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Effect of eccentricity of twist drill and candle stick drill on delamination in drilling composite materials
International Journal of Machine Tools & Manufacture 45 (2005) 125–130 www.elsevier.com/locate/ijmactool
Effect of eccentricity of twist drill and candle stick drill on delamination in drilling composite materials C.C. Tsaoa,*, H. Hochengb a Department of Automatic Engineering, Ta-Hua Institute of Technology, Hsinchu 307, Taiwan, ROC Department of Power Mechanical Engineering, National Tsing-Hua University, Hsinchu 300, Taiwan, ROC
b
Received 19 April 2004; accepted 4 August 2004 Available online 6 October 2004
Abstract Drilling is the most frequently employed operation of secondary machining for fiber-reinforced materials owing to the need for structure joining. Delamination is one of the serious concerns during drilling. Practical experience shows that an eccentric twist drill or an eccentric candle stick drill can degrade the quality of the fiber reinforced material. Comprehensive delamination models for the delamination induced by an eccentric twist drill and an eccentric candle stick drill in the drilling of composite materials have been constructed in the present study. For an eccentric twist drill and an eccentric candle stick drill, the critical thrust force that will produce delamination decreases with increasing point eccentricity x. The results agree with industrial experience. The need for control of drill eccentricity during drill regrinding has been proved analytically by the proposed models. q 2004 Elsevier Ltd. All rights reserved. Keywords: Twist drill; Candle stick drill; Eccentricity; Delamination; Drilling; Composite materials
1. Introduction The technological and commercial interest in composite materials lies in their superior properties of strength-toweight, stiffness-to-weight, fatigue and thermal expansion compared to metals. Various cutting methods are available for hole making, but drilling is by far the most common way in the practice of structural joining. The mechanics of drilling composite materials have been studied along with the quality of the hole and the effects of tool geometry and tool material [1,2]. Twist drills are widely used in industry to produce holes rapidly and economically. The point of a twist drill can be designed for various drilling conditions, while mostly the design has a chisel edge. A significant portion of the thrust force is due to the chisel edge [3–5]. Fujii et al. [6] also investigated the effects of the chisel edge on conical drill performance for optimum output. Increasing * Corresponding author. Tel.: C886 3 592 7700 2665; fax: C886 3 592 1047. E-mail address: [email protected] (C.C. Tsao). 0890-6955/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2004.08.001
the chisel edge length results in an increase in the thrust force. Investigators have studied analytically and experimentally how delamination in drilling is correlated to the thrust force during drilling and there is a critical thrust force below which no damage occurs [7]. Hocheng and Dharan [8] employed a linear elastic fracture mechanics method and plate bending theory and solved for the critical thrust force that related the delamination of composite laminates to material properties. Hocheng and Tsao [9–11] developed a series of analytical models for various drills (candle stick drill, saw drill, core drill and step drill) for correlating the thrust force at the onset of delamination. In practical machining operations, wear of cutting tool occurs and causes concern for machining quality. Clearly any tool improvements in increasing tool life will be beneficial, such as tool regrinding. In drill regrinding, however, the point of the twist drill can deviate from the centerline generating eccentricity of the drill point. The eccentric twist drill will cause scatter and enlarge the hole in drilling, while the delamination damage in drilling composite materials becomes more serious. Al-Hamdan [12]
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investigated the effects of drill misalignment on the cutting force signature in drilling. The axial thrust force at the same spindle rotational speed shows that the amplitudes of the different harmonics increases with the misalignment. While the existing research contributes to the practice using ideal drills, the problem of eccentric twist drill and eccentric candle stick drill produced by inaccurate tool regrinding has not been discussed. This paper presents a comprehensive analysis of the delamination caused by the eccentricity in twist and candle stick drills. The critical thrust force at the onset of delamination is predicted and compared with that for the ideal drills.
2. Delamination analysis 2.1. Physical model At the propagation of delamination, the drill movement of distance dX is associated with the work done by the thrust force FA, which is used to deflect the plate as well as to propagate the interlaminar crack, as shown in Fig. 1(a). The energy balance equation gives GIC dA Z FA dX K dU
(1)
where dU is the infinitesimal strain energy, dA is the increase in the area of the delamination crack, and GIC is the critical crack propagation energy per unit area in mode I. The value of GIC is assumed to be a constant, a mild function of strain rate [13]. 2.2. Mathematical analysis 2.2.1. Concentrated central load (twist drill) In Fig. 1(a), the center of the circular plate is loaded by a twist drill of diameter d. FA is the thrust force, X is the displacement, H is the workpiece thickness, h is the uncut depth under the tool, and a is the radius of delamination. Isotropic behaviour and pure bending of the laminate were assumed in the model. In Eq. (1), one notes that dA Z pða C daÞða C daÞ K pa2 Z 2pa da
(2)
For a circular plate subject to clamped ends and a concentrated load, the stored strain energy U is UZ
FA a 2 32pM
(3)
where M is the stiffness per unit width of the fiber reinforced material given by MZ
Eh3 12ð1 K v2 Þ
Fig. 1. Circular plate model for delamination analysis subject to twist drill.
