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# 02 Para Gleici - item5-01

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Research paper

Experimental investigation of thermal aspects in a cutting tool using comsol and inverse problem

R.F. Brito a, S.R. Carvalho b, S.M.M. Lima E Silva a, *Heat Transfer Laboratory e LabTC, Institute of Mechanical Engineering e IEM, Federal University of Itajub a e UNIFEI, Campus Prof. Jos e Rodrigues Seabra,

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Nonlinear inverse problem and COMSOL to estimate heat ﬂux on a turning cutting tool. Improvements on previous work to study the complex geometry of machining processes. Several tests using cemented carbide tools were performed to check the methodology. COMSOL adjusts any boundary conditions and models the geometries.

article i nf o

Keywords: COMSOL Inverse problems Machining process Heat ﬂux estimation Cutting tool abstract

The direct measurement of the temperature in a machining process is difﬁcult to accomplish due to the movement of the piece as well as the presence of chips. Thus, the use of inverse heat conduction techniques convey a good alternative to obtain these temperatures, since these techniques allow the use of experimental data obtained from accessible regions. This work proposes the use of a nonlinear inverse problem technique in connection with COMSOL to estimate the heat ﬂux and the temperature ﬁeld on a turning cutting tool in transient regime. The main purpose of the present work is to show the improvements performed in relation to the authors’ previous work to develop the complex geometry of a machining process. Speciﬁcation function, which is an inverse problem technique, was implemented in a MATLAB program to estimate the heat ﬂux applied on the tool, from the experimental temperature records. Once the heat ﬂux is known, COMSOL is again utilized to obtain the temperature ﬁeld on the cutting tool. A comparison of the numerical and experimental temperature results validates the methodology. © 2015 Elsevier Ltd. All rights reserved.

1. Introduction

Several engineering processes have their performance and quality affected by high temperature values. A typical example is the machining process in which cutting tool temperatures may be higher than 900 C [1]. High temperatures change the microstructure and physical properties of the tool during machining, thus reducing their capacity to resist mechanical stress [2]. The direct consequence of these alterations is the reduction of their lifespan and performance. This leads to high operation costs and reduction of the end product quality. The right knowledge of the temperature values and applied heat ﬂux, in this kind of process, results in advantages like the development of more efﬁcient cooling techniques as well as better speciﬁcations of the cutting parameters in machining processes. These temperatures have a controlling inﬂuence on the wear rate of the cutting tool as well as on the friction between the chip and the tool. However, the direct measurementof the temperature in a machining process is difﬁcult to accomplish due to the movement of the piece as well as the presence of chips. The application of inverse heat conduction techniques has proven to be a good option to achieve these temperatures. Inverse problems consist of obtaining the value of a variable through the measurement of another variable measured directly [3]. These

E-mail addresses: rogbrito@unifei.edu.br (R.F. Brito), srcarvalho@mecanica.ufu br (S.R. Carvalho), metrevel@unifei.edu.br (S.M.M. Lima E Silva).

Contents lists available at ScienceDirect

Applied Thermal Engineering journal homep age: w.elsevier.com/l ocate/apthermeng techniques often use optimization algorithm in order to minimize the error between the calculated and real value of the variable in question. Nowadays, several researchers have proposed the combination of inverse techniques and numerical heat transfer solutions to analyze the thermal ﬁelds during machining processes.

Conveying a greater availability of computational resources, the use of numerical methods gained terrain, and it did not take long before they started being used, along with experimental methods in the studies of temperature ﬁelds on cutting tools. A threedimensional ﬁnite difference-based model to predict temperature in machining processes was presented in Ulutan et al. [4]. The FDM based model proposed in this paper offered very rapid and reasonablyaccurate solutions. The simulated results were validated with infrared thermal measurements which were determined from the machining of AISI 1050 and AISI H13 materials under various cutting conditions. In the study of Wang et al. [5] an analytical and numerical model for cutting temperature prediction of 316L stainless steel was developed. The simulation model was set up in commercial FEM software of Abaqus 6.8, which is good at nonlinear dynamic calculation. An ALE ﬁnite element model, which combines the advantages of both Lagrangian and Eulerian techniques, was used. The JohnsoneCook plasticity model was used to model the workpiece material. The analytical modeling and FEM modeling results match very well. In Yang et al. [6] the temperature distribution of the micro-cutter in the micro-end-milling process was investigated by numerical simulations and experimental approach. Micro-end-milling processes were modeled by the threedimensional ﬁnite element method coupling thermalemechanical effects. The micro-cutter cutting temperature distribution, the effect of various tool edge radii on cutting force, and the effective stress during micro-end-milling of aluminum alloy Al2024-T6 using a tungsten-carbide micro-cutter were investigated on. The simulation results showed that the greater the tool edge radius the higher cutting forces, while the effective stress and mean cutting temperature decrease slightly.

