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j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 2 ( 2 0 0 8 ) 475–485
journa l homepage: www.e lsev ier .com/ locate / jmatprotec
n-process high-speed photography applied torthogonal turning
. Pujana ∗, P.J. Arrazola, J.A. Villaraculty of Engineering, Mondragon University, Loramendi 4, 20500 Arrasate, Gipuzkoa, Spain
r t i c l e i n f o
rticle history:
eceived 18 April 2007
eceived in revised form
September 2007
ccepted 1 October 2007
a b s t r a c t
Material behaviour understanding is a basic pillar for the building of predictive models
applied to machining processes and the majority of the formulated material flow rules that
are intimately associated to strain and strain rate. The use of high-speed filming allows
observing a sequence of frozen images focused on the chip formation area when machining
steel in orthogonal turning tests. This article presents the set-up and images acquired over
square grid marked tube work-pieces on 42CrMo4 steel. Variables such as chip geometry,
shear angle, strain, strain rate, chip thickness, and tool vibration amplitude are measured.
eywords:
igh-speed photography
achining
train
low patterns
Information acquired by the displacement of flow patterns allows measuring of plastic vari-
ables. Strain and strain rate results are calculated and compared to analytical modelling
results. Industrial machining speeds and feeds are analysed by means of short shutter
times, high image acquisition rates, and high magnifications achieving a good compromise
between image quality, recording continuity, and cost of the equipment and experiments.
calculated erroneously.
. Introduction
he understanding and explanation of the cutting processnvolves different research areas such as plasticity, thermody-amics, vibrations, wear, etc. Traditionally, because of specificnowledge of these areas, analytical models (Merchant, 1945;xley, 1989; Tounsi et al., 2002) have been formulated toxplain the cutting process. Lately, the development of fasteromputers and the generalization of numerical simulationrograms, generally based on finite element method, FEM
Arrazola, 2003; Chuzhoy et al., 2003; Simoneau and Elbestawi,007), has led to make an effort on more comprehensiveimulation models. Inside this framework, the experimentalnderstanding of the process is focused on specific charac-erization areas such as temperature measurement (Davies
t al., 2003; M’saoubi and Chandrasekaran, 2004), frictionnalysis (Filice et al., 2007), high-speed filming (Klocke andoppe, 2004), material behaviour characterization (Haman et∗ Corresponding author. Tel.: +34 943794700; fax: +34 943791536.E-mail address: [email protected] (J. Pujana).
924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.jmatprotec.2007.10.007
© 2007 Elsevier B.V. All rights reserved.
al., 2002; Jaspers and Dautzenberg, 2002a; Chandrasekaranand M’saoubi, 2005), and post-mortem chip and tool studies(Brown, 1987; Trent, 1991).
The study of strain, strain rates and chip formation inmachining operations has mostly been performed by meansof quick-stop devices (QSDs) (Brown, 1975; Vorm, 1976; Wagerand Brown, 1980; Griffiths, 1986; Jaspers and Dautzenberg,2002b; Chern, 2005). The use of quick-stop devices allowsextracting the chip root as it strains in the real process, butthere exists a tool–chip separation delay which is dependenton the design of the employed QSD. This delay time mightalter the deformation state to which the material is subjectedduring machining and if it is reasonably high, values of shearangle and strain calculation in the primary shear zone will be
There exist several methods of marking the material tomachine in order to measure the strains given in the pri-mary shear zone into the coated grids, there exist three main
n g t
476 j o u r n a l o f m a t e r i a l s p r o c e s s itechniques: the joining with adhesives, printing methods andphotochemical coating methods. When dealing with sinkedgrids, mechanical abrasion, thermal abrasion and chemicalabrasion should be mentioned (Leopold and Meisel, 2001).The analyses of strain in the primary shear zone (PSZ) havemainly been carried out producing a grid of lines or chessboard grids. Mechanical abrasion methods for producing gridlines were described by Baraya et al. (1963) as satisfactory formost work when milling cutters are employed, achieving up to4 lines/mm. Childs (Childs, 1971) employed a micro-hardnessdiamond for scratching the work-piece surface achieving adensity of 40 lines/mm. The principal drawback of mechan-ical methods is that they tend to be laborious and thequality of the scratches might not be appropriate once thedeformation occurs, especially when filming at high speedswhere light reflection has paramount importance. Nowadays,the use of electrochemical and photographic techniques ismore common. Electrochemical printing methods are usu-ally employed in forming process (Vogel et al., 1992) whereperiodic circular and square grid masks are employed. Thismethod is mostly used in large parts and inaccuracies asso-ciated with this technique have been analysed by Bruneel(2000) where real systematic errors of the order of 2–2.4%have been calculated. The use of chemical abrasion, photo-etching lithographic printing methods is more common incutting process. Researchers like Bao (1977), Oxley (1989) andLeopold and Schmidt (2000) have used this technique. Veryhigh resolutions, of the order of micrometers, can be achievedwith this printing method when the process is applied inclean rooms. Even so, this technique offers two main dis-advantages. It is fairly expensive and it is applied on flatsurfaces.