XZ
F A a2 16pM
(5)
The thrust force at the onset of crack propagation can be calculated [8], to be
(4)
E is Young’s modulus and n is Poisson’s ratio for the material, and the displacement X is
1=2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 8GIC Eh3 FA Z p 32GIC M Z p 3ð1 K n2 Þ
(6)
C.C. Tsao, H. Hocheng / International Journal of Machine Tools & Manufacture 45 (2005) 125–130
2.2.2. Eccentric concentrated load (eccentric twist drill) Fig. 1(b) depicts an eccentric twist drill and the induced delamination, where e is the chisel eccentricity of the twist drill. The deflection of the circular plate by an eccentric load (FEA) is found [14], for (i) 0%r%e (inner portion) FEA XZ ð1 K x2 Þða2 K 2er C r 2 Þ 16pM ð1 K x2 Þ2 r 3 2 C 2ðr K eÞ ln x K e
127
The total strain energy is then U Z U1 C U2 F 2 e2 1 25 7 2 43 19 2 C x K x ln x Z EA K C 4 4 16pM 2x2 32 8 1 1 C ðx2 K 5Þln2 x C lnx3 2 3
ð12Þ
Differentiation of Eq. (12) with respect to a yields ð7Þ
(ii) e%r%a (outer portion) FEA Ke3 K 2erð1 K x2 Þ C ð1 C x2 Þða2 K r 2 Þ XZ 16pM r xð2 K x2 Þr 3 r 2 C 2ðr K eÞ ln C ð8Þ a a where xZe/a.
2 dU FEA e 1 43 17 2 3 Z K x C 3x C 5 C x xln x da 16pM x 4 2 Kð1 C x2 Þx ln2 x
ð13Þ
The critical thrust force (FEA) at the onset of crack propagation can be derived, to be sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 32GIC M FEA Z p
2 4 1 C 11 x C 7x K 5x2 ln x C ð1 C x2 Þx2 ln2 x 4 (14)
At rZe A comparison of FEA and FA in Eqs. (14) and (6) gives
dX F e Z EA da 8pM
1 K 4x C 5x3 x
(9)
FEA 1 Z qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
FA 1 C 11 x2 C 7x4 K 5x2 ln x C ð1 C x2 Þx2 ln2 x 4
(15) as illustrated in Fig. 2.
when the higher order terms of x are neglected. The stored strain energy is from [15]. (i) 0%r%e (inner portion) 2 # ð e " 2 d X 1 dX U1 Zp M C r dr dr 2 r dr 0
2.2.3. Concentrated centered load associated with distributed circular load (candle stick drill) Fig. 3 depicts the schematics of a candle stick drill and the induced delamination. Candle stick drills are extensively used for drilling composite materials. The thrust force of
2 2 FEA e 185 151 2 17 13 2 2 K x C K x lnxC2ln x Z 16 4 2 16pM 64 (10) (ii) e%r%a (outer portion) "
ða U2 Z p
M e
d2 X 1 dX C r dr dr 2
2 # r dr
2 2 FEA e 1 235 165 2 C x K Z 64 16 16pM 2x2 13 7 2 1 2 1 3 2 C x ln x C ðx K 9Þln x C ln x C 2 4 2 3 (11)
Fig. 2. Critical thrust force ratio between eccentric twist drill and twist drill.
