-
hne
hinain 150
Received in revised form 16 October 2014Accepted 3 March
2015Available online 14 March 2015
Keywords:
that the vibration was assumed as a steady simple harmonic
motion and was only mea-
especially in the case of precision mold inserts of opticalparts
used for injection molding process. On the otherhand, SPDT is a
complicated process inuenced easily by
achining theory,cial inteln uniqueachining
based approach together with the experimental invtion approach
appears to be the most promising appCombining the two approaches
allows the accuratetion of surface roughness along with this
approach aidingwith the evaluation and improvement of machine
toolperformance.
http://dx.doi.org/10.1016/j.measurement.2015.03.0040263-2241/
2015 Elsevier Ltd. All rights reserved.
Corresponding author at: No. 438, Hebei Avenue, Qinhuangdao,
HebeiProvince, China. Tel.: +86 15227248304.
E-mail address: [email protected] (J. Chen).
Measurement 69 (2015) 2030
Contents lists available at ScienceDirect
Measurement
journal homepage: www.elseviproducts, surface roughness is an
important index ofproduct quality and technical requirement [2]. In
somecases, the surface roughness is required to be kept withina
certain range rather than the possible lowest value,
through the use of approaches based on mexperimental
investigation and arti[2,48]. Each approach possesses its owtages
and disadvantages. However,
mligenceadvan-theoryestiga-roach.predic-Single point diamond
turning (SPDT) is a promising toolbased machining technology, which
can be used for manu-facturing optical components and precision
molds. Themain feature of SPDT is its ability to produce
high-qualitysurface nish on the order of nanometers while
meetingtight form tolerances on the order of micrometers [1].
For
and high spindle speed [3]. Consequently, the investigationon
prediction of surface roughness in SPDT is signicantand necessary
in order to control the desired surfaceroughness of product in a
fast and effective manner.
Many researchers are interested in the prediction ofsurface
roughness and research in this eld has yieldedsome useful ndings
along with successful experiencePrediction modelRelative tool-work
vibrationSwelling effectSurface roughnessSingle-point diamond
turning
1. Introductionsured before turning process. In this study, an
improved method is presented to evaluatethe actual relative
tool-work vibration. By using this method the vibration
informationobtained is more credible, as it contains the components
caused by machine tool error,cutting force, material property and
changing of cutting parameters. Moreover, the swel-ling effect is
analyzed using a new evaluating method and taken into account for
predictingsurface roughness. On the basis of analyzing both the
relative vibration and the swellingeffect, a model is proposed for
predicting surface roughness Ra in single point diamondturning.
Prediction results prove that this model is a closer approximation
of the actualturning process as compared to the previous models and
shows a higher predictingaccuracy of surface roughness.
2015 Elsevier Ltd. All rights reserved.
the material swelling effect because of a ne feed rateArticle
history:Received 9 June 2014
The relative tool-work vibration is not generalized enough to
represent the actual displace-ment between tool and workpiece in
previous prediction models. This is due to the factA model for
predicting surface rougdiamond turning
Junyun Chen a,, Qingliang Zhao baCollege of Vehicles and Energy,
Yanshan University, Qinhuangdao 150001, CbCenter for Precision
Engineering (CPE), Harbin Institute of Technology, Harb
a r t i c l e i n f o a b s t r a c tss in single-point
001, China
er .com/ locate /measurement
-
empirical data suggests and supports that material swel-
achieve both the required hardness and goodmachinability,
J. Chen, Q. Zhao /Measurement 69 (2015) 2030 21In machining
theory based approach, a model based onthe theory of machining is
used to simulate the creation ofthe machined surface prole and
visualize the surfacetopography along with assessing surface
roughness [2].The surface roughness prole is generated with the
rep-etition of the tool tip prole at intervals of feed per
rev-olution (ideal surface roughness prole) plus a
relativedisplacement between the tool and workpiece. Sata et al.[9]
found that the roughness prole was composed of toolfeed component,
swelling of workpiece, spindle rotationerror and chatter vibration
error using spectrum analysismethod. Takasu et al. [10] estimated
the surface roughnessprole as a function of both the ratio of
vibration ampli-tude to geometrical roughness and the phase shift
of thevibration to work rotation. He established a theoreticalmodel
for creation of roughness prole and also indicatedthat, due to the
tool interference, surface roughness inthe tool feed direction can
be made much ner than thesum of whole vibration amplitude and
geometrical rough-ness. On the basis of the model created by Takasu
et al.,Cheung et al. [11] established a three-dimensional
surfacetopography simulation model, which takes into accountthe
tool geography, the machining condition as well asthe relative
tool-work vibration in the kinematics of dia-mond turning process.
The surface topography was gener-ated by a linear mapping of the
predicted surfaceroughness proles on the surface elements of a
cross lat-tice. Lee et al. [12] presented a dynamic surface
topographymodel for the prediction of nano-surface generation
inwhich an additional displacement caused by materialinduced
vibration was introduced into the model as com-pared to the
previous model.
