Effects of peripheral drilling moment on delamination using special drill bits

Transcription

1 journl of mterils processing technology 01 ( journl homepge: Effects of peripherl illing moment on delmintion using specil ill bits C.C. Tso,, H. Hocheng b Deprtment of Automtion Engineering, T Hu Institute of Technology, Tiwn b Deprtment of Power Mechnicl Engineering, Tsing Hu University, Tiwn rticle info bstrct Keywords: Thrust force Delmintion Peripherl moment Specil ills The delmintion dmge cused by the illing thrust hs been recognized s one of the mjor problems during illing. Bsed on the erlier concentrted-lod model proposed, the thrust force is the min cuse to delminte t the ill exit in workpiece. However, the centrl concentrted loding (twist ill is considered specil cse of the generl condition lso with circulr loding (sw ill, cndle stick ill nd core ill. A comprehensive criticl thrust force model considering the effects of the peripherl moment for sw ill, cndle stick ill nd core ill compred with twist ill is constructed in the present study. In this nlysis, the criticl thrust force ssocited with the effect of distributed peripherl moment cusing the onset of delmintion in use of specil ills is predicted nd discussed. 007 Elsevier B.V. All rights reserved. 1. Introduction Drilling is the most commonly employed opertion of secondry mchining for fiber-reinforced mterils owing to the need for structure joining. The delmintion dmge cused by the tool thrust hs been recognized s one of the mjor problems during illing. The fct tht rpid increse in feed rte t the end of illing will cuse the crcking round the exit edge of the hole ws first reported (Kobyshi, The ill geometry ws lso considered importnt for illing results (Gllowy, Twist ills re widely used in industry to produce holes rpidly nd economiclly. The delmintion in illing hs been correlted to the thrust force of the twist ill. Hocheng nd Dhrn firstly employed liner elstic frcture mechnics (LEFM method nd solved for the criticl thrust force tht reltes the delmintion of composite lmintes to illing prmeters nd composite mteril properties (Hocheng nd Dhrn, Chnsekhrn et l. proposed mechnistic pproch nd found tht the thrust force is primrily function of feed rte nd tool geometry (Chnsekhrn et l., Hocheng nd Tso developed series of nlyticl models for sw ill, cndle stick ill nd core ill for correlting the thrust force t the onset of delmintion (Hocheng nd Tso, 003. Although significnt efforts hve been mde to relize the illing-induced delmintion for sw ill, cndle stick ill nd core ill, there hve been few ppers reporting the effect of distributed peripherl moment on delmintion in illing composite mterils bsed on the mechnicl nd energy nlysis. This pper presents series of illing model to explin the effect of the peripherl moment on delmintion in illing composite mterils by sw ill, cndle stick ill nd core ill. The criticl thrust force with the effect of distributed peripherl moment ws compred with the sw ill, cndle stick ill nd core ill without the effect of peripherl Corresponding uthor. E-mil desses: etcc@msdb.thit.edu.tw (C.C. Tso, hocheng@pme.nthu.edu.tw (H. Hocheng /$ see front mtter 007 Elsevier B.V. All rights reserved. doi: /j.jmtprotec

2 47 journl of mterils processing technology 01 ( Fig. 1 Circulr plte model of delmintion for twist ill without distributed peripherl Fig. Circulr plte model of delmintion for sw ill with peripherl. Delmintion nlysis.1. Physicl model At the propgtion of delmintion, the ill movement of distnce is ssocited with the work done by the thrust force F, which is used to deflect the plte s well s to propgte the interlminr crck. The energy blnce eqution gives G IC da = F du (1 where du is the infinitesiml strin energy, da is the increse in the re of the delmintion crck, nd G IC is the criticl crck propgtion energy per unit re in Mode I. The vlue of G IC is ssumed constnt to be mild function of strin rte (Sghizdeh nd Dhrn, Mthemticl nlysis..1. Twist ill without peripherl moment In Fig. 1, the center of the circulr plte is loded by twist ill of dimeter d. F A is the thrust force, X is the displcement, H is the workpiece thickness, h is the uncut depth under tool, nd is the rdius of delmintion. For circulr plte subject to clmped ends nd concentrted lod, the thrust force t the onset of crck propgtion cn be clculted (Hocheng nd Dhrn, 1990 F A = 8GIC Eh 3 3(1 1/ = 3G IC M ( The deflection of the circulr plte is found (Timoshenko nd Woinowsky-Keiger, 1959: ( X = F SD (c r ln c 8M 1 ( r 1 c ( X = F SD (c r ln r 8M 1 ( r 1 c The stored strin energy is given s follows (Timoshenko nd Woinowsky-Keiger, 1959: U 1 =M c 0 ( d X = F SD c (1 U = M = F SD 3M ( d X c ( d (1 ( X 1 r (3 (4 r 1 r ( 4ln c 1 c4 4ln c 4 c 4c ln c 1 r r c c4 4c ln c c6 4 4c4 ln c (5 (6 where M is flexurl rigidity of the plte, E is Young s modulus, nd is Poisson s rtio.... Sw ill with peripherl moment Fig. depicts sw ill with distributed peripherl moment nd the induced delmintion, where c is the rdius of sw ill. F SD is the thrust force of sw ill with distributed peripherl The totl strin energy is then U = U 1 U = c c4 F SD { c c6 4 4c ln c 4c4 ln c } c6 4 4c ln c 4c ln c 4c4 ln c (7