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The energy balance equation can be expressed as follows dX1 dX2 dU1 dU2 C p2 K C GIC 2pa Z p1 da da da da p2 a p2 2c2 c4 aK C 3 (17) Z 1 C 2 16pM 16pM a a where the subscripts 1 and 2 denote the variables for the central concentrated force and the peripheral circular force, respectively. Let p2 Z ap1 The thrust force p1 can be calculated [9], to be sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 32GIC M p1 Z p 1 C a2 ð1 K 2s2 C s4 Þ
(18)
(19)
Substituting Eqs. (18) and (19) into Eq. (16), the thrust force for the candle stick drill at the onset of crack propagation is given by sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 32GIC M FC Z pð1 C aÞ (20) 2 1 C a ð1 K 2s2 C s4 Þ A comparison of FC and FA in Eqs. (20) and (6) gives FC ð1 C aÞ Z pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi FA 1 C a2 ð1 K 2s2 C s4 Þ
(21)
2.2.4. Eccentric concentrated load associated with distributed circular load (eccentric candle stick drill) Candle stick drills are extensively used for quality drilling of composite materials. Fig. 3 depicts the schematics of an eccentric candle stick drill and the induced delamination. The thrust force of the eccentric candle stick drill can be considered as a concentrated eccentric load (pe1) plus the distributed circular load (pe2). Namely, the thrust force FEC can be expressed as FEC Z pe1 C pe2
Fig. 3. Circular plate model for delamination analysis subject to candle stick drill.
the candle stick drill can be considered as a concentrated center load (p1) plus a distributed circular load (p2). Using the method of superposition, the thrust force FC can be expressed as follows FC Z p 1 C p 2
(16)
(22)
The energy balance equation can be expressed as follows dX1 dX2 dU1 dU2 GIC 2pa Z pe1 C pe2 C K da da da da 2 2 4 2 p 11e 7e 5e e C 3 K ln Z e1 a C a 16pM 4a a a 2 e e4 pe2 2c2 c4 2 e C 3 ln aK C 3 C C a a 16pM a a a (23) where the subscripts 1 and 2 denote the variables for the concentrated eccentric force and the peripheral circular force, respectively. Let pe2 Z ape1
(24)
C.C. Tsao, H. Hocheng / International Journal of Machine Tools & Manufacture 45 (2005) 125–130
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damage, which affects productivity. The results agree with industrial experience. The dimensional accuracy during tool reconditioning can produce the undesired eccentricity then significantly affects the drilling-induced damage. It explains the clear scattering in the reported hole quality in drilling composite materials. When the same nominal drill is used, the different drill eccentricity produced by tool regrinding causes the scattering. 3.2. Effect of eccentric candle stick drill on critical thrust force The candle stick drill exerts a thrust force on the laminate, which is composed of the concentrated central force and the peripheral circular force As pointed out by DiPaolo et al. [16], delamination of a size less than the drill Fig. 4. Critical thrust force ratio between eccentric candle stick drill and diameter is not of concern because it is drilled out twist drill. afterwards. When the delamination grows beyond the drill radius, the candle stick drill (applying the circular force p2 and the concentrated force p1 as shown in Fig. 3) can sustain The thrust force pe1 can be calculated as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 32GIC M (25) pe1 Z p
2 4 2 1 C 11 x C 7x K 5x ln x C ð1 C x2 Þx2 ln2 x C a2 ð1 K 2s2 C s4 Þ 4 Substituting Eqs. (24) and (25) into Eq. (22), the thrust force of the eccentric candle stick drill at the onset of crack propagation as
much larger thrust force than the twist drill (applying the concentrated force only as shown in Fig. 1). Fig. 4 shows this result. When the eccentricity is zero, the value ratio of sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 32GIC M FEC Z pð1 C aÞ
(26) 4 2 11 2 1 C 4 x C 7x K 5x ln x C ð1 C x2 Þx2 ln2 x C a2 ð1 K 2s2 C s4 Þ A comparison of FEC and FA in Eqs. (6) and (26) gives FEC ð1 C aÞ ffi Z qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
FA 1 C 11 x2 C 7x4 K 5x2 ln x C ð1 C x2 Þx2 ln2 x C a2 ð1 K 2s2 C s4 Þ
(27)
4
as shown in Fig. 4.
3. Results and discussions 3.1. Effect of eccentric twist drill on critical thrust force Fig. 2 depicts the ratio between the critical thrust force of an eccentric twist drill and an ideal twist drill as a function of the eccentricity ratio (x). The value of the thrust force ratio decreases rapidly with increasing x. In Fig. 2, the negative influence of eccentricity of twist drill is clearly reflected in the reduction of the critical thrust force. Namely, the threshold thrust force beyond which delamination occurs is lowered, thus the drilling-induced damage becomes more liable. A lower feed rate has to be used with an eccentric twist drill to prevent delamination
force larger than one illustrates this fact. Since the total thrust force is distributed towards the periphery at a ratio of a, the drill with larger a is expected to be advantageous in allowing for a larger critical thrust force, i.e. higher feed rate, at the onset of delamination. This fact remains the same for both the ideal and eccentric candle stick drill. The results of the critical thrust force predicted by the eccentric candle stick drill are presented in Fig. 4. It illustrates that the more the thrust force is distributed toward the periphery (larger a), the larger becomes the critical threshold. On the other hand, the value of thrust force ratio decreases with increasing point eccentricity x. It illustrates the incorrect tool regrinding can lead to very serious damage during drilling. The various degree of eccentricity of the same nominal drills will cause various degree of damage, respectively.