2. Previous theoretical models
The basic idea for the theoretical models mentionedabove is the
fact that the actual surface roughness proleis formed by an ideal
surface roughness prole plus a rela-tive displacement between the
tool and workpiece, whichis achieved by theoretic calculation.
Ideal surface rough-ness prole is determined by cutting conditions,
while arelative displacement between tool and workpiece
wasconsidered as the relative tool-work vibration. In the caseof
the primary models, materials were assumed ashomogeneous and
isotropic and the relative vibrationwas assumed as a steady simple
harmonic motion. For ani-sotropy of crystalline materials, an
enhanced model, whichadds material induced vibration to the primary
model, wasused. Although, they are able to predict surface
roughnesswith low error, there are two major issues impacting
pre-diction accuracy in previous theoretical models. First,
therelative tool-work vibration was assumed as invariable,and it
was measured before turning process. The secondis related to the
material swelling effect, which wasignored in previous models.
In the cutting process, the actual relative tool-workvibration
was caused by machine tool error, cutting force,material property
and change in cutting parameters.Some scholars have tried to
analyze the relative vibrationusing the spectrum method or by
measuring the force incutting process [9,1315]. However, no
research workthe compounding of coating solutionwas optimized to
gen-erate medium-phosphorus NiP, which possesses a coatingdepth of
more than 50 lm and a hardness of 50HRC.Table 1 tabulates the
cutting conditions in the tests study-ing relative tool-work
vibration and the swelling effect.
The surface prole was measured about 10 mm inlength by contact
probe prolometer, Form Talysurf PGI1240 (Taylor Hobson Ltd.) in 2D,
while the surface topogra-phy was measured by a non-contact type
surface measure-ment system, White Light Interferometer Veeco
NT1100(WLI, Veeco Metrology Group) in 3D for each sample.
Themeasurement data was then processed with MATLAB soft-ware. The
diamond tool wear was observed by a scanningelectronic microscope
(SEM, Hitachi S-4700) and an opticalmeasuring microscope (STM6,
Olympus, Japan).
4. The relative tool-work vibration
4.1. Evaluating the relative tool-work vibration
Relative vibration may be caused by machine tool error,cutting
force, material properties and change in cuttingling obviously
changes the surface roughness prole [3].However, no report predicts
surface roughness while con-sidering the effect of material
swelling.
In the present study, a prediction model is presented topredict
the surface roughness in the SPDT process, whichtakes both actual
tool-work vibration and material swel-ling into account. It is
almost impossible to measure theactual tool-work vibration directly
in cutting process. Toovercome this challenge, a concept of
equivalent ampli-tude was proposed to aid with the evaluation of
the actualtool-work vibration with the assistance of
experiments.Furthermore, the swelling proportion of every
materialwas dened to quantify the swelling effect, and the
rela-tion between the swelling effect and cutting parameterswas
investigated by means of experiments.
3. Experimental setup
A series of face cutting tests were conducted on a four-axis CNC
ultra-precision machine tool (made by Nachi-Fujikoshi Corp., Japan)
shown in Fig. 1 (left). A diamondtool used in tests is shown in
Fig. 1 (right), with a rakeangle of 0, a front clearance angle of 6
and a tool-noseradius of 0.5 mm.
The tests were carried out on three kinds of materialsincluding
copper (Cu), aluminum alloy (Al7075-T6) andelectroless-nickel (NiP)
during studying relative tool-workvibration and the swelling
effect. Aluminum alloy and cop-per were available in market, while
samples of NiP wereprepared on an aluminum alloy rod (7075-T6). In
order tohas been reported which takes the actual relative tool-work
vibration into account when establishing a model.On the other hand,
according to the results of roughnessprole based on the spectrum
analysis, it can be concludedthat the material swelling is an
important part contribut-ing to the surface roughness prole [9,13].
Additionally,
-
(left)
Tn
1111111122
22 J. Chen, Q. Zhao /Measurement 69 (2015) 2030Fig. 1. CNC
ultra-precision machine tool
Table 1Cutting conditions for experiments.
TermNo.
Spindle speed(rpm)
Feed rate(mm/min)
Depth of cut(lm)
Tool-noseradius (mm)
1 1000 25 2 0.52 1000 30 2 0.53 1000 35 2 0.54 1000 40 2 0.55
1000 40 4 0.56 1000 40 6 0.57 1000 40 8 0.58 1500 25 2 0.59 1500 30
2 0.5
10 1500 35 2 0.511 1500 40 2 0.5parameters during the cutting
process. The relative vibra-tion between the tool and workpiece
translates onto themachined surface and is very difcult to be
measureddirectly. Therefore it is feasible and applicable to
extractthe vibration information from the machined surface.After
which, the relationship between the relative vibra-tion and each
corresponding factor can be analyzed to pre-dict the surface
roughness.
Previous models consider the amplitude of basic fre-quency of
spindle to be the amplitude of simple harmonicmotion, which
indicates that the amplitude of relativevibration rather than
frequency has a dominant impacton surface roughness. As a result,
considerable attentionneeds to be given to the amplitude of actual
tool-workvibration, and then a denition of equivalent amplitudewas
proposed to evaluate it.