An alternative method to the use of QSDs for studying thestrain and strain rate field in machining operations could bethe high-speed filming. When frozen images are to be achievedusing high-speed filming devices, very short exposure timesare necessary, and event continuity is ensured increasing theframe rate acquisition. Early in the 1980s, Komanduri andBrown (1981) presented a work on the mechanics of chip seg-mentation where images up to 3300 frames per second (fps)were recorded working at cutting speeds up to 55 m/min. Theemployed lighting systems were a high-intensity xenon arclamp, and a mercury vapour lamp. In 2000, Ackroyd et al. pub-lished a study where the high-speed photography was notused for chip segmentation studies but used for characteriz-ing the chip–tool interface by means of transparent sapphiretools. In this work, images at 3000 fps reaching lineal cuttingspeeds of 90 m/min are recorded. No clue about the employedlighting system is given in this work. Recently, Sutter (2005)published a work where high-speed filming was presentedas an alternative to chip formation studies where QSDs areemployed. As stated by the author, QSDs are very time con-suming, there is a time delay in the tool retraction process, andthe experimental arrangement of QSDs is fairly problematic.In that work, Sutter analyses the length of tool–chip contactand shear angle as the real process occurs at lineal cutting
speeds of 1020–3600 m/min. The lighting system is based ontwo synchronised high-power flash lights properly balancedfor avoiding the shadows. Particle image velocimetry (PIV)is a different approach for strain and strain rate calculatione c h n o l o g y 2 0 2 ( 2 0 0 8 ) 475–485
when employing high-speed photography. This technique isbased on the two-dimensional analysis of flow fields, usuallyapplied in fluids, comparing the position of different parti-cles at two consecutive images with a very short time delaybetween them. Lee et al. made use of the PIV for the analy-sis of strain in the orthogonal cutting process (Sutter, 2005).The plane strain state is ensured constraining the work-piecebetween soft glass blocks and linearly machining at 0.6 m/minon 2-mm-thick and 50-mm-long work-pieces. 250 fps acquisi-tion rates are used and no data on the used exposure time andlighting system are given.
This article analyses the application of high-speed photo-graphic technique applied to the orthogonal turning processof cylindrical work-pieces, and the use of the acquired imagesfor different variable measurements such as shear angle,deformed chip thickness, and tool vibration. A new methodol-ogy for the assessment of strain and strain rate measurementin the primary shear zone over cylindrical work-pieces is alsodescribed in detail. Appropriate lighting and the printing ofsquared grids allow the employment of visioplasticity whileimages are acquired in real time, presenting the high-speedfilming as an alternative to the use of QSDs for the analysis ofthe PSZ.
2. Experimental set-up
2.1. Image acquisition equipment
Two main elements compose the image acquisition equip-ment: lighting and camera. Filming the machining process atcommon industrial cutting speeds can be considered as prob-lematic because the relation of motion speed to sample sizeis very high, of the order of 50,000 s−1, and also the size ofthe area to be viewed is relatively small, around 1 mm2. Thisfact implies that images have to be captured at very shortexposure times and the lighting intensity on the viewing areahas to be high also. In order to overcome these requirements,a fibre optic guided metallic halide lighting system of 270 Wand 2 s 540 W boost power has been employed. The electricalwave that generates the discharge in the lamp has been con-verted into a square shape wave in order to make the voltagepolarization change time minimum. In conjunction with thehigh-colour temperatures of metallic halide lamps, details ofthe material flow pattern in the primary shear zone have beenrecorded. Fig. 1 illustrates the experimental arrangement ofthe camera and lighting on the lathe, and the detail of thefibre optic light guide which has been placed close to the tooltip, focusing all the luminous power in an approximately 25-mm-diameter spot.