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4. Conclusions A comprehensive analysis for delamination caused by eccentric twist drill and eccentric candle stick drill in drilling of composite materials has been developed in the present study. The analytical results were obtained based on classical elasticity, linear elastic fracture mechanics and energy conservation. For eccentric twist drill and eccentric candle stick drill, the critical thrust force is reduced with increasing x. The results agree with industrial experience, that the worse drilling quality in use of the same nominal drill can be traced to the various degree of drill eccentricity produced in tool reconditioning process. A lower critical thrust force results if an eccentric twist drill or an eccentric candle stick drill is used so that a lower feed rate has to be used to prevent delamination damage. A guide for drill design and tool regrinding can be developed based on the proposed models, especially when the eccentric ratio (x) affects the critical thrust force. This approach can be extended to examine the similar eccentricity effects of various drills.
References [1] H. Hocheng, H. Puw, On drilling characteristics of fiber-reinforced thermoset and thermoplastics, International Journal of Machine Tools & Manufacture 32 (4) (1992) 583–592. [2] W.C. Chen, Some experimental investigations in the drilling of carbon fiber-reinforced plastic (CFRP) composite laminates, International Journal of Machine Tools & Manufacture 37 (8) (1997) 1097–1108. [3] S. Jain, D.C.H. Yang, Effects of feed rate and chisel edge on delamination in composite drilling, Processing and Manufacturing of Composite Materials PED-49/MD-27, 1991, pp. 37–51.
[4] M.S. Won, C.K.H. Dharan, Chisel edge and pilot hole effects in drilling composite laminates, Transactions of the ASME, Journal of Manufacturing Science and Engineering 124 (2002) 242–247. [5] C.C. Tsao, H. Hocheng, The effect of chisel length and associated pilot hole on delamination when drilling composite materials, International Journal of Machine Tools & Manufacture 43 (11) (2003) 1087–1092. [6] S. Fujii, M.F. DeVries, S.M. Wu, An analysis of the chisel edge and the effect of the d-theta relationship on drill point geometry, Transactions of the ASME, Journal of Engineering for Industry 93 (1971) 1093–1105. [7] W. Koenig, C. Wulf, P. Grass, H. Willerscheid, Machining of fiber reinforced plastics, Annals of the CIRP 34 (2) (1985) 538–548. [8] H. Hocheng, C.K.H. Dharan, Delamination during drilling in composite laminates, Transactions of the ASME, Journal of Engineering for Industry 112 (1990) 236–239. [9] H. Hocheng, C.C. Tsao, Comprehensive analysis of delamination in drilling of composite materials with various drill bits, Journal of Materials Processing Technology 140 (2003) 335–339. [10] H. Hocheng, C.C. Tsao, Analysis of delamination in drilling composite materials using step drill, Proceedings of 18th National Conference on Mechanical Engineering, Taipei, Taiwan (4) 2001; 895–900. [11] H. Hocheng, C.C. Tsao, Analysis of delamination in drilling composite materials using core drill, Australasian Journal of Mechanical Engineering 1 (1) (2003) 49–53. [12] A. Al-Hamdan, Effect of misalignment on the cutting force signature in drilling, Journal of Materials Processing Technology 124 (2002) 83–91. [13] H. Saghizadeh, C.K.H. Dharan, Delamination fracture toughness of graphite and Aramid epoxy composites, Transactions of the ASME, Journal of Engineering Materials and Technology 108 (1986) 290–295. [14] S. Timoshenko, S. Woinowsky-Keiger, Theory of Plates and Shells, 2nd ed., McGraw Hill, New York, 1959 (pp. 51–59 see also pages 290–293, 345–346). [15] P. Szilard, Theory and Analysis of Plates: Classical and Numerical Methods, Prentice-Hall, Englewood Cliffs, NJ, 1974. p. 218. [16] G. DiPaolo, S.G. Kapoor, R.E. DeVor, An experimental investigation of the crack growth phenomenon for drilling of fiber-reinforced composite materials, Transactions of the ASME, Journal of Engineering for Industry 118 (1996) 104–110.