A part of measured surface prole was shown in Fig. 2.The
location of diamond tool tip xi;Yixi can be extractedfrom the
measured surface roughness prole to form thetool locus in radial
direction, which represents the dis-placement between the tool and
workpiece, i.e., the rela-tive tool-work vibration.
By taking X-axis along the tool feed and Y-axis along theinfeed
cutting direction, the number of cutting edgesduplicated on the
machined surface along radial directionis given as
N dL x1=se 1where L is the length of measured surface roughness
pro-le, s is tool feed per work revolution, and de meansand diamond
tools used in tests (right).
ermo.
Spindlespeed (rpm)
Feed rate(mm/min)
Depth of cut(lm)
Tool-noseradius (mm)
2 1500 40 4 0.53 1500 40 6 0.54 1500 40 8 0.55 2000 25 2 0.56
2000 30 2 0.57 2000 35 2 0.58 2000 40 2 0.59 2000 40 4 0.50 2000 40
6 0.51 2000 40 8 0.5rounding down to the nearest whole unit. In the
measuredsurface roughness prole, the location of every point
form-ing tool locus can be extracted according to X value,
asfollows:
xi x1 i 1Dx x1 i 1s 2with i 1;2; . . . ;N. Consequently, the
location of everypoint xi;Yixi can be achieved from the measured
rough-ness prole, as shown in Fig. 2. The tool locus, i.e. the
actualrelative tool-work vibration can be dened as
Ytxi Yixi minfyixig 3with i 1;2; . . . ;N. This vibration will
increase the surfaceroughness of machined surface. In order to
evaluate thevibration easily, the actual relative tool-work
vibrationwas simplied as a simple harmonic motion. The principleof
simplication lies on an assumption that both the rela-tive
tool-work vibration and simple harmonic motion havethe same impact
on surface roughness. That is, both theprole of tool locus and the
curve of simple harmonicmotion were regarded as surface roughness
proles andhad the same arithmetic roughness value Ra. As a
result,the amplitude of simple harmonic motion is dened
asequivalent amplitude, which represents the degree ofchanging
surface roughness with respect to the actual rela-tive tool-work
vibration. The simplication procedure forthe vibration is described
below.
Assuming a simple harmonic motion as
Yhx A1 cos2pfx 4
-
TMillime
e mea
J. Chen, Q. Zhao /Measurement 69 (2015) 2030 23Rah 1N1XN1i1
Yhxi Yhxi
7
Let Eq. (6) equal Eq. (7), then the equivalent amplitudeA can be
calculated as
A N21PN
i1 NYtxi PN
i1Ytxi
N2PN1
i1 N1 1 cos pDxi1s
PN1i1 1 cos pDxi1s
8
4.2. Effect of cutting parameters
When depth of cut is set as 2 lm, the actual relativetool-work
vibration as a function of the change of feed rateis shown in Fig.
3 at different spindle speeds. It can be seenthat the equivalent
amplitude has no obvious uctuationexcept for Al7075 under spindle
speed of 2000 r/min,which may be caused by the inhomogeneous
materialproperties of the aluminum alloy. As the feed rate can
onlydetermine the overlap of the tool prole in radial direction,it
does not contribute to the amplitude. Therefore, theactual relative
tool-work vibration can be regarded as con-and its discretization
form can be expressed as
Yhxi A1 cos2pfDxi 1 5where Dx 1=mf and f was assumed as 1=2s, m
is an opti-mized positive integer, i 1;2; . . . ;N1, N1 dNs=Dxe.
Thearithmetic roughness value Rat calculated from the proleof tool
locus and the arithmetic roughness value Rah calcu-lated from the
curve of simple harmonic motion can begiven as Eqs. (6) and (7)
respectively.
Rat 1NXN
i1Ytxi
PNi1YtxiN
6
xYx))(,( 222 xYx
Mic
rom
eter
sFig. 2. Extract tool locus from thstant with increasing feed
rate for each material under anidentical spindle speed.
Fig. 4 presents the relationship between the equivalentamplitude
and depth of cut under feed rate of 40 mm/min.It is known that
depth of cut determines the contact condi-tion between tool and
workpiece and it would have adirect effect on cutting force
resulting in the relative vibra-tion. However, the depth of cut in
SPDT is too small toinuence the cutting force and the friction
conditionbetween tool and chip. So no direct relationship
betweendepth of cut and the relative vibration was found
accordingto the results shown in Fig. 4, which indicates that
theequivalent amplitude is maintained within a smaller rangeas the
depth of cut is changed. In other words, the relativevibration
during cutting process is almost unaffected bythe change in depth
of cut for each material.
