Solutions for Fundamentals of Modern Manufacturing , 5/e (published by Wiley) MPGroover 2012
20 THEORY OF METAL MACHINING Review Questions 20.1 20.1
Wht Wht re re the the three three bsi bsi!! !te"o !te"ories ries of #te #teri rill re#ov re#ovl l pro!e pro!esse sses$ s$ Answer. %s or"ni&ed in this te't, the three bsi! !te"ories of #teril re#ovl pro!esses re (1) !onventionl #!hinin", (2) brsive pro!esses, nd () nontrditionl pro!esses.
20.2 20.2
Wht Wht disti distin"u n"uish ishes es #!h #!hini inin" n" fro# fro# other other #nu #nuf! f!tur turin" in" pro!es pro!esses$ ses$ Answer. n #!hinin", #teril is re#oved fro# the *or+ prt so tht the re#inin" #teril is the desired prt "eo#etry "eo#e try..
20. 20.
dentify dentify so#e so#e of the the resons resons *hy *hy #!hini #!hinin" n" is !o##er !o##er!i !illy lly nd nd te!hnol te!hnolo"i o"i!l !lly ly i#port i#portnt nt.. Answer. he resons in!lude the follo*in"- (1) it is ppli!ble to #ost #terils (2) it !n produ!e vriety of "eo#etries to prt () it !n !hieve !loser tolern!es thn #ost other pro!esses nd () it !n !rete "ood surf!e finishes.
20. 20.
#e #e the the thr three ee #os #ostt !o## !o##on on #!h #!hin inin in" " pro! pro!es esse ses. s. Answer. he three !o##on #!hinin" pro!esses re (1) turnin", (2) drillin", nd () #illin".
20.5
Wht re the the t*o t*o bsi! bsi! !te"ories !te"ories of !uttin" !uttin" tools in #!hini #!hinin"$ n"$ Give t*o e'#ples e'#ples of of #!hinin" #!hinin" opertions tht use e!h of the toolin" types. Answer. he t*o !te"ories re (1) sin"lepoint tools, used in opertions su!h s turnin" nd borin" borin" nd (2) (2) #ultipleed" #ultipleed"ee !uttin" !uttin" tools, tools, used used in opertions opertions su!h su!h s #illin" #illin" nd drillin" drillin"..
20.
Wht re the the pr#eter pr#eterss of #!hinin" #!hinin" opertion opertion tht re in!lude in!luded d *ithin *ithin the s!ope of !uttin" !uttin" !onditions$ Answer. 3uttin" !onditions in!lude speed, feed, depth of !ut, nd *hether or not !uttin" fluid is used.
20.4 20.4
'pli 'plin n the differ differen!e en!e bet* bet*een een rou"h rou"hin" in" nd nd finishi finishin" n" opert opertion ionss in #!hini #!hinin". n". Answer. % rou"hin" opertion is used to re#ove lr"e #ounts of #teril rpidly nd to produ!e prt "eo#etry "eo#etry !lose to the desired shpe. % finishin" finishin" operti opertion on follo*s follo*s rou"hi rou"hin" n" nd is used used to !hieve the finl "eo#etry nd surf!e finish.
20.6
Wht is is #! #!hine to tool$ Answer. % #!hine tool !n be defined s po*erdriven #!hine tht positions nd #oves tool reltive to the *or+ to !!o#plish #!hinin" or other #etl shpin" pro!ess.
20.7 20.7
Wht Wht is n orth ortho" o"on onl l !utt !uttin in" " ope oper rti tion on$$ Answer. 8rtho"onl !uttin" involves the use of *ed"eshped tool in *hi!h the !uttin" ed"e is perpendi!ulr perpendi!ulr to the the dire!tion dire!tion of of speed #otion into the *or+ *or+ #teril. #teril.
20.10
Why is the ortho"o ortho"onl nl !uttin" !uttin" #odel useful in the the nlysis nlysis of of #etl #!hini #!hinin"$ n"$ Answer. 8rtho"onl !uttin" is useful in the nlysis of #etl #!hinin" be!use it si#plifies the rther !o#ple' threedi#ensionl #!hinin" sitution to t*o di#ensions. n ddition, the toolin" in the ortho"onl #odel hs only t*o pr#eters (r+e n"le nd relief n"le), *hi!h is si#pler "eo#etry thn sin"lepoint tool.
20.11 20.11
#e nd nd briefly briefly des!ribe des!ribe the the four four types of !hips !hips tht tht o!!ur o!!ur in #etl #etl !uttin". !uttin".
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Solutions for Fundamentals of Modern Manufacturing , 5/e (published by Wiley) MPGroover 2012
Answer. he four types re (1) dis!ontinuous, in *hi!h the !hip is for#ed into seprted se"#ents (2) !ontinuous, in *hi!h the !hip does not se"#ent nd is for#ed fro# du!tile #etl () !ontinuous *ith builtup ed"e, *hi!h is the s#e s (2) e'!ept tht fri!tion t the tool!hip interf!e !uses dhesion of s#ll portion of *or+ #teril to the tool r+e f!e, nd () serrted, *hi!h re se#i!ontinuous in the sense tht they possess s*tooth ppern!e tht is produ!ed by !y!li!l !hip for#tion of lterntin" hi"h sher strin follo*ed by lo* sher strin.
20.12
dentify dentify the four four for!es for!es tht !t !t upon the the !hip in in the ortho"on ortho"onl l #etl !uttin !uttin" " #odel but !nnot !nnot be #esured dire!tly in n opertion. Answer. he four for!es tht !t upon the !hip re (1) fri!tion for!e, (2) nor#l for!e to fri!tion, () sher for!e, nd () nor#l for!e to fri!tion.
20.1
dentify dentify the t*o for!es for!es tht tht !n be #esured #esured in the ortho"o ortho"onl nl #etl #etl !uttin" !uttin" #odel. #odel. Answer. he t*o for!es tht !n be #esured in the ortho"onl #etl !uttin" #odel re (1) !uttin" for!e nd (2) thrust for!e.
20.1
Wht is the the reltionship reltionship bet*een bet*een the the !oeffi!ient !oeffi!ient of of fri!tion fri!tion nd the fri!tion fri!tion n"le n"le in the ortho"on ortho"onl l !uttin" #odel$ Answer. he reltionship is tht the !oeffi!ient of fri!tion is the tn"ent of the fri!tion n"le ( 9 9 tn ). ).
20.15 20.15
:es!ri :es!ribe be in *ords *ords *ht *ht the the Mer!hn Mer!hntt e;uti e;ution on tells tells us. us. Answer. he Mer!hnt e;ution sttes tht the sher plne n"le in!reses *hen r+e n"le is in!resed nd fri!tion n"le is de!resed.