The employed camera is a Photron’s Ultima APX-RS modelwith a maximum record rate of 250,000 fps, and a maxi-mum resolution of 1024 × 1024 pixels up to 3000 fps. Whenacquiring images, minimum exposure times of 1 �s, havebeen employed. These short exposure times limit the blur-ring distance to acceptable values of the order of 2.5–5 �m
at the employed conditions. For the consecution of magnifiedimages, as it is appreciated in Fig. 1, a microscopic 12 mm Nav-itar 12× lens with a 100 mm extension tube is attached to thecamera.
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c
Fig. 1 – Disposition of high-speed photography equipmenti
sqbsetts
2
Odcwro
dmespw(twsw1irctrupwts
n the lathe.
Although the use of high-speed photography techniquesuch as the ones applied in particle image velocimetry, fre-uently employing pulsed laser lighting (Cu) systems, oftenehave better than conventional lighting systems, the cost ofuch equipment and the security reasons associated with themitted high intensities, make its use in machining opera-ions rather delicate. The use of metallic halides has proveno give good quality results once the light is concentrated in aufficiently small area.
.2. Work-piece preparation
rthogonal turning tests over 45-mm-long and 85-mm-iameter work-pieces with a wall thickness of 3 mm arearried out. Employed material is a 42CrMo4 steel machinedith uncoated WC P10 SPUN120308 tool inserts which have a
ake angle of +6◦, a clearance angle of +5◦, and an edge radiusf 5 �m.
For the consecution of micro-scale grid printings, threeifferent grid marking methods have been analysed: ther-al abrasion by means of laser marking, electrochemical
tching and photochemical etching. The aim of this analy-is was to find a simple, fast and reasonable accurate gridrinting method for its use in steel samples. Worst resultsere achieved when electrochemical serigraphic methods
Bruneel, 2000) were used reaching minimum line separa-ions of 0.25 mm. More accurate results on flat steel samplesere attained by means of photochemical milling. Chess type
quare grids were printed on steel by means of plastic masksith UV exposure times of 8 s, and chemical etching times of
2 s employing ferric chloride. At these conditions the orig-nal square marks were transformed into round marks withesolutions down to 0.125 mm between two consecutive cir-les. One important drawback when using this technique washe lack of uniformity on the generated print marks. The bestesults were achieved with laser printing method reachingniform marks at relatively reduced dimensions. After work-
ieces were polished to a Ra roughness lower than 0.8 �m,ork-pieces were mounted in a rotary laser machine wherehe laser head marked the work-pieces with square lengthizes of 0.065 mm. Fig. 2 in next section shows an image of the
h n o l o g y 2 0 2 ( 2 0 0 8 ) 475–485 477
laser marked grid during the chip formation process. Betterresolutions were probably attained by employing clean roomphotochemical methods (Bao, 1977), but the high cost of theprocess, difficult accessibility to the marking equipment andthe use of cylindrical work-pieces led to the use of laser mark-ing.
3. Results
3.1. Image acquisition
All images have been acquired at a frequency of22,500–25,000 fps with exposure times of 1 �s. At highesttested cutting speeds, Vc: 300 m/min, the travelling distancefrom one image to the next one is 0.22 mm; and the blurringdistance, the distance that work-piece moves while shutteris open is 5 �m, around 8% of the grid size. In Fig. 2, twoinstantaneous images of the work-pieces are photographedwhile machining at Vc: 150, 300 m/min and feeds of f: 0.3 and0.2 mm, left and right images, respectively.