During cutting process, the increase of spindle speedcan augment
spindle vibration contributing to the relativevibration between
tool and workpiece, but also increasesthe cutting times at the same
location to reduce the cuttingforce and further reduce the relative
vibration. Fig. 5 showsthe effect of spindle speed on the relative
vibration at dif-ferent feed rates and depths of cut for three
materials.Fig. 5(a) shows that the equivalent amplitude has no
dis-tinct change under a certain spindle speed for NiP, butchanges
from less than 5 nm to near 15 nmwith increasingspindle speed,
which means spindle speed affects the rela-tive vibration more
signicantly than feed rate and depthof cut for NiP. It can be
explained that spindle speed mainlyinuences spindle vibration in
cutting homogeneous NiP.The evaluated equivalent amplitude is found
to remain inthe range of 1018 nm for machining Cu at different
spin-dle speeds, as shown in Fig. 5(b). During the cutting of
Cumaterial, the increase of spindle speed may lead to largerspindle
vibration and smaller cutting force at the sametime. Whereas, for
Al7075 shown in Fig. 5(c), there is a sig-nicant change in the
equivalent amplitude at differentspindle speeds while the
equivalent amplitude decreaseswith increasing spindle speed. It is
inferred that theincrease of spindle speed mainly reduces the
cutting force,as Al7075 is a typical inhomogeneous alloy.
In general, it can be concluded that the actual
relativetool-work vibration is signicantly inuenced by thechange in
spindle speed, but not by feed rate and depthof cut. Thus, among
the cutting parameters, we only needto take into account the effect
of spindle speed on thevibration when a model is established for
predicting sur-face roughness.
ool locus))(,( iii xYx
Measured surface profile
ters
sured surface roughness prole.4.3. Effect of material
property
The surface topography and surface prole of themachined surfaces
are shown in Fig. 6 for every materialunder same cutting parameters
(spindle speed: 1000 r/min, feed rate: 25 mm/min, depth of cut: 2
lm). A dash-dot-line was drawn by connecting a series of tool
noselocations in the prole to observe the relative
tool-workvibration directly. It can be observed that the
dash-dot-lineis almost straight for material NiP, which implies
that themeasured prole is close to the ideal prole and the
rela-tive tool-work vibration is negligible. Moreover, based on
-
0 rate (
Spind
24 J. Chen, Q. Zhao /Measurement 69 (2015) 203025 30
5
10
15
20
Equi
vale
nt a
mpl
itude
(nm
)
Equi
vale
nt a
mpl
itude
(nm
)
25 30 35 400
10
20
30
40
50
NiPCuAl7075
Feed rate (mm/min) Feed(a)
Fig. 3. Relationship between the equivalent amplitude and feed
rate. (a)2000 r/min.
15
20
25
30
30
40
50
NiPCum
plitu
de (n
m)
ampl
itude
(nm
)analyzed results, the equivalent amplitude was less than10 nm
for a spindle speed of 1000 r/min, as shown inFig. 7. This
phenomenon can be explained from the mate-rial property of NiP
shown in Fig. 8. NiP has amorphousstructure, in which the atomic
arrangement does not fea-ture with long-range order and translation
cyclicity. As aresult, the solid solution structure of NiP is
homogeneousand does not have grain boundaries, dislocations,
twincrystals and other defects. In addition, the passivating
lmcovered on the surface of NiP basal body also has homoge-neous
structure without any dislocation. Therefore, therelative vibration
is very small in the case of machiningNiP because of the high
isotropy of this material.
It can be observed from Fig. 6(b), that there is a
largeuctuation for the displacement between tool and work-piece
when machining Cu as compared to NiP. The resultsof equivalent
amplitude also support this conclusion and itcan be seen that, the
magnitude of all the values wasgreater than 10 nm, as shown in Fig.
7. This fact can be
2 3 4 50
5
10
2 3 4 5 6 7 80
10
20 Al7075
Equi
vale
nt a
Equi
vale
nt
Depth of cut (m) Depth of (a)
Fig. 4. Relationship between equivalent amplitude and depth of
cut. (a) Spind2000 r/min.
1000 1200 1400 1600 1800 20000
5
10
15
20
Equi
vale
nt a
mpl
itude
(nm
)
Equi
vale
nt a
mpl
itude
(nm
)
(a)1000 1200 14000
5
10
15
20
Spindle speSpindle speed (r/min)
Fig. 5. Relationship between equivalent amplitude and spindle
speEqui
vale
nt a
mpl
itude
(nm
)
25 30 35 400
5
10
15
20
NiPCuAl7075
(c)35 40
NiPCuAl7075
(b) Feed rate (mm/min)mm/min)
le speed: 1000 r/min; (b) spindle speed: 1500 r/min; (c) spindle
speed:
10
15
20
mpl
itude
(nm
)
NiPCuAl7075explained on the basis that copper (Cu) is a
polycrystallinealloy material and does not have a similar
homogeneousstructure as NiP. However, copper has some
deoxidizingelements and other elements in the bulk material
besidespure Cu in order to improve material performance, as
seenfrom the metallurgical structure of Cu shown in Fig. 9.
