Indi an Journal of Engineerin g & M aterials Sciences Vo l. 10. Apr il 2003. pp. 123- 130
Effects of tool feed rate in single point diamond turning of aluminium-6061 alloy Gufrall Sayccu Khan;!, Ram a Gopal V Sarcpa ka". K D Chattopacl hyay". P K lain" & V M L arasimham" "Advan ced Opti ca l Processing Di vision. hlndo-Sw i ss Training Cen tre Central Sc ientilic Instruments Organ isati on. Sec tor 30-C. Chandigarh. 160030. India R('('('il'ed 21 .lIllIe 2002: a('cepted 14 .IallllillT 2003
Durin g single po int dia illond turning. th e effec ts of too l feed rate on surface fi gure and fini sh o f alu m iniulll -606 1 alloy are eva luated. Th e studi es are conductcd on 60 mm diameter optica l fl at surfaces. Twenty-s ix specimens are diamond turned for va ry ing too l feed rates (0.3 ~lin/rev to 30.0 ~lin/rev) keep ing all the oth er machining IXlrameters co nstant. The alumin iulll surfaces thu s mac hined. show a typ ica l roughness of 15 nm. ,md surface fi gure o f be tt er than a half wave peak-to-va lley (PV) for op timum too l feed rate . Th e too l fe ed rate betwee n o f I .S-8.0 ~lin/rev is fou nd to be optim um for a gi ve n sc t of other machining parameters to get th e acceptab le surface fi gure as we ll as roughness va lues. A n empirica l forilluia w ith best fit has been formulat ed to find out the practica l ro ughness ach ievab le for the machining condit ions under stu dy.
Single point dia mond turning (S POT) of optics can be defi ned as the use of a diamond tool on a precision lath e under very precise ly controlled machine and environmental co nditions to fabric ate a fi ni shed opti cal co mponent!.:!. As is in th e case of turn ed surfaces, SPOT also yields onl y rotationall y sy mm etri c surfaces. albeit of op ti cal quality'. The diamond turnin g mac hin e is so phi sticated eq uipm ent th at produ ces th e final surface, which typica ll y docs not need the trad iti onal poli shin g operati on. There are advantages of using diamond turnin g: incl uding th e abi lity to produce good op ti ca l su rfaces up to th e edge of th e element , to fabri cate soft ductil e materials th at are difficult to po li sh , and to fabrica te shapes that are difficu.lt to do by ot her methods. Thi s process prod uces finished surfaces by very accurat ely cutting away a thin chip or layer of th e surface . It is ge nerall y app licable to ducti le materi als th at machine well rather than hard brittl e mat eri als traditi onally used for opti cal elements. However, by usi ng a gri ndin g head on a diamondturnin g ma ch ine in place of th e too l, hard brittle material s like glasses and ceram ic. can be machin ed ~. In diamond turnin g. th e intended shape and surface prod uced depe nd on th e machine tool accuracy and other mac hinin g parameters. In traditional optical fab ri cation, lappi ng and poli shin g wi th an abras iveloaded lap produce the final shape and surface of optical elements. The fundamental di ITerence between diamond turning and traditional op tical fab ri cation is th at diamond turning is a di splacement-co ntrnlled process while conventional optical fab ri cation is a
force-co ntroll ed process. The operatin g parameters of a prec ision machinin g process on a g iven pi ece of material wi II vary considerab ly depending on production rates req uired, work-p iece and mac hin e characteri stics, and all ot her process variables such as coo lant, too l cond iti on. depth of cut, tool feed rates. Tool feed rates, cutting speeds, and depths o f cut are typ icall y mu ch lower in diamond turnin g process compared to turning with co nventi onal machining too ls. For a given material, under different co mbinations of machining parameters (w ithin th eir optimum range), similar surface figure and fini sh res ults ca n ofte n be ob tained. The main machining parameters are too l feed rates, spindle speed and depth of cut('. The tool feed rate is norm all y exp ressed in terms o f either di stan ce tra ve ll ed by th e too l per unit time (mll1 per min ) or di stan ce travelled per unit rotation (mm per revo luti on). It is most co mmon to see the di sta nce per revo luti on as it is direct ly related to th e anticipated th eo reti cal surface finish. For a given too l feed rate, larger the too l nose radius. lower th e roughn ess and better the optical surface fini sh. The surface quality depends to a great ex ten t on th e materia l characteri sti cs like: grain size, microstructure of crystal boundary, crys lal uniformit y and ann ea ling proced ures adopted 7 . In thi s paper, the effec ts of tool feed rate on the surface figu re and surface ro ughness are stu died under similar mach ining conditions. The materia l unde r study is Aluminium-6061 all oy. It is proposed that for optical quality !lat compo nen t fab ri catio n, it is always advisable to explore ancl optim ise the tool feed rate
INDIAN 1. ENG. MATER. SCI. . APRIL 2003
124
range and other corres pondin g machining parameters before batch production.
