Elliptic vibration-assisted cutting of fibre-reinforced polymer composites: Understanding the...

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Elliptic vibration-assisted cutting of fibre-reinforced polymercomposites: Understanding the material removal mechanisms

Weixing Xu a, L.C. Zhang a,⇑, Yongbo Wu b

a School of Mechanical and Manufacturing Engineering, The University of New South Wales, NSW 2052, Australiab Department of Machine Intelligence & Systems Engineering, Akita Prefectural University, 84-4 Tsuchiya-ebinokuchi, Yirihonjou, Akita 015-0055, Japan

a r t i c l e i n f o

Article history:Received 18 October 2013Received in revised form 4 December 2013Accepted 9 December 2013Available online 22 December 2013

Keywords:A. FibresB. FractureB. WearC. Finite element analysisVibration-assisted cutting

a b s t r a c t

This paper develops an elliptic vibration-assisted (EVA) technique to effectively cut fibre-reinforced poly-mer (FRP) composites using a simple tool. A novel vibrator was invented to work at the anti-resonant fre-quency to realize stable and high variational velocities. A three-dimensional microstructure-based finiteelement model was also established to explore the material removal mechanisms in the EVA cutting. Itwas found that the application of vibration can significantly decrease the cutting forces and reduce thesubsurface damage in a workpiece. The vibration in the cutting direction is more effective in reducingthe cutting force, but that normal to the cutting direction has the advantage of chip removal. Whenthe vibration is applied to both the directions in the EVA cutting, an optimal cutting process can bereached, providing much smaller cutting forces, a much improved surface integrity, and an extended toollife. The study concluded that the ratio of the tool-feed-rate to the maximum vibration velocity in the cut-ting direction, and the ratio of the cutting distance in a single tool vibration cycle to the fibre diameter arethe key parameters. To maximise the advantage of the EVA cutting, it is necessary that these two param-eters are below their critical values.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Fibre-reinforced polymer (FRP) composites have been widelyused in industry due to their high strength and stiffness to weightratio. However, machining of FRP composite products is quite dif-ficult, because of the significant difference in mechanical proper-ties of fibres and matrix. As a result, a machined FRPs usuallycontains various damages, such as fibre pull-out, fibre fracture, ma-trix cracking, fibre–matrix debonding and delamination [1–4]. Todate, most experimental investigations on the machining of FRPcomposites are on the following issues: effect of fibre or matrixtypes [5,6], influence of fibre volume fraction and orientations[2,7], role of tool materials and geometries [8–10], contributionof the depth of cut [11], and selection of processing parameters[12–14]. However, these studies are limited to traditional machin-ing methods, such as turning, milling, drilling and grinding, and arestill facing the poor surface integrity problems highlighted above.In order to reveal the machining mechanisms, corresponding theo-retical analysis has also been carried out, using various modellingmethods [3,4,15–19]. The finite element (FE) analysis has also beenconducted, of which some were based on the consideration ofequivalent homogenous materials [20–23] and some others

involved the microstructures of FRP composites [24–26]. Neverthe-less, these are still insufficient to reflect the real complex structureof FRPs, especially in the understanding of the dynamic materialremoval process in machining.

On the other hand, it has been a common understanding thatgrinding is more appropriate for machining FRP composites[27–29], because in grinding the depth of cut of individual cuttingedges is usually smaller than the diameter of a fibre [2]. However,in many cases, grinding is often inefficient. This raises an importantquestion: Can a FRP composite be cut at a nominally large depth ofcut but with a small tool–composite interaction to improve thesurface integrity while using a simple tool?

Vibration-assisted cutting may provide a satisfactory answer tothe above question, because this kind of cutting methods adds adisplacement of a micro-scale amplitude with an ultrasonic fre-quency to the tip motion of a cutting tool. The process effectivenesshas been experimentally evidenced by the machining of many sin-gle phase materials such as metals and ceramics [30,31]. Theadvantage is that the ultrasonic vibration alters the tip trajectoryof a tool, which consequently makes the instant depth of cut muchsmaller than a fibre diameter. This may in turn improve the surfaceintegrity as pointed out by Zhang and Xu [2,32]. However, theimmediate challenge is as follows: (1) what vibration amplitude,frequency and tool tip trajectory would be appropriate for a highperformance FRP cutting? (2) how can the material removal

0266-3538/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.compscitech.2013.12.011

⇑ Corresponding author. Tel.: +61 2 9385 6078.E-mail address: [email protected] (L.C. Zhang).