As shown in Table 2, Al, Zn, Mg and Cu are the main ele-ments
that make up Al7075. It can form solid solutionstructure or a
chemical compound in the basal body of Altermed as trapped phase,
which has a different physicaland mechanical property from the
basal body. As a result,this material was strengthened by the
trapped phase,thereby increasing the hardness. However, the
existenceof trapped phase makes the material non-homogeneous.The
metallurgical structure in Fig. 9 shows the trappedphase in Al7075
has a higher proportion and a bigger sizeas compared to Cu. The
machined surface prole ofAl7075 exhibits the largest displacement
between tooland workpiece along with the largest equivalent
2 3 4 5 6 7 80
5 NiPCuAl7075
Equi
vale
nt a
(c)6 7 8
(b)cut (m) Depth of cut (m)
le speed: 1000 r/min; (b) spindle speed: 1500 r/min; (c) spindle
speed:
1000 1200 1400 1600 1800 20000
10
20
30
40
50
(c)(b)
Equi
vale
nt a
mpl
itude
(nm
)
1600 1800 2000
ed (r/min) Spindle speed (r/min)
ed. (a) Material: NiP; (b) material: Cu; (c) material:
Al7075.
-
(a)Millimeters
J. Chen, Q. Zhao /Measurement 69 (2015) 2030 25crom
eter
s M
icro
met
ers amplitude, i.e., Al7075 exhibits the biggest relative
tool-work vibration among the three materials as shown inFigs. 6
(c) and 7. It can be concluded that material proper-ties can
largely inuence the actual relative tool-workvibration in SPDT,
thus we must consider the effect ofmaterial properties on the
vibration behavior when pre-dicting surface roughness.
4.4. Effect of tool wear
In the machining process for Al7075, serious wear ofdiamond tool
occurred due to its higher hardness. Fig. 10shows the degree of
tool wear when the machining wascompleted. It can be seen that the
circular part of diamond
(b)
(c)
Millimeters
Mi
Millimeters
Mic
rom
eter
s
Fig. 6. Three-dimensional topography and surface prole of
machined surface. (a) Material: NiP; (b) material: Cu; (c)
material: Al7075.
0
10
20
30
40
50
NiP Cu Al7075
Equi
vale
nt a
mpl
itude
(nm
)
Fig. 7. Relationship between equivalent amplitude and
materialproperty.
20 40 60 80 1000
500
1000
1500
2000
Intensity (cps)
2theta (deg.)
Fig. 8. X-ray spectra of NiP.
Basal body
Trapped phase
Basal body
Trapped phase
Fig. 9. Metallurgical structure of Cu (left) and Al7075
(right).
-
tool has to cut the hard trapped phase and soft basal body
n
.3
26 J. Chen, Q. Zhao /Measurement 69 (2015) 2030of Al
alternately, resulting in the repeating change of cut-ting state
and cutting force in the turning process. The rela-tive tool-work
vibration for cutting this material must begreater than cutting
homogeneous materials. However,when the diamond tool wears out, the
length of contactzone may increase to 100 lm, as shown in Fig.
10.Accordingly, the part of workpiece in contact with the dia-mond
tool is composed of the hard trapped phase and softbasal body
simultaneously, leading to a steadier materialremoval process as
compared to before the tool wear.Therefore, the relative tool-work
vibration gets smallerwith increase in tool wear, and the effect of
tool wear onthe vibration must be considered in the turning
process.
5. The material swelling effect
5.1. Method of quantifying the swelling effect
In the SPDT process, as the tool has two edges includingcutting
edge and burnishing edge, the latter burnishes andindents the
freshly machined surface besides cutting thematerials via cutting
edge in turning process. Meanwhile,the metal left behind the
cutting edge undergoes highpressure, which results in a material ow
toward the sideof the active cutting edge [16]. The material left
behindthe ank face recovers after burnishing [3]. Moreover,
thecutting force along the main cutting edge pushes asidethe work
material near the tool nose, causing it to owtoward the free
surface [17]. The combined effect of plasticow, burnishing, and
elastic recovery is called the swellingtool contacting the
workpiece during the machining hasworn out into a straight shape.
Further analysis of Fig. 10revealed that the worn part had a height
of 7.6 lm and awidth of 95.8 lm. It is generally agreed that tool
wearmay lead to a larger relative tool-work vibration. On
thecontrary, it is found in this study that the equivalentamplitude
becomes smaller with the increase in cuttingdistance and with the
aggravation in tool wear, as shownin Fig. 11. The equivalent
amplitude decreases from44 nm to 4 nm, indicating that the relative
tool-workvibration was reduced gradually.
This can be explained from the metallurgical structureshown in
Fig. 9 (right), in which the size of trapped phaseis about 20 lm in
material of Al7075, while the length ofcontact zone between tool
and workpiece during the turn-ing process is not larger than 10 lm.
Thus, the diamond
Table 2Chemical composition of Al7075.
Composition Cu Si Fe M
Mass percent (%) 1.22.0 0.4 0.5 0effect [13], which causes the
change of tool marks genera-tion on the machined surface, as shown
in Fig. 12.
Liu et al. [18] showed plastic side ow could
increasepeak-to-valley roughness due to the material piling up
atthe trailing edge of the tool. Sata et al. [9] found workmaterial
swells at the end of the active cutting edge caus-ing a greater
tool mark on the machined surface becausethe swelling increases the
peaks height of the feed compo-nents in spectrum. However, in some
cases, the swellingeffect was found to decrease the surface
roughness whenplastic ow for ductile materials is overwhelmed by
theeffect of materials recovery [3]. The amount of recoveryis
decided by the material properties and forces on theank face [13].