20.1
20.14 20.14
Wht Wht is the the spe!if spe!ifi! i! ener" ener"y y in #et #etll #!hin #!hinin" in"$$ Answer. Spe!ifi! ener"y is the #ount of ener"y re;uired to re#ove unit volu#e of the *or+ #teril.
20.16 20.16
Wht Wht does does the ter# ter# si&e si&e effe!t effe!t #en #en in in #etl #etl !utti !uttin"$ n"$ Answer. he si&e effe!t refers to the f!t tht the spe!ifi! ener"y in!reses s the !rossse!tionl re of the !hip (t ( t o ' w in ortho"onl !uttin" or f or f ' ' d in in turnin") de!reses.
20.17 20.17
Wht Wht is too tool! l!hi hip p ther ther#o #o!o !oup uple le$$ Answer. % tool!hip ther#o!ouple is !o#prised of the tool nd !hip s the t*o dissi#ilr #etls for#in" the ther#o!ouple =un!tion s the tool!hip interf!e hets up durin" !uttin", s#ll volt"e is e#itted fro# the =un!tion tht !n be #esured to indi!te !uttin" te#perture.
Probles %ns*ers to proble#s lbeled !A" re listed in n %ppendi' %ppendi' t the b!+ of the boo+. C#i$ For%tion %n& For'es in M%'#inin(
20.1
!A" (S units) he r+e n"le in n ortho"onl !uttin" opertion 9 12 . he !hip thi!+ness before the !ut 9 0.0 ##, nd the resultin" !hip thi!+ness fter the !ut 9 0.40 ##. 3l!ulte () the sher plne n"le n"le nd nd (b) the the sher sher strin strin for the opertion opertion.. )olution- () r 9 9 t o/t c 9 0.0/0.40 9 0.26
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Solutions for Fundamentals of Modern Manufacturing , 5/e (published by Wiley) MPGroover 2012
9 9 tn1(0. 26 !os 12/(1 0. 26 sin 12)) 9 tn 1(0.02) 9 2*+, (b) Sher strin 9 9 !ot 2.4 > tn (2.4 15) 9 2.14 > 0.22 9 2+-.. 20.2 20.2
(S units) units) n Prob Proble# le# 20.1, 20.1, supp suppose ose the r+e r+e n"le n"le *ere !hn"ed !hn"ed to 0 0 . %ssu#in" tht the fri!tion n"le re#ins the s#e, deter#ine () the sher plne n"le, (b) the !hip thi!+ness, nd (!) the sher strin for the opertion. )olution- ?ro# Proble# 20.1, 9 9 12 12 nd 9 9 2.4 2.4. @sin" the Mer!hnt ;ution, ;ution (20.1) 9 9 5 > /2 /2 /2 /2 rerrn"in", 9 9 2(5) > 2 2 9 9 2(5) > $ 2( 2( ) 9 70 > 15 A 2(2.4) 9 52. 52. o*, o*, *ith 9 9 0 nd re#inin" re#inin" the s#e t 52. 52. , 9 9 5 > 0/2 A 52./2 9 /+,
(b) 3hip thi!+ness t 9 9 0- t c 9 t o/tn 9 9 0.0/tn 16.4 9 0+1 (!) Sher strin 9 9 !ot 16.4 > tn (16.4 0) 9 2.75 > 0.6 9 -+2.2 20. 20.
(@S3S (@S3S units) units) he he tool tool in n orth ortho"o o"onl nl !utt !uttin" in" oper operti tion on is 0.25 0.250 0 in *ide *ide nd hs hs r+e r+e n"le n"le 9 5 . he #!hine tool is set for !hip thi!+ness before the !ut of 0.012 in, nd !uttin" speed 9 100 ft/#in. %fter the !ut, the defor#ed !hip thi!+ness 9 0.01 in. 3l!ulte () the sher plne n"le, (b) the sher strin for the opertion, nd (!) #teril re#ovl rte. 9 t o/t c 9 0.012/0.01 9 0.641 )olution- () r 9 1 9 9 tn (0. 641 !os 5/(1 0. 641 sin 5)) 9 tn 1(0.760) 9 2/+, (b) Sher strin 9 9 !ot 21.4 > tn (21.4 A 5) 9 2.512 > 0.00 9 2+/2 (!) % (!) % &% 9 't ow 9 100(12)(0012)(0.250) 9 -+1 in-in
20. 20.
(S units units)) n turnin turnin" " opert opertion ion,, !uttin" !uttin" speed speed 9 1.6 1.6 #/s. #/s. ?eed 9 0.0 0.0 ##/rev ##/rev nd nd depth depth of of !ut 9 2. 2. ##. B+e n"le 9 6 6. %fter the !ut, the defor#ed !hip thi!+ness 9 0.5 ##. :eter#ine () sher plne n"le, n"le, (b) sher sher strin, strin, nd (!) #teril #teril re#ovl re#ovl rte. @se @se the ortho"onl ortho"onl !uttin" !uttin" #odel s n ppro'i#tion of the turnin" pro!ess. 9 t o/t c 9 0.0/0.5 9 0.5 )olution- () r 9 1 9 9 tn (0. 5 !os 6/(1 A 0. 5 sin 6)) 9 tn 1(0.54) 9 2.+ (b) 9 9 !ot 27.6 > tn (27.6 6) 9 1.4 > 0.00 9 2+/*1 (!) % (!) % &% 9 (1.6 #/s ' 10 ##/#)(0.)(2.) 9 /*0* -s
20.5
!A" (S units) he !uttin" for!e nd thrust for!e in n ortho"onl !uttin" opertion re 140 nd 1567 , respe!tively. B+e n"le 9 5 , *idth of the !ut 9 5.0 ##, !hip thi!+ness before the !ut 9 0., nd !hip thi!+ness rtio 9 0.6. :eter#ine () the sher stren"th of the *or+ #teril nd (b) the !oeffi!ient of fri!tion in the opertion. )olution- () 9 9 tn1(0.6 !os 5/(1 0.6 sin 5)) 9 tn 1(0.71) 9 21.6 21.6 ( s 9 140 !os 21.6 A 1567 sin 21.6 9 467. A s 9 (0.)(5.0)/sin 21.6 9 .0/. 9 6.2 ## 2 S 9 9 467./6.2 9 75.7 /## 2 9 .3+. MP%
(b) 9 9 5 > /2 /2 /2 /2 rerrn"in", 9 9 2(5) > 2 2 9 9 2(5) > $ 2( 2( ) 9 70 > 5 A 2(21.6) 9 52.2 52.2 9 9 tn 52.2 9 /+2./ 20. 20.
