set point temperature. It is notable that the same set of adjoint equations is used to solve both problems.     

Modeling of Heat Transfer Across the Interface in Two-Fluid Flows

A model is presented in this article to deal with heat transfer across the interface separating two immiscible fluids. It is suitable to be incorporated into interface-tracking methods, such as volume-of-fluid (VOF) methods, because a sharp interface is available in these approaches. The temperature at the interface and the heat flux through it are calculated in such a way that the continuity of the two properties at the contact surface is satisfied explicitly. With use of these values, the temperature either at the centroid or on a face of the interface cell can be estimated, which serves as Dirichlet boundary condition for the energy equation. The temperature field is then calculated by solving the energy equations for the two fluids simultaneously in an implicit way. This method is first assessed via testing on two heat conduction problems in which two solids are in contact. Good agreement between numerical solutions and theory is obtained. To demonstrate its capability, it is applied to two kinds of heat transfer problems, one being the collapse of a heated water column in a cavity, and the other the falling of a molten tin droplet in an oil tank. The effect of fluid flow on the heat transfer is clearly illustrated.     

Methodology for Estimation of Local Convective Heat Transfer Coefficient for Vapor Condensation

This paper aims to present an effective two-dimensional inverse heat conduction technique and an experimental design for accurately estimating the local convective heat transfer coefficient of vapor condensation over a conical surface, given temperature measurements at some interior locations. The functional form for the heat transfer coefficient is not known a priori. The method uses a sequential procedure together with Beck's function specification approach. Solution accuracy and the effects of experimental errors are examined using simulated temperature data. It is concluded that a good estimation of space-variable heat transfer coefficient can be made from the knowledge of transient temperature recordings using the proposed inverse heat conduction problem method. The method is also used in a series of numerical experiments to provide the optimum experimental design for condensation heat transfer investigation.     

Inverse problem of estimating the heat flux at the roller/workpiece interface during a rolling process

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to estimate the unknown space-dependent heat flux at the roller/workpiece interface during rolling process from the knowledge of temperature measurements taken within the roller. It is assumed that no prior information is available on the functional form of the unknown heat flux; hence the procedure is classified as the function estimation in inverse calculation. The temperature data obtained from the direct problem are used to simulate the temperature measurements, and the effect of the errors in these measurements upon the precision of the estimated results is also considered. The results show that an excellent estimation on the space-dependent heat flux can be obtained for the test cases considered in this study.     

Estimation of heat generation at the interface of cylindrical bars during friction process

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to estimate the unknown time-dependent heat generation at the interface of cylindrical bars during friction process from the knowledge of temperature measurements taken within the bar. It is assumed that no prior information is available on the functional form of the unknown heat generation; hence the procedure is classified as the function estimation in inverse calculation. The temperature data obtained from the direct problem are used to simulate the temperature measurements, and the effect of the errors in these measurements upon the precision of the estimated results is also considered. Results show that an excellent estimation on the time-dependent heat generation can be obtained for the test case considered in this study. The current methodology can be applied to the prediction of heat generation in continuous-drive friction welding or in breaking systems.     

Estimation of Internal Heat Generation in a Fin Involving All Modes of Heat Transfer Using Golden Section Search Method

The present work deals with the application of the golden section search method (GSSM) for predicting the internal rate of heat generation to reconstruct a given temperature distribution within a rectangular fin involving all modes of heat transfer. The thermal conductivity has been assumed to be temperature-dependent. The forward problem is numerically solved using an implicit fourth-order Runge–Kutta method, whereas, an inverse problem has been solved using GSSM. In conjunction with GSSM, for the inverse analysis, the effect of inverse crime has been addressed using a different solver operating on fifth-order accurate Runge–Kutta method than that used for synthesizing the input data. A case study of Hastelloy generally used in gas turbine applications is also presented and the effect of measurement error in the temperature distribution has been reported. For pure temperature data, an exact estimation of the internal heat generation rate is done, whereas, even with noisy data, a satisfactory estimation of the heat generation rate is also achieved which is verified from the reconstructed temperature distributions.     

生物组织热边界条件反演研究

对肿瘤热疗过程中生物组织表面热流及内部温度协同反演进行了研究。首先介绍了激光辐照下生物组织内部光热传输模型，并采用有限体积法和离散坐标法相结合求解生物组织内光热传输问题。然后介绍了模糊推理方法基本原理，并采用改进分散模糊推理方法同时反演了激光诱导肿瘤热疗过程中生物组织表面入射热流及内部温度场。最后分析了热流形式和测量误差对反演结果的影响。结果表明，改进分散模糊推理方法可以准确地同时反演组织表面热流及内部温度分布，并具有较强稳定性和抗误差干扰能力。     

A three-dimensional inverse problem in estimating the applied heat flux of a titanium drilling – Theoretical and experimental studies

The applied heat flux on the drilling surface of drilling tool is estimated in the present three-dimensional inverse heat conduction problem. The inverse algorithm utilizing the Steepest Descent Method (SDM) and a general purpose commercial code CFX4.4 is applied successfully in this study based on the simulated and measured temperature distributions with time at four sensors embedded on the drilling surfaces. The numerical experiments are considered at the first stage to illustrate the validity of inverse determination of the unknown heat flux using exact and error measurements. Experimental data are then used to estimate the actual heat flux along the drilling edge at two different drill peripheral cutting speeds. Results of both the numerical and experimental examinations show that the reliable estimated heat flux can be obtained by using the present inverse algorithm.     

A Markov Chain Monte Carlo-Metropolis Hastings Approach for the Simultaneous Estimation of Heat Generation and Heat Transfer Coefficient from a Teflon Cylinder

This paper reports the use of Markov Chain Monte Carlo (MCMC) and Metropolis Hastings (MH) approach, to solve an inverse heat transfer problem. Three-dimensional, steady state, conjugate heat transfer from a Teflon cylinder of dimensions 100 mm diameter and 100 mm length with uniform volumetric internal heat generation is considered. The goal is to estimate volumetric heat generation and heat transfer coefficient, given the temperature data at certain fixed location on the surface of the cylinder. The internal volumetric heat generation is specified as input and the temperature and heat transfer coefficient values are obtained by a numerical solution to the governing equation. The temperature values also depend on heat transfer coefficient which is obtained by solving Navier–Stokes equation to obtain flow information. In order to reduce the computational cost, a neural network is trained from the computational fluid dynamics simulations. This is posed as an inverse problem wherein volumetric heat generation and heat transfer coefficient are unknown but the temperature data is known by conducting experiments. The novelty of the paper is the simultaneous determination of volumetric heat generation and heat transfer coefficient for the experimentally measured steady-state temperatures from a Teflon cylinder using MCMC-MH as an inverse model in a Bayesian framework and finally, the estimates are reported in terms of mean, maximum a posteriori, and the standard deviation which is the uncertainty associated with the estimated parameters.