research article analyses of effects of cutting parameters

Research ArticleAnalyses of Effects of Cutting Parameters on Cutting EdgeTemperature Using Inverse Heat Conduction Technique

Marcelo Ribeiro dos Santos1 Sandro Metrevelle Marcondes de Lima e Silva2

Aacutelisson Rocha Machado1 Maacutercio Bacci da Silva1 Gilmar Guimaratildees1

and Solidocircnio Rodrigues de Carvalho1

1 College of Mechanical Engineering Federal University of Uberlandia Campus Santa Monica Bloco MAvenida Joao Naves de Avila 2121 38408-100 Uberlandia MG Brazil

2 Institute of Mechanical Engineering Federal University of Itajuba Campus Professor Jose Rodrigues SeabraAvenida BPS 1303 37500-903 Itajuba MG Brazil

Correspondence should be addressed to Solidonio Rodrigues de Carvalho srcarvalhomecanicaufubr

Received 17 February 2014 Revised 2 April 2014 Accepted 23 April 2014 Published 1 June 2014

Academic Editor Caner Ozdemir

Copyright copy 2014 Marcelo Ribeiro dos Santos et al This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Duringmachining energy is transformed into heat due to plastic deformation of theworkpiece surface and friction between tool andworkpiece High temperatures are generated in the region of the cutting edge which have a very important influence on wear rate ofthe cutting tool and on tool life This work proposes the estimation of heat flux at the chip-tool interface using inverse techniquesFactors which influence the temperature distribution at the AISI M32C high speed steel tool rake face during machining of aABNT 12L14 steel workpiece were also investigated The temperature distribution was predicted using finite volume elements Atransient 3D numerical code using irregular and nonstaggered mesh was developed to solve the nonlinear heat diffusion equationTo validate the software experimental tests were made The inverse problem was solved using the function specification methodHeat fluxes at the tool-workpiece interface were estimated using inverse problems techniques and experimental temperatures Testswere performed to study the effect of cutting parameters on cutting edge temperatureThe results were compared with those of thetool-work thermocouple technique and a fair agreement was obtained

1 IntroductionNowadays several researchers proposed the combination ofinverse techniques and analytical or numerical heat transfersolutions to analyze the thermal fields during machiningprocesses One method to study the heat transfer problem isto adopt a known heat flux and calculate the temperature atthe chip-tool interface from the solution of the heat diffusionequation In literature this methodology is called directproblem in heat transfer However during machining theexperimental heat flux is unknown and inverse techniqueshave to be used to predict this parameter This proposal esti-mates the transient heat flux with a numerical model basedon the heat diffusion equation using inverse techniques andexperimental temperatures measured at accessible regions ofthe sample

In Chen et al [1] the inverse technique used was basedon the sequential function specification method proposedby Beck et al [2] The numerical technique used was thefinite volume method and the temperatures were obtainedby inserting a thermocouple in the tool In both methodsthe model took into account only the insert and some dis-crepancies were observed between calculated and measuredtemperatures

Lazard and Corvisier [3] considered the problem ofestimating the transient temperature and the heat flux atthe chip-tool interface during a turning process using aninverse approach The heat transfer model was based on aquadrupole formulation commonly used to solve ordinarydifferential equations in the Laplace domain The results oftemperature obtained with the analytical model used were

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 871859 11 pageshttpdxdoiorg1011552014871859

2 Mathematical Problems in Engineering

(a)

q998400998400(x y t)

Aq(x y)

h Tinfin uarruarruarr

z

x

y

(b)

x

y

147134

1465

42

(c)

Figure 1 (a) High speed steel tool (b) three-dimensional physical model and (c) tool dimensions in millimeters (mm) where the coordinateldquo119911rdquo is 95 (mm)

in good agreement with those obtained with FLUENT Theauthors assumed that the temperature measurements wereavailable for the inverse analysis

In the work of Yvonnet et al [4] an innovative approachwas proposed The work was based on a simple inverseprocedure to identify both the heat flux flowing into thetool through the rake face and the heat transfer coefficientbetween the tool and the environment during a typicalorthogonal cutting process To determine the heat flux andconvection heat transfer coefficient an iterative Newton-Raphson procedure was used to minimize the error definedby the difference between experimental and calculated tem-peratures Four different tools were used three of themweremanufactured by electrical dischargemachining (EDM)cutting the last slot with different distances between the tooltip and the slot 035 050 and 060mm The last tool wasinstrumented with a thermocouple to measure the averageheat flux flowing into the tool through the rake face

Woodbury et al [5] demonstrated the solution of a three-dimensional inverse heat conduction problem using an evo-lutionary algorithm (EA) The heat flux from the workpieceinto the tool during the turning process was determinedusing evolutionary operations combined with measurementsof surface temperature on the tool The three-dimensionalconduction in the tool and tool holder was simulated usingFLUENT

A numerical prediction of the three-dimensional temper-ature fields inmoving chip stationary tool andmovingwork-piece during machining operations using a finite differencemethod was presented in Ulutan et al [6] First the authorsstudied the chip and tool together to create a heat balancedue to the friction on the rake face Then an investigationof the effect of the chip and tool interface temperature onthe temperature field of the workpiece taking into accountthe heat generated at the shear plane was made A finitedifference model was employed to describe the process andthe results were in good agreement with experimental datapresented in the literature The advantage of this methodin relation to finite element method (FEM) models is thecomputational time which decreased substantially and the

advantage in relation to curve fitting methods is that themethod is based on the physical phenomenon

In Samadi et al [7] the sequential function specificationmethodwas usedwith simulated temperature data to estimatethe transient heat flux imposed on the rake face of a cuttingtool during the cutting operation with two different hypothe-sesThe thermal conductivity was considered constant in oneand in the other it varied with temperature The cutting toolwas modeled as a three-dimensional object The influence ofnonlinearity and different sensor locations were investigatedin order to determine an optimal experimental procedureFinally typical temperature data during turning was used torecover the heat flux at the cutting tool surface consideringlinear and nonlinear solutions

The aim of the present paper is to estimate the heat fluxand calculate the temperature field at the cutting interfaceof the high speed steel tool In addition the influence ofthe cutting parameters (cutting speed cutting depth andfeed rate) on the tool-chip interface temperature was alsoinvestigated The novelty in this work compared to otherspresented in the literature is the joint solution and analysis ofthe following problems a nonlinear tridimensional thermalmodel an inverse technique to estimate the heat flux thethermal analyses of a machining process and the finalcomparison of the results with those obtained from a fullyexperimental methodology proposed to Evangelista Luiz[8] based on the tool-workpiece thermocouple technique(TWTT)

2 The Direct Problem Thermal Model

Figure 1 shows the high speed steel tool the model usedand the dimensions of the tool The interface contact area119860119902(119909 119910) was subjected to the heat flux 11990210158401015840(119909 119910 119905) generatedby contact between the tool and the workpiece At theremaining boundaries a constant convective heat transfercoefficient of 20 (Wm2 K) was considered

The three-dimensional physical problem was solved inCartesian coordinates using finite volume technique with

Mathematical Problems in Engineering 3

Table 1Thermal properties of high speed steel tool according to Taylor Specials Steels Ltda (2009) Material AISI M32 C with 10 of cobalt

Temperature range (∘C) 0 le 119879 le 400 119879 gt 400

Thermal conductivity (WmK) 00105 119879 + 238 minus0005 119879 + 30

Thermal diffusivity (m2s) minus503 times 10minus10119879 + 702 sdot 10

minus6minus594 times 10

minus9sdot 119879 + 919 times 10

minus6

irregular mesh The objective is to obtain the temperaturedistribution in the tool using the direct problem and infollowing estimate the heat flux generated at the chip-toolinterface with inverse techniques

The choice of the high speed steel tool is due to its largeapplication in industry and also because Evangelista Luiz [8]presented a thermal analysis using toolwork thermocoupletechnique (TWTT) thus permitting the comparison with theresults obtained using a different technique

The thermal problem shown in Figure 1(b) is described bythe heat diffusion equation as in Carvalho et al [9]