Effect of eccentricity of twist drill and candle stick drill on delamination in drilling composite materials C.C. Tsaoa,*, H. Hochengb a Department of Automatic Engineering, Ta-Hua Institute of Technology, Hsinchu 307, Taiwan, ROC Department of Power Mechanical Engineering, National Tsing-Hua University, Hsinchu 300, Taiwan, ROC
b
Received 19 April 2004; accepted 4 August 2004 Available online 6 October 2004
Abstract Drilling is the most frequently employed operation of secondary machining for fiber-reinforced materials owing to the need for structure joining. Delamination is one of the serious concerns during drilling. Practical experience shows that an eccentric twist drill or an eccentric candle stick drill can degrade the quality of the fiber reinforced material. Comprehensive delamination models for the delamination induced by an eccentric twist drill and an eccentric candle stick drill in the drilling of composite materials have been constructed in the present study. For an eccentric twist drill and an eccentric candle stick drill, the critical thrust force that will produce delamination decreases with increasing point eccentricity x. The results agree with industrial experience. The need for control of drill eccentricity during drill regrinding has been proved analytically by the proposed models. q 2004 Elsevier Ltd. All rights reserved. Keywords: Twist drill; Candle stick drill; Eccentricity; Delamination; Drilling; Composite materials
1. Introduction The technological and commercial interest in composite materials lies in their superior properties of strength-toweight, stiffness-to-weight, fatigue and thermal expansion compared to metals. Various cutting methods are available for hole making, but drilling is by far the most common way in the practice of structural joining. The mechanics of drilling composite materials have been studied along with the quality of the hole and the effects of tool geometry and tool material [1,2]. Twist drills are widely used in industry to produce holes rapidly and economically. The point of a twist drill can be designed for various drilling conditions, while mostly the design has a chisel edge. A significant portion of the thrust force is due to the chisel edge [3–5]. Fujii et al. [6] also investigated the effects of the chisel edge on conical drill performance for optimum output. Increasing * Corresponding author. Tel.: C886 3 592 7700 2665; fax: C886 3 592 1047. E-mail address: [email protected] (C.C. Tsao). 0890-6955/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2004.08.001
the chisel edge length results in an increase in the thrust force. Investigators have studied analytically and experimentally how delamination in drilling is correlated to the thrust force during drilling and there is a critical thrust force below which no damage occurs [7]. Hocheng and Dharan [8] employed a linear elastic fracture mechanics method and plate bending theory and solved for the critical thrust force that related the delamination of composite laminates to material properties. Hocheng and Tsao [9–11] developed a series of analytical models for various drills (candle stick drill, saw drill, core drill and step drill) for correlating the thrust force at the onset of delamination. In practical machining operations, wear of cutting tool occurs and causes concern for machining quality. Clearly any tool improvements in increasing tool life will be beneficial, such as tool regrinding. In drill regrinding, however, the point of the twist drill can deviate from the centerline generating eccentricity of the drill point. The eccentric twist drill will cause scatter and enlarge the hole in drilling, while the delamination damage in drilling composite materials becomes more serious. Al-Hamdan [12]
126
C.C. Tsao, H. Hocheng / International Journal of Machine Tools & Manufacture 45 (2005) 125–130
investigated the effects of drill misalignment on the cutting force signature in drilling. The axial thrust force at the same spindle rotational speed shows that the amplitudes of the different harmonics increases with the misalignment. While the existing research contributes to the practice using ideal drills, the problem of eccentric twist drill and eccentric candle stick drill produced by inaccurate tool regrinding has not been discussed. This paper presents a comprehensive analysis of the delamination caused by the eccentricity in twist and candle stick drills. The critical thrust force at the onset of delamination is predicted and compared with that for the ideal drills.
2. Delamination analysis 2.1. Physical model At the propagation of delamination, the drill movement of distance dX is associated with the work done by the thrust force FA, which is used to deflect the plate as well as to propagate the interlaminar crack, as shown in Fig. 1(a). The energy balance equation gives GIC dA Z FA dX K dU
(1)
where dU is the infinitesimal strain energy, dA is the increase in the area of the delamination crack, and GIC is the critical crack propagation energy per unit area in mode I. The value of GIC is assumed to be a constant, a mild function of strain rate [13]. 2.2. Mathematical analysis 2.2.1. Concentrated central load (twist drill) In Fig. 1(a), the center of the circular plate is loaded by a twist drill of diameter d. FA is the thrust force, X is the displacement, H is the workpiece thickness, h is the uncut depth under the tool, and a is the radius of delamination. Isotropic behaviour and pure bending of the laminate were assumed in the model. In Eq. (1), one notes that dA Z pða C daÞða C daÞ K pa2 Z 2pa da
(2)
For a circular plate subject to clamped ends and a concentrated load, the stored strain energy U is UZ
FA a 2 32pM
(3)
where M is the stiffness per unit width of the fiber reinforced material given by MZ
Eh3 12ð1 K v2 Þ
Fig. 1. Circular plate model for delamination analysis subject to twist drill.