(@S3S (@S3S units) units) he he !uttin !uttin" " for!e for!e nd thrust thrust for!e for!e hve hve been been #esured #esured in in n ortho"o ortho"onl nl !utti !uttin" n" opertion to be 00 lb nd 271 lb, respe!tively. B+e n"le 9 10 nd *idth of !ut 9 0.200 in. 3hip
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Solutions for Fundamentals of Modern Manufacturing , 5/e (published by Wiley) MPGroover 2012
thi!+ness before the !ut 9 0.015 in, nd !hip thi!+ness rtio 9 0.. :eter#ine () the sher stren"th of the *or+ #teril nd (b) the !oeffi!ient of fri!tion in the opertion. 9 tn1(0. !os 10/(1 0. sin 10)) 9 tn 1(0.2) 9 22.7 22.7 )olution- 9 ( s 9 00 !os 22.7 271sin 22.7 9 12.7 lb. A s 9 (0.015)(0.2)/sin 22.7 9 0.0044 in 2 S 9 9 12.7/0.0044 9 2/4/1, lbin2 9 9 2(5) > $ 2( 2( ) 9 70 > 10 2(22.7) 9 5.1 5.1 9 tn 5.1 9 /+- 9 20.4 20.4
(@S3S (@S3S units) units) %n ortho ortho"on "onl l !utti !uttin" n" opert opertion ion is is perfor#e perfor#ed d usin" usin" r+e r+e n"le n"le of 15 . 3hip thi!+ness before the !ut 9 0.012 in nd *idth of !ut 9 0.100 in. he !hip thi!+ness rtio is #esured fter the !ut to be 0.55. :eter#ine () the !hip thi!+ness fter the !ut, (b) sher n"le, (!) fri!tion n"le, (d) !oeffi!ient of fri!tion, nd (e) sher strin. )olution- () r 9 9 t o/t c, t c 9 t o/r 9 9 0.012/0.55 9 0+022 in
(b) 9 9 tn1(0.55 !os 15/(1 0.55 sin 15)) 9 tn 1(0.17) 9 -/+ (!) 9 9 2(5) > $ 2( 2( ) 9 70 > 15 2(1.6) 9 */+3 (d) 9 9 tn 1.5 9 0+ (e) 9 9 !ot 1.6 > tn(1.6 15) 9 1.15 > 0.01 9 /+.2 20.6
!A" (@S3S units) he ortho"onl !uttin" opertion des!ribed in previous Proble# 20.4 involves *or+ #teril *hose sher stren"th 9 0,000 lb/in 2. Csed on your ns*ers to the previous proble#, proble#, !o#pute !o#pute () sher for!e, for!e, (b) (b) !uttin" !uttin" for!e, for!e, (!) thrust for!e, nd nd (d) fri!tion fri!tion for!e. for!e.
() A s 9 (0.012)(0.10)/sin 1.6 9 0.00226 in 2 )olution- () A ( s 9 A 9 A sS 9 9 0.00226(0,000) 9 ./+2 lb (b) ( (b) ( c 9 71.2 !os (1.5 15)/!os (1.6 > 1.5 15) 9 /33 lb (!) ( (!) ( t t 9 9 71.2 sin (1.5 15)/!os (1.6 > 1.5 15) 9 ,,+2 lb (d) ( (d) ( 9 9 155 sin 15 44.2 !os 15 9 //3 lb 20.7 20.7
(S units) units) n n n ortho ortho"on "onl l !utt !uttin" in" operti opertion, on, the r+e r+e n"le n"le 9 5 5 , !hip thi!+ness before the !ut 9 0.2 ##, nd *idth of !ut 9 .0 ##. he !hip rtio 9 0.. :eter#ine () the !hip thi!+ness fter the !ut, (b) sher n"le, (!) fri!tion n"le, (d) !oeffi!ient of fri!tion, nd (e) sher strin. )olution- () r 9 9 t o/t c, t c 9 t o/r 9 0.2/. 9 0+3
(b) 9 9 tn1(0. !os(A5)/(1 0. sin(A5))) 9 tn 1(0.651) 9 2/+/ (!) 9 9 2(5) > $ 2( 2( ) 9 70 > (5) 2(21.6) 9 *2+. (d) 9 9 tn 2.7 9 0+.(e) 9 9 !ot 1.6 > tn(1.6 15) 9 2.574 > 0.67 9 -+0. 20.10
(@S3S units) units) he sher stren"t stren"th h of !ertin !ertin *or+ *or+ #teril #teril 9 50,000 50,000 lb/in lb/in 2. %n ortho"onl !uttin" opertion is perfor#ed usin" tool *ith r+e n"le 9 20 t !uttin" speed 9 100 ft/#in, !hip thi!+ness before the !ut 9 0.015 in, nd *idth of !ut 9 0.150 in. he resultin" !hip thi!+ness rtio 9 0.50. :eter#ine () the sher plne n"le, (b) sher for!e, (!) !uttin" for!e nd thrust for!e, nd (d) fri!tion for!e. )olution- () 9 9 tn1(0.5 !os 20/(1 0.5 sin 20)) 9 tn 1(0.56) 9 2.+3
(b) A (b) A s 9 (0.015)(0.15)/sin 27.5 9 0.005 in 2. '!erpts fro# this *or+ #y be reprodu!ed by instru!tors for distribution on notforprofit bsis for testin" or instru!tionl purposes only to students enrolled in !ourses for *hi!h the te'tboo+ hs been dopted. Any other reproduction reproduction or translation of this work work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyriht Act without the permission of the copyriht owner is unlawful!
