IOP PUBLISHING MEASUREMENT SCIENCE AND TECHNOLOGY

Meas. Sci. Technol. 22 (2011) 025106 (13pp) doi:10.1088/0957-0233/22/2/025106

A calibrated dual-wavelength infraredthermometry approach withnon-greybody compensation formachining temperature measurementsA Hijazi1, S Sachidanandan2, R Singh2 and V Madhavan2

1 Department of Mechanical Engineering, The Hashemite University, Zarka, Jordan2 Department of Industrial and Manufacturing Engineering, Wichita State University, Wichita, KS, USA

E-mail: hijazi@hu.edu.jo

Received 20 September 2010, in final form 19 November 2010Published 11 January 2011Online at stacks.iop.org/MST/22/025106

AbstractWe report the development of a new approach for determining temperatures using thedual-wavelength infrared thermometry technique, which does not presume greybodybehaviour and compensates for the spectral dependence of emissivity. This approach is basedon Planck’s radiation equation and explicitly accounts for the wavelength-dependent responseof the IR detector and the losses occurring due to each of the elements of the IR imagingsystem that affect the total radiant energy sensed in different spectral bands. A thoroughcalibration procedure is utilized to determine a compensation factor for the spectraldependence of emissivity, which is referred to as the non-greybody compensation factor(NGCF). Calibration and validation experiments are carried out on Aluminum 6061-T6 targetswith two different surface roughnesses. Results show that this alloy does not exhibit greybodybehaviour, even though the two spectral bands used were relatively close to each other, andthat the spectral dependence of emissivity is influenced by the surface finish. It is found thatnon-greybody behaviour of low emissivity surfaces can lead to significant systematic error indual-wavelength IR thermometry. The inclusion of the NGCF eliminates the systematic errorcaused by the invalidity of greybody assumption and thus improves the accuracy of themeasurements. Non-greybody-compensated dual-wavelength thermography is used tomeasure the chip temperature along the tool–chip interface during orthogonal cutting of Al6061-T6 and sample results at three different cutting speeds are presented.

Keywords: infrared thermometry, thermography, pyrometry, dual-wavelength IR, two-colourIR, emissivity, non-greybody compensation, IR calibration, microscopic IR, machiningtemperatures

(Some figures in this article are in colour only in the electronic version)

1. Introduction

Machining (or metal cutting) is a process in which a hard,sharp, wedge-shaped cutting tool removes unwanted materialfrom the surface of a softer workpiece by relative motionunder interference. A large amount of deformation (straingreater than 100%) takes place in the primary shear zone (PSZ)

and the speed at which the material flows through the PSZcan reach tens of meters per second, which results in strainrates between 104 and 106. This high strain rate generatesa considerable amount of heat during a very short period oftime (i.e. the transit time of the material in the PSZ, which istypically much less than a millisecond) and that results in asignificant increase in temperature. In addition, a significant

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Meas. Sci. Technol. 22 (2011) 025106 A Hijazi et al

amount of heat is also generated at the chip–tool interface dueto the friction between the chip and the rake face of the tool,which results in a further increase in temperature. As a result,the temperatures encountered during high speed machiningcan reach hundreds of degrees and can reach close to meltingtemperatures in some cases. There are several factors thatinfluence the temperature increase, such as the work material,cutting speed, feed, rake angle, tool-nose radius, tool material,tool coating and cutting fluids.

The quantification and control of the temperaturesencountered during machining have been of great interest toresearchers since the temperature is the key factor controllingtool wear and life [1] and has a considerable influenceon the surface finish, microstructure and residual stressesalong the machined surfaces [2, 3]. Several experimentaltechniques, with varying degrees of applicability and accuracy,have been developed and used by researchers to measuretemperatures during metal cutting. These techniques includethe intrinsic thermocouple (or the work–tool thermocouple)technique, the extrinsic (or direct) thermocouple technique, themetallurgical technique, the thermo-sensitive paints techniqueand infrared pyrometry [2–4]. The measurement of machiningtemperatures based on the emitted infrared radiation, thoughone of the earliest techniques, remains the most widely usedtechnique. The key contributor to uncertainty in radiation-based temperature measurements is the uncertainty in thevalue of emissivity used for inferring temperatures. Duringmachining, the material is subjected to large deformationswhich change the surface characteristics and therefore itsemissivity changes as well. In order to account forthis, researchers have adopted the use of dual-wavelengthpyrometry (or a ratio technique) for the measurement ofmachining temperatures [5–9]. The most important advantageof the dual-wavelength technique is that, as long as thegreybody assumption (i.e. the emissivity does not depend onwavelength) is applicable, the ratio of radiance in differentspectral bands can be related to the temperature, and theactual value of the emissivity value does not need to beknown. Although most metallic surfaces do not exhibitgreybody behaviour, it is usually assumed that, by choosingthe two spectral bands carefully enough or close to each other,the assumption of greybody behaviour is realistic [5–9]. Inthe error analysis of their two-colour pyrometer, Muller andRenz [7] concluded that the primary source of error in themeasured absolute temperature is due to the deviation ofthe surface emissivity from the greybody behaviour. Otherstudies have shown that it is impossible to reliably estimatethe uncertainty in the temperature measured with a multi-wavelength pyrometer, of any complexity, in the absence ofany valid experimental or theoretical knowledge of the spectraldependence of emissivity [10, 11].

In this paper we report the development of a new approachfor determining temperatures using the dual-wavelengthtechnique, which does not presume greybody behaviour andcompensates for the spectral dependence of emissivity. Thefull theoretical development of our approach is presented.A thorough calibration procedure is utilized to determinea compensation factor for the emissivity spectral behaviour

which is referred to as the non-greybody compensation factor(NGCF). The inclusion of this NGCF eliminates the systematicerror in dual-wavelength temperature measurements (due tothe invalidity of greybody assumption) and thus the overallerror decreases significantly. Calibration and validationexperiments were carried out on Aluminum 6061-T6 alloytargets with two different surface finishes. This approach wasused to measure the chip temperature distribution along thetool–chip interface during orthogonal cutting of Al 6061-T6tubes and sample results at three different cutting speeds arepresented.

2. Machining temperatures measurement usingradiation thermometry

The measurement of machining temperatures based on theemitted infrared (IR) radiation (using a single point pyrometer,scanner or camera) is by far the most used technique[2–4]. Some researchers have even measured the radiationemitted in the visible range, using intensified cameras, toinfer temperatures during machining [12]. However, suchmeasurements are applicable to temperatures greater than600 ◦C due to the very weak radiation in the visiblerange at lower temperatures. Also, in general, temperaturemeasurements based on visible radiation are less accuratethan those based on IR radiation due to the lower signal tonoise ratio. The first reported use of IR radiation for themeasurement of machining temperatures was by Schwerd [13]in the 1930s where he used a pyrometer that focuses radiationon a thermocouple using an optical condenser. Boothroyd[14] was the first to use thermography for obtaining a full-fieldmeasurement of machining temperatures where he used anIR-sensitive film. Later, with the development of solid-statedetectors, IR cameras with solid-state FPAs became more andmore commonly used for mapping the full-field temperaturedistribution during machining [2–4].