XZ
F A a2 16pM
(5)
The thrust force at the onset of crack propagation can be calculated [8], to be
(4)
E is Young’s modulus and n is Poisson’s ratio for the material, and the displacement X is
1=2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 8GIC Eh3 FA Z p 32GIC M Z p 3ð1 K n2 Þ
(6)
C.C. Tsao, H. Hocheng / International Journal of Machine Tools & Manufacture 45 (2005) 125–130
2.2.2. Eccentric concentrated load (eccentric twist drill) Fig. 1(b) depicts an eccentric twist drill and the induced delamination, where e is the chisel eccentricity of the twist drill. The deflection of the circular plate by an eccentric load (FEA) is found [14], for (i) 0%r%e (inner portion) FEA XZ ð1 K x2 Þða2 K 2er C r 2 Þ 16pM ð1 K x2 Þ2 r 3 2 C 2ðr K eÞ ln x K e
127
The total strain energy is then U Z U1 C U2 F 2 e2 1 25 7 2 43 19 2 C x K x ln x Z EA K C 4 4 16pM 2x2 32 8 1 1 C ðx2 K 5Þln2 x C lnx3 2 3
ð12Þ
Differentiation of Eq. (12) with respect to a yields ð7Þ
(ii) e%r%a (outer portion) FEA Ke3 K 2erð1 K x2 Þ C ð1 C x2 Þða2 K r 2 Þ XZ 16pM r xð2 K x2 Þr 3 r 2 C 2ðr K eÞ ln C ð8Þ a a where xZe/a.
2 dU FEA e 1 43 17 2 3 Z K x C 3x C 5 C x xln x da 16pM x 4 2 Kð1 C x2 Þx ln2 x
ð13Þ
The critical thrust force (FEA) at the onset of crack propagation can be derived, to be sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 32GIC M FEA Z p
2 4 1 C 11 x C 7x K 5x2 ln x C ð1 C x2 Þx2 ln2 x 4 (14)
At rZe A comparison of FEA and FA in Eqs. (14) and (6) gives
dX F e Z EA da 8pM
1 K 4x C 5x3 x
(9)
FEA 1 Z qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
FA 1 C 11 x2 C 7x4 K 5x2 ln x C ð1 C x2 Þx2 ln2 x 4
(15) as illustrated in Fig. 2.
when the higher order terms of x are neglected. The stored strain energy is from [15]. (i) 0%r%e (inner portion) 2 # ð e " 2 d X 1 dX U1 Zp M C r dr dr 2 r dr 0
2.2.3. Concentrated centered load associated with distributed circular load (candle stick drill) Fig. 3 depicts the schematics of a candle stick drill and the induced delamination. Candle stick drills are extensively used for drilling composite materials. The thrust force of
2 2 FEA e 185 151 2 17 13 2 2 K x C K x lnxC2ln x Z 16 4 2 16pM 64 (10) (ii) e%r%a (outer portion) "
ða U2 Z p
M e
d2 X 1 dX C r dr dr 2
2 # r dr
2 2 FEA e 1 235 165 2 C x K Z 64 16 16pM 2x2 13 7 2 1 2 1 3 2 C x ln x C ðx K 9Þln x C ln x C 2 4 2 3 (11)
Fig. 2. Critical thrust force ratio between eccentric twist drill and twist drill.