Previous research implies that the amountof swelling depends upon
the properties of the materialbeing cut. Softer and more ductile
material show higherswelling of the tool marks [9]. In order to
quantify theswelling effect, Sata et al. [9] dened the swelling
ratioas the ratio of power between the rst order feed compo-nent of
the measured roughness spectrum and the idealroughness spectrum.
Then, Cheung et al. [13] proposed alocal swelling ratio SRi at the
ith radial section of themachined surface which is dened as the
square root ofthe ratio of the power spectral density for the rst
feedcomponents of the measured and the ideal surface rough-ness
spectrum.
In present study, the effect of material swelling on sur-face
roughness is required to consider in the predictionmodel, so it is
not feasible to process the measured rough-ness prole by means of
spectrum method. Therefore, aswelling proportion SP was proposed to
quantify the swel-ling effect based directly on measured roughness
prole. Itis dened as a proportion between the average height oftool
mark on measured surface and the height of ideal toolmark:
SP Pn
i1HrinHc
9
where Hri is the height of the ith tool mark after both
reco-vering and plastic owing on machined surface, as shownin Fig.
12, Hc is the calculated height of ideal tool markHc s2=8R; s is
tool feed per work revolution, R is the toolnose radius) and n is
the number of tool marks evaluated. Itcan be deduced that the
effect of plastic ow will be largerthan the effect of recovery on
roughness prole and thus toincrease the surface roughness, if SP
> 1; while the effect ofplastic ow will be smaller than the
effect of recovery onroughness prole and thus to reduce the surface
rough-ness, if SP < 1.
5.2. Effect of cutting parameters
Sata et al. [9] studied the swelling ratio of C45 and brassat
the different feed rates. It was found that the swelling
Mg Zn Cr Ti Al
2.12.9 5.16.1 0.4 0.06 90ratios remain nearly constant within a
certain feed raterange. Cheung et al. [13] analyzed the
distribution ofswelling ratio on machined surface of aluminum
singlecrystal and Al6061 to evaluate the materials
anisotropy.However, no report was found to predict surface
roughnesstaking into account the swelling effect. Therefore,
theeffect of cutting parameters on the material swelling and
-
0) an
J. Chen, Q. Zhao /Measurement 69 (2015) 2030 27Fig. 10. Image of
tool wear (left, magnication 20the change of surface roughness
caused by the swellingeffect is still far from understand very well
and needs tobe further studied.
For the purpose of correlating a prediction model of sur-face
roughness with the swelling effect, it was analyzed atdifferent
cutting parameters for NiP, as shown in Fig. 13.The swelling
proportion is in the ranges of 1.211.39,1.041.11 and 0.961.08 at
varying spindle speeds of1000 r/min, 1500 r/min and 2000 r/min
respectively underdifferent feed rates and depths of cut. The
result impliesthat the swelling proportion nearly keeps invariable
withthe changing feed rates and cutting depths for a xed spin-dle
speed. However, it decreases obviously when the spin-dle speed was
increased, which means machined surface
5.5 6.0 6.5 7.0 7.5 8.0 8.50
10
20
30
40
50
Cutting distance (km)
Equi
vale
nt a
mpl
itude
(nm
)
Fig. 11. Relationship between equivalent amplitude and tool
wear.
Hc
HrHfIdeal surface calculated
Surface after plastic flow Surface after recovery
Fig. 12. Schematic illustration for the effect of swelling on
surfacegeneration (Hc height of ideal tool mark calculated, Hf
height of toolmark after plastic ow, Hr height of tool mark after
recovery).1
1.5
Swel
ling
prop
ortio
n
d size of worn part (right, magnication 1000).becomes smoother
at a higher spindle speed. This can beexplained based on the fact
that at higher spindle speedthe same position on the fresh machined
surface will beburnished and indented many times, which cause a
largerresidual stress onto the surface, with a larger recovery
andthus a lower height of tool mark. The results reveal that
thematerials swelling effect was mainly affected by thespindle
speed, which is very useful and signicant forthe proposed
prediction model in this study, because theroughness prole after
plastic ow and recovery can beclearly known based on the swelling
proportion at differ-ent spindle speeds.
6. A prediction model of surface roughness
6.1. Creation of a prediction model
Based on above analysis, the main factors affecting therelative
tool-work vibration are spindle speed, materialproperty and tool
wear. In addition, the swelling effect ofa material will change
mainly with the change in spindlespeed. Therefore, in the
prediction model, experimentsare necessary to determine the
relative tool-work vibrationand the swelling effect at different
spindle speeds for eachmaterial. As shown in Fig. 14, the roughness
prole wasrst measured on the machined surface in radial
direction,and then processed by the methods discussed in the
1000 1200 1400 1600 1800 20000.5
Spindle speed (r/min)
Fig. 13. The swelling ratio of NiP at different cutting
parameters.