120597

120597119909

(120582

120597119879

120597119909

) +

120597

120597119910

(120582

120597119879

120597119910

) +

120597

120597119911

(120582

120597119879

120597119911

) = 120588119862

120597119879

120597119905

(1)

The boundary conditions imposed are

minus120582

120597119879

120597120578

= ℎ (119879 minus 119879infin) (2)

at the regions exposed to the environment and

minus120582

120597119879

120597120578

= 11990210158401015840(119909 119910 119905) (3)

at the interface defined by119860119902 where 120578 is the outward normalin coordinates 119909 119910 and 119911 119879 is the temperature 119879infin is theroom temperature 120582 is the thermal conductivity 120588119862 is thevolumetric heat capacity and ℎ the heat transfer coefficientThe initial condition is given by

119879 (119909 119910 119911 0) = 119879119900 (4)

where 119879119900 is the initial temperature of the tool shim and toolholder

The above equations were implemented in C++ Analgorithm called Inverse3D or Inv3D was developed Thiscomputational algorithm has been developed over the last 14years by the research group of the Laboratory of Heat andMass Transfer College of Mechanical Engineering FederalUniversity of Uberlandia It has been extensively validatedand has led to several articles published in scientific journalsand conferences such as Brito et al [10] Brito et al [11] Sousaet al [12] and Carvalho et al [9]

The thermal properties of the tool obtained from TaylorSpecial Steels Ltd [13] are shown in Table 1

Several factors are responsible for the errors or uncer-tainties in the mathematical model Comparing Figures 1(a)and 1(b) there are several simplifications in geometry of thethermal model compared to the cutting tool The model didnot include the rake and relief angles typical of any cuttingtool Such simplifications imply an increase in volume of themodel of 147 compared to the tool In spite of this smallincrease no significant changeswere identified in the thermalfield calculated by the model of the cutting tool

As for the uncertainties in the thermalmodel the thermalproperties of the tool were obtained from scientific papersOther sources of uncertainties are the correct location of thethermocouples and the presence of noise in the experimentalsignal of the temperature In this work we opted for the tech-nique of capacitive discharge to weld the thermocouples tothe tool thus minimizing uncertainty regarding the thermalcontact resistance

An HP 75000 series B data acquisition system withE1326B voltmeter controlled by a PC connected to a stabi-lized power source was used The temperature acquisitioninterval was 025 seconds Based on the procedures and theequipment adopted it was estimated that the measurementerror of the entire system (thermocouplemultimeter) wasless than plusmn03∘C

Also an average ℎ of 20Wm2 K for the entire surfaceof the tool was used The correct determination of the heattransfer coefficient by convection is not an easy task Ananalysis of the influence of this important parameter on thecalculated temperature at the cutting interface is shown inFigure 2

Figure 2(a) shows that the heat transfer coefficients byconvection (ℎ) in the range tested (10ndash30Wm2 K) has littleinfluence on the final temperature at the cutting interfaceAdopting an average ℎ of 20Wm2 K as reference andcomparing the calculated temperature with those obtainedfor other values of ℎ a maximum deviation of less than 074was obtained during machining as shown in Figure 2(b)With this result it was concluded that for the range of valuesof ℎ considered the calculation of the temperature at thecutting interface was not compromised Hence the value of20Wm2 K was adopted

Figure 3 shows the heat transfer rate by convection at thecutting interface for different values of ℎ

Figure 3 shows that as ℎ increases the rate of heat transferbecomes more significant Besides within the range of valuesanalyzed (10ndash30Wm2 K) a maximum difference of only 1 Win relation to ℎ = 20Wm2 K occurred Thus it is concludedthat ℎ has little influence on the interface temperature Theenergy lost by convection represents 61 of the energygenerated at the cutting interface (ℎ = 20Wm2 K)

3 The Inverse Problem FunctionSpecification Procedure

The inverse technique adopted in this work is the SequentialFunction Estimation Beckrsquos Method [2] This techniquerequires the sensitivity coefficients (120601) which are the deriva-tives of the calculated temperatures (119879) with respect to theheat flux (11990210158401015840)


0 20 40 60 80 100 120 140

Time (s)

Tem

pera

ture

(∘C)

700

600

500

400

300

200

100

0

h = 10 (Wm2K)

h = 18 (Wm2K)

h = 20 (Wm2K)

h = 22 (Wm2K)

h = 30 (Wm2K)

(a)

0 20 40 60 80 100 120 140

Time (s)

6

4

2

0

minus2

minus4

minus6

R = Th=20 minus Th=30R = Th=20 minus Th=22


Max

imum

dev

iatio

n R

(∘C)

(b)

Figure 2 Analysis of the influence of the heat transfer coefficient by convection (a) cutting interface temperature for different values of ℎand (b) analysis of uncertainty considering ℎ = 20Wm2 K as reference Cutting conditions feed rate 0138mmrot cutting speed 142mmin(900 rpm) and depth of cut 10mm

0 20 40 60 80 100 120 140

Time (s)

5

4

3

2

1

0

Hea

t tra

nsfe

r rat

e (W

)

h = 10 (Wm2K)

h = 18 (Wm2K)

h = 20 (Wm2K)

h = 22 (Wm2K)

h = 30 (Wm2K)

Figure 3 Heat transfer rate by convection for different valuesof ℎ Cutting conditions feed rate 0138mmrot cutting speed142mmin (900 rpm) and depth of cut 10mm

Numerically the sensitivity coefficients (120601) were calcu-lated at the thermocouples positions (Table 2) as shown inFigure 4(a)The direct problem is solved considering (1) with11990210158401015840= 1 (unit value) initial temperature equal to zero (119879 =

0) ℎ equal to 20Wm2 K and constant thermal propertiescalculated for 119879 = 30∘C using Table 1 The numerical tech-nique is based on Duhamelrsquos summation and Stolz method[2]

Basically the Sequential Function Estimation minimizesa squared error function based on numerical (119879) and exper-imental temperatures (119884) to estimate the heat flux (11990210158401015840) at

Table 2 Thermocouple locations following the coordinate systemdefined in Figure 1

Position Thermocouple1 2 3 4 5

119909 (mm) 061 270 00 330 200119910 (mm) 720 850 90 700 340119911 (mm) 00 00 50 950 950

chip-tool contact area for each time step (119872) The basic ideais to reduce a continuous function to a set of parameters byspecifying an underlying nature of the function In this worka constant sequential function was adopted Thus accordingto Beck et al [2] the heat flux can be estimated as given in

11990210158401015840

119872=

sum119903

119894=1sum119869

119895=1(119884119895119872+119894minus1 minus

119879119895119872+119894minus1|119902119872=sdotsdotsdot=0

) 120601119895119894

sum119903

119894=1sum119869

119895=1120601119895119894

2 (5)

where 119872 is the time 119869 is the number of sensors 119903 isthe number of future time steps and 119884 and 119879 are theexperimental and calculated temperatures respectively

In the estimation process 10 future time steps were usedfor each cutting condition The transient heat flux for eachexperiment was estimated as shown in Figure 4(b)

Finally according to Figure 4(c) the direct problem isagain solved considering the nonlinear thermal model (1)in which the thermal properties vary with temperatureresulting in the temperature distribution in the cutting tool

4 Experimental Procedure

The machining test was carried out in a conventional IMORMAXI-II-520-6CV lathe without coolant The material used


Direct problem Input data

Initial and boundary conditions (2) and (3)T0 = 0 (∘C) and q998400998400 = 1 (Wm2)

Thermal properties calculated for T = 30∘C

Time = 2 nt

Time = 2 nt

Solve linear system (1)

Output data

Time = ntYes

No

Sensitivity coefficients

Estimated heat flux

Experimental temperatures

Future time steps ldquor = 10rdquo

Function

specification

Solve (5)


(a)

(b)

(c)


Calculation of thermal properties Table (1)

Solve linear system (1)Calculation of thermal properties Table (1)

Yes

Yes

No

No

Output data

Time = nt

T converged

Numerical temperatures

Initial and boundary conditions (2) to (4)

Figure 4 Computational algorithm (a) calculation of the sensitivity coefficients (b) Beckrsquos method for the solution of the inverse problem(c) solution of the nonlinear thermal model