can be used for rough cuts an d to produce an y reference surfaces, while th e oth er tool is used for finishin g the optical surface.
Machine Description Base machine
Spray mist coolant system
In thi s stud y, th e work-pi eces arc turn ed on Nan o form -250, a preci sion diamond turning Illachin e fro lll Taylor-H obso n (Fi g. I). The machin e is havin g 8.6 nm positi on feedback with th e X hori zo ntal strai ghtn ess 0.30 ).lin over 350 Illm trave rse. Z horizo ntal strai ghtn ess 0.20 ~lm ove r 250 mill traverse, X ve rti cal strai ghtn ess 0.75 ~ll1l over 350 mm tra ve rse, Z ve rti cal strai ghtn ess 0.50 ~lm ove r 250 mm trave rse, and X to Z squareness 0.50 arc seconds.
Mos t diamond machinabl e materi als require a spray mi st cool ant of so me type. For those material s (like PMMA ). whi ch do not require a spray mi st coo la nt. a hi gh-press ure jet o f air can be supp li ed fro m thi s sys tem.
L VDT tool set station
The LVDT tool settin g stati on is used to adjust th e height of th e di amond too l as we ll as X and Z pos itions relati ve to th e spindl e ce ntreline. The ve rti cal LVDT air-bearin g probe is used to accurat ely se t diamond too l height. The hori zo ntal LVDT airbearin g probe is used to autolllati ca ll y calculate th e di amond too l's nose radiu s and relati ve X and Z pos iti ons, in relati on to th e spindl e's ce ntreline. Iiero height adjust tool holders
The mi cro- height adjuster inco rporates an adjustm ent mec hani sm for initial loca ti on of the tool , and in additi on, acc urately es tab li shes th e exact height 01" the too l relati ve to th e ce ntreline. The tool ho lder asse mbl y includes a Ve nturi type chip ex tracti on sys tem uti Iizing th e co mpressed ai r be ing suppl ied to th e machine. A seco nd too l holde r with height adjus tm ent , fitted al ongs ide th e firs t too l holder. permits simultaneo us set-up of two tools. One too l
...