3 journl of mterils processing technology 01 ( Using superposition theorem of twist ill nd sw ill, the thrust force p 1 cn be clculted s: 3G IC M p 1 = 1 (C 1 C (14 Substituting Eqs. (13 nd (14 into Eq. (1, one obtins the thrust force of the cndle stick ill with distributed peripherl moment t the onset of crck propgtion. 3G IC M F CD = (1 1 (C 1 C (15 Fig. 3 Circulr plte model of delmintion for cndle stick ill with peripherl Differentition of Eq. (7 with respect to yields du d = F SD 16M { c c4 3 c6 5 c ln c c4 3 ln c } c c4 3 At r = c ( d = F SD c 8M c4 3 c6 5 c ln c c4 3 ln c The criticl thrust force of sw ill with distributed peripherl moment (F SD t the onset of crck propgtion cn be derived by substitution of Eqs. (8 nd (9 into Eq. (1 3G IC M F SD = (10 C 1 C where C 1 =1 (3 lnss (3 lnss 4 s 6, C =(1 ln ss (lnss 4 s 6 nd s = c/. The comprison of F SD nd F A in Eqs. (10 nd ( gives F SD F A = 1 C 1 C (11 (8 (9 The comprison of F CD nd F A in Eqs. (15 nd ( gives F CD 1 = (1 (16 F A 1 (C 1 C..4. Core ill with peripherl moment Fig. 4 depicts the schemtics of core ill with distributed peripherl moment nd the induced delmintion. The deflection of circulr plte of rdius, which is clmped nd subjected to distributed lod over n nnulus externl nd internl rdii c nd c*, respectively, is given by (Timoshenko nd Woinowsky-Keiger, X = F RD 4 3(c c r (c c 4(c c ln c 4c 4 (c c ln(1 ˇ 8r ln c 8r c (c c ln(1 ˇ X = F RD r (c c ln r 3M 4r ln r (c c r (c c (17 ( Cndle stick ill with peripherl moment Fig. 3 depicts the schemtics of cndle stick ill with distributed peripherl moment nd the induced delmintion. The thrust force of the cndle stick ill with distributed peripherl moment (F CD cn be expressed s follows: F CD = p 1 p (1 where p 1 nd p re the centrl concentrted force nd the peripherl circulr force, respectively, s shown in Fig. 3. Let p = p 1 (13 Fig. 4 Circulr plte model of delmintion for core ill with peripherl

4 474 journl of mterils processing technology 01 ( where F RD is the thrust force of the core ill with distributed peripherl c* nd c re the inner nd outer rdii of core ill, respectively. t is the thickness of core ill, nd ˇ is the rtio of thickness to rdius of core ill (nmely, ˇ = t/c. Differentition of Eq. (18 with respect to yields d = F RD 8 8r 4(c c 4r (c c 3 The stored strin energy is U 1 = M c 0 ( d X 1 r r = F RD c (1 56M ( d X (1 1 r (19 16ln c 16c 4 (c c ln (1 ˇ 8(c c ln c (c c 4 3c (c c ln(1 ˇln c 8c (c c (c c ln(1 ˇ (0 d X U = M c 1 r r = F RD c (c c 8c ln c 4c (c c ln c c (c c 4 The totl strin energy is (1 Differentition of Eq. ( with respect to yields du d = F RD { 4 8c ln c 8c c (c c ln(1 ˇ (c c 3 4c (c c 3 ln c c (c c 3 4c c (c c 3 (c c ln(1 ˇ c (c c 5 8c ln c 8c c (c c ln(1 ˇ c (c c 3 4c c (c c 3 (c c c (c c 5 } ln(1 ˇ 4c (c c 3 ln c (3 Substituting Eqs. (19 nd (3 into Eq. (1, one obtins the thrust force of core ill with distributed peripherl moment t the onset of crck propgtion s 3G IC M F RD = (4 C 3 C 4 ( C 3 = 1 ˇ 3 ˇ (1 ˇ ln s ˇ( ˇ ln(1 ˇ { ( ˇ ˇ ( ˇ ˇ ln s } (1 ˇ ˇ( ˇ ln(1 ˇ s 4 ( ˇ ˇ s 6 4 C 4 = ln s { (1 ˇ ˇ( ˇ ln(1 ˇ s ( ˇ ˇ s } 1 (1 ˇ ln s ˇ( ˇ ln(1 ˇ s 4 U = U 1 U = F RD {8 8c (c c 56M 16c ln c 16c c 4 (c c ln (1 ˇ 8c (c c ln c 3c c (c c ln(1 ˇln c 8c c (c c (c c ln(1 ˇ c (c c 4 16c ln c 16c c (c c ln (1 ˇ 8c (c c ln c 3c c (c c ln(1 ˇln c 8c c (c c (c c ln(1 ˇ c (c c 4 } ( ( ˇ ˇ s 6 4 The comprison of F RD nd F A in Eqs. (4 nd ( gives F RD F A = 1 C 3 C 4 (5 3. Results nd discussion 3.1. Effect of sw ill on threshold thrust force Fig. 5 depicts the theoreticl criticl thrust rtio for sw ill with nd without peripherl It is seen tht the thrust rtio for sw ill without peripherl moment is slightly lrger thn the thrust rtio for sw ill with peripherl moment