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Solutions for Fundamentals of Modern Manufacturing , 5/e (published by Wiley) MPGroover 2012
( s 9 A 9 A sS 9 9 0.005(50,000) 9 22 lb (!) 9 9 2(5) > $ 2( 2( ) 9 70 > 20 2(27.5) 9 50.7 50.7 ( c 9 226 !os (50.7 20)/!os (27.5 > 50.7 20) 9 -., lb ( t t 9 9 226 sin (50.7 20)/!os (27.5 > 50.7 20) 9 2- lb (d) ( (d) ( 9 9 74 sin 20 > 26 !os 20 9 -3. lb 20.11 20.11
(@S3S units) units) Solve Solve previous previous Proble# Proble# 20.10, 20.10, e'!ept e'!ept tht the r+e r+e n"le n"le hs been been !hn"ed !hn"ed to 5 nd the resultin" !hip thi!+ness rtio 9 0.5. 9 tn1(0.5 !os(A5)/(1 0.5 sin(5))) 9 tn 1(0.6) 9 /+, )olution- () 9 (b) A (b) A s 9 (0.015)(0.15)/sin 16.4 9 0.00402 in 2. ( s 9 A 9 A sS 9 9 0.00402(50,000) 9 -3/ lb (!) 9 9 2(5) > $ 2( 2( ) 9 70 > (5) 2(16.4) 9 4. ( c 9 51 !os(4. (5))/!os(16.4 > 4. (5)) 9 113 lb ( t t 9 9 51 sin(4. (5))/!os(16.4 > 4. (5)) 9 ,0 lb (d) ( (d) ( 9 9 5 sin (5) > 640 !os (5) 9 0. lb
20.12
(@S3S units) units) 3onsider 3onsider the the dt in in Proble# Proble# 20.10, 20.10, e'!ept tht tht r+e n"le n"le is vrible, vrible, nd its its effe!t effe!t on the for!es in prts (b), (!), nd (d) is to be evluted. () @sin" spredsheet !l!ultor, !o#pute the vlues of sher for!e, !uttin" for!e, thrust for!e, nd fri!tion for!e s fun!tion of r+e n"le over rn"e of r+e n"les bet*een the hi"h vlue of 20 in Proble# 20.10 nd lo* vlue of 10 . @se intervls of 5 5 bet*een these li#its. he !hip thi!+ness rtio de!reses s r+e n"le is redu!ed nd !n be ppro'i#ted by the follo*in" reltionship- r 9 9 0.6 > 0.00 0.00 , *here r 9 9 !hip thi!+ness nd 9 9 r+e n"le. (b) Wht observtions !n be #de fro# the !o#puted results$ )olution- () he uthorDs spredsheet !l!ultions (usin" '!el) returned the follo*in" results-
r
( s (lb)
( c (lb)
( t t (lb) (lb)
( (lb) (lb)
20 15 10 5 0 5 10
0.5 0.4 0. 0.1 0.6 0.5 0.2
226 25 25 266 14 51 7
74 5 60 51 572 5 45
26 07 77 515 4 640 1150
57 11 4 557 4 607 1001
(b) 8bservtions- (1) %ll for!es in!rese s r+e n"le de!reses. (2) he !hn"e in for!es *ith r+e n"le in!reses t n !!elertin" rte s r+e n"le is redu!ed. () hrust for!e is less thn !uttin" for!e t hi"h r+e n"les (e."., 20 ) but in!reses t fster rte thn !uttin" for!e so tht its vlue is "reter t lo* nd ne"tive r+e n"les. () 3hip thi!+ness rtio de!reses *ith de!resin" r+e n"le, s indi!ted by the "iven reltionship r 9 9 0.6 > 0.00 0.00 . 20.1
(@S3S units) units) % !rbon steel steel br br *ith di#eter di#eter 9 4. in hs hs tensile tensile stren"th stren"th of of 5,000 lb/in lb/in 2 nd sher stren"th of 5,000 lb/in 2. he di#eter is redu!ed in turnin" opertion t !uttin" speed of 50 ft/#in. ?eed 9 0.011 in/rev nd depth of !ut 9 0.120 in. he r+e n"le on the tool in the dire!tion of !hip flo* 9 1 1 . he !uttin" !onditions result in !hip rtio of 0.52. @sin" the ortho"onl #odel s n ppro'i#tion of turnin", deter#ine () sher plne n"le, (b) sher for!e, (!) !uttin" for!e nd feed for!e, nd (d) !oeffi!ient of fri!tion bet*een the tool nd !hip. 9 tn1(0.52 !os 1/(1 0.52 sin 1)) 9 tn 1(0.546) 9 2.+ )olution- () 9
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Solutions for Fundamentals of Modern Manufacturing , 5/e (published by Wiley) MPGroover 2012
(b) A (b) A s 9 t ow/sin 9 9 (0.011)(0.12)/sin 27.6 9 0.0025 in 2. ( s 9 A 9 A sS 9 9 0.0025(5,000) 9 //.+- lb (!) 9 9 2(5) > $ 2( 2( ) 9 70 > 10 2(27.6) 9 . . ( c 9 ( 9 ( s!os (E A F)/!os ( ( > E A F) ( c 9 117. !os (. 1)/!os (27.6 > . 1) 9 20, lb ( t t 9 ( 9 ( ssin (E A F)/!os ( ( > E A F) ( t t 9 9 117. sin (. 1)/!os (27.6 > . 1) 9 /2/ lb (d) ) (d) ) 9 9 tn * tn * 9 9 tn . 9 0+.*2 20.1
!A" (S units) o* !rbon steel hvin" tensile stren"th 9 00 MP nd sher stren"th 9 220 MP is turned t !uttin" speed 9 2.5 #/s. ?eed 9 0.20 ##/rev nd depth of !ut 9 .0 ##. he r+e n"le 9 5 5 in the dire!tion of !hip flo*. he resultin" !hip rtio 9 0.5. @sin" the ortho"onl #odel to ppro'i#te turnin", deter#ine the !uttin" for!e nd feed for!e. )olution- 9 9 tn1(0.5 !os 5/(1 0.5 sin 5)) 9 tn 1(0.) 9 25.0 25.0 2 A s 9 t ow/sin 9 9 (0.2)(.0)/sin 25.0 9 1.2 ## . ( s 9 A 9 A sS 9 9 1.2(220) 9 12 9 9 2(5) > $ 2( 2( ) 9 70 > 5 2(25.0) 9 5.0 5.0 ( c 9 ( 9 ( s!os ( * A A $)/!os ( ( > * > * A A $) ( c 9 12 !os(5 5)/!os(25.0 > 5.0 5) 9 311 N ( t t 9 ( 9 ( ssin( * A A $)/!os( )/!os( > * > * A A $) ( t t 9 9 12 sin(5 5)/!os(25.0 > 5.0 5) 9 *,* N
20.15
(@S3S units) units) % turnin" turnin" opertion opertion is #de #de *ith *ith r+e r+e n"le n"le of 10 , feed of 0.010 in/rev nd depth of !ut 9 0.100 in. he sher stren"th of the *or+ #teril is +no*n to be 50,000 lb/in 2, nd the !hip thi!+ness rtio fter the !ut 9 0.0. :eter#ine the !uttin" for!e nd the feed for!e. @se the ortho"onl !uttin" #odel s n ppro'i#tion of the turnin" pro!ess. 9 tn1(0. !os 10/(1 0. sin 10)) 9 tn 1(0.2) 9 22+. )olution- 9 A s 9 (0.010)(0.10)/sin 22.7 9 0.00254 in 2 ( s 9 A 9 A sS 9 9 0.0025(50,000) 9 /2 lb 9 9 2(5) > $ 2( 2( ) 9 70 > 10 2(22.7) 9 5.1 5.1 ( c 9 126 !os (5.1 10)/!os (22.7 > 5.1 10) 9 2-1 lb ( t t 9 9 126 sin (5.1 10)/!os (22.7 > 5.1 10) 9 22. lb
20.1
Sho* ho* ho* ;ution ;ution (20.) (20.) is derived derived fro# fro# the definiti definition on of !hip !hip rtio, rtio, ;ution ;ution (20.2), (20.2), nd ?i"ure ?i"ure 20.5(b). 9 t o/t c 9 sin /!os /!os ( ( ) )olution- Ce"in *ith the definition of the !hip rtio, ;ution (20.2)- r 9 Berrn"in", r !os !os ( ( ) 9 sin @sin" the tri"ono#etri! identity !os( ) 9 !os !os !os > > sin sin sin r (!os !os !os > > sin sin sin ) 9 sin :ividin" both sides by sin , *e obtin r !os !os /tn /tn > > r sin sin 9 9 1 r !os !os /tn /tn 9 9 1 r sin sin Berrn"in", tn 9 9 r !os !os /(1 /(1 r sin sin ) H..:.