Fi g. l - Na no rorm 250 lathe (Tay lor-Hobson)
Single-crystal diamond tool
When co mbin ed with an ultra- prec isio n vibratio nfree machine, a co mpact ri gid too l ho ld er. stable and well -balan ced fi xturing, sin gle crys tal natural diam ond cutti ng tool s wi II re move mat erial fro m substrates cleanl y and effec ti ve ly. Because of th e ex treme level of sharpn ess on the diamond-cuttin g too l, very slllall force s are ge nerated durin g th e machinin g process. The end res ult is a surface th at ex hibits opti cal qualiti es in both sur face fini sh and form accuracy. Extreme leve l o f sharpn ess , minimal tool wear. cutting edge quality, edge waviness control. low coeffici ent of fri cti on and th ermal ex pansion and hi gh th erm al condu eti vity, mak e di amond the bes t cUlli ng too l for ultra prec ision machinin g. There are two types o f too ls: with control led wav iness and noncontroll ed wav iness at th e too l tip . Co ntroll ed wav iness di ctates that th e radius shape of" th e tool ti p dev iates from a tru e circle by a gu aranteed va lue ranging betwee n 1.0-0.05 mi crons. [n th ese inves ti gati ons, single-crys tal natural cliamond too ls ha ving a 0.5 mm nose radius. 100° arc and 0° rake angle are used. The wav iness of" too l is des ignat ed to be 0.40 ~m. SUI-face Eva[uation There are three types o f errors th at may occ ur on th e machin ed surface, i.e., f"orm , fi gure and fini sh. [t is impossible to say, at what point does fini sh error become fi gure error. [t is better to se parate fini sh. fi gure and form according to their cause, as thi s relates to the performance factors. Roughn ess is du e to the irregularities, which are inherent in th e x producti on process (e.g. cutting tool and feed rate ) . The rou ghn ess also depends on th e materi al composition and heat treatment 7.'). Figure error may result from vibration s, chatter or work de ri ee ri ons and stra ins in the material. Form is genera l shape of th e surface, neglecting variation s due to rou ghn ess and
KHAN el 01.: EFFECTS OF TOOL FEED RATE IN SINGLE POINT D IAMOND TUR ING .
fi gure error. Th e mos t commonly accepted parameters to evaluate surface figure and surface finish are peakto-va lley and roughness (Ra) respec ti ve ly. The term peak-to-valley is the di fference between th e hi ghest and lowes t poi nts in any su rface trace, w hereas Ra is th e arithmetic mean of th e departures of th e profi Ie fro m th e mean line over the sa mpli ng length II). There are oth er stati st ica l parameters for ro ughness measurements like Rz., Rq , skew ness, and kurtos is ll also . Rz is the average of fi ve hi ghest peaks and th e average of five lowes t va lleys. Skewness describes th e asy mmetry of a profile, while kurtosis describes th e peakedness or spikiness of a profile.
A standard Form T alys urf Series 2 (PG I) Profilometer from Tay lor-H obson is used for the surface evaluation. A diamond conical sty lus ha vi ng th e tip radiu s 2 J1.m and 10 mm vertical ran ge is used to measure th e figure error and surface roughness. Droughts and airborn e vibrations are avoi ded during the measurements. The profi lometer is mounted on an epoxy granite co nstructio n on anti-vibration mounts, and provides a finn support for th e co lumn and work piece. Measurements are taken w ith th e sty lus movement speed of 0.5 mm/s. Theoretical surface fini sh during tuming
The resultant ro ughness produced during turning operation is due to th e co mbinati on effec t of two independent quantities such as ideal roughness and natural roughness. Ideal ro ughness is due to the tool geometry and its feed . It is a geometri ca l ph enomenon and is the minimum possible magnitude of th e uneven ness, which results from a machining operation. Movement of a cutting tool across th e surface o f the turning component produces the diamond turn ed surface, th erefore, it always has some period ic surface ro ughness . The surface texture is directly related to the co mbinati on of th e tool shape and radius , and the tool's path over the su rface. The machine ' s operating cond itions affect this surface figure and fi ni sh in the direct quan ti ta tive manner indicated in the theoret ica l 4 sur face finish equat ion given as :
125
on di amond-turned parts is influenced by other factors such as: slides straightness error, sp indl e rotati on error, external and self-induced vibrati ons, material impurities, roughness of th e edge of th e tool. Natural roughness in actual turning operati on is the result of formati on of a built up edge and vibrati on, w hi ch adversely affect th e surface finish. Wh en th e cutting co nditi ons are properl y chosen, th e vibrati on may be avoided. Since th e built up edge formati on depends w hether coo lant is being used or dry machining is performed and the proper cutting speed is used or not, it is expected that natural roughness to vary with actual cutting speeds. 4 Cutting speed ca n be defined as the speed by which the tool moves over th e length o f th e job per unit time.