Grid printed images are appropriate for strain analysisof the primary shear zone although other variables, suchas contact lengths, chip thickness, and shear angles, arebetter interpreted in plane, non-printed work-pieces. Oneof the advantages that high-speed photography offers withrespect to the analytical or numerical predictive models isthe capability of shear angle, chip thickness, strain, and strainmeasurement over non-continuous chip formation conditionsas those shown in Fig. 3. Once images are acquired for a givenset of working conditions and serrated and continuous chipsoccur within the same millisecond, the appropriate imagescan be chosen for its analysis whereas the use of QSDs doesnot allow to selectively choosing the desired chip morphologyin one shot.
Another effect observed in some tests is the apparition ofvibration. Due to the vibration of the tool with respect to thework-piece, a variable thickness chip is formed. The amplitudeand frequency of the vibration can easily be measured on theimage and consequently the chip thickness. If vibration is anon-desired effect, experiments can be repeated and if the aimof the experiment is the analysis of vibration associated withchip formation, high-speed photography allows sampling atfrequencies higher than conventional dynamometers. Vibra-tion on tool has been observed at two feeds, namely f: 0.05 and0.1 mm. The resulting feed, f, and chip thickness, t2, variationsare plotted in Fig. 4 at machining speeds of Vc: 300 m/min.Although feed and chip vary significantly, it has been observedthat shear angle keeps apparently constant through the entireset of images. Calculating the shear angle variation accordingto Eq. (1),
� = tan−1
((f/t2) cos(˛)
1 − (f/t2) sin(˛)
), (1)
where � indicates the shear angle, and ˛ indicates the rakeangle; it is observed that its value does not vary more than±1.7◦, value that well might be committed in other circum-stances due to experimental measurement errors.
478 j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 2 ( 2 0 0 8 ) 475–485
ple
Fig. 2 – Two images acquired with 0.065 mm/square grid sam0.2 mm (right).Average chip thickness and shear angle values obtainedfrom high-speed photography images are given in Table 1.Another variable that has been measured by some authors(Klocke and Hoppe, 2004; Sutter, 2005) is the contact length.
In this work, contact length has not been measured becauseof the ambiguity on measurement. Low chip slopes make thecontact zone area definition rather difficult, and it has beenobserved that apparently it doubles its length within the sameFig. 3 – Two sequence of images acquired at a frequency of 22,50when machining at Vc: 300 m/min and a feed of f: 0.3 mm.
at Vc: 150 m/min, f: 0.3 mm (left) and Vc: 300 m/min, f:
millisecond, so, the use of microscope is believed to be a moreaccurate way for contact length estimation.
3.2. Strain calculation
Calculation of strain and consequently strain rate is based onthe manual measurement of the grid patterns shown eitherin Figs. 2 and 3. Although automated methods have been long
0 Hz the upper sequence and 25,000 Hz the lower sequence,
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 2 ( 2 0 0 8 ) 475–485 479
F ece ad
dGgottX
stnda
ε
wid
ac
Fc
ig. 5 – Representation of a deformed grid shape on work-pieformation under plane strain conditions.
eveloped (Vogel et al., 1992; Lee et al., 2006; Novotny andeiger, 2003; Manthey et al., 1993) for strain measurementsiving good results in stamped parts, the correct interpretationf severely deformed flow patterns is doubtful. Fig. 5 illustrateshe basic square deformation according to the strains at whichhe material is subjected over an original square of dimensions
and Y.In the free face of the chip where images are acquired, plane
train condition does not fulfil. But, it has been consideredhat shear strain components in the z axis of the strain tensor,amely, εxz, εyz are null being the z direction, a principal strainirection. Thus, the strain tensor components are calculatedccording to Eqs. (2) and (3).
i,j˛˛ = ∂ui,j
∂˛, ˛ = x, y, z, where ui,j = ˛∗ij − ˛ (2)
here ˛ indicates the non-deformed length of the basic cuben each of the three spatial directions, and ˛*i,j indicates theeformed basic length for the i, j element.
The angular deformations of the cube are calculatedccording to Eq. (3) since the angular strains in z direction areonsidered to be null. Eq. (3) is similar to the addition of angles
ig. 4 – Variation on feed and chip thickness, t2, at twoutting conditions due to the vibration of the tool.
nd chip obtained from experiments and the basic square
�1 and �2 from Fig. 5.