The most important issue affecting the accuracy ofradiation-based temperature measurement is the accuracyof the value of emissivity used for inferring temperatures.In the earliest work, researchers coated the surfaces beingimaged with a black layer having a ‘known’ high emissivity[14, 15]. However, this cannot be used for cases involvinglarge deformation of the surface, or rapid changes intemperature, since there is a finite time constant for diffusionof heat from the substrate to the coating. The increasedsensitivity of IR cameras has enabled uncoated surfaces tobe imaged, the emissivity values of which are obtainedfrom the literature or through calibration experiments carriedout on the same material. However, the fact that theemissivity of metallic surfaces does not depend only on thematerial composition, but also on several other factors such asthe surface finish, condition and temperature as well as theradiation wavelength, makes the issue of uncertainty of theemissivity value of concern. This concern is especiallylegitimate in machining where the surface roughness andcondition change considerably as the material passes throughthe PSZ. Davies et al [16] developed an IR microscopesystem to measure temperature fields during machining and

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Meas. Sci. Technol. 22 (2011) 025106 A Hijazi et al

they introduced a thorough approach for calibration andinferring temperatures from the measured radiation field. Theyused the IR microscope to measure the chip temperaturedistribution along the chip–tool interface during orthogonalcutting of AISI 1045 steel and they elaborately discussed thesources of uncertainty in the measured temperatures wherethey reported an uncertainty of ±52 ◦C at the maximummeasured temperature of 800 ◦C. The biggest contribution tothe uncertainty value was reported to be from changes in theemissivity as a result of changes in surface roughness. Theydetermined the mean emissivity value (over the wavelengthband of their camera) of the workpiece material indirectly,based on Kirchhoff’s law, by measuring the 8◦/hemispherereflectivity using a FT-IR spectrometer. However, someconcern might arise with such an indirect measurement whereit is based on some assumptions one of which is the greybodybehaviour [17] and the fact that the microscopic objectivedoes not collect radiation over the entire hemisphere (NA =0.5). This might lead to an additional error in the measuredtemperatures which is not accounted for. In later work,Davies et al [18] measured the emissivity directly using the IRmicroscope system in an additional calibration step. Pujanaet al [19] also used microscopic IR imaging for temperaturemeasurement during orthogonal cutting of different grades ofsteel. However, instead of measuring the temperature of thechip they measured the temperature of the cutting tool wherethe emissivity of the cutting tool can be determined with higherconfidence.

In order to avoid the error in temperature measurementsarising from the uncertainty in the emissivity value, severalresearchers have adopted the use of dual-wavelength (or ratio)thermometry [4]. For a greybody, the emissivity of whichis constant over the entire spectrum, the ratio of radiationintensities over two different wavelength ranges will be afunction of temperature only. Ueda and coworkers [5, 6]developed a dual-wavelength pyrometer using two detectors(InSb and Ge as well as InSb and HgCdTe in another variationof the system) linked to an optical fibre inserted into thecutting tool to measure temperature of the rake and flankfaces. Similarly, Muller and co-workers [7, 8] developeda fibre-optic dual-wavelength (1.7 and 2.0 μm) pyrometerwith a few microseconds temporal resolution and 0.5 mm2

spatial resolution and used it to measure temperatures onthe chip and the workpiece during high speed machining.Narayanan et al [9] used a mid-wavelength IR camerafor mapping the temperature distribution over the chip–toolinterface using dual-wavelength thermometry by switchingbetween two different band-pass filters (3.16–3.8 μm and4.31–4.95 μm) mounted on a filter wheel placed in front ofthe camera. They observed the chip–tool interface directlythrough special cutting tools, made out of sapphire, whichare transparent to IR radiation [20]. In all of the above dual-wavelength thermometry work, temperatures were determinedunder the assumption of greybody behaviour. Althoughthe greybody assumption is not valid for metallic surfaces,for which the spectral dependence of emissivity is widelydocumented in the literature [21–23], it is often argued thatby choosing two wavelengths carefully enough or them being

fairly close to each other, the spectral dependence of emissivitycan be neglected. However, when the two wavelengths arevery close to each other, the radiation intensities in the twowavelengths will be close to each other and the change inthe radiation intensity ratio with temperature will be veryslow, thus causing the effect of random noise in the signalof each detector on the error in measured temperatures to bemore significant [10]. Inagaki and Ishii [24] theoreticallyinvestigated the effect of a emissivity drift (due to spectraldependence) on the error in temperature predictions using thedual-wavelength technique. For instance, their results indicatethat by using an InSb sensor (2–5 μm) and a HgCdTe sensor(8–13 μm), a relative emissivity drift of 40% will result inmore than 40 ◦C error in the predicted temperature at near-ambient temperatures. The relative emissivity drift is definedas �ε = [εi − εj ]/[(εi + εj )/2] and a drift of 40% (�ε = 0.4)can result from ε1 = 0.15 and ε2 = 0.1. From this, it isapparent that even small changes in emissivity can cause largedrifts in relative emissivity when the emissivity value is small(such as the case of polished metallic surfaces). Furthermore,Wen and Mudawar [22] studied the emissivity characteristicsfor some aluminium alloys at wavelengths between 2 and4.7 μm and their results show considerable variation inemissivity with wavelength and more interestingly that thespectral behaviour of emissivity, in some cases, changes withsurface roughness.

3. Theory

IR radiation is part of the electromagnetic spectrum andoccupies frequencies between visible light and radio waves.The IR spectrum includes radiation of wavelengths from 0.7to 1000 μm. Within this wave band, only frequencies between0.7 and 20 μm are typically used for temperature measurement.All forms of matter at any temperature above absolute zeroemit radiation of varying intensity across the entire wavelengthspectrum. The spectral distribution of this radiation intensityacross the wavelength spectrum is given by Planck’s law whichstates that the hemispherical radiance (power per unit area)emitted by a blackbody at an absolute temperature T as afunction of a wavelength λ is given by [23]

Ibb(λ, T ) = C1

λ5[e

C2λT − 1

] (1)

where Ibb(λ, T ) is the hemispherical radiance emitted by a unitsurface area of an ideal blackbody at an absolute temperatureT , per unit wavelength λ, and C1, C2 are Planck’s radiationconstants.

A blackbody is defined as a body which absorbs allradiation incident on it and emits, for any given temperature,the maximum possible radiation. A real body always emitsradiation intensity of a lower magnitude than a blackbody. Theemissivity of a body is defined as the ratio of radiance emittedby a unit surface area of that body, at any given wavelength andtemperature, to the radiance emitted by a unit surface area ofan ideal blackbody at the same wavelength and temperature.In general, the emissivity could be a function of the body’stemperature and of the wavelength of emitted radiation. The

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Meas. Sci. Technol. 22 (2011) 025106 A Hijazi et al

radiance of a real body, of an emissivity ε, at a wavelength λ,and an absolute temperature T , is thus given by

I (λ, T ) = ε(λ, T )C1

λ5[e

C2λT − 1

] . (2)

Thus, the total radiance emitted (per unit surface area) by areal body in a wavelength interval bounded by λ1 and λ2 isfound by integrating between the two wavelengths:

I1,2(T ) =∫ λ2

λ1

ε(λ, T )C1

λ5[e

C2λT − 1

] dλ

= ε1,2(T )

∫ λ2

λ1

C1

λ5[e

C2λT − 1

] dλ (3)

where ε1,2(T ) is the mean spectral emissivity value over thewavelength band between λ1 and λ2.