Inverse techniqueshave alreadybeenused tostudytemperature ﬁelds on a cutting tool. The solution of a three-dimensional inverse heatconductionproblemusingan EvolutionaryAlgorithm(EA)was demonstrated in Woodbury et al. [7]. The heat ﬂux on the tool during the turning process was determined by using evolutionary operations combined with measured temperatures on the tool surface. The three-dimensional conduction in the tool and tool holder was simulated using FLUENT. In Luchesi and Coelho [8],a n inverse method was proposed to estimate the heat sources in the transient two-dimensional heat conduction problem in a rectangular domain with convective bounders. The nonhomogeneous partial differential equation (PDE) is solved by using the Integral

Transform Method. The test function for the heat generation term was obtained by the chip geometry and thermomechanical cutting. Then the heat generation term was estimated by the conjugated gradient method (CGM) with adjoint problem. The sequential function speciﬁcation method was used to estimate the transient heat ﬂux imposed on the rake face of a cutting tool during the cutting operation with two different assumptions [9]. In one of them, the thermal conductivity is assumed to be constant, and in the other one it varies with the temperature. The cutting tool was modeled as a three-dimensional object. Simulated temperature data was used to recover the heat ﬂux on the cutting tool surface using linear as well as nonlinear solutions.

This work proposes the use of inverse problem techniques with thecommercialsoftwareCOMSOL®5.0toestimatetheheatﬂuxand thetemperatureﬁeldinthecontactareaundertransientregime,ina turning cutting tool. A MATLAB program, with the Speciﬁcation Functiontechnique,wasdevelopedtoestimatetheheatﬂuxapplied on the cutting tool, by usingexperimental temperaturerecords.The nonlinear problem was considered which means that the thermal model took into account the dependence of the thermal properties on temperature. The validation of the proposed methodology was accomplished in controlled experiments in laboratory.

2. Theoretical formulation 2.1. Temperature model

The problem dealt with in this work is represented by Fig. 1a, which shows a set consisting of a hard metal cutting tool, a wedge positioned under the cutting tool between the tool and the tool holder. There is also a staple and a bolt to ﬁx the set. Fig.1a presents the schematic model for the thermal problem of machining. The heat generation during the machining process is indicated by a distribution of unknown heat ﬂux q”(x,y,t), over the arbitrary area by x and y. A blown up view of the set is shown in Fig. 1b.

The heat diffusion equation ruling this problem is the nonlinear transient three-dimensional system given as:

vx kðTÞvT vx þ v vy kðTÞvT vy þ v vz kðTÞvT vz ¼ rcðTÞvT vt (1) subject to the following boundary conditions kðTÞvT vz on the contact interface with the workpiece (Fig. 1b),

Nomenclature c speciﬁc heat, WsKg 1 K 1 F objective function h heat transfer coefﬁcient, Wm 2 K 1 k thermal conductivity, Wm 1 K 1 M general time index, s q 0 unknown heat ﬂux, Wm 2 qM estimated heat ﬂux, Wm 2 r number of future time steps

T numerical temperature, C t time, s

T∞ the medium temperature, C

T0 initial temperature, C Y experimental temperatures, C x Cartesian coordinate, m y Cartesian coordinate, m z Cartesian coordinate, m

Greek a thermal diffusivity, ms 2 h the outward drawn normal to the surface

Subscripts j index of sensors p index of future time steps

Superscript np number of points ns number of sensors

Fig. 1. a) Thermal problem scheme and b) detail of the contact interface between the tool and the workpiece. Fig. 2. a) The tetrahedral grid with 108058 elements and b) a closer view.

Fig. 3. Sketch of the experimental apparatus used in the validation.

Fig. 4. a) Experimental and estimated heat ﬂux, b) experimental and calculated temperatures, and c) temperature residuals. Fig. 5. Experimental apparatus used to acquire the temperature signals in the tool during machining.

kðTÞvT vh ¼hðT T∞Þ; intheremainingregionsof theset (3) and having the following as the initial condition where T is the calculated temperature, h is heat transfer coefﬁcient byconvection, T∞ the room temperature, q 0 theunknown heatﬂux, and k(T) and c(T) temperature dependent thermal conductivity and speciﬁc heat, respectively.