n x D xN Cutting speed (m/mi n) = - - - 1000
.. . (2)
where D is diameter of the wo rk -piece in mm, N is sp indl e's rotational speed (rpm). In the experimental set-up, as th e cutting tool is approach ing nearer to th e centre, the CUlling speed becomes lower as th e diameter is approach ing zero. It is expected th at for a give n set of cutt ing cond itions, the natural roughness w ill vary with th e CUllin g speed. It is also ex pected that excep t for low cutting speed. th e intensity of built up edge formation decreases with th e cutting speed , so the maximum height of su r fac e unevenness is also expected to decrease with th e cu ttin g speed.
Experimental Results Twenty-six alu1l1inium-606 1 work- pieces. each o f 60 mm diameter are . ingle-point-diamond-turned to study the effects of tool feed rate on surface figure and roughn ess. A 11 the speci men s are machi nt'd under
Maximunt he ight or une venne ss =
(feed/rev) 2
." ( I )
8x (tool nose radi us)
In add ition to the theoretical fini sh based on the ' cu sp' structure (Fi!!. 2), th e meas ured surface fin ish
Fig. 2-Ex panded view opti c:." e k me nt
or "C usp"
surfa ce of dianlll lld- llII'ncd
INDIA
126
J. E G. MATER. SC I.. APR I L 2003
roughness was 26. 5 nm and it impro ves at 4.0 ~lInlrev to 13.6 nm and deteri orate after 8 I1mlrev. Fig. 5 shows th e surface fi gure (P-V and its rm s va lue) versus tool feed rate.
the same co nditi ons with th e exception of tool feed rate. The tool feed rate is selec ted to vary from 0.3 11m/rev to 30.0 I1mlrev. The depth of cut is kept at 2 11111 and spindl e's rate at 3000 rpm . Th e depth of cut was vari ed from I I..un to IS 11111, and sp indle's rate frol11 1000 rpm to 5000 rpm. It was observed th at va ri ati on of depth of cut does not affect the su rface roughness much but it affec ts th e surface figure. The depth of cu t of 2 11m and sp ind le's rpm 3000 is found to be optil11 unl for 60 mm dial11eter aluminiul11 workpi ece to get the desired surface roughness and surface fig ure. All the specimens are (urn ed w hil e too l is moving fro m edge to ce ntre. Th e surfaces thu s turn ed are evaluated for their surface fi gure (P-V and rm s PV) and surface roughness ( Ra). These results are presented in Table I . Th e practical optimum ran ge of tool feed rate is found to be 1.5-8.0 )..lmlrev. Th e surface finish is almost constant in this range. Average of the ro ugh ness in thi s range is around I S nm. Standard deviation from th e mean ro ughness is 1.24824. The surface fini sh is affected signifi cantl y ou tside thi s prescribed ran ge. This variat ion occurs due to process conditions e.g., vibrati on, chattering, built -up-edges, and wear oul at tool tip . Figs 3a, 3b and 3c show the surface figure P- V at th e tool feed rates of 0.3 11m/rev, 1.0 11m/rev and 4.0 ~lIn/rev respectively. At 0.3 I1l11lrev th e surface figure is 1.9480 11m (nns PV 0.5796 ~lm ) and it improves at 4.0 I1mlrev to 0. 1882 )..lm (rms PV 0.0428 11m ). Figs 4a, 4b and 4c show the roughness at the tool feed rates o/" 0.3 )..lm/ rev, 4.0 )..lmlrev and 30 )..lmlrev respectively . At 0.3 11m/ rev tool feed rate, the