Dual-wavelength thermometry (also called two-colouror ratio technique) involves measuring the radiance at twodifferent wavelengths and inferring the temperature from theratio of the spectral radiances. While the measurement ofradiances at two wavelengths, rather than one, introducessome difficulties, including requiring more sophisticatedexperimental apparatus and data processing, dual-wavelengthpyrometers are preferred in many applications (such as thoseinvolving partial or occluded targets) since they can givesignificantly more accurate temperature measurements [23].Measurement of temperature using this technique utilizes thefact that, for a greybody, whose emissivity is constant at allwavelengths, the ratio of radiant intensities obtained at twodifferent wavelengths is a function of temperature only, and theneed for prior knowledge of the target emissivity is eliminated.Using the expression of equation (3), if I1,2(T ) and I3,4(T ) arethe radiances in two wavelength bands (λ1–λ2) and (λ3–λ4),respectively, then the ratio of the two radiances, rI (T ), can bewritten as

rI (T ) = I1,2(T )

I3,4(T )= ε1,2(T )

ε3,4(T )

∫ λ2

λ1

C1

λ5[

eC2λT −1

] dλ

∫ λ4

λ3

C1

λ5[

eC2λT −1

] dλ

= rε(T )

∫ λ2

λ1

C1

λ5[

eC2λT −1

] dλ

∫ λ4

λ3

C1

λ5[

eC2λT −1

] dλ(4)

where rε(T ) is the ratio of the mean spectral emissivities inthe two wavelength bands. This equation shows that that theratio of radiances, rI (T ), will be independent of emissivityonly if the emissivities in the two wavelength bands areequal for all temperatures. This assumption, though notreasonable in many cases, is usually made when measuringtemperatures using dual-wavelength thermometry. Besidesdual-wavelength thermometry, there is also multi-wavelengththermometry where three, four, or even six wavelengths areused [19]. A study involving the use of multi-wavelengthand dual-wavelength thermometry concluded that there is noadvantage in using more than two wavelength bands for theratio technique, since the results obtained with three and fourbands did not reveal any significant reduction in error over theresults obtained with two bands [25].

In the work presented herein, we compensate for thenon-greybody behaviour by including the spectral emissivityratio rε(T ) in our calculations. This ratio which we referto as the ‘non-greybody compensation factor (NGCF)’ isdetermined through an additional calibration step using thesame surface of interest. Although the idea of compensatingfor the non-greybody behaviour is not new and severalstudies have developed methods for this [23, 26–30], thesemethods are mostly based on Wien’s approximation (whichis only accurate for wavelength–temperature products (λT ) ofless than 3000 μm K [31]). Additionally, they deal withdual-wavelength pyrometers utilizing two monochromatic(narrowband) detectors. Our approach extends this to handlewideband dual-wavelength thermometry based on Planck’sequation. We also introduce a novel systematic calibrationprocedure for determining the spectral and temperaturedependence of emissivity.

4. Experimental setup

In this study we used a mid-wavelength infrared (MWIR)camera (Merlin MidTM by Indigo Systems Corp.) whichincorporates an indium antimonide (InSb) focal plane array(FPA) cooled to 77 K by a Stirling cycle cooler. The FPAhas a resolution of 320 × 256 pixels with 30 μm pixel size.The InSb detector is sensitive to radiation in the 1.0–5.4 μmrange; however, the camera incorporates a cold filter whichrestricts the spectral response to the 3.0–5.0 μm range. Thecamera has a 12-bit dynamic range (i.e. 4096 intensity counts),an adjustable integration time that can be varied from 2 μs to16 ms and can capture 60 full resolution frames per second.The lens used in our experiments is a SAXET VIS-IRTM

reflecting microscope objective with 15× magnification (itprojects a 1.2 mm × 1 mm area of the object plane onto theFPA). The lens has a 24.5 mm working distance, 0.28 NA,negligible astigmatic aberration and no chromatic or sphericalaberrations. In order to measure the radiation intensitywithin two-wavelength bands, two IR bandpass filters withcentral transmission wavelengths of 4.03 and 4.65 μm, with0.19 μm FWHM bandwidth for both, were mounted on atwo-position translating filter holder that is positioned in frontof the objective lens. For the sake of brevity, these filterswill be referred to as the 403 and 465 filters henceforth.Care was taken in choosing the wavelength bands of the twofilters to avoid the strong atmospheric attenuation wavelengthband centred at 4.3 μm (due to CO2 molecules). With thebandpass filters used in our experiments, it was found that anintegration time of 1 ms was sufficient to obtain a reasonabledetector response for the expected range of temperatures ofaluminium workpieces. After setting the video offset permanufacturer recommendations, a two-point non-uniformitycorrection (NUC) was defined and saved. The aim of theNUC is to ensure that all individual pixels of the FPA willhave a quantitatively ‘uniform’ response when imaging atarget surface of uniform temperature. The two-point NUCis the most accurate NUC available for the Merlin MidTM

camera and it is defined by imaging a smooth black surfaceof uniform temperature, with the image slightly defocused to

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Meas. Sci. Technol. 22 (2011) 025106 A Hijazi et al

ensure higher uniformity, at two different temperatures (lowtemperature and high temperature).

For the initial blackbody calibration a polished copperplate (10 × 10 mm with 2 mm thickness), with two K-type thermocouples attached to the surface 5 mm apart, wasuniformly coated with a black temperature-resistant paint(KrylonTM ultra-flat black) which has a reported emissivityof 0.96. The back surface of the plate was stuck to a smallcoil heater using thermally conducting, electrically insulating,potting agent (OmegaTM CC high temperature cement). Thecoil-heater was potted inside a tube using a curable insulator(CotronicsTM Resbond) to minimize stray radiation gettingout of the heater. The readings of the thermocouples arerecorded using a data logger that can be run in synchronizationwith the IR camera. For the second calibration step aimedat determining the NGCF, two calibration targets made ofAluminum 6061-T6 (the same workpiece material used inthe cutting experiments), but having different surface finishes,were prepared using a similar procedure to that used for theblack calibration target. The two different surface finisheswere obtained by polishing one of the surfaces using 600-gritsilicon carbide abrasive paper and the other with 1500-gritpaper. The surface finishes of the two calibration targets weremeasured using an optical profilometer (MicroXAMTM 3D)and they were found to be Ra = 0.34 μm, Rq = 0.47 μm andRa = 0.11 μm, Rq = 0.1 μm for the 600-grit and 1500-gritsamples, respectively. Figure 1(a) shows an image of the setupfor calibration.

The orthogonal cutting experiments were performed on ahigh speed, high rigidity custom-built lathe. The workpiece isa thin-walled Al 6061-T6 tube (48 mm outer diameter and2 mm wall thickness) held on the machine spindle and itis fed axially against a stationary tool to allow continuousobservation of the chip formation process from an Eulerianframe of reference using the IR camera. The tube wasmachined to final dimensions from a larger diameter bar andthe final OD turning was carried out with very small depthand feed to give a smooth surface. Then it was polishedusing 600-grit silicon carbide abrasive paper to remove theturning marks and replace them with a finish equivalent tothat of the calibration surface polished with the 600-gritpaper. A modified Kennametal TD6P cutting insert groundto a +20◦ rake angle was used for the cutting experiments.Figure 1(b) shows an image of the setup during a typicalcutting experiment. The two IR filters used for the cuttingexperiments presented in this paper are the 403 filter indicatedearlier and another filter having a centre wavelength of 3.43and 0.3 μm FWHM bandwidth. This different filter wasused instead of the 465 filter in order to accommodate thehigher temperatures expected at high cutting speeds withoutexceeding the linear response range of the camera and withouthaving to use different integration times for each of the twofilters. Although not presented in this paper, a calibrationprocedure similar to that described later (in section 6) wasused for this set of filters.