Composites Science and Technology 92 (2014) 103–111

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mechanisms be explored such that a deep understanding can beachieved for optimising a cutting process?

The objective of this paper is to develop a vibration-assistedtechnique for the effective cutting of FRPs and explore the materialremoval mechanisms associated with the process. Both experi-mental and numerical methods will be employed to establish thefundamentals.

2. Principle and modelling

2.1. Principle

A fibre in an FRP composite is often made of a brittle material,such as carbon and glass. To facilitate the breakage of such fibresin cutting the composite, an elliptic tool tip motion as illustratedin Fig. 1a can be effective, because the tip motion, when properlyapplied, can generate a local tensile stress in the fibre. For conve-nience, this process is called an elliptic vibration-assisted (EVA)cutting, of which the cutting tool feeds at a nominal feed rate, v,while vibrates elliptically at an ultrasonic frequency and a microscale amplitude in the xz-plane. The feed rate is smaller than themaximum vibration speed in x-direction, such that an intermittentcutting [33–35] is generated in each vibration cycle of the tool. Ineach cycle, cutting takes place only when the tip wedges into theworkpiece, and hence a chip is mainly pulled up when the toolmoves upward in the chip flow direction. To facilitate the breakageof the fibres and matrix, the cutting distance within a cycle of thetool vibration, D, is set to be smaller than the fibre diameter, D.

Consequently, the surface quality can be improved as concludedby Wang and Zhang [2] from a qualitative mechanics analysis.

2.2. Micro-scale modelling

To understand the material removal mechanisms in an EVA cut-ting, a 3D microstructure-based FE model (Fig. 1b) was establishedby ABAQUS. The model was constructed with three layers: a micro-structured layer, an equivalently homogeneous material (EHM)layer and an infinite elements layer. The microstructured layerwas in the middle of the model, whose thickness was set to bethe same as that of the cutting tool as shown in the figure. Thislayer consisted of three phases of unique material properties, i.e.,the fibre, the matrix and the fibre–matrix interface, and wasmeshed by 8-noded brick elements. For the sake of computationalefficiency but without losing the generality, the material layersthat sandwiched the microstructured layer were treated as anEHM. To avoid the boundary effect, infinite elements (CIN3D8)were arranged around the control volume, except its front andtop surfaces. The material properties of the infinite elements wereset to be the same as the EHM. The cutting tool was regarded as arigid body and its motion was supposed as follows:

xToolðtÞ ¼ a cosð2pftÞ zToolðtÞ ¼ b cosð2pft þ wÞ ð1Þ

where a and b are the vibration amplitudes in x- and z-directions,respectively; f is the vibration frequency; and w is the phase differ-ence. The relative instantaneous cutting speed of the tool to theworkpiece is therefore

mxðtÞ ¼ �2pfa sinð2pftÞ þ m mzðtÞ ¼ �2pfb sinð2pft þ wÞ: ð2Þ

Based on the relative motion of the tool vibration to the feeddirection, there can be three types of vibration-assisted cutting:(1) cutting-directional vibration-assisted (CDVA) cutting wherethe tool vibrates in the cutting direction only (i.e., a – 0 butb = 0), (2) normal-directional vibration-assisted (NDVA) cutting(i.e., a = 0 but b – 0), and (3) EVA cutting (i.e., a – 0 and b – 0).

3. The ultrasonic vibrator

3.1. The EVA cutting system

Fig. 2 shows a schematic illustration of the EVA cutting system,consisting of a vibrator to generate an elliptic high frequency vibra-tion, a cutting tool, a support system and a power supply system.The vibrator was designed by bonding four axis-symmetric distrib-uted piezoelectric (PZT) actuators, denoted by A, B, C and D, on acylindrical body made of stainless steel SUS304. In order to realizethe ultrasonic vibrations in both cutting and vertical directions,

Fibre

Chip

Tool

Locus of cutting edge

Ellipticalvibration

Matrix

v

X

Z

ab

ap

Workpiece

Δ

(a)

Tool

Fibre

MatrixInterface

EHM

X

ZY

(b) Fig. 1. Illustration of (a) EVA cutting of FRP composite and (b) its FE micro-scalemodel.