(a) (b)

Figure 5 (a) Thermocouples on the tool and (b) equipment

in the experimental tests was cylindrical ABNT 12L14 [8] barswith an external diameter of 502mm Figure 5 shows thetemperatures measured at accessible locations of the insertusing type T thermocouples and an HP 75000 series B dataacquisition system with an E1326B voltmeter controlled by aPC

Table 2 gives the thermocouple locations according tothe coordinate system shown in Figure 1 To evaluate theinfluence of the machining parametersmdashdepth of cut (119886119901)feed rate (119891) and cutting speed (119881119888)mdashon temperature at chip-tool interface the following tests given in Tables 3 4 and 5were made

The chip-tool contact area of each test was defined byan imaging system The device consists of a Hitachi model

Table 3 Depth of cut (constant parameters 119891 = 0138mmrot and119881119888 = 56 mmin)

Unit (mm)119886119901 05 10 15 20

KP-110 CCD video camera an AMD K6 450MHz computerand a software processer of images (the Global Lab Image)Figure 6 shows a photograph of the contact area (119860119902 = 119871 sdot119867)for cutting conditions 119886119901 = 10mm 119891 = 0138mmrot and119881119888 = 56mmin (scale 25 1)

Figure 7 shows the results of the chip-tool contact areasfor the cutting conditions of Tables 3 to 5


Figure 6 Chip-tool contact area for cutting conditions 119886119901 = 10mm 119891 = 0138mmrot and 119881119888 = 56mmin scale 25 1

16

14

12

1

08

06

04

02

00 25 50 75 100 125 150

Vc (mmmin)

Con

tact

area

(mm

2)

(a)

18

0 05 1 15 2 25

16

14

12

1

08

06

04

02

0

Con

tact

area

(mm

2)

ap (mm)

(b)

f (mmrot)0138 0162 0176 0204 0242 0298

18

16

14

12

10

08

06

Con

tact

area

(mm

2)

(c)

Figure 7 Chip-tool contact area for the following conditions (a) 119886119901 = 10mm 119891 = 0138mmrot and 119881119888 variable (b) 119891 = 0138mmrot119881119888 = 56mmin and 119886119901 variable (c) 119886119901 = 10mm 119881119888 = 56mmin and 119891 variable

Table 4 Feed rate (constant parameters 119886119901 = 10mm and 119881119888 =56mmin)

Unit (mmrot)119891 0138 0162 0176 0204 0242 0298

Increase of the cutting parameters increases the chip-tool contact area The development of an accurate methodto measure the chip-tool contact area represents a greatchallenge because direct observations during cutting are notpossible Most of the available theories of the identificationof the chip-tool contact area are derived from the study of

the interface after cutting had been interrupted In this workthe methodology is also based on the analysis of the contactarea after cuttingHowever evenwith the enlarged areas fromanalysis software identification of the contact area is notan easy task and requires experience and knowledge of theresearcher Normally approximate areas are obtained becauseeven with the various existing theories it is difficult or evenimpossible to identify the real chip-tool contact area

In this work the area was approximated as a rectangle inwhich the energy is distributed evenly Thus

11990210158401015840(119909 119910 119905) = 119902

10158401015840(119905) (6)


20

15

10

5

0

0 20 40 60 80 100 120 140

Time (s)

Hea

t tra

nsfe

r rat

e (W

)

q998400998400(x y t) =

q998400998400(x y t) =

(6)(7)

(a)

700

600

500

400

300

200

100

00 20 40 60 80 100 120 140

Time (s)

Tem

pera

ture

(∘C)

TA119902calculated with


(6)(7)

(b)

Figure 8 (a) Comparison of the average heat transfer rates and (b) temperatures at the cutting interface

Table 5 Cutting speed (constant parameters 119886119901 = 10mm and 119891 = 0138mmrot)

Unit (mmin)119881119888 44 71 88 112 142 177 221 284 353 442 56 883 112 142

However metallographic techniques such as thoseapplied by Dearnley [14] showed that the correct methodol-ogy would be to adopt an irregular area and a nonuniformheat flux distribution at the cutting interface Howeverthe combination of both parameters in the thermal modelthat is irregular heat flux and irregular area would leadto countless possible results Thus as the area had beenpreviously measured it was decided to change only thedistribution of the heat flux at the cutting interface Thethermal model was simulated in two stages initially auniform heat flux at the cutting interface was adopted (6)and in the following stage an exponential heat flux was usedas in

11990210158401015840(119909 119910 119905) = 119902

10158401015840

119886sdot 119890(minus11198972

119909)sdot(119909minus119909119900)

2+(minus1119897

2

119910)sdot(119910minus119910119900)

2

(7)

The variables119909 and119910define the coordinates of the contactarea 11990210158401015840

119886is the maximum value of instantaneous heat flux at

the contact area 119897119909 and 119897119910 are the dimensions of the contactarea and 1199090 and 1199100 are the points of maximum value Thevariables 119897119909 119897119910 119909119900 and 119910119900 were adjusted for each cuttingcondition using the contact areas shown in Figure 7

Thus with the cutting parameters the chip-tool contactarea and the experimental temperatures measured for eachcase this work proposes to solve the inverse problemestimate the heat flux at the interface and obtain the three-dimensional temperature distribution in the tool The resultswere comparedwith those obtained by the experimental tool-work thermocouple method [8]

5 Results and Discussions

Figure 8 shows the heat transfer rate and the average temper-ature at the cutting interface during the most severe cuttingcondition feed rate 119891 = 0138mmrot cutting speed 119881119888 =142mmin (900 rpm) and cutting depth 119886119901 = 10mm

Figure 8(a) shows that the average heat transfer rateestimated with an exponential heat flux (7) is quite similar tothat estimated with a uniform heat flux (6) Consequently theaverage temperatures at the cutting interface are quite similar(Figure 8(b))

Figure 9 shows a comparison of experimental and calcu-lated temperatures of each methodology

Figure 9(a) shows good agreement between calculatedand experimental temperatures However Figure 9(b) showsthat the residue is lower for temperatures calculated withexponential heat flux (7)

Figure 10 shows the temperature profile in the tool for thefollowing cutting conditions feed rate 119891 = 0138mmrotcutting speed 119881119888 = 142mmin (900 rpm) and cutting depth119886119901 = 10mm where the maximum temperature calculated atthe chip-tool interface was 600∘C

Analyzing Figures 10(b) and 10(c) the isotherms in a realmachining process tend to behave as shown in Figure 10(c)that is the maximum temperature in the contact area isat a certain distance from the main cutting edge as foundin the literature such as Dearnley [14] Thus the use of anexponential heat flux gives results more consistent with thoseidentified in a real turning process


Y1T1T1

calculated with calculated with

0 20 40 60 80 100 120

Time (s)

Tem

pera

ture

(∘C)

140

120

100

80

60

40

20

(6)(7)

(a)

4

3

2

1

0

minus1

minus2

minus3

minus4

minus5

minus6

R = Y1 minus T1R = Y1 minus T1

0 20 40 60 80 100 120


Time (s)

Resid

ual t

empe

ratu

reR

(∘C)

(6)(7)

(b)

Figure 9 (a) Comparison between experimental and calculated temperatures and (b) residual temperatures

Figure 11 shows the average maximum temperature at thecutting interface for the cutting conditions defined in Tables3 to 5 These values were calculated using the numericalmethodology proposed in this work (considering (6) and (7)uniform and exponential heat flux) and measured with theexperimental technique TWTT [8]

As in Trent [15] the temperature at the cutting interfaceincreases with the increase in cutting parameters In otherwords increasing the cutting parameters increases the chip-tool contact area and the rate of deformation thus generatingmore energy and consequently higher temperatures at thecutting interface

Figure 11 also shows the difference between temperatureprofiles measured with TWTT and calculated by numericaltechniques With the experimental TWTT technique as areference there is a significant difference between experi-mental and numerical temperatures Figure 11(c) shows thatthis difference decreases when the cutting speed increasesTrent [15] showed that cutting speeds between 100 and200mmin give temperatures at cutting interface between600∘C and 800∘C which agrees with the values obtained inthis work