(a)

(b)

Figure 1. Images of the typical experimental setup; (a) calibration,(b) cutting experiment.

5. Approach

The processing of broadband IR thermometry data is based onequation (3). The IR sensor of the pyrometer (or FPA of thecamera) receives a portion of the radiance emitted by the targetand transfers it into an electronic signal that is proportional tothe emitted radiation. The detector signal is then transformedby the pyrometer (or camera) electronics (after offsetting,amplification and digitization) into an intensity count. Fora detector that receives radiation between wavelengths λx andλy , the detector intensity count reading can be related to theradiation emitted by the target within this wavelength band(equation (3)) as

DRx,y(T ) = CBx,yIx,y(T ) + F

= CBx,yεx,y(T )

∫ λy

λx

C1

λ5[e

C2λT − 1

] dλ + F (5)

where CBx,y is the constant of proportionality between theradiation emitted by the target and the detector reading (withinthe linear regime of the detector’s response), and F is anoffset. The value of CBx,y, which is a ‘calibration constant’,depends on many factors such as the optics being used(their magnification, numerical aperture, and transmittance),

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Meas. Sci. Technol. 22 (2011) 025106 A Hijazi et al

sensitivity of the sensor, integration time, gain, etc. The valueof the offset F depends on the settings of detector parameters(integration time, gain and offset) and on the amount ofradiation received by the detector from internal sources suchas the internal surfaces of the lens or microscope being used.Usually, these two constants are not evaluated individuallybut rather they are obtained collectively by calibrating thepyrometer (or camera) against a blackbody (ε ∼= 1) of knowntemperature and obtaining a calibration curve that relates thedetector reading to the blackbody temperature. During acalibration experiment, the temperature of the body of theobjective lens will slightly increase and therefore the offsetF will not remain constant, but will also increase. Thisincrease of the value of F , even though it is relatively small,influences the accuracy of calibration especially when using amicroscopic objective (since the amount of radiation receivedfrom the target surface is very small due to the very small fieldof view). The only way to determine the value of the offset F isby imaging a target surface at 0 K. Instead, we can introduce aquantity called the ‘differential detector reading’ �DRx,y(T )

which is the difference between the detector reading at anytemperature above ambient and that at ambient temperature.Mathematically it is expressed as

�DRx,y(T ) = DRx,y(T ) − DRx,y (Tambient) (6)

where DRx,y (Tambient) is the detector reading obtained byimaging the target surface at ambient temperature. Bysubstituting equation (5) into (6), the offset F will cancelout and the equation will become

�DRx,y(T ) = CBx,yεx,y(T )

×∫ λy

λx

⎡⎣ C1

λ5[e

C2λT − 1

] − C1

λ5[e

C2λTambient − 1

]⎤⎦ dλ. (7)

The calibration constant for any wavelength band CBx,y

depends on several factors where some of them are wavelengthdependent while the rest are wavelength independent. Since,the transmittance of optical elements (e.g., lens and filter)and atmosphere as well as the detector response (i.e. quantumefficiency) are wavelength dependent, the calibration constantcan be expressed as

CBx,y = ks

∫ λy

λx

τoptical elements(λ)τatmosphere(λ)Sdetector(λ) dλ

(8)

where τ(λ) and S(λ) are the spectral transmittance andresponse, respectively, and ks is a constant that dependson integration time, gain, dynamic range, magnification andaperture. Therefore, for the camera used in our experiments,the calibration constant for any of the two wavelength bandsis

CBx,y = ks

∫ λy

λx

τbandpass filter(λ)[ρlens(λ)τcold filter(λ)SInSb(λ)] dλ

= ks

∫ λy

λx

τbandpass filter(λ)β(λ) dλ (9)

where ρ(λ) is the spectral reflectance of the microscopicreflective lens being used in our setup and β is the product

of all the terms within the square brackets. The atmospherictransmittance was not included since no specific data isavailable for such a small path length. Substituting equation(9) into (7), the differential detector reading for our camera,with either of the two bandpass filters, is found to be

�DRx,y(T ) = ksεx,y(T )

∫ λy

λx

τbandpass filter(λ)β(λ)

×

⎡⎢⎣ C1

λ5[e

C2λT − 1

] − C1

λ5[e

C2λTambient − 1

]⎤⎥⎦ dλ. (10)

Thus, the ratio of the differential detector readings r�DR(T ) inthe two wavelength bands, (λ1, λ2) and (λ3, λ4), is

r�DR(T ) = Cfrε(T )

×

∫ λ2

λ1τ403 filter(λ)β(λ)

[C1

λ5[

eC2λT −1

] − C1

λ5[

eC2

λTambient −1]]

dλ

∫ λ4

λ3τ465 filter(λ)β(λ)

[C1

λ5[

eC2λT −1

] − C1

λ5[

eC2

λTambient −1]]

dλ

(11)

where Cf is a correction factor, rε(T ) is the ratio of themean spectral emissivities in the two wavelength bands, andτ403 filter and τ465 filter are the spectral transmittances for the twobandpass filters used in our setup. The correction factor Cf isused to account for any inaccuracies in the spectral response,transmittance or reflectance curves used in the equation andfor any other spectrally dependent terms that are not included(such as the atmospheric transmittance in our case). It shouldbe noted that the constant ks has canceled out from the ratiosince its value does not depend on wavelength and the samecamera parameter settings were used with both filters. Thisequation is analogous to equation (4) but it includes the specificparameters of the IR imaging system used in our experiments,and most importantly it compensates for the drift in the offsetof the camera readings which might be caused by the heatingof the objective lens. Furthermore, this equation can be usedto obtain temperatures with no need for calibration if thegreybody assumption is applicable or if the ratio of spectralemissivities in the two wavelength bands is known (assumingthat all the transmittance, reflectance and response curvesbeing used are accurate and the atmospheric attenuation isnegligible, i.e. Cf = 1). If the emissivity ratio is not known,it can be determined using a simple calibration proceduredescribed in the next section.

Figure 2 shows the spectral curves for the components ofour imaging system. Using these curves, equation (11) wasevaluated using numerical integration to obtain the relationshipbetween the temperature and the differential detector readingratio. For the sake of accuracy, the limits of integration foreach of the two wavelength bands were set to be 3.8 to 4.4 μmfor the 403 filter and 4.1 to 5 μm for the 465 filter, significantlybroader than the FWHM values (as seen from the filterstransmission curves shown in figure 2). The resultingrelationship between the temperature and the differentialdetector signal ratio for temperatures from 360 to 900 K (usingTambient = 298 K) is shown in figure 3. As can be seen from the

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Meas. Sci. Technol. 22 (2011) 025106 A Hijazi et al

Figure 2. Spectral response, transmittance and reflectance curvesfor the different components of the imaging system.