Metal elastic body

C

DPZT actuator

Tool

X

Z Y

B

A

BC

D

Generator

Amplifier

FPZ

FPX

Fig. 2. Illustration of EVA cutting system.

104 W. Xu et al. / Composites Science and Technology 92 (2014) 103–111


four alternating current signals, VA, VB, VC and VD, were applied tothe PZT actuators, respectively. If their frequencies were set atthe same value of f and their amplitudes were Vp, then VA =Vpsin(2pft), VB = Vpsin(2pft + p), VC = Vpsin(2pft + w) and VD =Vpsin(2pft + w + p), where the phase shift between VA and VC wasw, that between VA and VB was p, and that between VC and VD

was p. When f is set to be the same as or close to the resonantor anti-resonant frequencies of the third-bending-mode of theassembled body (including the actuators, cylindrical body and cut-ting tool), the vibrator will vibrate in two modes simultaneously.As a result, the tip of the cutting tool at the end of the vibrator willvibrates elliptically. It should be mentioned that to obtain ellipticvibrations in a flexible range, the cylindrical body should be sup-ported at the nodal points of its bending vibration modes. To betterbalance the cutting force and improve the stiffness of the vibratorduring the cutting process, preloads of FPX in cutting direction andFPZ in vertical direction were applied at the free end. In addition, awave function generator (WF1946B by NF Corporation) and its cor-responding amplifiers (HSA4052) were used as the power supplyto produce sinusoidal signals with the same frequencies and re-quired phase shifts.

3.2. Performance of the vibrator

To determine the dimensional design of the ultrasonic vibrator,FE analysis was carried out with the condition of fAB = fCD, where fAB

and fCD are the frequency of the third-bending-mode in thexy-plane (Mode 1) and yz-plane (Mode 2) respectively. Fig. 3ashows the results of the frequency response using a PZT deviceanalysis software (PIEZO by Dynus Co., Ltd.), under the conditionof Vp = 1 V, fAB = fCD = 17.38 kHz and w = 90�. Clearly, an ellipticmotion occurred on the tip of the cutting tool. The vibrator wasthen manufactured and Fig. 3b shows the resonant frequenciesmeasured by an impedance analyser (4294A by Agilent Co., Ltd.).Obviously, the resonant frequencies of the Mode 1 and 2 were17.386 kHz and 17.382 kHz, respectively. Therefore, the designedvibrator has met the requirements.

Fig. 3a also shows that the impedances for the two modesreached their maxima at 17.43 kHz, indicating that the power con-sumption would be the lowest when the voltages with these fre-quencies were applied. This is the anti-resonance phenomenon. Ithas been a common understanding that in general a high poweris required to obtain high vibration velocities in vibration-assistedmachining. The vibrators in the current manufacturing practice aremostly arranged to vibrate at the resonant frequencies, leading to abig electric-mechanical loss, sharp temperature rise and unstablevelocities as sacrifice [36]. In contrast, working at the anti-resonant

frequency can not only avoid these problems but also reach thesame high but more stable vibration velocity [33,37–39]. The ear-lier works by the authors have proven that vibrating at the anti-resonance frequency outstands that at the resonance frequencyunder the high power condition [40–43]. In this study, therefore,the vibrator was set to vibrate at the anti-resonance frequency of17.43 kHz. In addition, to keep the vibration characteristics un-changed under different cutting forces, preloads on the free endof the vibrator were set as FPX = FPZ = 30 N according to [41,42,44].