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The energy balance equation can be expressed as follows dX1 dX2 dU1 dU2 C p2 K C GIC 2pa Z p1 da da da da p2 a p2 2c2 c4 aK C 3 (17) Z 1 C 2 16pM 16pM a a where the subscripts 1 and 2 denote the variables for the central concentrated force and the peripheral circular force, respectively. Let p2 Z ap1 The thrust force p1 can be calculated [9], to be sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 32GIC M p1 Z p 1 C a2 ð1 K 2s2 C s4 Þ
(18)
(19)
Substituting Eqs. (18) and (19) into Eq. (16), the thrust force for the candle stick drill at the onset of crack propagation is given by sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 32GIC M FC Z pð1 C aÞ (20) 2 1 C a ð1 K 2s2 C s4 Þ A comparison of FC and FA in Eqs. (20) and (6) gives FC ð1 C aÞ Z pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi FA 1 C a2 ð1 K 2s2 C s4 Þ
(21)
2.2.4. Eccentric concentrated load associated with distributed circular load (eccentric candle stick drill) Candle stick drills are extensively used for quality drilling of composite materials. Fig. 3 depicts the schematics of an eccentric candle stick drill and the induced delamination. The thrust force of the eccentric candle stick drill can be considered as a concentrated eccentric load (pe1) plus the distributed circular load (pe2). Namely, the thrust force FEC can be expressed as FEC Z pe1 C pe2
Fig. 3. Circular plate model for delamination analysis subject to candle stick drill.
the candle stick drill can be considered as a concentrated center load (p1) plus a distributed circular load (p2). Using the method of superposition, the thrust force FC can be expressed as follows FC Z p 1 C p 2
(16)
(22)
The energy balance equation can be expressed as follows dX1 dX2 dU1 dU2 GIC 2pa Z pe1 C pe2 C K da da da da 2 2 4 2 p 11e 7e 5e e C 3 K ln Z e1 a C a 16pM 4a a a 2 e e4 pe2 2c2 c4 2 e C 3 ln aK C 3 C C a a 16pM a a a (23) where the subscripts 1 and 2 denote the variables for the concentrated eccentric force and the peripheral circular force, respectively. Let pe2 Z ape1
(24)
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damage, which affects productivity. The results agree with industrial experience. The dimensional accuracy during tool reconditioning can produce the undesired eccentricity then significantly affects the drilling-induced damage. It explains the clear scattering in the reported hole quality in drilling composite materials. When the same nominal drill is used, the different drill eccentricity produced by tool regrinding causes the scattering. 3.2. Effect of eccentric candle stick drill on critical thrust force The candle stick drill exerts a thrust force on the laminate, which is composed of the concentrated central force and the peripheral circular force As pointed out by DiPaolo et al. [16], delamination of a size less than the drill Fig. 4. Critical thrust force ratio between eccentric candle stick drill and diameter is not of concern because it is drilled out twist drill. afterwards. When the delamination grows beyond the drill radius, the candle stick drill (applying the circular force p2 and the concentrated force p1 as shown in Fig. 3) can sustain The thrust force pe1 can be calculated as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 32GIC M (25) pe1 Z p
2 4 2 1 C 11 x C 7x K 5x ln x C ð1 C x2 Þx2 ln2 x C a2 ð1 K 2s2 C s4 Þ 4 Substituting Eqs. (24) and (25) into Eq. (22), the thrust force of the eccentric candle stick drill at the onset of crack propagation as
much larger thrust force than the twist drill (applying the concentrated force only as shown in Fig. 1). Fig. 4 shows this result. When the eccentricity is zero, the value ratio of sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 32GIC M FEC Z pð1 C aÞ
(26) 4 2 11 2 1 C 4 x C 7x K 5x ln x C ð1 C x2 Þx2 ln2 x C a2 ð1 K 2s2 C s4 Þ A comparison of FEC and FA in Eqs. (6) and (26) gives FEC ð1 C aÞ ffi Z qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
FA 1 C 11 x2 C 7x4 K 5x2 ln x C ð1 C x2 Þx2 ln2 x C a2 ð1 K 2s2 C s4 Þ
(27)
4
as shown in Fig. 4.
3. Results and discussions 3.1. Effect of eccentric twist drill on critical thrust force Fig. 2 depicts the ratio between the critical thrust force of an eccentric twist drill and an ideal twist drill as a function of the eccentricity ratio (x). The value of the thrust force ratio decreases rapidly with increasing x. In Fig. 2, the negative influence of eccentricity of twist drill is clearly reflected in the reduction of the critical thrust force. Namely, the threshold thrust force beyond which delamination occurs is lowered, thus the drilling-induced damage becomes more liable. A lower feed rate has to be used with an eccentric twist drill to prevent delamination
force larger than one illustrates this fact. Since the total thrust force is distributed towards the periphery at a ratio of a, the drill with larger a is expected to be advantageous in allowing for a larger critical thrust force, i.e. higher feed rate, at the onset of delamination. This fact remains the same for both the ideal and eccentric candle stick drill. The results of the critical thrust force predicted by the eccentric candle stick drill are presented in Fig. 4. It illustrates that the more the thrust force is distributed toward the periphery (larger a), the larger becomes the critical threshold. On the other hand, the value of thrust force ratio decreases with increasing point eccentricity x. It illustrates the incorrect tool regrinding can lead to very serious damage during drilling. The various degree of eccentricity of the same nominal drills will cause various degree of damage, respectively.