Figure 3. Temperature as a function of the differential detectorreading ratio (from 360 to 900 K with 298 K ambient).

figure, this relationship can be perfectly fitted using a third-order polynomial, and thus temperature can be found as

T = 1872.1(r�DR/Cf rε)3 − 2922.5(r�DR/Cf rε)

2

+ 2289.8(r�DR/Cf rε) − 262.3. (12)

6. Calibration

Although the specific parameters of our IR imaging systemwere included in the development of equation (11), and thusequation (12) may be directly used to infer temperatures,calibration experiments are still needed. Firstly, thesetheoretical equations are valid only as long as the detectorreading is linearly proportional to the intensity of radiationemitted by the target, and thus the linear range of the detector

response needs to be identified. Secondly, the atmosphericattenuation of the radiation in the two wavelength bands,assumed to be negligible due to the short path length, should beverified to be small indeed (i.e. the correction factor Cf needsto be evaluated). Finally, and most importantly, the validityof the greybody assumption for the surfaces of interest mustbe verified and if it is found to be inapplicable, the emissivityratio rε(T ) or the NGCF needs to be determined. In orderto satisfy these requirements, a two-step calibration procedurehas been adopted. In the first step, a black surface is heatedto different known temperatures to verify the linearity of thedetector response and to identify deviations from the expectedtheoretical behaviour given in equations (10) and (11). In thesecond step, this procedure is repeated using the surface ofinterest, which helps to determine the NGCF.

According to equation (6), the differential camera readingcan be determined by subtracting the average camera intensitycount for a target surface at ambient temperature fromthe intensity count when the same surface is at highertemperature. However, when imaging different target surfaces(with different emissivity values) at ambient temperature, itwas found that the difference in the camera average intensitycount is negligible (it was in the range of random error of theintensity readings). This indicates that the biggest contributionto the camera intensity count when imaging a target surfaceat ambient temperature is from the radiation reflected andemitted by the inner surfaces of the lens body, filter, etc. It isunderstandable that the contribution of the radiation emittedby the target surface is small, because of the low surfacetemperature and the high optical magnification. It was alsofound that almost the same reading can be obtained by simplyblocking the view of the camera using a sheet of paper insertedimmediately in front of the bandpass filter (which is the mostfront optical element). Therefore, this simpler approach wasadopted for determining the baseline average camera intensityreading which is referred to as the ‘background reading’.

The value of the background reading was found to befairly sensitive to the temperature of the objective lens body.Holding the outer body of the lens by hand for few secondswas enough to cause a noticeable change in the backgroundreading. It was also observed that the background readingvaries slightly with time even after the camera is run for a longenough time for the Stirling cooler to maintain the temperatureof the FPA stably at 77 K. This variation may be attributable toslight changes in the heat dissipated by the Stirling cooleraffecting the temperature of the camera and lens bodies.Therefore, during the cutting experiments, the differentialcamera intensity readings were obtained by subtracting thebackground reading, obtained by blocking the view using asheet of paper, immediately before starting each experiment.On the other hand, during the calibration experiments, whichextend over a longer time duration, the heat radiated fromthe hot calibration target causes the temperature of the lensbody to continuously increase, thereby slowly increasing thebackground reading. To compensate for this, backgroundreadings were taken at uniform time intervals during thecalibration experiments. This is one more reason why it isextremely important to base the experimental measurements

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Meas. Sci. Technol. 22 (2011) 025106 A Hijazi et al

on differential intensity readings rather than absolute intensityreadings; in the presence of variation in the baseline value,absolute readings will lead to undetected errors in the measuredtemperatures.

The first calibration step was done using the black paintedcopper plate described previously. The IR camera was usedwith one of the bandpass filters to image the region in betweenthe two thermocouples. The camera was set to capture animage every 2 s, in synchronization with the thermocouplereadings. The plate was gradually heated up to 330 ◦C bypassing an increasing current through the heater coil. Thenthe current was switched off and the plate was allowed tocool down to 80 ◦C. The second bandpass filter was thenused and the same heating and cooling cycle was repeated.To ensure higher reliability of the calibration data, two morerepeats of the heating and cooling cycles were carried out withthe first and second bandpass filters. This resulted in fourtemperature versus camera intensity count curves for each ofthe two filters, two obtained during heating and two duringcooling. To keep track of the drift of the background readingduring the calibration experiment, a background reading wastaken every 30 s by blocking the view of the camera for a fewseconds using a sheet of paper.

Figure 4(a) shows the camera intensity count readings ofthe target and the background versus the frame number duringthe calibration experiment. It can be clearly observed from thefigure that the background reading continuously increases dueto the heating of the lens body and the filters. The figure showsthat there was a total drift in the background reading of about150 intensity counts (which corresponds to less than a 10 ◦Cincrease in the temperature of the lens body) during the fourheating and cooling cycles which took about an hour.

Figure 4(b) shows the camera intensity count readingsversus the thermocouple temperature readings during the twoheating and cooling cycles for each of the two filters. It canbe seen from the figure that there is a clear difference betweenthe four curves corresponding to each filter and this differenceis more obvious at lower temperatures. This difference is dueto the drift in the background reading and thus it becomesmore pronounced at lower temperatures since the amount ofradiation received from the target surface is relatively small.

Figure 4(c) shows the ‘differential’ camera intensityreadings versus the thermocouple temperature readings duringthe two heating and cooling cycles with each of the twofilters. The differential intensity readings were obtained bysubtracting the interpolated background reading at the sametime instance, seen in figure 4(a), from each of the cameraintensity readings. It can be seen from figure 4(c) that the fourcurves corresponding to each of the two filters became almostidentical after removing the background. This results in twodistinct curves, each representing the relationship between thedifferential camera intensity reading and temperature for eachof the two filters. These two curves are fitted using higher orderpolynomials to obtain the ‘experimental’ differential cameraintensity (DCI) reading as a function of temperature for eachof the two filters. The two resulting curve fit equations areDCI403 = −5 × 10−11T 6 + 7 × 10−8T 5

− 3 × 10−5T 4 + 0.0089T 3

− 1.2852T 2 + 96.512T − 2930.7 (13)

DCI465 = −7 × 10−11T 6 + 8 × 10−8T 5

− 4 × 10−5T 4 + 0.0092T 3

− 1.2284T 2 + 86.654T − 2480.1 (14)

where the temperature is in ◦C (with goodness of fit R2 =0.9997 for both). The relations given by these experimentalcurves are analogous to the theoretical relation given byequation (10). Figure 4(d) compares the experimentalvalues of the differential camera intensity (obtained fromequations (13) and (14) with the corresponding theoreticalvalues of the differential detector reading (obtained fromequation (10)) for the same temperature values for each of thetwo filters. From this figure it is clear that the experimentalvalues are linearly proportional to the theoretical values.

As a matter of fact, the aim of our calibration procedureis to correlate the experimental and theoretical differentialintensity values for both filters as shown in figure 4(d), sincea lot of useful information can be obtained from such a figure.Firstly, this figure helps identify the linear range of the detectorresponse. It is necessary to have a linear detector response tobe able to predict temperatures using the theoretical relationgiven by equation (12). For instance, it is found that thedetector response starts to deviate from linearity at ‘absolute’intensity readings greater than 3200 counts which, for oursetup, corresponds to a differential intensity count of about1300 counts. Thus, these data points are eliminated fromfigure 4(d) and care was taken to ensure that the absolutecamera intensity reading did not exceeded 3200 counts inthe subsequent measurements. Secondly, since the camerasettings are the same when each of the two filters is used andthe emissivity of the black plate used in this first calibrationstep is believed to be independent of wavelength, the productof the camera settings constant and spectral emissivity (ksεx,y

in equation (10)) should be the same for both filters. If all thespectral curves (transmittance, reflectance, and response) usedfor each of the two filters are accurate, the two curves infigure 4(d) should be the same and overlap one another.However, it can be seen from the figure that there is a smalldifference in the slopes of the two lines. This small differencein the slope values may be attributed to a variety of factors, butis likely due to the difference in the atmospheric transmittancein the two wavelength bands (which was not included inequation (10)). The transmittance in the range of the 465filter is expected to be slightly lower than that in the rangeof the 403 filter since similar trend can be observed for thelonger path-length data reported in the literature. Since theslopes of the two lines are different, the correction factor Cf

in equation (11) can be simply calculated as the ratio of thetwo slopes. From the equations of the trendlines shown infigure 4(d), the correction factor Cf can be calculated to be3.193/3.101 = 1.03. Finally, if the background compensationapproach is valid and the obtained background readings areaccurate, then the values of the y intercepts for both linesshould be equal to zero. From the figure, it can be seen thatthe y intercepts for both lines are very small, in the rangeof the random noise in camera intensity readings, and can beneglected. This confirms that our approach of obtaining the