Tah le I- E ITecls of feed rale on surface fi g ure c,nd surface lini sh Su rface fi g ure
Feed rale ( ~l11/rev)
0.3 0.5 075 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 X.O 10.0 12.0 14 .0 15 .0 16.0 IX.O 20.0 22.0 25.0 30. 0
(P-V)
Surface figure ( rln s 1'- V )
( ~lIn)
(~lIn J
1.!l322 1.1 !l54 0.878 1 0.6884 0.423D 0.3439 0.3625 0.4270 O.30n 0.2228 0.2558 0.248 1 0.234 1 0.5963 0.4790 0.3205 0.2782 0.2 199 0.2474 0.2875 0.3367 0.2725 0.3254 0.310 1 0.3299 0. 1976
0.551 3 0.2832 0.26 18 0.1 657 0.0569 OJlS09 0.0656 D.I 037 0.0665 0.0462 0.0568 0.0671 D. IOn 0.1 534 0.1 329 0.06!l6 00596 O.D504 0.0525 0.060 I O.OXM 0.0572 0.0697 0.0702 O.OMI 0.0347
R()u ghlles~
(in nl11 over 5.6 111111 ran ge)
25.30 18.05 19.25 18.XO 17.60 16.35 16.28 16.·Hl 15.33 14.45 14. 10 1390 14.10 13.55 15.DO 15. 20 17 .35 19.55 24.35 24.DO 26.65 30.90 35 .30 40.45 49.70 65.70
2.0 15 10 05 V>
c
e ~
00 ·05 ·10 ·15 ·20 25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
millimetres
Pa
o. 5196
urn
1, 9480
urn
I
Fig . 3a-S urfaee fi g ure (1'- V) a l feed rUle 0.3 ~lInlrev
105
110
11 5 120
125
KH AN et at.: EFFECTS OF TOOL FEED RATE IN SINGLE POI T DI A MOND T UR ING
0.5
0.5
04
0.4
0.3
0.3
02
02
o1
01
00
00
-0 1
::}
-02
-jr.
127
-01
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-0;
/
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-03
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.·f 25
30
p,
40
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55
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ut:
0. 1351
60
: : : t:
65
70
75 80 millimetres
85
90
95
100
105
110
115 120
125
I
Fi g. 3b- Surfaee fi gure (P- V) at feed rate 1.0
~t11llre v
04 03 0.2 01 ~
c
e
00
.~
-0 1 -0 2
/
-03
-03 -0.4
-04 30
P.
35
0.Ol69
40
45
50
55
60
65
70
75
80
85
90
95
100 105
110
11 5
120
125
130
mllhmetres
ut;
Fig. 3e- Surfaee fi gure ( P- V) at feed rate 4.0
~11l1/ rev
1.2 ~-------~--'--------'----------/0 /;-------~ 12 / 1.0 10 ./
08
08
/ /.
06
'"
~
.~
06
04
/ --
"
02 00
/.
~'.
- 02
t-----------~·~~~~~~~~~~~~~~~~/T·c~C-------_+OO /
-0 .2
./
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-0 .4
-0 4 /
25
30
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60
65
70
75
80
85
90
95
100
m illimetres
Ra
o. 0265
Uml Rg
o. 0395
um I
Fi g. 4a- Surfaee roughn ess at feed rate 0.3
~lInlrev
105
110
115
120 125
INDI AN J. ENG. MATER . SCI. , APR IL 2003
128 ./
04 03
~
I
.. j
I
/
1
0 .4
03
'j-'
0.2 0.1 00
-01
/
-0 .2
-02
;,-
....;
-03
30
35
40
45
-0 .3
SO
55
60
65
70
75
80
85
90
95
100
105
110
115
120
125
130
millimetres
O. 0118
vm
I
Fig. 4b-Surface ro ughness at feed rate 4.0 J..llll/rev
(I)
c
g f:
04
04
0.3
0.3
0.2
0.2
0.1
0.1
0.0
0.0
-0 .1 -0.2
0.2
-0 .3
03
-0.4
-35
-30
-25
-20
-15
-10
-5
5
10
15
20
25
30
35
40
45
50
55
60
65
milllmetres
o.0768
Ra
urn
I
Fig. 4c- Su rfaee roughness at feed rate 30.0 J..llll/rev Relationship of surface figure with feed rate Comparison of Theoretica l and Pract ica l Surface finish
-+- Peak-Ie-Valley
1.8 ..
c: ~
I ~ "u::'"
i- - Peak -Ie-Va lley (rms)
1.6 1.4
1.2
10
15
j
10
~
~
'0
-+-+-::----; 20
100
u.