Both TWTT and numerical methodology have sourcesof errors which can influence directly the measured andcalculated temperatures which can justify the differencesshown in Figure 11

For the numerical methodology the uncertainties arerelated to the dimensions and the simplifications adopted tosimulate the thermal behavior of tool the correct identifica-tion of the thermal properties of the high speed steel the con-vective heat transfer coefficient the measured temperaturesduring turning and the correct identification of the chip-toolcontact area for each cutting condition

According to Evangelista Luiz [8] the uncertainties inTWTT technique are related to the calibration of the systemand the assembly of the experimental components TheTWTT basically consists of an electric circuit which involvesthe tool the workpiece and the lathe The tool and theworkpiece forming the thermocouple had to be previouslycalibrated as any conventional sensor and the experimentalprocedure is strongly dependent on the equipments and theability of the operator Besides during turning a mercurychamber had to be used to connect the components of thesystem due to the rotation of the workpiece as shown inFigure 5(a) Also the attrition between tool and workpiecegenerates noise in the signal of the temperature that hadto be minimized using statistical tools to remove excessivenoise and to define the mean temperature and the standarddeviation

6 Conclusions

This work is an interdisciplinary study involving two majorareas of mechanical engineering heat transfer and manu-facturing processes Based on the knowledge of these twoareas a new computational algorithm for solving problemsof heat transfer applied to manufacturing processes focusingon turning process was developed

The simulations optimize the numerical model proposedanalyzing the numerical mesh computational cost conver-gence quality of numerical results and possible sources oferror in order to obtain a favorable cost-benefit solution of thethermal problem Furthermore in experiments in this studyit was sought to minimize the likely sources of experimentalerrors


(b) (c)

(a)

X Y

Z

Figure 10 Temperature profile for feed rate 119891 = 0138mmrot cutting speed 119881119888 = 142mmin (900 rpm) and cutting depth 119886119901 = 10mm(a) tool (b) cutting interface temperatures for exponential heat flux (7) and (c) cutting interface temperatures for uniform heat flux (6)

Regarding the thermal effects studied it was possible tocalculate and analyze the three-dimensional temperature dis-tribution in the thermal machining model as well as at chip-tool interface The numerically temperatures were comparedwith experimental data which can increase the reliability andcredibility of the results found Besides temperature in thisstudy the heat flux at the contact interface which allowed aquantitative analysis of the thermal energy generated in themachining process was estimated

This work studied the thermal effects during turning andalso analyzes the influence of the cutting conditions (cuttingspeed feed rate and depth of cut) on the temperature gen-erated at chip-tool interface Analyzing the results as in theliterature the temperature at the cutting interface increaseswith the increase in cutting conditions The results do not fit

perfectly with those presented by Evangelista Luiz [8] usingthe experimental method of tool-workpiece thermocoupletechnique This fact is attributed to the possible sources oferror in each methodology which have direct influence onthe results Thus there is no existing technique that canbe universally accepted as a standard There are attemptsto understand the fundamentals of the thermal exchangesduring turning and it is believed that the understanding isthe next step to predict the performance of a manufacturingprocess [16]

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper


450

400

350

300

04 06 08 10 12 14 16 18 20 22

YTA119902

calculated with TA119902

calculated with

Tem

pera

ture

(∘C)

04 06 08 10 12 14 16 18 20 22

140

120

100

80

60

40

20

R = YTWTT

TWTT

minus TA119902with

R = Y minus TA119902with

TWTT

ap (mm) ap (mm)

Resid

ual t

empe

ratu

reR

(∘C)

(6)(7)

(6)(7)

(a)

015 020 025 030 035

f (mmrot)

100

80

60

40

20

0

minus20

minus40

minus60

550

500

450

400

350

015 020 025 030 035

f (mmrot)

YTA119902


calculated with

R = YTWTT

TWTT

minus TA119902with


TWTT

Resid

ual t

empe

ratu

reR

(∘C)

Tem

pera

ture

(∘C)

(6)(7)

(6)(7)

(b)

120

0

0 20 40 60 80 100 120 140 160

Vc (mmin)

100

80

60

40

20

minus20

minus40

700

600

500

400

300

200

100

0 20 40 60 80 100 120 140 160

Vc (mmin)

YTA119902


calculated with

R = YTWTT

TWTT

minus TA119902with


TWTT

Resid

ual t

empe

ratu

reR

(∘C)

Tem

pera

ture

(∘C)

(6)(7)

(6)(7)

(c)

Figure 11 Chip-tool interface temperature and residual for TWTT and data from (a) Table 3 (b) Table 4 and (c) Table 5


Acknowledgments

The authors thank CNPq FAPEMIG and CAPES for thefinancial support without which this work would not bepossible

References

[1] W C Chen C C Tsao and P W Liang ldquoDetermination oftemperature distributions on the rake face of cutting tools usinga remote methodrdquo International Communications Heat MassTransfer vol 24 pp 161ndash170 1997

[2] J V Beck B Blackwell andC St Clair InverseHeat ConductionIll-Posed Problems Wiley-Interscience New York NY USA1985

[3] M Lazard and P Corvisier ldquoInverse method for transienttemperature estimation duringmachiningrdquo inProceedings of the5th International Conference on Inverse Problems in EngineeringTheory and Practice Cambridge UK 2005

[4] J Yvonnet D Umbrello F Chinesta and F Micari ldquoA sim-ple inverse procedure to determine heat flux on the tool inorthogonal cuttingrdquo International Journal of Machine Tools andManufacture vol 46 no 7-8 pp 820ndash827 2006

[5] K A Woodbury S Duvvuri Y K Chou and J Liu ldquoUseof evolutionary algorithms to determine tool heat fluxes in amachining operationrdquo in Proceedings of the Inverse ProblemsDesign and Optimization Symposium (IPDO rsquo) Miami BeachFla USA 2007

[6] DUlutan I Lazoglu andCDinc ldquoThree-dimensional temper-ature predictions in machining processes using finite differencemethodrdquo Journal of Materials Processing Technology vol 209no 2 pp 1111ndash1121 2009

[7] F Samadi F Kowsary andA Sarchami ldquoEstimation of heat fluximposed on the rake face of a cutting tool a nonlinear complexgeometry inverse heat conduction case studyrdquo InternationalCommunications in Heat and Mass Transfer vol 39 no 2 pp298ndash303 2012

[8] N Evangelista Luiz Usinabilidade do aco de corte facil baixocarbono ao chumbo abnt 12l14 com diferentes nıveis de ele-mentos quımicos residuais (cromo nıquel e cobre) [doctoratethesis] School of Mechanical Engineering Federal Universityof Uberlandia Uberlandia Brazil 2007

[9] S R Carvalho S M M Lima e Silva A R Machado andG Guimaraes ldquoTemperature determination at the chip-toolinterface using an inverse thermal model considering the tooland tool holderrdquo Journal of Materials Processing Technology vol179 no 1ndash3 pp 97ndash104 2006

[10] R F Brito S R Carvalho S M M Lima e Silva and J RFerreira ldquoThermal analysis in TIN and AL

2O3coated iso K10

cemented carbide cutting tools using Design of Experiment(DoE) methodologyrdquo Journal of Machining and Forming Tech-nologies vol 3 pp 1ndash12 2011

[11] R F Brito S R D Carvalho S M M D Lima e Silvaand J R Ferreira ldquoThermal analysis in coated cutting toolsrdquoInternational Communications in Heat and Mass Transfer vol36 no 4 pp 314ndash321 2009

[12] P F B Sousa S R Carvalho and G Guimaraes ldquoDynamicobservers based on Greenrsquos functions applied to 3D inversethermal modelsrdquo Inverse Problems in Science and Engineeringvol 16 no 6 pp 743ndash761 2008

[13] Taylor Specials Steels Ltda 2005 httpwwwtaylorspecial-steelscoukpdfdownloadm35pdfsearch=rsquoM3520thermal20properties

[14] P A Dearnley ldquoNew technique for determining temperaturedistribution in cemented carbide cutting toolsrdquoMetals Technol-ogy vol 10 no 6 pp 205ndash214 1983