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Meas. Sci. Technol. 22 (2011) 025106 A Hijazi et al

(a) (b)

(c) (d)

Figure 4. Calibration approach (black plate data); (a) camera intensity readings for the hot target surface and the background, (b) cameraintensity versus thermocouple temperature readings, (c) differential camera intensity versus temperature, (d) differential camera intensity(experimental) versus differential detector reading (theoretical).

background reading by blocking the view of the camera usinga sheet of paper is quite adequate.

After identifying the linear range of the camera responsethrough the black plate calibration, the same calibrationprocedure was repeated with each of the two Al 6061-T6calibration targets. The results of the calibration procedure forthe two aluminium targets, finished with 600-grit and 1500-grit abrasives, are shown in figures 5(a) and (b), respectively.From the figures it can again be noted that there is a linearrelationship between the experimental differential intensityvalue and that expected theoretically. It can be noted that theslopes of the curves are lower than those of the curves obtainedfor the blackbody (figure 4(d)), due to the lower emissivity ofthe aluminium plates as compared to that of the black plate.Although determining the emissivity values is not necessaryfor inferring the temperatures using this approach, the actualemissivity of a given target in a given wavelength range (εx,y)can be obtained as the ratio of the slopes of the calibrationlines for the target to that for the black plate (whose emissivity

ε is known to be 0.96) in that wavelength range. The spectralemissivity of the surface finished with 600-grit abrasives wasfound to be ε403 = 0.644 and ε465 = 0.622, with the 403 and465 bandpass filters, respectively. The corresponding valuesfor the surface finished with the 1500-grit abrasive are foundto be ε403 = 0.256, and ε465 = 0.271. This indicates thatthe greybody assumption is not applicable to either of the twotargets.

The NGCF (i.e. the spectral emissivity ratio rε) for each ofthe two targets can be determined from the figure by dividingthe slopes of the two lines representing the two bandpassfilters then dividing that by the correction factor Cf obtainedfrom the black plate calibration. Therefore, the NGCFs for the600-grit and 1500-grit targets are found to be 1.035 and 0.944,respectively. This indicates that the greybody assumption isnot applicable to either of the two targets since the NGCFis not unity. It should be obvious that the ratio of theslopes of the two lines in figures 5(a) or (b) is simply theproduct of the correction factor Cf and the NGCF for that

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Meas. Sci. Technol. 22 (2011) 025106 A Hijazi et al

(a)

(b)

Figure 5. Differential camera intensity versus differential detectorsignal for Al 6061-T6 targets with different surface finishes;(a) 600 grit, (b) 1500 grit.

corresponding target and this product can be directly usedfor calculating temperatures from equation (12). While thismight suggest that the black plate calibration is not needed,the black plate calibration is necessary to identify the rangeof linear response of the camera. Furthermore, it should berealized that the relationships between the experimental andtheoretical differential intensity values will not be linear if theemissivity of the surface changes with temperature (thoughit was not the case here but it might be expected in somecases). In such a case, the spectral emissivity ratio mightbe temperature dependent as well and it can be evaluated bynumerically dividing the two curve fit equations correspondingto the two filters and obtaining a new curve fit equation for theemissivity ratio as a function of temperature, rε(T ). Thistemperature-dependent ratio can still be used for predictingtemperatures using equation (12), but an iterative solution willbe needed in such a case.

The linearity of the curves in figure 5 indicates thatemissivity values do not change with temperature within thetemperature range used in the calibration experiments (upto about 350 ◦C). Additionally, since the emissivity of thealuminium targets is lower than that of the black target,they can be heated to temperatures higher than 350 ◦C

without exceeding the limit of the linear response range of thedetector. However, higher temperatures were avoided duringthe calibration experiments in order to avoid the buildup ofan oxide layer that can cause the emissivity to change. Wenand Mudawar [22] showed that the emissivity of differentaluminium alloys changes with temperature for temperaturesfrom 327 to 527 ◦C, and attributed this change in emissivityto the formation of a relatively thick oxide layer at highertemperatures. While temperatures above 400 ◦C may beencountered in the cutting zone during the machining ofaluminium, oxidation will not be an issue since the totaltime period from the moment the material is heated to hightemperature in the cutting zone until it exits the field of viewof the camera is less than 1 ms. Therefore, it is reasonable toassume that the ratio of the emissivities in the two wavelengthranges obtained from our calibration experiments can also beused at higher temperatures.

7. Validation and error assessment

7.1. Validation experiments

The results of the calibration experiments show that, not onlydo the aluminium targets not exhibit greybody behaviour, butalso the spectral emissivity ratio for the aluminium targetschanges with surface finish. In order to test the accuracy ofour approach, validation experiments were done by imagingeach of the two aluminium targets (600 grit and 1500 grit) atthree known temperature values 150, 225 and 300 ◦C. The truetemperatures were read by the thermocouples and temperaturepredictions were made using the dual-wavelength approach(equation (12)) with different values of the NGCF. Figures 6(a)and (b) show the relative errors of the predicted temperaturesfor the 600-grit and 1500-grit targets, respectively. From thefigure it can be clearly seen that the dual-wavelength approachcannot predict the temperature accurately for either of the twosurfaces under the assumption of greybody behaviour (rε = 1).Under the greybody assumption, the absolute error averageswere 9.5% and 13% (for the 600-grit and 1500-grit targets,respectively) where these errors are mainly systematic. Also,it can be seen from the figure that the average errors will be evenhigher if temperature predictions of any of the two surfaceswere made based on the NGCF of the other surface. Whenthe appropriate NGCF is used for each of the two targets,rε = 1.035 for 600 grit and rε = 0.944 for 1500 grit, theaverage absolute error reduces to be 1.5% and 1.8% for thetwo targets, respectively.

7.2. Machining temperatures error assessment

The data presented in figure 6 clearly show that assuminggreybody behaviour leads to a relatively large systematic errorin temperature predictions obtained using the dual-wavelengthapproach and that the accuracy of temperature predictions ishighly sensitive to the value of the NGCF being used. Theuse of the correct value of the NGCF eliminates the systematicerror and the remaining error will be completely random. Themagnitude of random error is inversely proportional to thefourth power of temperature since at lower temperatures the

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Meas. Sci. Technol. 22 (2011) 025106 A Hijazi et al

(a)

(b)

Figure 6. Relative errors in temperature predictions using differentvalues of the NGCF for the two targets; (a) 600 grit, (b) 1500 grit.

amount of radiation received by the detector will be lower andthat reduces the signal to noise ratio and thus increases randomerror. The fact that differential detector readings are used inour approach leads to a significant increase in the random errorin temperature predictions for temperatures close to ambient,and the error quickly reduces as temperature increases. Inorder to obtain a realistic quantitative estimate of the expectedrandom error, the maximum temperature error was determinedtheoretically at a detector signal level in the middle of the linearresponse range of our detector (an intensity reading of about2600 counts). For our camera system, the maximum randomvariation in the detector signal at a fixed temperature is found tobe ±4 counts and that leads to a maximum random temperatureerror of less than ±2%. This magnitude of maximum randomerror corresponds to a temperature of about 300 ◦C for the 600-grit target and the error will be smaller at higher temperatures.However, as a conservative measure, the same magnitude ofmaximum random error is assumed for temperatures higherthan 300 ◦C.