5 journl of mterils processing technology 01 ( up to s It mens tht the peripherl moment cn contribute to the delmintion in ddition to thrust force in illing composite mterils. As pointed out by DiPolo et l., the splling occurred vi Mode I (opening nd Mode III (tering dmge mechnism (DiPolo et l., The Mode III ws subjected to the illing torque nd twisting due to the combintion of the downwrd thrust force nd the bck rke ngle long the cutting lips. Fig. 5 lso shows tht the incresing Poisson s rtio (lrge hs mild effect on the growth of the criticl thrust force for the sw ill with peripherl 3.. Effect of cndle stick ill on threshold thrust force Fig. 5 Theoreticl criticl thrust rtio for sw ill with nd without peripherl The results of the theoreticl criticl thrust rtio for cndle stick ill with nd without peripherl moment re presented in Fig. 6(. Since the totl thrust force of cndle stick ill is distributed towrd the periphery t rtio, the ill is expected to be dvntgeous in llowing higher threshold thrust force t the onset of delmintion. Fig. 6( illustrtes tht the more the thrust force is distributed towrd the periphery (lrger Fig. 6 Theoreticl criticl thrust rtio for cndle stick ill ( with nd without peripherl moment nd (b with peripherl moment t vrying Poisson s rtio ( = 0.5. Fig. 7 Theoreticl criticl thrust rtio for core ill ( with nd without peripherl moment, (b with peripherl moment t vrying Poisson s rtio (ˇ = 0..

6 476 journl of mterils processing technology 01 ( , the lrger the criticl threshold becomes. In generl, is relted to the geometry of cndle stick ill. From this figure, it cn be seen tht the thrust force vrying within nrrow rnge s s increses t Fig. 6(b depicts tht the incresing Poisson s rtio (lrge hs mild effect on the increse of the criticl thrust force for the cndle stick ill with peripherl 3.3. Effect of core ill on threshold thrust force Fig. 7( compres the theoreticl criticl thrust rtio of core ill with nd without peripherl moment with vrying s. In this figure, the criticl thrust rtio of core ill with nd without peripherl moment increses with the reduction of ˇ. The criticl thrust rtio of core ill without peripherl moment is much higher thn core ill with peripherl Fig. 7(b shows tht the incresing Poisson s rtio (lrge hs little difference on the growth of the criticl thrust force for the core ill with peripherl However, the criticl thrust rtio of core ill with peripherl moment is below 1 t certin s vlue between 0 nd Conclusions A comprehensive nlysis for criticl thrust rtio ssocited with the peripherl illing moment using specil ills (sw ill, cndle stick ill nd core ill in illing of composite mterils is developed in the present study. The nlyticl results re obtined bsed on clssicl elsticity, liner elstic frcture mechnics nd energy conservtion. The results revel tht, the criticl thrust force of the specil ills considering peripherl illing moment is lower thn those without peripherl In other words, the peripherl moment cn cuse lrger delmintion t the ill exit in the workpiece. Acknowledgment This work is prtilly supported by Ntionl Science Council, Tiwn, ROC, under contrct NSC95-1-E references Chnsekhrn, V., Kppor, S.G., DeVor, R.E., A mechnistic pproch to predicting the cutting forces in illing: with ppliction to fiber-reinforced composite mterils. ASME J. Eng. Ind. 117, DiPolo, G., Kpoor, S.G., DeVor, R.E., An experimentl investigtion of the crck growth phenomenon for illing of fiber-reinforced composite mterils. ASME J. Eng. Ind. 118, Gllowy, D.F., Some experiments on the influence of vrious fctors on ill performnce. Trns. ASME 79, Hocheng, H., Dhrn, C.K.H., Delmintion during illing in composite lmintes. ASME J. Eng. Ind. 11, Hocheng, H., Tso, C.C., 003. Comprehensive nlysis of delmintion in illing of composite mterils with vrious ill bits. J. Mter. Process. Technol. 140, Kobyshi, A., Mchining of Plstics. McGrw-Hill, New York. Sghizdeh, H., Dhrn, C.K.H., Delmintion frcture toughness of grphite nd rmid epoxy composites. ASME J. Eng. Mter. Technol. 108, Timoshenko, S., Woinowsky-Keiger, S., Theory of Pltes nd Shells. McGrw-Hill, New York.