[15] E M Trent Metal Cutting Butterworths London UK 2ndedition 1984

[16] A R Machado and M B Silva Usinagem dos Metais 8thedition 2004

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


(a)

q998400998400(x y t)

Aq(x y)

h Tinfin uarruarruarr

z

x

y

(b)

x

y

147134

1465

42

(c)

Figure 1 (a) High speed steel tool (b) three-dimensional physical model and (c) tool dimensions in millimeters (mm) where the coordinateldquo119911rdquo is 95 (mm)

in good agreement with those obtained with FLUENT Theauthors assumed that the temperature measurements wereavailable for the inverse analysis

In the work of Yvonnet et al [4] an innovative approachwas proposed The work was based on a simple inverseprocedure to identify both the heat flux flowing into thetool through the rake face and the heat transfer coefficientbetween the tool and the environment during a typicalorthogonal cutting process To determine the heat flux andconvection heat transfer coefficient an iterative Newton-Raphson procedure was used to minimize the error definedby the difference between experimental and calculated tem-peratures Four different tools were used three of themweremanufactured by electrical dischargemachining (EDM)cutting the last slot with different distances between the tooltip and the slot 035 050 and 060mm The last tool wasinstrumented with a thermocouple to measure the averageheat flux flowing into the tool through the rake face

Woodbury et al [5] demonstrated the solution of a three-dimensional inverse heat conduction problem using an evo-lutionary algorithm (EA) The heat flux from the workpieceinto the tool during the turning process was determinedusing evolutionary operations combined with measurementsof surface temperature on the tool The three-dimensionalconduction in the tool and tool holder was simulated usingFLUENT

A numerical prediction of the three-dimensional temper-ature fields inmoving chip stationary tool andmovingwork-piece during machining operations using a finite differencemethod was presented in Ulutan et al [6] First the authorsstudied the chip and tool together to create a heat balancedue to the friction on the rake face Then an investigationof the effect of the chip and tool interface temperature onthe temperature field of the workpiece taking into accountthe heat generated at the shear plane was made A finitedifference model was employed to describe the process andthe results were in good agreement with experimental datapresented in the literature The advantage of this methodin relation to finite element method (FEM) models is thecomputational time which decreased substantially and the

advantage in relation to curve fitting methods is that themethod is based on the physical phenomenon

In Samadi et al [7] the sequential function specificationmethodwas usedwith simulated temperature data to estimatethe transient heat flux imposed on the rake face of a cuttingtool during the cutting operation with two different hypothe-sesThe thermal conductivity was considered constant in oneand in the other it varied with temperature The cutting toolwas modeled as a three-dimensional object The influence ofnonlinearity and different sensor locations were investigatedin order to determine an optimal experimental procedureFinally typical temperature data during turning was used torecover the heat flux at the cutting tool surface consideringlinear and nonlinear solutions

The aim of the present paper is to estimate the heat fluxand calculate the temperature field at the cutting interfaceof the high speed steel tool In addition the influence ofthe cutting parameters (cutting speed cutting depth andfeed rate) on the tool-chip interface temperature was alsoinvestigated The novelty in this work compared to otherspresented in the literature is the joint solution and analysis ofthe following problems a nonlinear tridimensional thermalmodel an inverse technique to estimate the heat flux thethermal analyses of a machining process and the finalcomparison of the results with those obtained from a fullyexperimental methodology proposed to Evangelista Luiz[8] based on the tool-workpiece thermocouple technique(TWTT)

2 The Direct Problem Thermal Model

Figure 1 shows the high speed steel tool the model usedand the dimensions of the tool The interface contact area119860119902(119909 119910) was subjected to the heat flux 11990210158401015840(119909 119910 119905) generatedby contact between the tool and the workpiece At theremaining boundaries a constant convective heat transfercoefficient of 20 (Wm2 K) was considered

The three-dimensional physical problem was solved inCartesian coordinates using finite volume technique with








minus6




120597

120597119909

(120582

120597119879

120597119909

) +

120597

120597119910

(120582

120597119879

120597119910

) +

120597

120597119911

(120582

120597119879

120597119911

) = 120588119862

120597119879

120597119905

(1)


minus120582

120597119879

120597120578

= ℎ (119879 minus 119879infin) (2)


minus120582

120597119879

120597120578

= 11990210158401015840(119909 119910 119905) (3)


119879 (119909 119910 119911 0) = 119879119900 (4)














0 20 40 60 80 100 120 140

Time (s)

Tem

pera

ture

(∘C)

700

600

500

400

300

200

100

0

h = 10 (Wm2K)

h = 18 (Wm2K)

h = 20 (Wm2K)

h = 22 (Wm2K)

h = 30 (Wm2K)

(a)

0 20 40 60 80 100 120 140

Time (s)

6

4

2

0

minus2

minus4

minus6



Max

imum

dev

iatio

n R

(∘C)

(b)


0 20 40 60 80 100 120 140

Time (s)

5

4

3

2

1

0

Hea

t tra

nsfe

r rat

e (W

)

h = 10 (Wm2K)

h = 18 (Wm2K)

h = 20 (Wm2K)

h = 22 (Wm2K)

h = 30 (Wm2K)







119909 (mm) 061 270 00 330 200119910 (mm) 720 850 90 700 340119911 (mm) 00 00 50 950 950


11990210158401015840

119872=

sum119903

119894=1sum119869

119895=1(119884119895119872+119894minus1 minus


) 120601119895119894

sum119903

119894=1sum119869

119895=1120601119895119894

2 (5)










Time = 2 nt

Time = 2 nt


Output data

Time = ntYes

No


Estimated heat flux



Function

specification

Solve (5)


(a)

(b)

(c)




Yes

Yes

No

No

Output data

Time = nt

T converged




(a) (b)






Unit (mm)119886119901 05 10 15 20





16

14

12

1

08

06

04

02

00 25 50 75 100 125 150

Vc (mmmin)

Con

tact

area

(mm

2)

(a)

18

0 05 1 15 2 25

16

14

12

1

08

06

04

02

0

Con

tact

area

(mm

2)

ap (mm)

(b)

f (mmrot)0138 0162 0176 0204 0242 0298

18

16

14

12

10

08

06

Con

tact

area

(mm

2)

(c)



Unit (mmrot)119891 0138 0162 0176 0204 0242 0298




11990210158401015840(119909 119910 119905) = 119902

10158401015840(119905) (6)


20

15

10

5

0

0 20 40 60 80 100 120 140

Time (s)

Hea

t tra

nsfe

r rat

e (W

)

q998400998400(x y t) =

q998400998400(x y t) =

(6)(7)

(a)

700

600

500

400

300

200

100

00 20 40 60 80 100 120 140

Time (s)

Tem

pera

ture

(∘C)



(6)(7)

(b)



Unit (mmin)119881119888 44 71 88 112 142 177 221 284 353 442 56 883 112 142


11990210158401015840(119909 119910 119905) = 119902

10158401015840

119886sdot 119890(minus11198972

119909)sdot(119909minus119909119900)

2+(minus1119897

2

119910)sdot(119910minus119910119900)

2

(7)













Y1T1T1


0 20 40 60 80 100 120

Time (s)

Tem

pera

ture

(∘C)

140

120

100

80

60

40

20

(6)(7)

(a)

4

3

2

1

0

minus1

minus2

minus3

minus4

minus5

minus6


0 20 40 60 80 100 120


Time (s)

Resid

ual t

empe

ratu

reR

(∘C)

(6)(7)

(b)








6 Conclusions




(b) (c)

(a)

X Y

Z








450

400

350

300

04 06 08 10 12 14 16 18 20 22

YTA119902


calculated with

Tem

pera

ture

(∘C)

04 06 08 10 12 14 16 18 20 22

140

120

100

80

60

40

20

R = YTWTT

TWTT

minus TA119902with


TWTT

ap (mm) ap (mm)

Resid

ual t

empe

ratu

reR

(∘C)

(6)(7)

(6)(7)

(a)

015 020 025 030 035

f (mmrot)

100

80

60

40

20

0

minus20

minus40

minus60

550

500

450

400

350

015 020 025 030 035

f (mmrot)