-
Then, both the roughness prole after the swellingeffect YSx and
the curve of equivalent simple harmonicmotion Yhx were produced
with the method of additionof waveforms on MATLAB/Simulink
software, where Yhxis given by Eq. (4) and shown in Fig. 15(c). So,
the additionof two waveforms resulted in a new roughness prole
Y(x),as shown in Fig. 15(d). Finally, predicted arithmetic
rough-ness value Ra was calculated with export data of the
rough-ness prole Y(x) on MATLAB/Simulink software. It is notedthat
the roughness prole Y(x) contains both the relativetool-work
vibration and the swelling effect, is only usedto calculate
roughness value but not actual roughness pro-le of machined
surface.
In conclusion, there are three aspects of signicant fea-ture in
the prediction model presented in this paper, as
Experiments Measure roughness profile
Data processing
Cutting parameters
Materials property
Relative tool-work vibration
The swelling proportion
Ideal roughness profile
Roughness profile after swelling effect
Equivalent vibration
Addition of waveforms and data processing
Surface roughness
28 J. Chen, Q. Zhao /Measurement 69 (2015) 2030previous section.
As a result, the actual relative tool-workvibration was simplied as
a simple harmonic motion tocalculate the equivalent amplitude A,
while swelling pro-portion SP of each material can be determined
accordingto Eq. (9).
Once the cutting parameters are conrmed, the idealroughness
prole in radial direction shown in Fig. 15(a)can be expressed
as
YIx x2
2Rif 0 6 x 6 s=2 10
YIx x ns2
2Rif x > s=2 11
where s is tool feed per work revolution, R is the tool
noseradius and n = dx s=2=sede means rounding down tothe nearest
whole unit). Since the swelling effect cannotbe avoided, both
plastic ow and recovery of the materialwere taken into account to
evaluate a roughness proleafter swelling effect YSx, which is
calculated on the basisof the ideal roughness prole as well as the
calculated
Fig. 14. A block diagram of the prediction model of surface
roughness.swelling proportion SP, as shown in Fig. 15 (b).
YSx SPYIx 12
x0 s 2s 3s
Ys(x) (b)
After swelling effect
2s
(a)
x0 3s
c
Y (x)
H
cHrH
s
1
Fig. 15. The schematic diagram of predicting process of surface
roughness. (a) Idshown in Fig. 12; (c) equivalent simple harmonic
motion; (d) roughness prolefollows:
(1) The evaluated vibration is more credible and close tothe
actual vibration in the turning process becauseof the relative
tool-work vibration coming from themachined surface.
(2) The swelling effect, i.e., the material plastic ow
andrecovery in turning is rst taken into account in theprediction
of surface roughness.
(3) This prediction model adopts the approach combin-ing
machining theory with experimentalinvestigation.
6.2. Verication of the prediction model
Verication tests of face cutting were carried out formaterials
NiP and Cu. The tests were conducted on afour-axis CNC
ultra-precision machine tool (made byNachi-Fujikoshi Corp., Japan)
and a diamond tool used intests has a rake angle of 0, a front
clearance angle of 6and a tool-nose radius of 0.5 mm. The cutting
conditionsare tabulated as Table 3. By using the model proposed
inthe present study, the equivalent amplitude A and
swellingproportion SP were rst evaluated under varying
cuttingparameters for NiP and Cu, as shown in Table 4. Then
sur-face roughness values Ra were predicted.
The predicted values, measured values and ideal valuesare shown
in Fig. 16, in which the ideal values were calcu-lated from the
ideal roughness prole YIs given by Eqs.(10) and (11). It can be
seen that there are three kinds of
x
Yh(x)
0
A2
A
x
Y(x)
0
Addition of waveforms
(c)
(d)
eal roughness prole; (b) roughness prole after swelling effect,
Hc and Hrcontaining both the relative tool-work vibration and the
swelling effect.
-
surface roughness values, which increases with theincrease in
feed rate, as illustrated in Fig. 16(a) and (c).This can be
explained that a bigger feed rate will makethe tool marks deeper
and wider in ideal roughness prole,
and lead to a larger ideal value of surface roughness ascompared
to a smaller feed rate. Additionally, it was foundthat there was a
good accordance between the predictedand the measured values,
indicating the prediction errorwas small or close to negligible in
this case.
Fig. 16(b) and (d) presents the measured surface rough-ness
having no obvious uctuation when the depth of cutincreases, which
supports that the effect of depth of cuton the relative vibration
and the swelling effect can beignored in the prediction model. The
little uctuation formeasured surface roughness may be caused due to
thechange of the machine tool error or the swelling propor-tion
with the change in depth of cut. However, the resultsfor the
measured and predicted values were in goodagreement.
It is noticed that the two materials (NiP and Cu) weremachined
with the same diamond tool, the same machinetool and the same
cutting parameters, theoretically,
Table 3Cutting conditions of verication tests.
Termno.
Spindle speed(rpm)
Feed rate(mm/min)
Depth of cut(lm)
Tool-noseradius (mm)
Termno.