εi,jxy = 1
2
(∂ui,j
∂y+ ∂vi,j
∂x
)(3)
The strain tensor, ε, is built from Eqs. (2) and (3); and solvingEq. (4), the eigenvalues of the strain tensor are calculated.
∣∣∣∣(
εi,jxx ε
i,jxy
εi,jxy ε
i,jyy
)− �I
∣∣∣∣ = 0 (4)
Principal strains, ε11 and ε22 are defined as the eigenval-ues of the strain tensor and the equivalent strain is calculatedfrom Eq. (5).
εeq. =√
23
(ε : ε) (5)
The third principal strain, ε33, is calculated assuming theincompressibility of the material according to Eq. (6), which isone of the invariants of the strain tensor.
ε11 + ε22 + ε33 = 0 (6)
Strain rates will be approximated according to Eq. (7) wherethe differential time quantity is substituted by an incrementaltime that is dependent on the cutting speed and the size of theprinted grid, L.
εeq. = ∂εeq.
∂t∼= (εeq.(i, j + 1) − εeq.(i, j))Vc
L(7)
Fig. 6 depicts the principal strain values on XY plane for thetested four working conditions. The linear fitting equations foreach set of points are indicated in the legend.
In an ideal plane strain condition, the set of points drawnin Fig. 6 should be over a ε = −ε line. The measured results
11 22agree reasonably well with plane strain conditions and twomain groups of points are depicted in Fig. 6. One of the groupsis close to the (0, 0) point, non-deformed material in the work-piece. The second group is placed around (−0.8, 0.8) strains
480 j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 2 ( 2 0 0 8 ) 475–485
Tabl
e1
–R
esu
lts
exp
erim
enta
llym
easu
red
and
calc
ula
ted
Con
dit
ion
sEx
per
imen
tal
An
alyt
ical
3Dn
um
eric
al
Vc
(m/m
in)
f(m
m)
t 2(m
m)
Shea
ran
gle,
˚(◦
)A
vera
geSt
rain
,εA
vera
geSt
rain
rate
,ε(s
−1)
t 2(m
m)
Shea
ran
gle,
˚(◦
)A
vera
geSt
rain
,εA
vera
geSt
rain
rate
,ε(s
−1)
t 2(m
m)
Shea
ran
gle,
˚(◦
)A
vera
geSt
rain
,εA
vera
geSt
rain
rate
,ε(s
−1)
150
0.3
0.40
380.
7110
,700
0.41
390.
7422
,000
0.47
29.5
0.70
29,8
0020
00.
20.
2841
0.67
22,0
000.
2538
0.66
47,0
000.
3129
.20.
7655
,750
300
0.2
0.26
400.
6733
,700
0.26
400.
6969
,000
0.30
270.
7289
,800
300
0.3
0.39
390.
7328
,700
0.40
400.
7146
,000
0.45
300.
8065
,000
Fig. 6 – Representation of the two principal strains
calculated from Eq. (4) for the tested four workingconditions.belonging to the chip. Smaller quantities of points are alsodepicted in intermediate positions corresponding to the dif-ferent deformation stages encountered in the primary shearzone.
Fig. 7 shows the calculated strains after applying the Eqs.(2)–(6) calculation methodology. Distances have been manu-ally measured and as it can be noted in Fig. 7, the bordersof each original square are visible. An uncertainty of around5–10% the length of each square is estimated to commit inthe measurement accuracy. Due to the large dimensions ofeach original printed square, the calculation of strain variationinside each square is implemented by means of a numeri-cal algorithm that divides the basic square in as many piecesas desired. Even so, and due to the discontinuity in flow pat-tern derivatives from one square to the next, original squareborders can be appreciated in Fig. 7. Although strains in thesecondary shear zone (SSZ) are higher than in the PSZ and inthe average chip, the lack of optical and serigraphic definitiondo not allow the analysis of this zone, being QSD and metallo-graphic studies over the chip still necessary for the completionof a thorough study over the cutting area.