0.4
~
r - - - Practical fimsh
.!1
0.8
0: _
i eu I
j 06 ~ '
.,
..........- Theo~et j Cal finish
1000
25
....o
om I
• 30
0.1
0.1
35
10
100
Surface Fi nish (microns )
Feedrate (microns/rev.)
Fig. 5- S ul fac e figure (P-V ;md rm s va lue) ve rsus tool feed rate
Fi g. 6- Theo reti cal and prac ti ca l surface fin is h versus tool feed rate
I
KH AN ef al.: EFFECTS O F TOOL FEED RATE IN S INGLE PO I T DIAMOND TU RNING
A co mpari son o f th e theo reti ca l surface fini sh and th e o btain ed surface fini sh is prese nted in Tab le 2. It is observed th at sma ll e r th e too l feed rate, bette r th e surface roughn ess. The surface roug hness, however, beco mes almos t co nstant w he n the too l feed rate is betwee n 1.5-8 .0 /-lin/rev as show n in Fi g . 6. Th e ro ug hn ess va lu e in creases as the too l feed rate goes dow n to I /-lin/rev or less. Beyo nd 8 /-lin/re v too l feed rate theoretica l ro ughness is hi g he r th an practica l o ne. There fo re fro m Fi g. 6, it can be co nc luded th at th eoreti ca l fo rmul a does no t ho ld good beyond 8.0 J..un/ rev too l feed rate.
f
is th e too l feed rate : coeffic ients ao, al a nd a2 are de fin ed as:
ao= 12 .4 109;
= 4 .05 29
a2= 0 .23 17
a nd
Tab le 3-Confidcnce in terva ls for the values of variab les Variab le
An e mpiri cal fo rmul a is deri ved fro m the prac ti ca l surface fini sh versus th e too l feed rate (Fi g. 6 and Table 2) as:
(I f) . (I , . (I ,
Confidence inte rva ls
Value
68 %
90%
95 %
9'Y,I
(1 0
12.4 109
0.435836
0.734926
O.88706()
1.203 78
(I,
4.0529
0.420552
0.709 153
0.855957
1.1 6 1565
(I ,
0.23 17
0.00549
0.00926
O. III X
(>.0 15 18
70 •
(2
where A
aI
The first term A has been added to the exis ting th eore ti cal fo rmul a ( I). Thi s re lati o nship (3), in stead of the o ne give n by Eq . ( I) will sati sfac to ril y provide the practi ca l ro ug hness unde r th e mac hin ing
Em pir ical fo rm ula for practical roughness
Roughness
129
= A + a ~ -'-
- 8R
a
= a o +-l f
... (4)
__ Practical Roughness
i
... (3)
___ Best fi tted curve
60 .
I
50
. en en
c:
~
Ol :J
o
0::
Table 2-Compar iso n of theoretica l and obtained surface fini sh Feed rate (~lIll lrev)
Theoreti cal fini sh (Roughness in nm )
Prac ti ca l fini sh (Ro ughness in nl11 )
0. 3 0.5 0.75 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 8.0 10.0 12.0 14.0 15.0 16.0 18.0 20.0 22 .0 25.0 30.0
0.0225 0.0625 0. 1406 0.2500 0.5625 1.0000 1.5625 2.2500 3.0625 4.0000 5.0625 6.2500 7.5625 9.0000 10.5625 16.0000 25.0000 36.0000 49.0000 56.2500 64.0000 8 1.0000 100.0000 12 1.0000 156.2500 225.0000
25.30 18.05 19.25 18.80 17.60 16.3 5 16.28 16.40 15.33 14.45 14. 10 13.90 14. 10 13.5 5 15.00 15.20 17.35 19.55 24.35 24.00 26.65 30.90 35.30 40.45 49.70 65 .70
10
o o
10
5
15
20
25
30
35
Feedrate in micro n/rev.