YTA119902


calculated with

R = YTWTT

TWTT

minus TA119902with


TWTT

Resid

ual t

empe

ratu

reR

(∘C)

Tem

pera

ture

(∘C)

(6)(7)

(6)(7)

(b)

120

0

0 20 40 60 80 100 120 140 160

Vc (mmin)

100

80

60

40

20

minus20

minus40

700

600

500

400

300

200

100

0 20 40 60 80 100 120 140 160

Vc (mmin)

YTA119902


calculated with

R = YTWTT

TWTT

minus TA119902with


TWTT

Resid

ual t

empe

ratu

reR

(∘C)

Tem

pera

ture

(∘C)

(6)(7)

(6)(7)

(c)



Acknowledgments


References











2O3coated iso K10















Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















minus6




120597

120597119909

(120582

120597119879

120597119909

) +

120597

120597119910

(120582

120597119879

120597119910

) +

120597

120597119911

(120582

120597119879

120597119911

) = 120588119862

120597119879

120597119905

(1)


minus120582

120597119879

120597120578

= ℎ (119879 minus 119879infin) (2)


minus120582

120597119879

120597120578

= 11990210158401015840(119909 119910 119905) (3)


119879 (119909 119910 119911 0) = 119879119900 (4)














0 20 40 60 80 100 120 140

Time (s)

Tem

pera

ture

(∘C)

700

600

500

400

300

200

100

0

h = 10 (Wm2K)

h = 18 (Wm2K)

h = 20 (Wm2K)

h = 22 (Wm2K)

h = 30 (Wm2K)

(a)

0 20 40 60 80 100 120 140

Time (s)

6

4

2

0

minus2

minus4

minus6



Max

imum

dev

iatio

n R

(∘C)

(b)


0 20 40 60 80 100 120 140

Time (s)

5

4

3

2

1

0

Hea

t tra

nsfe

r rat

e (W

)

h = 10 (Wm2K)

h = 18 (Wm2K)

h = 20 (Wm2K)

h = 22 (Wm2K)

h = 30 (Wm2K)







119909 (mm) 061 270 00 330 200119910 (mm) 720 850 90 700 340119911 (mm) 00 00 50 950 950


11990210158401015840

119872=

sum119903

119894=1sum119869

119895=1(119884119895119872+119894minus1 minus


) 120601119895119894

sum119903

119894=1sum119869

119895=1120601119895119894

2 (5)










Time = 2 nt

Time = 2 nt


Output data

Time = ntYes

No


Estimated heat flux



Function

specification

Solve (5)


(a)

(b)

(c)




Yes

Yes

No

No

Output data

Time = nt

T converged




(a) (b)






Unit (mm)119886119901 05 10 15 20





16

14

12

1

08

06

04

02

00 25 50 75 100 125 150

Vc (mmmin)

Con

tact

area

(mm

2)

(a)

18

0 05 1 15 2 25

16

14

12

1

08

06

04

02

0

Con

tact

area

(mm

2)

ap (mm)

(b)

f (mmrot)0138 0162 0176 0204 0242 0298

18

16

14

12

10

08

06

Con

tact

area

(mm

2)

(c)



Unit (mmrot)119891 0138 0162 0176 0204 0242 0298




11990210158401015840(119909 119910 119905) = 119902

10158401015840(119905) (6)


20

15

10

5

0

0 20 40 60 80 100 120 140

Time (s)

Hea

t tra

nsfe

r rat

e (W

)

q998400998400(x y t) =

q998400998400(x y t) =

(6)(7)

(a)

700

600

500

400

300

200

100

00 20 40 60 80 100 120 140

Time (s)

Tem

pera

ture

(∘C)



(6)(7)

(b)



Unit (mmin)119881119888 44 71 88 112 142 177 221 284 353 442 56 883 112 142


11990210158401015840(119909 119910 119905) = 119902

10158401015840

119886sdot 119890(minus11198972

119909)sdot(119909minus119909119900)

2+(minus1119897

2

119910)sdot(119910minus119910119900)

2

(7)













Y1T1T1


0 20 40 60 80 100 120

Time (s)

Tem

pera

ture

(∘C)

140

120

100

80

60

40

20

(6)(7)

(a)

4

3

2

1

0

minus1

minus2

minus3

minus4

minus5

minus6


0 20 40 60 80 100 120


Time (s)

Resid

ual t

empe

ratu

reR

(∘C)

(6)(7)

(b)








6 Conclusions




(b) (c)

(a)

X Y

Z








450

400

350

300

04 06 08 10 12 14 16 18 20 22

YTA119902


calculated with

Tem

pera

ture

(∘C)

04 06 08 10 12 14 16 18 20 22

140

120

100

80

60

40

20

R = YTWTT

TWTT

minus TA119902with


TWTT

ap (mm) ap (mm)

Resid

ual t

empe

ratu

reR

(∘C)

(6)(7)

(6)(7)

(a)

015 020 025 030 035

f (mmrot)

100

80

60

40

20

0

minus20

minus40

minus60

550

500

450

400

350

015 020 025 030 035

f (mmrot)

YTA119902


calculated with

R = YTWTT

TWTT

minus TA119902with


TWTT

Resid

ual t

empe

ratu

reR

(∘C)

Tem

pera

ture

(∘C)

(6)(7)

(6)(7)

(b)

120

0

0 20 40 60 80 100 120 140 160

Vc (mmin)

100

80

60

40

20

minus20

minus40

700

600

500

400

300

200

100

0 20 40 60 80 100 120 140 160

Vc (mmin)

YTA119902


calculated with

R = YTWTT

TWTT

minus TA119902with


TWTT

Resid

ual t

empe

ratu

reR

(∘C)

Tem

pera

ture

(∘C)

(6)(7)

(6)(7)

(c)



Acknowledgments


References











2O3coated iso K10















Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 20 40 60 80 100 120 140

Time (s)

Tem

pera

ture

(∘C)

700

600

500

400

300

200

100

0

h = 10 (Wm2K)

h = 18 (Wm2K)

h = 20 (Wm2K)

h = 22 (Wm2K)

h = 30 (Wm2K)

(a)

0 20 40 60 80 100 120 140

Time (s)

6

4

2

0

minus2

minus4

minus6



Max

imum

dev

iatio

n R

(∘C)

(b)


0 20 40 60 80 100 120 140

Time (s)

5

4

3

2

1

0

Hea

t tra

nsfe

r rat

e (W

)

h = 10 (Wm2K)

h = 18 (Wm2K)

h = 20 (Wm2K)

h = 22 (Wm2K)

h = 30 (Wm2K)







119909 (mm) 061 270 00 330 200119910 (mm) 720 850 90 700 340119911 (mm) 00 00 50 950 950


11990210158401015840

119872=

sum119903

119894=1sum119869

119895=1(119884119895119872+119894minus1 minus


) 120601119895119894

sum119903

119894=1sum119869

119895=1120601119895119894

2 (5)










Time = 2 nt

Time = 2 nt


Output data

Time = ntYes

No


Estimated heat flux



Function

specification

Solve (5)


(a)

(b)

(c)




Yes

Yes

No

No

Output data

Time = nt

T converged




(a) (b)






Unit (mm)119886119901 05 10 15 20





16

14

12

1

08

06

04

02

00 25 50 75 100 125 150

Vc (mmmin)

Con

tact

area

(mm

2)

(a)

18

0 05 1 15 2 25

16

14

12

1

08

06

04

02

0

Con

tact

area

(mm

2)

ap (mm)

(b)

f (mmrot)0138 0162 0176 0204 0242 0298

18

16

14

12

10

08

06

Con

tact

area

(mm

2)

(c)



Unit (mmrot)119891 0138 0162 0176 0204 0242 0298




11990210158401015840(119909 119910 119905) = 119902

10158401015840(119905) (6)


20

15

10

5

0

0 20 40 60 80 100 120 140

Time (s)

Hea

t tra

nsfe

r rat

e (W

)

q998400998400(x y t) =

q998400998400(x y t) =

(6)(7)

(a)

700

600

500

400

300

200

100

00 20 40 60 80 100 120 140

Time (s)