20.14 20.14
Sho* Sho* ho* ;u ;utio tion n (20.) (20.) is deriv derived ed fro# fro# ?i"ure ?i"ure 20.. 20.. )olution- n the fi"ure, 9 AC 9 AC / +, 9 +, 9 ( A, > A, > ,C ,C )/ )/ +, 9 +, 9 A, A,// +, > +, > ,C ,C / +, +, A,/ A,/ +, 9 +, 9 !ot nd ,C nd ,C / +, 9 +, 9 tn ( ( ) hus, 9 9 !ot > > tn ( ( ) H..:.
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Solutions for Fundamentals of Modern Manufacturing , 5/e (published by Wiley) MPGroover 2012
20.16 20.16
:eriv :erivee the the for!e for!e e;u e;ut tio ions ns for for ( ( , - , ( s, nd ( nd ( n (;s. (20.7) throu"h (20.12) in the te't) usin" the for!e di"r# of ?i"ure 20.11. nd F c )olution- ;ution (20.7)- n ?i"ure 2.11, !onstru!t line strtin" t the interse!tion of F t t nd tht is perpendi!ulr to the fri!tion for!e F . he !onstru!ted line is t n n"le *ith *ith F c. he ve!tor F is is divided into t*o line se"#ents, one of *hi!h 9 F c sin nd nd the other 9 F t t !os !os . hus, F 9 9 F c sin > > F t t !os !os . H..:. ;ution (20.10)- n ?i"ure 2.11, trnslte ve!tor N verti!lly verti!lly up*rd until it !oin!ides *ith the previously previously !onstr !onstru!ted u!ted line, line, *hose *hose len"th len"th 9 F c !os . e't, trnslte ve!tor F t t to to the ri"ht nd do*n*rd t n n"le until its bse is t the rro*hed of F . F t t no* no* #+es n n"le *ith F . he rro*hed of F t t *ill *ill no* be t the bse of the trnslted bse of N. he distn!e lon" the previously previously !onstr !onstru!ted u!ted line line bet*een bet*een the the F t t rro*hed rro*hed (bse of trnslted N ve!tor) ve!tor) nd F is is F t t sin sin . > F t t !os !os H..:.
Power %n& Ener(5 in M%'#inin(
20.17
!A" (S units) n turnin" opertion on stinless steel, !uttin" speed 9 150 #/#in, feed 9 0.25 ##/rev, nd depth of !ut 9 4.5 ##.
20.20
(S units) units) n Proble# Proble# 20.17, 20.17, !o#pute !o#pute the lthe lthe po*er po*er re;uire#ents re;uire#ents if feed 9 0.50 0.50 ##/rev ##/rev. )olution- his is the s#e bsi! proble# s the previous, e'!ept tht !orre!tion #ust be #de for the Lsi&e effe!t. @sin" ?i"ure 20.1, for f 9 9 0.50 ##, !orre!tion f!tor 9 0.64. ?ro# ble 20.2, U 9 9 2.6 K/## . With the !orre!tion ff!tor, !tor, U 9 2.6(0.64) 9 2. K/## . % &% 9 'fd 9 9 (150 #/#in)(10 ##/#)(0.50 ##)(4.5 ##) 9 52,500 ## /#in 9 7,45 ## /s . c 9 (7,45 ## /s)(2. K/## ) 9 22,66 K/s 9 22,66 W 9 22.6 +W %!!ountin" for #e!hni!l effi!ien!y, effi!ien!y, . 9 9 22.6/0.70 9 23+* 67
20.21
(@S3S units) units) n turnin turnin" " opertion opertion on lu#inu lu#inu#, #, !uttin" !uttin" speed 9 700 ft/#in, ft/#in, feed 9 0.020 in/rev in/rev,, nd depth of !ut 9 0.250 in. Wht horsepo*er is re;uired of the drive #otor, if the lthe hs #e!hni!l effi!ien!y 9 64J$ @se ble 20.2 to obtin the pproprite unit horsepo*er vlue.
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Solutions for Fundamentals of Modern Manufacturing , 5/e (published by Wiley) MPGroover 2012
)olution- ?ro# ble 20.2, /. 20.2, /. u 9 0.25 hp/(in /#in) for lu#inu#. Sin!e feed is "reter thn 0.010 in/rev in the tble, !orre!tion f!tor #ust be pplied fro# ?i"ure 20.1. ?or f 9 9 0.020 in/rev 9 t o, !orre!tion f!tor 9 0.7. /. c 9 /. 9 /. u ' % ' % &%, /. 9 /. 9 /. c/ % &% 9 'fd 9 9 700 ' 12(.020)(0.250) 9 5 in /#in /. c 9 0.7(0.25)(5) 9 12.2 hp /. 9 9 12.2/0.64 9 /*+0 #$
20.22
(S units) units) Plin !rbon steel steel *ith *ith Crinell Crinell hrdness hrdness of 245 245
he uthorDs spredsheet !l!ultions (usin" '!el) returned vlue !loser to f 8 8 0+*1 rev .