To collect the vibration characteristics of the tool tip, a measur-ing system consisting of two laser Doppler vibrometers (LV-1610by Ono Sokki) [44] was constructed. Fig. 4a shows the results underVp = 50 V and f = 17.43 kHz. Clearly, the cutting tool vibrates withsinusoidal patterns along the cutting direction with a = 1.76 lmand along the vertical direction with b = 1.45 lm when w = 90�.The synthesis of the two vibrations is a typical elliptic vibrationand the tool tip motion follows this pattern. The shape of the el-lipse also varies with the change of the phase shift. For instance,the elliptic pattern is nearly linear when w = 10� but becomes cir-cular when w = 150�. The influence of the voltage amplitude Vp onthe vibration amplitude is shown in Fig. 4b. As can be seen, Vp sig-nificantly affects the vibrations in both the cutting and verticaldirections. The amplitude a increases from 0.69 lm to 2.79 lmand b increases from 0.55 lm to 2.31 lm linearly as Vp increasesfrom 10 V to 90 V. This shows an important fact that a and b canbe altered accurately by changing the value of Vp.

For the other types of vibration-assisted cutting, the actuatorsA&B (Cases 1) and C&D (Cases 2) were excited separately andFig. 5 shows the vibration traces of the tool tip. The vibrationamplitudes were a = 1.95 lm and b = 0.12 lm in Case 1, anda = 0.08 lm and b = 1.31 lm in Case 2. Since only one third-bending-mode was excited by applying 180� phase shift voltagesto the parallel actuators, unidirectional vibrations in cutting direc-tion (CDVA cutting) and vertical direction (NDVA cutting) weregenerated in Cases 1 and 2, respectively. Consequently, they areused for the following cutting experiments.

4. Setup and conditions for experimental and numericalanalyses

The workpieces used in the study were unidirectional carbon fi-bre-reinforced polymer (CFRP). The conditions for the simulationand experimental cutting tests are listed in Table 1. Previousexperiments [2] have shown that when cutting CFRP, both the fibreand matrix exhibit brittle fracture. In the present FE analysis,therefore, the brittle cracking constitutive model in ABAQUS Expli-cit was used. Table 2 shows the properties used in the simulation.

Locus of elliptic vibration

X

Z

Y

Cutting tool

17.2 17.3 17.4 17.5 17.620

40

60

80

100

Resonance point

Gai

n dB

Frequency Hz

Mode1 Mode2

Antiresonance point

(a) (b)

Fig. 3. Frequency responses by (a) FEM and (b) measurement.

W. Xu et al. / Composites Science and Technology 92 (2014) 103–111 105


A material separation took place in the fibre, the matrix or theinterface when the maximum principal stress in that material ex-ceeds its tensile strength. The separation direction (or crackingdirection) was governed by the principal stress direction. To avoidthe penetration of elements after separation, a penalty contact con-dition was applied to insure that the surfaces of each element inthe microstructured layer would not interact with the surfaces ofits surrounding elements. The material properties of the fibre-epoxy interface were treated similarly to those of the epoxy matrix,but with smaller tensile and shear stress thresholds to reflect thefibre–matrix bonding strength. In addition, the friction factor

ψ =10° ψ =50°

ψ =90° ψ =150° ψ =180°

1μm

Vibrationdirection

1μm

1μm

1μm1μm

b a

1μm1μs

ψ =90°

(a)

0 20 40 60 80 1000.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Vib

ratio

n am

plitu

de μ

m

Input voltage Vp V

Amplitude a Amplitude b

(b) Fig. 4. Influence of (a) the phase shift and (b) the voltage amplitude on elliptic vibration.

2μm 1μm

Exciting PZT: A&B Phase shift: 180°

Exciting PZT: C&D Phase shift: 180°

Fig. 5. Actuator exciting methods and the locus of vibration on the tool tip.

Table 1Simulation and experimental conditions.

Tool and workpiece Cutting conditions

Tool material TiAlN/TiN coated tungsten carbide Input voltage frequency f (kHz) 17.43Tool clearance angle a (�) 7 Input voltage amplitude Vp (V) 20–80Tool rake angle c (�) 5 Input voltage shift phase w (�) 90Cutting edge radius re (lm) 2 Preload in cutting direction FPX (N) 30Workpiece material Unidirectional CFRP Preload in normal direction FPZ (N) 30Fibre orientation h (�) 90 Depth of cut ap (lm) 10–150Fibre diameter D (lm) 7 Tool feed rate v (m/min 0.3–15Fibre volume fraction Vf (%) 60 Coolant None



between the tool and workpiece was taken as 0.25 based on theexperimental measurements available [2].