While the estimate of ±2% random error holds for thevalidation experiments where the average camera intensityreading (over the entire FPA) is used and the target can beheld at constant temperature while the filters are switchedquickly, additional sources of random and systematic errors areexpected for temperature measurements during the machiningexperiments. The major source of random errors expected

during the machining experiments arises from the fact thatthe images captured using the two bandpass filters are notcaptured simultaneously, since each experiment is repeatedtwice, once with each filter. Our machining experimentsshowed that even after steady state conditions are reached(about 2 s after the start of the cut), consecutive IR imagescontinued to show some variation in the radiation level whichclearly indicates that some dynamic events are taking place.These dynamic events are also evident from examining thechip thickness where slight variations in the chip thicknesscan be detected. The most effective approach to eliminate theerror in the dual-wavelength temperature predictions resultingfrom this variation is to use two synchronized IR camerasthat capture images simultaneously in two wavelength bandsor to use a single IR camera with an image splitting opticthat enables the capture of two simultaneous images side byside on the same FPA [32]. However, our experimental setupemployed a single camera with switchable filters and for sucha setup the additional sources of error include (1) variationin the camera intensity readings for consecutive frames evenafter a steady state is achieved, (2) difficulty of obtaining aperfect, repeatable, spatial matching of images captured withthe same filter or with different filters especially that a slightchange in the tool position, due to vibration, is observed inconsecutive images, (3) slight non-uniformity in the responseof individual pixels to a constant uniform temperature, and(4) slight difference in the amount of random intensityvariation of individual pixels. These sources of error can leadto a dramatic increase in the expected error in the estimatedtemperatures. A thorough investigation of these sources oferror showed that the variation reduces significantly by usingtemporal averaging of several consecutive frames capturedwith each of the two bandpass filters and spatial averaging oversubsets of 4 × 4 pixels. This averaging of the camera intensitycounts needs to take place before calculating temperaturesusing the dual-wavelength approach. With this temporal andspatial averaging approach, it was found that the variation inthe differential camera intensity readings can reach ±10 countsand that leads to ±3.5% error in temperature predictions.

Additional systematic error might arise from the deviationof the actual NGCF from the value determined fromcalibration. The ideal approach for determining the valueof the NGCF is to use actual chips, observed from the side,for calibration. However, it was not possible to use chipsfor the calibration due to their very small thickness (less than0.5 mm) and the waviness of their surfaces which make itextremely difficult to attach thermocouples or get reliabletemperature readings for the calibration. It was observedthat when machining tubes having highly polished surfaces,the surface roughness on the side of the produced chip willbe higher than the original roughness of the surface and thisincrease in surface roughness is attributed to the large plasticdeformation that takes place in the PSZ. On the other hand, fortubes having relatively rough surfaces, such as those polishedwith 600-grit paper, there will be very small difference insurface roughness between the original tube surface and theside surface of the produced chip. Since the calibrationexperiments showed that the NGCF is strongly influenced by

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Meas. Sci. Technol. 22 (2011) 025106 A Hijazi et al

surface roughness, the tubes used in the cutting experimentshad a relatively rough surface finish. The tubes were onlypolished using the 600-grit paper to remove turning marks andthus the NGCF of the 600-grit target was used for temperaturecalculations. In order to account for any minor differences insurface roughness between the side of the chip and the 600-gritcalibration target, a ±2% variation in the value of the NGCFwas assumed. This small variation in the NGCF will lead tolarger variation in the estimated temperatures and theoreticalanalysis showed that its effect slightly reduces as temperatureincreases. The ±2% variation in the NGCF was found tocause ±5% error in the estimated temperature at 300 ◦C and,as a conservative measure, the same percentage of error wasassumed for higher temperatures. Combining the estimatesof random and systematic errors gives a total maximum errorof ±8.5% for the machining temperatures predicted using thedual-wavelength approach compensated for spectral variationsin emissivity.

Using the same calibration procedure for the two filtersthat were used for temperature measurements in the cuttingexperiments presented in this paper, which are the 3.43 andthe 4.03 μm (as indicated earlier in section 4), the NGCF wasdetermined to be 1.069 for the 600-grit target. The theoreticalerror assessment yielded a slightly higher value for the randomerror due to the slightly lower signal to noise ratio for the3.43 μm filter and the estimated total maximum error wasfound to be ±8.7%.

8. Machining temperature results

Orthogonal cutting experiments were conducted on Al 6061-T6 tubes at a constant feed of 160 μm rev−1. Three differentcutting speeds of 2, 5 and 8 m s−1 were used in the experimentsto demonstrate the effect of cutting speed on machiningtemperatures. The chip–tool interface temperature distributionprofiles were obtained along a line parallel to the rake face ofthe tool and located about 20 μm inside the chip. Figure 7shows the temperature distribution profiles obtained for thethree different cutting speeds plotted as a function of thedistance from cutting edge. It should be noted that, due tothe spatial averaging, temperatures cannot be resolved at thefull spatial resolution of the FPA (i.e. for each individual pixel),but rather one temperature data point was obtained for every12 pixels, with a spatial resolution of 0.05 mm. The figureclearly shows the dependence of machining temperatureson cutting speed and the average and maximum rake facetemperatures are given in table 1. Each of the temperatureprofiles shows that the material is already at a high temperaturewhen it reaches the cutting edge and the temperature continuesto increase further as the chip slides over the rake faceof the tool. Toward the end of contact, the temperaturebegins to decrease. The figure clearly indicates that thetemperature increase in the secondary shear zone is relativelysmall for the higher cutting speeds where more heating willtake place in the PSZ due to more of the heat remainingin the work material (i.e. less heat is lost and the processbecomes more adiabatic). The higher temperature of thechip causes its shear strength to be lower, which reduces

Figure 7. Al 6061-T6 chip temperature distribution profiles alongthe rake face at different cutting speeds (160 μm rev−1 feed, +20◦

rake angle).

Table 1. Al 6061-T6 chip temperature along the rake face atdifferent cutting speeds (160 μm rev−1 feed, +20◦ rake angle).

Average MaximumCutting speed temperature temperature(m s−1) (◦C) (◦C)

2 256 2835 328 3388 429 442

the heat production due to secondary shear deformation.For the low cutting speed (2 m s−1) the temperature increasein the secondary shear zone is more pronounced. The trend ofthese rake face temperature profiles is in close agreement withthe trend of rake face temperature profiles obtained by Davies[16] for the machining of AISI-1045 steel.