Tem

pera

ture

(∘C)



(6)(7)

(b)



Unit (mmin)119881119888 44 71 88 112 142 177 221 284 353 442 56 883 112 142


11990210158401015840(119909 119910 119905) = 119902

10158401015840

119886sdot 119890(minus11198972

119909)sdot(119909minus119909119900)

2+(minus1119897

2

119910)sdot(119910minus119910119900)

2

(7)













Y1T1T1


0 20 40 60 80 100 120

Time (s)

Tem

pera

ture

(∘C)

140

120

100

80

60

40

20

(6)(7)

(a)

4

3

2

1

0

minus1

minus2

minus3

minus4

minus5

minus6


0 20 40 60 80 100 120


Time (s)

Resid

ual t

empe

ratu

reR

(∘C)

(6)(7)

(b)








6 Conclusions




(b) (c)

(a)

X Y

Z








450

400

350

300

04 06 08 10 12 14 16 18 20 22

YTA119902


calculated with

Tem

pera

ture

(∘C)

04 06 08 10 12 14 16 18 20 22

140

120

100

80

60

40

20

R = YTWTT

TWTT

minus TA119902with


TWTT

ap (mm) ap (mm)

Resid

ual t

empe

ratu

reR

(∘C)

(6)(7)

(6)(7)

(a)

015 020 025 030 035

f (mmrot)

100

80

60

40

20

0

minus20

minus40

minus60

550

500

450

400

350

015 020 025 030 035

f (mmrot)

YTA119902


calculated with

R = YTWTT

TWTT

minus TA119902with


TWTT

Resid

ual t

empe

ratu

reR

(∘C)

Tem

pera

ture

(∘C)

(6)(7)

(6)(7)

(b)

120

0

0 20 40 60 80 100 120 140 160

Vc (mmin)

100

80

60

40

20

minus20

minus40

700

600

500

400

300

200

100

0 20 40 60 80 100 120 140 160

Vc (mmin)

YTA119902


calculated with

R = YTWTT

TWTT

minus TA119902with


TWTT

Resid

ual t

empe

ratu

reR

(∘C)

Tem

pera

ture

(∘C)

(6)(7)

(6)(7)

(c)



Acknowledgments


References











2O3coated iso K10















Volume 2014




Journal of











Journal of


Function Spaces






Algebra













Time = 2 nt

Time = 2 nt


Output data

Time = ntYes

No


Estimated heat flux



Function

specification

Solve (5)


(a)

(b)

(c)




Yes

Yes

No

No

Output data

Time = nt

T converged




(a) (b)






Unit (mm)119886119901 05 10 15 20





16

14

12

1

08

06

04

02

00 25 50 75 100 125 150

Vc (mmmin)

Con

tact

area

(mm

2)

(a)

18

0 05 1 15 2 25

16

14

12

1

08

06

04

02

0

Con

tact

area

(mm

2)

ap (mm)

(b)

f (mmrot)0138 0162 0176 0204 0242 0298

18

16

14

12

10

08

06

Con

tact

area

(mm

2)

(c)



Unit (mmrot)119891 0138 0162 0176 0204 0242 0298




11990210158401015840(119909 119910 119905) = 119902

10158401015840(119905) (6)


20

15

10

5

0

0 20 40 60 80 100 120 140

Time (s)

Hea

t tra

nsfe

r rat

e (W

)

q998400998400(x y t) =

q998400998400(x y t) =

(6)(7)

(a)

700

600

500

400

300

200

100

00 20 40 60 80 100 120 140

Time (s)

Tem

pera

ture

(∘C)



(6)(7)

(b)



Unit (mmin)119881119888 44 71 88 112 142 177 221 284 353 442 56 883 112 142


11990210158401015840(119909 119910 119905) = 119902

10158401015840

119886sdot 119890(minus11198972

119909)sdot(119909minus119909119900)

2+(minus1119897

2

119910)sdot(119910minus119910119900)

2

(7)













Y1T1T1


0 20 40 60 80 100 120

Time (s)

Tem

pera

ture

(∘C)

140

120

100

80

60

40

20

(6)(7)

(a)

4

3

2

1

0

minus1

minus2

minus3

minus4

minus5

minus6


0 20 40 60 80 100 120


Time (s)

Resid

ual t

empe

ratu

reR

(∘C)

(6)(7)

(b)








6 Conclusions




(b) (c)

(a)

X Y

Z








450

400

350

300

04 06 08 10 12 14 16 18 20 22

YTA119902


calculated with

Tem

pera

ture

(∘C)

04 06 08 10 12 14 16 18 20 22

140

120

100

80

60

40

20

R = YTWTT

TWTT

minus TA119902with


TWTT

ap (mm) ap (mm)

Resid

ual t

empe

ratu

reR

(∘C)

(6)(7)

(6)(7)

(a)

015 020 025 030 035

f (mmrot)

100

80

60

40

20

0

minus20

minus40

minus60

550

500

450

400

350

015 020 025 030 035

f (mmrot)

YTA119902


calculated with

R = YTWTT

TWTT

minus TA119902with


TWTT

Resid

ual t

empe

ratu

reR

(∘C)

Tem

pera

ture

(∘C)

(6)(7)

(6)(7)

(b)

120

0

0 20 40 60 80 100 120 140 160

Vc (mmin)

100

80

60

40

20

minus20

minus40

700

600

500

400

300

200

100

0 20 40 60 80 100 120 140 160

Vc (mmin)

YTA119902


calculated with

R = YTWTT

TWTT

minus TA119902with


TWTT

Resid

ual t

empe

ratu

reR

(∘C)

Tem

pera

ture

(∘C)

(6)(7)

(6)(7)

(c)



Acknowledgments


References











2O3coated iso K10















Volume 2014




Journal of











Journal of


Function Spaces






Algebra











16

14

12

1

08

06

04

02

00 25 50 75 100 125 150

Vc (mmmin)

Con

tact

area

(mm

2)

(a)

18

0 05 1 15 2 25

16

14

12

1

08

06

04

02

0

Con

tact

area

(mm

2)

ap (mm)

(b)

f (mmrot)0138 0162 0176 0204 0242 0298

18

16

14

12

10

08

06

Con

tact

area

(mm

2)

(c)



Unit (mmrot)119891 0138 0162 0176 0204 0242 0298




11990210158401015840(119909 119910 119905) = 119902

10158401015840(119905) (6)


20

15

10

5

0

0 20 40 60 80 100 120 140

Time (s)

Hea

t tra

nsfe

r rat

e (W

)

q998400998400(x y t) =

q998400998400(x y t) =

(6)(7)

(a)

700

600

500

400

300

200

100

00 20 40 60 80 100 120 140

Time (s)

Tem

pera

ture

(∘C)



(6)(7)

(b)



Unit (mmin)119881119888 44 71 88 112 142 177 221 284 353 442 56 883 112 142


11990210158401015840(119909 119910 119905) = 119902

10158401015840

119886sdot 119890(minus11198972

119909)sdot(119909minus119909119900)

2+(minus1119897

2

119910)sdot(119910minus119910119900)

2

(7)













Y1T1T1


0 20 40 60 80 100 120

Time (s)

Tem

pera

ture

(∘C)

140

120

100

80

60

40

20

(6)(7)

(a)

4

3

2

1

0

minus1

minus2

minus3

minus4

minus5

minus6


0 20 40 60 80 100 120


Time (s)

Resid

ual t

empe

ratu

reR

(∘C)

(6)(7)

(b)








6 Conclusions




(b) (c)

(a)

X Y

Z








450

400

350

300

04 06 08 10 12 14 16 18 20 22

YTA119902


calculated with

Tem

pera

ture

(∘C)

04 06 08 10 12 14 16 18 20 22

140

120

100

80

60

40

20

R = YTWTT

TWTT

minus TA119902with


TWTT

ap (mm) ap (mm)

Resid

ual t

empe

ratu

reR

(∘C)

(6)(7)

(6)(7)

(a)

015 020 025 030 035

f (mmrot)

100

80

60

40

20

0

minus20

minus40

minus60

550

500

450

400

350

015 020 025 030 035

f (mmrot)