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4. Conclusions A comprehensive analysis for delamination caused by eccentric twist drill and eccentric candle stick drill in drilling of composite materials has been developed in the present study. The analytical results were obtained based on classical elasticity, linear elastic fracture mechanics and energy conservation. For eccentric twist drill and eccentric candle stick drill, the critical thrust force is reduced with increasing x. The results agree with industrial experience, that the worse drilling quality in use of the same nominal drill can be traced to the various degree of drill eccentricity produced in tool reconditioning process. A lower critical thrust force results if an eccentric twist drill or an eccentric candle stick drill is used so that a lower feed rate has to be used to prevent delamination damage. A guide for drill design and tool regrinding can be developed based on the proposed models, especially when the eccentric ratio (x) affects the critical thrust force. This approach can be extended to examine the similar eccentricity effects of various drills.
References [1] H. Hocheng, H. Puw, On drilling characteristics of fiber-reinforced thermoset and thermoplastics, International Journal of Machine Tools & Manufacture 32 (4) (1992) 583–592. [2] W.C. Chen, Some experimental investigations in the drilling of carbon fiber-reinforced plastic (CFRP) composite laminates, International Journal of Machine Tools & Manufacture 37 (8) (1997) 1097–1108. [3] S. Jain, D.C.H. Yang, Effects of feed rate and chisel edge on delamination in composite drilling, Processing and Manufacturing of Composite Materials PED-49/MD-27, 1991, pp. 37–51.
[4] M.S. Won, C.K.H. Dharan, Chisel edge and pilot hole effects in drilling composite laminates, Transactions of the ASME, Journal of Manufacturing Science and Engineering 124 (2002) 242–247. [5] C.C. Tsao, H. Hocheng, The effect of chisel length and associated pilot hole on delamination when drilling composite materials, International Journal of Machine Tools & Manufacture 43 (11) (2003) 1087–1092. [6] S. Fujii, M.F. DeVries, S.M. Wu, An analysis of the chisel edge and the effect of the d-theta relationship on drill point geometry, Transactions of the ASME, Journal of Engineering for Industry 93 (1971) 1093–1105. [7] W. Koenig, C. Wulf, P. Grass, H. Willerscheid, Machining of fiber reinforced plastics, Annals of the CIRP 34 (2) (1985) 538–548. [8] H. Hocheng, C.K.H. Dharan, Delamination during drilling in composite laminates, Transactions of the ASME, Journal of Engineering for Industry 112 (1990) 236–239. [9] H. Hocheng, C.C. Tsao, Comprehensive analysis of delamination in drilling of composite materials with various drill bits, Journal of Materials Processing Technology 140 (2003) 335–339. [10] H. Hocheng, C.C. Tsao, Analysis of delamination in drilling composite materials using step drill, Proceedings of 18th National Conference on Mechanical Engineering, Taipei, Taiwan (4) 2001; 895–900. [11] H. Hocheng, C.C. Tsao, Analysis of delamination in drilling composite materials using core drill, Australasian Journal of Mechanical Engineering 1 (1) (2003) 49–53. [12] A. Al-Hamdan, Effect of misalignment on the cutting force signature in drilling, Journal of Materials Processing Technology 124 (2002) 83–91. [13] H. Saghizadeh, C.K.H. Dharan, Delamination fracture toughness of graphite and Aramid epoxy composites, Transactions of the ASME, Journal of Engineering Materials and Technology 108 (1986) 290–295. [14] S. Timoshenko, S. Woinowsky-Keiger, Theory of Plates and Shells, 2nd ed., McGraw Hill, New York, 1959 (pp. 51–59 see also pages 290–293, 345–346). [15] P. Szilard, Theory and Analysis of Plates: Classical and Numerical Methods, Prentice-Hall, Englewood Cliffs, NJ, 1974. p. 218. [16] G. DiPaolo, S.G. Kapoor, R.E. DeVor, An experimental investigation of the crack growth phenomenon for drilling of fiber-reinforced composite materials, Transactions of the ASME, Journal of Engineering for Industry 118 (1996) 104–110.