(@S3S units) units) % rou"h turnin" turnin" opertio opertion n is perfor#ed perfor#ed on 20 hp lthe lthe tht hs 72J 72J effi!ien!y effi!ien!y.. he !ut is #de on lloy steel *hose hrdness is 25
20.2
(@S3S units) units) Suppose Suppose the the !uttin" !uttin" speed in Proble#s Proble#s 20.4 20.4 nd 20.6 20.6 9 00 ft/#in. ft/#in. ?ro# ?ro# your ns*ers to those proble#s, find () the horsepo*er !onsu#ed in the opertion, (b) #etl re#ovl rte in in /#in, (!) unit horsepo*er (hp#in/in ), nd (d) the spe!ifi! ener"y (inlb/in ). )olution- () ?ro# Proble# 20.6, ( 20.6, ( c 9 155 lb. /. lb. /. c 9 155(00)/,000 9 /+*/ #$
(b) % (b) % &% 9 'fd 9 9 (00 ' 12)(0.012)(0.100) 9 *+-2 in-in '!erpts fro# this *or+ #y be reprodu!ed by instru!tors for distribution on notforprofit bsis for testin" or instru!tionl purposes only to students enrolled in !ourses for *hi!h the te'tboo+ hs been dopted. Any other reproduction reproduction or translation of this work work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyriht Act without the permission of the copyriht owner is unlawful!
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Solutions for Fundamentals of Modern Manufacturing , 5/e (published by Wiley) MPGroover 2012
(!) /. (!) /. u 9 1.1/.2 9 0+-21 #$!in-in" (d) U 9 9 155(00)/.2 9 /04,1* 9t:lbin- 8 /2.4/1, in:lbin20.25
(S units) units) % turnin" turnin" opertion opertion is !rried !rried out on on lu#inu#. lu#inu#. Csed on the the spe!ifi! spe!ifi! ener"y vlues vlues in ble 20.2, deter#ine #teril re#ovl rte nd !uttin" po*er in the opertion under the follo*in" sets of !uttin" !onditions- () 3uttin" speed 9 5. #/s, feed 9 0.25 ##/rev, nd depth of !ut 9 2.0 ## nd (b) !uttin" speed 9 1. #/s, feed 9 0.45 ##/rev, nd depth 9 .0 ##. )olution- () ?ro# ble 20.2, U 9 9 0.4 #/## for lu#inu#. 9 5.(10 )(.25)(2.0) 9 2+!/0-" -s. % &% 9 'fd 9 . c 9 U % % &% 9 0.4(2.6)(10 ) 9 1.7(10 ) #/s 9 /.10 7
(b) Ce!use feed is "reter thn 0.25 ##/rev in the tble, !orre!tion f!tor #ust be pplied fro# ?i"ure 20.1. ?or f ?or f 9 9 0.45 ##/rev 9 t o, !orre!tion f!tor 9 0.60. % &% 9 'fd 9 9 1.(10 )(.45)(.0) 9 -+.!/0-" -s. . c 9 U % % &% 9 0.6(0.4)(.7)(10 ) 9 2.16(10 ) #/s 9 2/* 7 ote tht tht lthou"h lthou"h the po*er po*er in (b) is only bout bout 10J 10J "reter "reter thn thn in (), (), the #etl re#ovl re#ovl rte is l#ost 0J "reter. 20.2
(@S3S units) units) n turnin turnin" " opertion opertion on lo* lo* !rbon !rbon steel steel (145 C<), C<), !uttin" !uttin" speed speed 9 00 ft/#in, ft/#in, feed 9 0.010 in/rev, nd depth of !ut 9 0.045 in. he lthe hs #e!hni!l effi!ien!y 9 0.65. Csed on the unit horsepo*er vlues in ble 20.2, deter#ine () the horsepo*er !onsu#ed by the turnin" opertion nd (b) the horsepo*er tht #ust be "enerted by the lthe. )olution- () ?ro# ble 20.2, /. 20.2, /. u 9 0. hp/(in /#in) for lo* !rbon steel. /. c 9 /. 9 /. u ' % ' % &% % &% 9 'fd 9 9 00 ' 12(.010)(0.045) 9 . in /#in /. c 9 0.(.) 9 2+/1 #$
(b) /. (b) /. 9 9 2.1/0.65 9 2+3* #$ 20.24
!A" (@S3S units) % !st iron *or+pie!e is turned on lthe *hose #e!hni!l effi!ien!y 9 0.64. 3uttin" speed 9 00 ft/#in, feed 9 0.011 in/rev, nd depth of !ut 9 0.120 in. 3uttin" for!e 9 250 lb. :eter#ine () the horsepo*er !onsu#ed by the turnin" opertion (b) horsepo*er tht #ust be "enerted by the lthe (!) unit horsepo*er nd spe!ifi! ener"y for the *or+ #teril in this opertion. )olution- () Given ( Given ( c 9 250 lb, /. lb, /. c 9 ( 9 ( c'/,000 9 250(00)/,000 9 -+0- #$
(b) /. (b) /. 9 /. 9 /. c/ 9 9 .0/0.64 9 -+* #$ (!) % (!) % &% 9 12 'fd 9 9 (00 ' 12)(0.011)(0.120) 9 . in /#in /. u 9 /. 9 /. c/ % % &% 9 .0/. 9 0+*, #$!in-in" U 9 ( 9 ( c'/ % % &% 9 250(00 ' 12)/. 9 /.4-.* in:lbin20.26
(@S3S units) units) % turnin" turnin" opertion opertion is perfor#ed perfor#ed on n en"ine en"ine lthe lthe usin" tool tool *ith &ero &ero r+e n"le n"le in the dire!tion of !hip flo*. he *or+ #teril is n lloy steel *ith hrdness 9 25 Crinell. ?eed 9 0.015 in/rev, depth of !ut 9 0.125 in, nd !uttin" speed 9 00 ft/#in. %fter the !ut, the !hip thi!+ness rtio 9 0.5. () @sin" the pproprite vlue of spe!ifi! ener"y fro# ble 20.2, !o#pute the horsepo*er t the drive #otor, if the lthe effi!ien!y 9 65J. (b) Csed on horsepo*er, !o#pute your best esti#te of the !uttin" for!e for this turnin" opertion. @se the ortho"onl !uttin" #odel s n ppro'i#tion of the turnin" pro!ess. 9 . u 9 520,000 inlb/in for this lloy steel of the spe!ified )olution- () ?ro# ble 20.2, U 9 . hrdness. Sin!e feed is "reter thn 0.010 in/rev in the tble, !orre!tion f!tor #ust be pplied fro# ?i"ure 20.1. ?or f ?or f 9 9 0.015 in/rev 9 t o, !orre!tion f!tor 9 0.75. hus,