Fig. 8 shows the strain and strain rate calculation over fourflow patterns when original data and polynomial smoothedcurves are employed for assessing the cutting process at Vc:300 m/min and f: 0.3 mm. It is observed how strains have asimilar rising and stabilization tendency in all the four pat-terns. This fact implies that strains in the PSZ are constant.However, in the strain rate analysis, it can be appreciated thatthe outermost flow patterns, namely, x4 in Fig. 8, have smallerstrain rate values than the inner flow patterns. This differenceis of the order of 100% attending to measured flow patternsand of the order of 60% for the smoothed flow patterns. Theseresults qualitatively coincide with results shown by Shankaret al. (2006) in 2D orthogonal cutting of titanium, and it is dueto the variable primary shear zone thickness, reported by Leiet al. (1999) on the analytical strain rate calculation of the PSZ.
If the polynomial smoothed strain functions are employedin the calculation of strain fields as shown in Fig. 9, the PSZand chip boundary can easily be discerned. These images onlyshow the material behaviour that turns into chip not consider-
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 2 ( 2 0 0 8 ) 475–485 481
F , (B) V0
ims
ifTbfietci
Fa
ig. 7 – Strain calculation at (A) Vc: 150 m/min and f: 0.3 mm.2 mm and (D) Vc: 300 m/min and f: 0.3 mm.
ng the material that remains as work-piece. The work-pieceaterial strain calculation is shown in Fig. 7 where almost null
train values are given.Strain rate fields can also be deducted from the captured
mages. Attending to Eq. (7), the strain rates are calculatedrom the smoothed strain paths of Fig. 8 and depicted in Fig. 10.he strain rate field shown in Fig. 10 can also be smoothedy means of polynomials, achieving more uniform strain rateelds. From the analysis of Fig. 10, two main facts can be
xtracted. First, the strain rate near the tool edge is higher thanhe strain rate of the outer flow pattern material, not havingonstant strain rate along the shear plane as it is supposedn the majority of analytical models. Second, the maximumig. 8 – Two dimensional representation of strain and strain ratend f: 0.3 mm over a general strain field (upper small figure).
c: 200 m/min and f: 0.2 mm, (C) Vc: 300 m/min and f:
strain rate field is placed before the shear plane, making thehappening of material hardening process at different stages.
The measured average shear angles, chip thickness,strains, and strain rates are summarized in Table 1, and addi-tional analytical values for strain and strain rate in the primaryshear zone are calculated using the model of Tounsi et al.(2002) in order to analyse the ambiguity between experimentaland predicted results. Additionally, Abaqus ExplicitTM FiniteElement Method (FEM) software has been employed in order to
simulate the cutting process. A 3D orthogonal model has beenbuilt for the estimation of chip thickness, shear angles, strainand strain rate values (Arrazola, 2003). Fig. 5 shows the geome-try of the model, built using an Arbitrary Lagrangian–Eulerianover four strain paths, x1, x2, x3 and x4 for Vc: 300 m/min
482 j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 2 ( 2 0 0 8 ) 475–485
Fig. 9 – Representation of smoothed strain fields at the tested four conditions.
Fig. 10 – Strain rate distribution at the tested four conditions in the primary shear zone.
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c
Fig. 11 – 3D FEM model built using Abaqus ExplicitTM of theofi
(sC51wc
aoti
ostcrtrpc(wAnmmAmfdsseircsworp
rthogonal cutting process showing the equivalent straineld of the work material. Vc: 300 m/min and f: 0.2 mm.
ALE) formulation and square elements. Friction has been con-idered constant with a value of � = 0.23, and Johnson andook’s constitutive law has been employed with values of A:98 MPa, B: 768 MPa, n: 0.21, C: 0.0137 and m: 0.807 (Grolleau,996). Fig. 11 shows the geometry of the model with a 3 mmall thickness and the equivalent strain field during a 3 ms
utting time at Vc: 300 m/min and f: 0.2 mm.Results in Table 1 show good agreement between measured
nd analytically calculated strains with maximum differencesf the order of 5%. The numerical model differs around 10%he measured strain and chip thickness values, whereas theres an important difference with respect to the shear angle.