The direct problem consists in solving the heat diffusion equation according to the boundary conditions (Eqs. (1)e(4)). The COMSOL® 5.0 program, which solves thermal problems by using the ﬁnite element method, is used for this purpose. The use of COMSOL for the numerical resolutions of differential equations that rule the physical phenomenon investigated should be highlighted.

Also, COMSOL allows adjusting any boundary conditions, as well as modeling the geometry so as to faithfully represent the system investigated as presented in Fig. 2.

2.2. The inverse problem

The inverse technique adopted in this work is the Speciﬁcation Function. As the Inverse Heat Conduction Problem (IHCP) at hand is a nonlinear one, sensitivity coefﬁcients are function of qM, and the nextcomponentsofTaylorexpansionwouldnotbeequal tozero(as in the case for linear IHCP). Therefore, it is necessary to recalculate the sensitivity coefﬁcients at each time step [9,10]. In the Speciﬁcation Function technique, a determined value of futuretime steps r is used to estimate the heat ﬂux at present instant [3]. In the resolution of the inverse problem, the Speciﬁcation Function searches for a heat ﬂux value that minimizes the objective function given in Eq. (5), for each time step

F ¼ Xr

Xns

3. Validation of the methodology proposed

Ag reat difﬁculty in the solution of inverse heat conduction problems is the validation of the technique used. This difﬁculty is inherent to the problem, once the validation of the estimated

Fig. 6. a) Tool and tool holder assembly, b) detail of the positions of the thermocouples welded to the tool and c) a close view of the origin and orientation.

Table 1 Locations of the thermocouples shown in Fig. 6b.

Table 2 Cutting conditions.

Cutting parameters Test 1 Test 2

Feed rate 0.138 m/rev 0.138 m/rev Cutting speed 135.47 m/min 135.47 m/min Depth of cut 5.0 m 1.0 m Final diameter 72 m 76 m

Fig. 7. a) Image treatment of the contact area and b) contact area on the computational model.

Fig. 8. Comparison of three repeated experiments for the same turning condition on the chip-tool interface a) heat ﬂux and b) temperature. Fig. 9. a) Estimated heat ﬂux and b) comparison between experimental and estimated temperatures for thermocouples T , T and T .

heat ﬂux requires the previous knowledge of the experimental heat ﬂux. It is observed that in real inverse problems, as in machining process, the experimental heat ﬂux is not known. Thus, an alternative for the validation of the inverse technique is to carry out a controlled experiment, in which the heat ﬂux and the temperature are measured at the cutting tool (Fig. 3). In this case, before the analysis of the real machining process, a cemented carbide tool with dimensions of 0.0127 0.0127 0.0047 m was used for the controlled experiment. A heat ﬂux transducer and two thermocouples previously calibrated and a kapton electric heater were used on this tool. This heater was connected to a digital power supply (MCE). The heat ﬂux transducer was located between the heater and the tool in order to measure the heat supplied to the tool. The heat ﬂux and temperatures signals were acquired by a HP Series 75000 data acquisition system, controlled by a PC. Temperatures were measured by using type K thermocouples (30 AWG) welded by capacitive discharge and calibrated by using a bath temperature calibrator ERTCO with a stability of ±0.01 C.

The solution of the three-dimensional heat diffusion equation is obtained with the use of the ﬁnite element method, through the commercial software COMSOL® 5.0. For this, a computational thermal model was used to faithfully represent the experimental model of the sample. This model was discretized in a computational tetrahedral mesh. The validation results are presented in Fig. 4aec. Fig. 4a presents a comparison between the experimental and estimated ﬂux,whereas Fig. 4b compares the experimental and numerical temperatures. Fig. 4c presents the deviation between the experimental and numerical temperatures. The Speciﬁcation Function method for r equal to 10 future time steps was used in Fig. 4a. In this validation the values of the temperature-dependent thermal properties of the cemented carbide tool (WC) were obtained from Grzesik et al. [1].

4. Experimental assembly in a real machining process

The machining test wascarried out ina conventional latheIMOR

MAXIeIIe520e6CV without coolant. The material used in the experimental test was a cylindrical gray cast iron bar FC 20 EB 126 ABNT of 7 m in external diameter. The insert and tool holder used were cemented ISO SNUN12040408 K20/Brassinter and ISO CSBNR 20K12/SANDVIK COROMAT, respectively. The temperatures were measured on accessible locations of the insert, the shim and the toolholder byusing type K thermocouples (30 AWG) linked to a data acquisition system HP 75000 Series B controlled by a PC (Fig. 5). The insert-tool holder assembly is shown in Fig. 6a. Table 1 presents the location of the thermocouples shown in Fig. 6b. Fig. 6c presents the location of the origin and orientation of the axes.

(Parte **1** de 2)