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Solutions for Fundamentals of Modern Manufacturing , 5/e (published by Wiley) MPGroover 2012
U 9 9 520,000(0.75) 9 7,000 inlb/in 9 1,14 ftlb/in . % &% 9 00 ' 12(.015)(0.125) 9 .45 in /#in . c 9 U % &% 9 1,14(.45) 9 244,645 ftlb/#in /. c 9 244,645/,000 9 6.2 hp /. 9 9 6.2/0.65 9 .+. #$ (b) /. (b) /. c 9 '( c/,000. Berrn"in", ( Berrn"in", ( c 9 ,000 ( /. c/') 9 ,000(6.2/00) 9 .21 lb+ C#e'6 - @se unit horsepo*er fro# ble 20.2 rther thn spe!ifi! ener"y. /. u 9 1. hp/(in /#in). %pplyin" the !orre!tion f!tor !orre!tion f!tor 9 0.75, /. u 9 1.25 hp/(in /#in). % &% 9 00 ' 12(.015)(0.125) 9 .45 in /#in, s#e s before /. c 9 1.25(.45) 9 6. hp /. 9 9 6./0.65 9 .+ #$
(b) ( (b) ( c 9 ,000 (6./00) 9 ./- lb+ 20.27
(@S3S units) units) % lthe perfor#s perfor#s turnin" turnin" opertion opertion on *or+pie *or+pie!e !e *ith di#eter di#eter 9 .0 .0 in. Sher Sher 2 2 stren"th of the *or+ 9 0,000 lb/in nd tensile stren"th 9 0,000 lb/in . B+e n"le of the tool 9 . 3uttin" speed 9 400 ft/#in, feed 9 0.015 in/rev, nd depth 9 0.070 in. he !hip thi!+ness fter the !ut 9 0.025 in. :eter#ine () the horsepo*er re;uired in the opertion, (b) unit horsepo*er for this #teril under these !onditions, nd (!) unit horsepo*er s it *ould be listed in ble 20.2 for t o of 0.010 in. @se the ortho"onl !uttin" #odel s n ppro'i#tion of the turnin" pro!ess. )olution- () Must find ( find ( c nd ' to deter#ine /. deter#ine /. . r 9 9 0.015/0.025 9 0. 9 9 tn1(0. !os /(1 0. sin )) 9 tn 1 (0.) 9 2.5 2.5 9 9 2(5) > F 2( 2( ) 9 70 > 2(2.5) 9 1.0 1.0 A s 9 t ow/sin 9 9 (0.015)(0.07)/sin 2.5 9 0.00251 in 2 ( s 9 SA s 9 0,000(0.00251) 9 101 lb. ( c 9 ( 9 ( s !os ( * A A $)/!os ( ( > * > * A A $) ( c 9 101 !os(1 )/!os(2.5 > 1.0 A ) 9 140 lb. /. c 9 ( 9 ( c'/,000 9 140(400)/,000 9 -+1/ #$+
(b) % (b) % &% 9 400 ' 12(0.0045)(0.045) 9 11. in /#in /. u 9 /. 9 /. c / % % &% 9 .1/11. 9 0+-/. #$!in-in" (!) 3orre!tion f!tor 9 0.72 fro# ?i". 20.1 to !!ount for the f!t tht f 9 9 0.015 in/rev insted of 0.010 in/rev. +in" +in" this !orre!tion f!tor into !!ount, /. u 9 0.17/0.72 9 0+-*, #$!in-in" s it *ould pper in ble 20.2 for feed ( t o) 9 0.010 in/rev. in/rev. 20.0
(@S3S units) units) n turnin turnin" " opertion opertion on n n lu#inu# lu#inu# lloy lloy *or+pie!e, *or+pie!e, feed 9 0.020 in/rev in/rev,, nd depth of !ut 9 0.250 in. he #otor horsepo*er of the lthe is 20 hp, nd it hs #e!hni!l effi!ien!y 9 72J. Wht is the #'i#u# !uttin" speed tht !n be used on this =ob$ )olution- ?ro# ble 20.2, /. 20.2, /. u 9 0.25 hp/(in /#in) for lu#inu#. Sin!e feed is "reter thn 0.010 in/rev in the tble, !orre!tion f!tor #ust be pplied fro# ?i"ure 20.1. ?or f 9 9 0.020 in/rev 9 t o, !orre!tion f!tor 9 0.64. /. c 9 /. 9 /. u ' % ' % &%, /. 9 /. 9 /. c/ % &% 9 'fd 9 9 12' 12'(.020)(0.250) 9 0.0 ' in/#in /. c 9 0.64(0.25)(0.0 ') 9 0.01 ' hp /. 9 9 0.01 ' /0.72 9 0.0116 ' 9 20 hp ' 9 20/0.0116 9 110 ft/#in
20.1
8ne of the the fore#en in the #!hine #!hine shop shop !o#plins !o#plins of of proble# proble# *ith n n opertion opertion in the the turnin" turnin" se!tion. t see#s the lthe hs tenden!y to slo* do*n or stll in the #iddle of the !uttin"
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"0#1
Solutions for Fundamentals of Modern Manufacturing , 5/e (published by Wiley) MPGroover 2012
opertion, indi!tin" tht the #!hine is underpo*ered for the *or+ #teril nd !onditions of the !ut. Without +no*in" ny #ore bout the proble#, *ht !tions nd !hn"es !n be #de to #iti"te this po*er proble#$ )olution- ?ro# ble 20., there re severl !hn"es tht !n be #de to void this +ind of po*er proble# proble#- (1) redu!e redu!e !uttin" !uttin" speed, (2) redu!e redu!e feed nd/or nd/or depth depth of !ut, !ut, () perfor# perfor# the the opertion opertion on on lthe *ith hi"her po*er !pbility, () use !uttin" fluid, nd (5) use !uttin" tool tht hs lr"er r+e n"le. Cuttin( Te$er%ture
20.2
!A" (S units) 8rtho"onl !uttin" is perfor#ed on #etl *hose #ss spe!ifi! het 9 1.0 K/"3, density 9 2.7 "/!# , nd ther#l diffusivity 9 0.6 !# 2/s. 3uttin" speed 9 .5 #/s, un!ut !hip thi!+ness 9 0.25 ##, nd *idth of !ut 9 2.2 ##. 3uttin" for!e 9 750 . :eter#ine the !uttin" te#perture if the #bient te#perture 9 22 3. )olution- C C 9 9 (2.7 "/!# )(1.0 K/" K/" 3) 9 2.70 K/!# 3 9 (2.70'10 ) K/##3 9 9 0.6 !#2/s 9 60 ## 2/s U 9 ( 9 ( c'/ % % &% 9 750 ' .5 #/s/(500 ##/s ' 0.25 ## ' 2.2 ##) 9 1.424 #/## 2 9 9 0.U 0.U /( /( 3C 3C ) ' ('t ('t o/ )0. 2 9 9 22 > (0. ' 1.424 #/## /(2.70'10) K/##3) O500 ##/s ' 0.25 ##/60 ## 2/s0. 2 9 9 22 > (0.262 ' 10 3)(10.7) . 9 22 > 26.(2.22) 9 22 22 > 526 526 9 330 C
20.