YTA119902


calculated with

R = YTWTT

TWTT

minus TA119902with


TWTT

Resid

ual t

empe

ratu

reR

(∘C)

Tem

pera

ture

(∘C)

(6)(7)

(6)(7)

(b)

120

0

0 20 40 60 80 100 120 140 160

Vc (mmin)

100

80

60

40

20

minus20

minus40

700

600

500

400

300

200

100

0 20 40 60 80 100 120 140 160

Vc (mmin)

YTA119902


calculated with

R = YTWTT

TWTT

minus TA119902with


TWTT

Resid

ual t

empe

ratu

reR

(∘C)

Tem

pera

ture

(∘C)

(6)(7)

(6)(7)

(c)



Acknowledgments


References











2O3coated iso K10















Volume 2014




Journal of











Journal of


Function Spaces






Algebra










20

15

10

5

0

0 20 40 60 80 100 120 140

Time (s)

Hea

t tra

nsfe

r rat

e (W

)

q998400998400(x y t) =

q998400998400(x y t) =

(6)(7)

(a)

700

600

500

400

300

200

100

00 20 40 60 80 100 120 140

Time (s)

Tem

pera

ture

(∘C)



(6)(7)

(b)



Unit (mmin)119881119888 44 71 88 112 142 177 221 284 353 442 56 883 112 142


11990210158401015840(119909 119910 119905) = 119902

10158401015840

119886sdot 119890(minus11198972

119909)sdot(119909minus119909119900)

2+(minus1119897

2

119910)sdot(119910minus119910119900)

2

(7)













Y1T1T1


0 20 40 60 80 100 120

Time (s)

Tem

pera

ture

(∘C)

140

120

100

80

60

40

20

(6)(7)

(a)

4

3

2

1

0

minus1

minus2

minus3

minus4

minus5

minus6


0 20 40 60 80 100 120


Time (s)

Resid

ual t

empe

ratu

reR

(∘C)

(6)(7)

(b)








6 Conclusions




(b) (c)

(a)

X Y

Z








450

400

350

300

04 06 08 10 12 14 16 18 20 22

YTA119902


calculated with

Tem

pera

ture

(∘C)

04 06 08 10 12 14 16 18 20 22

140

120

100

80

60

40

20

R = YTWTT

TWTT

minus TA119902with


TWTT

ap (mm) ap (mm)

Resid

ual t

empe

ratu

reR

(∘C)

(6)(7)

(6)(7)

(a)

015 020 025 030 035

f (mmrot)

100

80

60

40

20

0

minus20

minus40

minus60

550

500

450

400

350

015 020 025 030 035

f (mmrot)

YTA119902


calculated with

R = YTWTT

TWTT

minus TA119902with


TWTT

Resid

ual t

empe

ratu

reR

(∘C)

Tem

pera

ture

(∘C)

(6)(7)

(6)(7)

(b)

120

0

0 20 40 60 80 100 120 140 160

Vc (mmin)

100

80

60

40

20

minus20

minus40

700

600

500

400

300

200

100

0 20 40 60 80 100 120 140 160

Vc (mmin)

YTA119902


calculated with

R = YTWTT

TWTT

minus TA119902with


TWTT

Resid

ual t

empe

ratu

reR

(∘C)

Tem

pera

ture

(∘C)

(6)(7)

(6)(7)

(c)



Acknowledgments


References











2O3coated iso K10















Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Y1T1T1


0 20 40 60 80 100 120

Time (s)

Tem

pera

ture

(∘C)

140

120

100

80

60

40

20

(6)(7)

(a)

4

3

2

1

0

minus1

minus2

minus3

minus4

minus5

minus6


0 20 40 60 80 100 120


Time (s)

Resid

ual t

empe

ratu

reR

(∘C)

(6)(7)

(b)








6 Conclusions




(b) (c)

(a)

X Y

Z








450

400

350

300

04 06 08 10 12 14 16 18 20 22

YTA119902


calculated with

Tem

pera

ture

(∘C)

04 06 08 10 12 14 16 18 20 22

140

120

100

80

60

40

20

R = YTWTT

TWTT

minus TA119902with


TWTT

ap (mm) ap (mm)

Resid

ual t

empe

ratu

reR

(∘C)

(6)(7)

(6)(7)

(a)

015 020 025 030 035

f (mmrot)

100

80

60

40

20

0

minus20

minus40

minus60

550

500

450

400

350

015 020 025 030 035

f (mmrot)

YTA119902


calculated with

R = YTWTT

TWTT

minus TA119902with


TWTT

Resid

ual t

empe

ratu

reR

(∘C)

Tem

pera

ture

(∘C)

(6)(7)

(6)(7)

(b)

120

0

0 20 40 60 80 100 120 140 160

Vc (mmin)

100

80

60

40

20

minus20

minus40

700

600

500

400

300

200

100

0 20 40 60 80 100 120 140 160

Vc (mmin)

YTA119902


calculated with

R = YTWTT

TWTT

minus TA119902with


TWTT

Resid

ual t

empe

ratu

reR

(∘C)

Tem

pera

ture

(∘C)

(6)(7)

(6)(7)

(c)



Acknowledgments


References











2O3coated iso K10















Volume 2014




Journal of











Journal of


Function Spaces






Algebra










(b) (c)

(a)

X Y

Z








450

400

350

300

04 06 08 10 12 14 16 18 20 22

YTA119902


calculated with

Tem

pera

ture

(∘C)

04 06 08 10 12 14 16 18 20 22

140

120

100

80

60

40

20

R = YTWTT

TWTT

minus TA119902with


TWTT

ap (mm) ap (mm)

Resid

ual t

empe

ratu

reR

(∘C)

(6)(7)

(6)(7)

(a)

015 020 025 030 035

f (mmrot)

100

80

60

40

20

0

minus20

minus40

minus60

550

500

450

400

350

015 020 025 030 035

f (mmrot)

YTA119902


calculated with

R = YTWTT

TWTT

minus TA119902with


TWTT

Resid

ual t

empe

ratu

reR

(∘C)

Tem

pera

ture

(∘C)

(6)(7)

(6)(7)

(b)

120

0

0 20 40 60 80 100 120 140 160

Vc (mmin)

100

80

60

40

20

minus20

minus40

700

600

500

400

300

200

100

0 20 40 60 80 100 120 140 160

Vc (mmin)

YTA119902


calculated with

R = YTWTT

TWTT

minus TA119902with


TWTT

Resid

ual t

empe

ratu

reR

(∘C)

Tem

pera

ture

(∘C)

(6)(7)

(6)(7)

(c)



Acknowledgments


References











2O3coated iso K10















Volume 2014




Journal of











Journal of


Function Spaces






Algebra










450

400

350

300

04 06 08 10 12 14 16 18 20 22

YTA119902


calculated with

Tem

pera

ture

(∘C)

04 06 08 10 12 14 16 18 20 22

140

120

100

80

60

40

20

R = YTWTT

TWTT

minus TA119902with


TWTT

ap (mm) ap (mm)

Resid

ual t

empe

ratu

reR

(∘C)

(6)(7)

(6)(7)

(a)

015 020 025 030 035

f (mmrot)

100

80

60

40

20

0

minus20

minus40

minus60

550

500

450

400

350

015 020 025 030 035

f (mmrot)

YTA119902


calculated with

R = YTWTT

TWTT

minus TA119902with


TWTT

Resid

ual t

empe

ratu

reR

(∘C)

Tem

pera

ture

(∘C)

(6)(7)

(6)(7)

(b)

120

0

0 20 40 60 80 100 120 140 160

Vc (mmin)

100

80

60

40

20

minus20

minus40

700

600

500

400

300

200

100

0 20 40 60 80 100 120 140 160

Vc (mmin)

YTA119902


calculated with

R = YTWTT

TWTT

minus TA119902with


TWTT

Resid

ual t

empe

ratu

reR

(∘C)

Tem

pera

ture

(∘C)

(6)(7)

(6)(7)

(c)



Acknowledgments


References











2O3coated iso K10















Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Acknowledgments


References











2O3coated iso K10















Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article analyses of effects of cutting parameters

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