Spindle speed(rpm)
Feed rate(mm/min)
Depth of cut(lm)
Tool-noseradius (mm)
1 1500 25 2 0.5 8 2000 25 2 0.52 1500 30 2 0.5 9 2000 30 2 0.53
1500 35 2 0.5 10 2000 35 2 0.54 1500 40 2 0.5 11 2000 40 2 0.55
1500 40 4 0.5 12 2000 40 4 0.56 1500 40 6 0.5 13 2000 40 6 0.57
1500 40 8 0.5 14 2000 40 8 0.5
Table 4Equivalent amplitude A and swelling proportion SP
calculated by themodel.
A (nm) and SP Spindle speed (rpm)1500 2000
Material NiP
A 8 12
SP 1.11 1.08
Material Cu
A 13 14
SP 0.82 0.85
J. Chen, Q. Zhao /Measurement 69 (2015) 2030 29(nm
) 60
7025 30 35 400
10
20
30
40
Surf
ace
roug
hnes
s Ra
(nm
)Su
rfac
e ro
ughn
ess R
a
Ideal
NiP Cu
(c)
25 30 35 400
10
20
30
40
50
Feed rate (mm/min)
Feed rate (mm/min)
Ideal
NiP Cu
(a)
Fig. 16. Model predicted surface roughness (dash dot line),
measured surface rouspeed: 1500 r/min, depth of cut: 2 lm; (b)
spindle speed: 1500 r/min, feed rate: 4speed: 2000 r/min, feed
rate: 40 mm/min.30
40
Surf
ace
roug
hnes
s Ra
(nm
)a
(nm
)
2 3 4 5 6 7 80
10
20
30
40
50
60
70
Depth of cut (m)
Ideal
NiP Cu
(b)(d)2 3 4 5 6 7 8
0
10
20
Ideal
NiP Cu Su
rfac
e ro
ughn
ess R
Depth of cut (m)
ghness (solid line) and ideal surface roughness for NiP and Cu.
(a) Spindle0 mm/min; (c) spindle speed: 2000 r/min, depth of cut: 2
lm; (d) spindle
-
the ideal surface should be identical, but the measured sur-face
roughness values were found to have a big differencein comparison
to the corresponded ideal value. This differ-ence could be caused
by the effect of material property onthe relative vibration and the
swelling effect. Especially formaterial Cu, most of predicted
surface roughness and mea-
the error is within 6.5%, which further proves the improve-ment
of the model proposed in the present study.
Acknowledgments
The authors would like to express their sincere thanks
30 J. Chen, Q. Zhao /Measurement 69 (2015) 2030sured surface
roughness are less than ideal value, which iscaused by the swelling
proportion SP < 1, i.e., Hr < Hc inFig. 15(b). Therefore, it
is necessary to consider the inu-ence of material property in order
to achieve high predic-tion accuracy when predicting the surface
roughness.Overall, using the prediction model in the present
study,a good accordance between the measured and predictedvalues is
realized. The average prediction error of surfaceroughness Ra is
found to be 5.1% as well as the error iswithin 6.5% in most
cases.
7. Conclusions
The actual relative tool-work vibration during the turn-ing
process is different from the relative vibration mea-sured before
turning. The swelling effect can obviouslyaffect the surface
roughness prole through changing thesize of tool mark, thus have to
be taken into account theprediction of surface roughness in
SPDT.
In machining a material with a homogeneous structure(e.g., NiP),
the actual relative tool-work vibration causedwas very smaller when
compared to inhomogeneousmaterials. This is due to the fact that
homogeneous materi-als do not present grain boundaries,
dislocations, com-pound twins and other defects. But for
inhomogeneousmaterials (e.g., Cu and Al7075), material induced
vibrationwas larger and mainly determined by the size of
trappedphase and the length of contact zone between tool
andworkpiece.
Among three types of cutting parameters, the spindlespeed has
the most dominant inuence on the relativevibration and the swelling
effect when compared to thatof the other two parameters of feed
rate and depth of cut.Moreover, it was found that a higher spindle
speed leadsto a lower swelling proportion and smoothermachined
sur-face, because the larger residual stress and amount ofrecovery
can be caused on the fresh machined surface.
Using the approach combining machining theory withexperimental
investigation, a prediction model of surfaceroughness in SPDT was
proposed. It takes into accountthe actual relative tool-work
vibration extracted from themachined surface and the swelling
effect, which representsthe complicated elastic and plastic
deformation in cutting.Therefore, this model is further close to
the actual cuttingprocess.
There is a good agreement between the model predictedand the
measured values. The average prediction error ofsurface roughness
Ra is found to be 5.1%while inmost casesto the National Scientic
Foundation of China (NSFC)(Contract No. 51205343) and Postdoctoral
ScienceFoundation of China (Contract No. 2012M520595) for
theirnancial support of the research work.
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A model for predicting surface roughness in single-point diamond
turning1 Introduction2 Previous theoretical models3 Experimental
setup4 The relative tool-work vibration4.1 Evaluating the relative
tool-work vibration4.2 Effect of cutting parameters4.3 Effect of
material property4.4 Effect of tool wear
5 The material swelling effect5.1 Method of quantifying the
swelling effect5.2 Effect of cutting parameters
6 A prediction model of surface roughness6.1 Creation of a
prediction model6.2 Verification of the prediction model
7 ConclusionsAcknowledgmentsReferences