(S units) units) 3onsider 3onsider turnin" turnin" operti opertion on perfor#ed perfor#ed on steel steel *hose *hose hrdness hrdness 9 225 225 7 9 .1* C
20.
(@S3S units) units) %n ortho"on ortho"onl l !uttin" !uttin" opertion opertion is is perfor#ed perfor#ed on !ertin !ertin #etl #etl *hose *hose volu#etri! volu#etri! 2 spe!ifi! het 9 110 inlb/in ? nd ther#l diffusivity 9 0.10 in /se!. he !uttin" speed 9 50 ft/#in, !hip thi!+ness before the !ut 9 0.006 in, nd *idth of !ut 9 0.100 in. 3uttin" for!e 9 200 lb. :eter#ine the !uttin" te#perture if the #bient te#perture 9 40 ?. )olution- ' 9 50 ft/#in ' 12 in/ft/0 se!/#in 9 40 in/se!. U 9 ( 9 ( c'/'t ow 9 200(40)/(40 ' 0.006 ' 0.100) 9 250,000 inlb/in . 2 9 9 40 > (0.@/ (0.@/ 3)(vto/Q)0. 9 2 9 9 40 > (0. ' 250,000/110)O40 ' 0.006/0.1 0. 9 40 > (707)() 0. 9 40 > 1 9 /301 F
20.5
(@S3S units) units) t is is desired desired to esti#te esti#te the the !uttin" !uttin" te#pertur te#perturee for !ertin !ertin lloy steel *hose *hose hrdness 9 20 Crinell. @se the pproprite vlue of spe!ifi! ener"y fro# ble 20.2 to !o#pute the !uttin" te#perture for turnin" opertion in *hi!h the !uttin" speed is 500 ft/#in, feed is 0.005
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Solutions for Fundamentals of Modern Manufacturing , 5/e (published by Wiley) MPGroover 2012
in/rev, nd depth of !ut is 0.040 in. he *or+ #teril hs volu#etri! spe!ifi! het of 210 in lb/in? nd ther#l diffusivity of 0.1 in 2/se!. %ssu#e #bient te#perture 9 66 ?. for lloy steel (10 C<) 9 20,000 inlb/in . )olution- ?ro# ble 20.2, U for Sin!e f Sin!e f 9 9 0.005 in/rev, !orre!tion f!tor 9 1.25. herefore U 9 9 20,000(1.25) 9 00,000 inlb/in . ' 9 500 ft/#in ' 12 in/ft/0 se!/#in 9 100 in/se!. 2 9 9 2 a > (0.U (0.U / C C)('t ) ('t o/ )0. 9 66 > (0. ' 00,000/210)(100 ' 0.005/0.1) 0. 9 66 > (42)(.125) 0. 9 66 > 111 9 /20/ F 20.
!A" (@S3S units) %n ortho"onl #!hinin" opertion re#oves #etl t 1.6 in /#in. 3uttin" for!e 9 00 lb. he *or+ #teril hs ther#l diffusivity 9 0.16 in 2/se! nd volu#etri! spe!ifi! het 9 12 inlb/in ?. f the feed 9 0.010 in nd *idth of !ut 9 0.100 in, !o#pute the !uttin" te#perture in the opertion "iven tht #bient te#perture 9 40 ?. )olution- % &% 9 't ow, ' 9 % 9 % &%/t ow 9 1.6/(0.01 ' 0.100) 9 1600 in/#in 9 0 in/se! U 9 ( 9 ( c'/'t ow 9 00(0)/(0 ' 0.010 ' 0.100) 9 00,000 inlb/in . 2 9 9 40 > (0.U (0. U / C C)('t ) ('t o/ )0. 9 40 > (0. ' 00,000/12)(0 ' 0.010/0.16) 0. 9 40 > (76)(1.4) 0. 9 40 > 114 9 /2/, F
20.4
(S units) units) n turnin" turnin" opertio opertion, n, !uttin" !uttin" speed speed 9 200 #/#in, #/#in, feed 9 0.25 ##/rev ##/rev,, nd depth depth of !ut 9 2 .00 ##. her#l diffusivity of the *or+ #teril 9 20 ## /s nd volu#etri! spe!ifi! het 9 .5 (10) K/##3. f the te#perture in!rese bove #bient te#perture (20 (20 ?) is #esured by tool!hip ther#o!ouple to be 400 3, deter#ine the spe!ifi! ener"y for the *or+ #teril in this opertion. )olution- Berrn"in" the 3oo+ e;ution, U 9 9 2 ( C C /0.)( /0.)( /'t o)0. U 9 9 (400 A 20)(.5 ' 10 /0.)(20/R(200/0)(10 )(0.25)) 0. U 9 60(6.45 ' 10 )(0.02)0. 9 5.75(0.2666) 9 /+,2 N:-
20.6
(S units) units) :urin" :urin" turnin" turnin" opertion opertion,, tool!hip tool!hip ther#o!oup ther#o!ouple le *s used used to #esure #esure !uttin" !uttin" te#perture. he follo*in" te#perture dt *ere !olle!ted durin" the !uts t three different !uttin" speeds (feed nd depth *ere held !onstnt)- (1) ' 9 100 #/#in, 2 9 9 505 5053, (2) ' 9 10 #/#in, 2 9 9 552 5523, () ' 9 10 #/#in, 2 9 9 572 5723. :eter#ine n e;ution for te#perture s fun!tion of !uttin" speed tht is in the for# of the ri""er e;ution, ;ution (20.2). 9 'm )olution- ri""er e;ution 2 9 ' 3hoose points (1) nd () nd solve si#ultneous e;utions usin" 2 9 ' 9 'm s the #odel. (1) 505 9 9 (100) (100)m nd () 572 9 9 (10) (10)m (1) ln 505 9 ln ln > > m ln 100 nd () ln 572 9 ln ln > > m ln 10 3o#binin" (1) nd ()- ln 505 m ln 100 9 ln 572 m ln 10 .22 A .052 m 9 .65 A 5.0452 m m 8 0+-- 0.4 m 9 0.1567 0.6 (1) (1) 9 9 505/100 9 505/.4 9 10. (2) (2) 9 9 572/100.6 9 572/5.51 9 10.5 @se K 8 /01+*3 e;ution *ith dt point (2)- 2 9 9 10.5(10) 0.6 9 551.643 (pretty !lose to the "iven vlue C#e'6 e;ution of 5523).
'!erpts fro# this *or+ #y be reprodu!ed by instru!tors for distribution on notforprofit bsis for testin" or instru!tionl purposes only to students enrolled in !ourses for *hi!h the te'tboo+ hs been dopted. Any other reproduction reproduction or translation of this work work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyriht Act without the permission of the copyriht owner is unlawful!
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