In the case of strain rates, the measured and analyticallyr numerically calculated values differ notoriously. The mea-ured average strain rate values are of the order of one-half ofhe analytically calculated values and one-third the numeri-ally calculated values. This fact might be due to the severaleasons. The wider experimental PSZ thickness compared tohe considered calculation thickness of the models is the maineason. The analytical strain rate has been calculated using arimary shear zone thickness of one-half the non-deformedhip thickness according to the employed analytical modelTounsi et al., 2002). Experimentally, it is observed that PSZ
idth lays in the 70–75% the non-deformed chip thickness.s the strain rate is inversely proportional to the PSZ thick-ess, there will be a difference between the predicted andeasured strain rate values because the wider the PSZ, theore time the material strains, and lower is the strain rate.nother cause of the difference encountered between experi-entation and analytical modelling is that deformation in the
ree face of the chip is considered to be under plane strain con-itions whereas the experimental images show the materialtraining perpendicularly to the free face, closely to a planetress condition. Due to this fact, a third strain componentxists, namely ε33, and consequently a strain rate componentn the z direction, ε33. Thus, the existence of a third main strainate component, ε33, leads to a lower strain rate than in thease of having a plane strain condition where ε33 = 0 is con-idered. Consequently, ε11, ε22 and εeq. will take higher values
hen plane strain conditions are assumed than in the casef assuming plane stress conditions. Thus, equivalent strainates in the analytical model will result in higher values com-ared to those experimentally measured. In the numericalh n o l o g y 2 0 2 ( 2 0 0 8 ) 475–485 483
model, several factors have influence on the predicted strainsand strain rates such as the edge radius, material constitu-tive law, friction coefficient, heat partition coefficient, materialand tool conductivity, etc. An experimental factor that mightcause the deviation of measurements from analytically andnumerically calculated results is the grid size. Although, themeasured flow lines have been smoothed by employing poly-nomials, more refined grid sizes would produce more accuratemeasurements.
The definition of the constitutive material law for its use inmachining models is a hard task (Tounsi et al., 2002; Hamanet al., 2002) and the frequently employed constitutive equa-tions (Johnson and Cook, 1983; Maekawa et al., 1983; Zerilli andArmstrong, 1987) are dependent on strain, strain rate and tem-perature. The definition of material constitutive equations atvery high-strain rates can be improved by the in-process strainand strain rate measurement and can be implemented withtemperature measurements (Davies et al., 2003), achievingmore accurate machining models and more realistic materialconstitutive equations (Pujana et al., 2007).
4. Conclusions
This work has presented a new methodology for the assess-ment of cutting variables such as shear angles, chip thickness,tool vibration amplitude, strain, strain rate, and chip topol-ogy associated studies by means of high-speed photographycombined with laser printed square grid patterns on the work-piece at industrial cutting speeds and feeds. Thus, high-speedphotography is presented as an alternative method to the useof QSDs for the above mentioned variable measurement andfor its use in the improvement of mainly numerical machiningmodels and the definition of constitutive equations.
Presented lighting and laser marking methods have provento be successful for strain analysis in the PSZ, achievinggood compromise between image continuity, blur control, andacquisition cost compared to the pulsed lighting systems.
Once observed the recorded different photographs itshould be noted that there is a notorious tendency on thelack of uniformity on chip topology under the specifiedfour working conditions. Inside some very generic limits,the chip formation of 42CrMo4 could be defined as a ran-dom process between serrated, transitional, and continuouschip. Experimental measurement error in strain field anal-ysis is calculated to lay in the 7–12% range and could beimproved with the use of automatic strain measurementtechniques.
Achieved results on average strains in the PSZ have showngood agreement between measured and calculated values.Strain rates of the order of one-half the analytically calcu-lated values have been measured. This difference might bedue to the higher measured PSZ thickness, to the existenceof a third principal strain rate component which is not takeninto account in the analytical model and to the employed gridsize. In the case of the 3D MEF numerical model, strain rates
three times higher than the experimentally measured oneshave been calculated. On the other hand, higher strain rates,of the order of double, have been measured in the vicinity ofthe cutting edge when compared to those encountered in the
n g t
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484 j o u r n a l o f m a t e r i a l s p r o c e s s i
work-piece surface confirming the results achieved in otherstudies.
Acknowledgements
The authors would like to thank the Basque and SpanishGovernments for the financial support given to the projectsTAF (IE05-148) and MAQUIMODEL (DPI2006-15502-C02-01). Theauthors also thank the reviewers for their input and com-ments.
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