9. Concluding remarks

In this study, we have presented a new approachfor determining temperatures using the dual-wavelengthtechnique while compensating for the spectral dependenceof emissivity. Our approach is based on Planck’s radiationequation and explicitly accounts for the wavelength-dependentresponse of the IR detector and the losses occurring due to eachof the elements of the IR imaging system that affect the totalradiant energy sensed in different spectral bands. A thoroughcalibration procedure is used to determine the NGCF, whichrelates the actual ratio of the differential radiation intensityreadings to the theoretically expected ratio. Use of differentialradiation intensity readings reduces the experimental errorduring calibration and measurements. This approach has beenvalidated using Al 6061-T6 targets having two different surfaceroughness values. The experiments show that neither of thetwo surfaces exhibits greybody behaviour, that the NGCFdepends on surface roughness, and that the accuracy of dual-wavelength thermometry is highly dependent on the value ofthe NGCF. With the inclusion of the correct value of the NGCF,temperatures can be measured with a maximum random errorof less than ±2%.

This approach was used to measure the chip temperaturedistribution along the tool–chip interface during orthogonal

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Meas. Sci. Technol. 22 (2011) 025106 A Hijazi et al

cutting of Al 6061-T6 tubes at three different cuttingspeeds. The estimated uncertainty in the measured machiningtemperatures is ±8.7% and the uncertainty can be furtherreduced by capturing simultaneous images in two wavelengthbands. From the results of this study, it is concluded that dual-wavelength thermometry, assuming greybody behaviour, canresult in significant errors in temperature estimation and thatthe spectral dependence of emissivity can be determined andused to improve the accuracy of the temperature estimates.

Acknowledgments

We are pleased to acknowledge support from the U.S.Army Research Office (grant number DAAD190310174,Program Manager Bruce LaMattina) which made thiswork possible. Special thanks to Jeff Leake of theLeake Co. for providing the Merlin IR camera used inthe experiments. The experiments were conducted in theManufacturing Processes Research Lab at Wichita StateUniversity (http://engr.wichita.edu/vmadhavan/MPRL.htm).

References

[1] Takeyama H and Murata T 1963 Basic investigations on toolwear Trans. ASME, J. Eng. Ind. 85 33–8

[2] Davies M, Ueda T, M’Saoubi R, Mullany B and Cooke A2007 On the measurement of temperature in materialremoval processes CIRP Ann. 56 581–604

[3] Komanduri R and Hou Z 2001 A review of the experimentaltechniques for the measurement of heat and temperaturesgenerated in some manufacturing processes and tribologyTrib. Int. 34 653–82

[4] Longbottom J and Lanham J 2005 Cutting temperaturemeasurement while machining—a review Aircr. Eng.Aerosp. Technol. 77 122–30

[5] Ueda T, Al Huda M, Yamada K and Nakayama K 1999Temperature measurement of CBN tool in turning of highhardness steel CIRP Ann. 48 63–6

[6] Al Huda M, Yamada K, Hosokawa A and Ueda T 2002Investigation of temperature at tool-chip interface in turningusing two-color pyrometer Trans. ASME, J. Manuf. Sci.Eng. 124 200–7

[7] Muller B and Renz U 2001 Development of a fast fiber-optictwo-color pyrometer for the temperature measurement ofsurfaces with varying emissivities Rev. Sci. Instrum.72 3366–74

[8] Muller B, Renz U, Hoppe S and Klocke F 2004 Radiationthermometry at a high-speed turning process Trans. ASME,J. Manuf. Sci. Eng. 126 488–95

[9] Narayanan V, Krishnamurthy K, Chandrasekar S, Farris Tand Madhavan V 2001 Measurement of the temperaturefield at the tool-chip interface in machining Proc. ASME Int.Mech. Eng. Cong. and Expos. (New York, NY) pp 1–8

[10] Coates P 1981 Multi-wavelength pyrometry Metrologia17 103–9

[11] Neuer G, Fiessler L, Groll M and Schreiber E 1992 Criticalanalysis of the different methods of multi-wavelengthpyrometry Temperature: Its Measurement and Control inScience and Industry vol 6 ed J F Schooley (New York:American Institute of Physics) pp 787–9

[12] Sutter G, Faure L, Molinari A, Ranc N and Pina V 2003 Anexperimental technique for the measurement of temperaturefields for the orthogonal cutting in high speed machiningInt. J. Mach. Tool. Manuf. 43 671–8

[13] Schwerd F 1933 Determination of the temperature distributionduring cutting Z. VDI 7 191–202

[14] Boothroyd G 1961 Photographic technique for thedetermination of metal cutting temperatures Br. J. Appl.Phys. 12 238–42

[15] Jeelani S 1981 Measurement of temperature distribution inmachining using IR photography Wear 68 191–202

[16] Davies M, Yoon H, Schmitz T, Burns T and Kennedy M 2003Calibrated thermal microscopy of the tool-chip interface inmachining Mach. Sci. Technol. 7 167–90

[17] Baehr H and Stephan K 2006 Heat and Mass Transfer 2nd edn(New York: Springer) p 540

[18] Davies M, Cooke A and Larsen E 2005 High bandwidththermal microscopy of machining AISI 1045 steel CIRPAnn. 54 63–6

[19] Pujana J, Del-Campo L, Perez-Saez R, Tello M, Gallego Iand Arrazola P 2007 Radiation thermometry applied totemperature measurement in the cutting process Meas. Sci.Technol. 18 3409–16

[20] Madhavan V, Chandrasekar S and Farris T 2002 Directobservation of the chip-tool interface in the low-speedcutting of pure metals J. Tribol. 124 617–26

[21] Kobayashi M, Ono A, Otsuki M, Sakate H and Sakuma F 1999A database of normal spectral emissivities of metals at hightemperatures Int. J. Thermophys. 20 299–308

[22] Wen C and Mudawar I 2004 Emissivity characteristics ofroughened aluminum alloy surfaces and assessment ofmultispectral radiation thermometry (MRT) emissivitymodels Int. J. Heat Mass Transf. 47 3591–605

[23] DeWitt D and Nutter G 1988 Theory and Practice of RadiationThermometry (New York: Wiley)

[24] Inagaki T and Ishii T 2001 Proposal of quantitativetemperature measurement using two-color techniquecombined with several infrared radiometers having differentdetection wavelength bands Opt. Eng. 40 372–80

[25] Khan M, Allemand C and Eager T 1990 Noncontacttemperature measurement I: interpolation based techniquesRev. Sci. Instrum. 62 392–402

[26] DeWitt D and Kunz H 1972 Theory and technique for surfacetemperature determinations by measuring the radiancetemperatures and the absorption ratio for two wavelengthsTemperature: Its Measurement and Control in Science andIndustry Part 1 vol 4 ed H H Plumb (Pittsburgh: InstrumentSociety of America) pp 599–610

[27] Linkoln R and Pettit R 1973 A two-wavelength technique forthe simultaneous measurement of high temperature and thetemperature dependence of spectral emittances High Temp.High Press. 5 421–32

[28] Ruffino G 1979 Surface temperature measurement throughradiance temperature and emissivity at two wavelengthsHigh Temp. High Press. 11 221

[29] Gardner J and Jones T 1980 Multi-wavelength radiationpyrometry where reflectance is measured to estimateemissivity J. Phys. E: Sci. Instrum. 13 306

[30] Tsai B, Shoemaker R, DeWitt D, Cowans B, Dardas Z,Delgass W and Dail G 1990 Dual-wavelength radiationthermometry: emissivity compensation algorithms Int. J.Thermophys. 11 269–81

[31] Golay M 1974 Introduction to Astronomical Photometry(Dordrecht: Reidel) p 14

[32] Hijazi A and Madhavan V 2009 An image-splitting-opticfor dual-wavelength imaging Proc. SPIE7494 749403

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