Fig. 7- Bes t-fit curve for surface ro ughness in term s of tool feed rate Percen tage Error of curve fitted data w ith p ra ctica l roughnes s
15
~ ~
10
1
5
!
~
w .
0
OJ
. .
~
c: ~
Q.
-5 , I
-10 '
I
-15 -20
1
I 0
5
10
15
20
25
30
35
Feedrate in m icron/rev.
Fig. 8- Percentage error between the best-fit curve and the practi cal roughness
130
IND IAN J. ENG. MATER. SCI.. APRIL 2003
condit ions described. As th e f eed rate is less than 1.5 ~lIn/rev th e first term of th e empirical formula dom in ates thu s deteriorating the surface roughness. Beyond 8. 0 )..tm/rev tool feed rate th eoretical roughness is hi gher than practical one. Th erefore from Fig. 6, it can be conc luded that theoretica l formula does not hold good beyond 8.0 )..tm/rev tool feed rate. Confidence intervals at 68%, 90%, 95 %, and 99% for thc co nstant va lues o()= 12.4 109, 01 = 4.0529 and 0 2 = 0.23 17 are presented in Table 3. Since surface roughness value remark ably increases as th e tool feed rate goes down to I )..tm/rev or less, thi s region has been excl uded w hile fitting the curve. Fig. 7 depi cts the bes t-fitted curve on the pl ot for roughness w ith too l feed rate . Th e bes t- f itted curve is as per the relati onship (3). It shows that th e practi ca l roughness and the roughness from the deri ved form ul a are in agreement. Fi g. 8 shows th e perce ntage error of th e bes t-fitted curve. At thc med ium tool fced rates 1.5-8.0 )..tm /rev , th e oth er machining parameters such as tool co ndition, spray mi st coo lant, chip extraction and vibration dominate over theoretical fini sh resulting in higher actua l surface roughness. A lso it is observed that at hi gher tool feed rates , th e oth er machini ng parameters lose th eir dom inance resulting in the theoretica l and actua l surface fini shes close to each oth er.
Conclusions The study has been carr ied out on aluminium-6061 alloy rIat wo rk-pieces o f 60 mm diameter w ith the 2 11m depth of cut and 3000 rpm of spindl e speed. It has been observed that th e tool feed rate of 1.5 to 8.0 pm/rev pro vides optimum surface figure and f ini sh under the above said machining parameters. Th e th eoreti ca l and practi ca l surface fini shes are co mpared. It is observed that. small er th e feed rate, better th e surface roughness. Th e surface roughn ess, however, becom es almos t co nstant when th e feed rate
is in between 1.5 to 8.0 )..tm/ rev . Th e ro ughness va lue significantly increases as th e feed rate red uces to I )..tm/rev or less. I t has also been observed that th e slower cutting speeds produced by facing to the cen tre of a j ob do not affect th e surface fini sh, however th ey affect th e sur face fi gure. An empiri ca l formula is deri ved to best f it th e practi ca l roughness obtained in thi s in ves ti gation. Thc pract ical roughness and roughness from th e empiri ca l formul a are In agreement. Th ere are two approaches to write the CNC program for flats and regul ar co ni cs. O ne is based on ISO code (G39 facin g cycl e) and another by using the Tool Path Generator (TPG) software. T he work-piece has been turn ed by both th e programs, and it was observed th at G39 cycl e gives better surface fi ni sh compared to TPG, giving lesser scatterin g and dispersion.
Acknowledgement Th e au th ors are grateful to Dr R P Bajpai , Director, CSIO, Chandi garh , for hi s co nstan t enco uragement throughout th e inves ti gati on.
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