In the cutting experiments, a micrograin grade TiAlN/TiNcoated tungsten carbide insert (rake angle 5� and clearance angle7�) was used as the cutting tool, and the workpieces (size:80 mm � 40 mm � 3 mm) were prepared from a unidirectionalCFRP laminate plate. The experiments were carried out on a CNCsurface grinder (SGT-315RPA by Nagase Integrecs Co. Ltd.) asshown in Fig. 6, and the cutting procedure was as follows.Firstly the vibrator was loaded on the worktable and its positionwas adjusted to make the cutting tool in parallel with theCNC spindle. The workpiece was fastened on the spindle with itssurface to cut to be perpendicular to the cutting tool. Nocoolant was used in all the experiments and the fibres werevertical to the cutting direction (i.e., h = 90�). To measure the aver-age cutting and vertical forces, a Kistler 3D dynamometer (9256A1,with 5 kHz natural frequency) was mounted beneath the vibrator[45,46].

5. Results and discussion

In the FRP cutting process, the fracture of fibres not only dom-inates the cutting force and plays an important role in the chip for-mation, but also determines the surface finish and subsurfacequality. As such, we will focus on the fracture of fibres in our cut-ting analysis.

5.1. Chipping mechanisms and surface integrity

Fig. 7 shows the fibre fracture of the second fibre under the cut-ting conditions of ap = 30 lm and v = 1 m/min. When the ultrasonicvibration was applied, the frequency used was f = 17.43 kHz. Withthe CDVA cutting mode, a = 2.07 lm and b = 0 lm; under theNDVA cutting mode, a = 0 lm and b = 1.67 lm; and under theEVA cutting mode, a = 2.07 lm and b = 1.67 lm.

Fig. 7a presents the fibre fracture in the traditional cutting pro-cess. It is clear that the wedging of the cutting edge does not re-move the fractured fibres effectively, but pushes the broken fibresegments into the zone in front of the cutting edge. This leads toobvious fibre-bending ahead of the cutting zone, brings about se-vere damages to the neighbouring fibres and the matrix material,and causes the fibres to crack even in the deep subsurface.

When a vibration is applied to the feeding direction, i.e., theCDVA cutting mode shown in Fig. 7b, it can be seen that somelocalised deformation zones appear, giving rise to certain smallerfibre fragments. The extent of the fibre-bending is reduced, re-flected by the straightness of the fibres. This is because of the fol-lowing facts: (1) In the CDVA cutting mode, the maximumvibration velocity in the cutting direction, 2pfa= 22.97 m/min, ismuch larger than the tool feed rate, v = 1 m/min; and (2) the cut-ting distance in each vibration cycle, D = v/f = 0.96 lm, is muchsmaller than the fibre diameter D. As a result, the vibration breaksa feed step down to many intermittent cutting actions. However,fibre fracture in the deep subsurface still occurs, caused by thereciprocating motion of the cutting edge.

When a vibration is applied to the vertical direction, i.e., theNDVA cutting mode in Fig. 7c, the fibre facture becomes localised,because the tool-fibre friction caused by the vertical vibration mo-tion of the cutting edge brings about additional tension and com-pression cycles in the fibre, particularly at the fibre-tool contactsurface. This role of such friction-induced tension–compression istwofold: (i) it facilitates the localised fracture of the fibre by

Table 2Material properties.

Material Densityq (kg/m3)

Yong’smodulusE (GPa)

Poisson’sratio m

Tensilestrengthrt (MPa)

Shearstrengthrs (MPa)

Carbon fibre 1750 230 0.2 2000 380Epoxy 1220 3.2 0.35 85 50Interface 1220 3.2 0.35 50 25EHM 1530 135 0.318

(1) Wave function generator(2-5) Power amplifier(6) AC singles display(7) Force sensor amplifier(8) Force display(9) CNC surface grinder(10) Worktable(11) Vibrator(12) Workpiece holder(13) Force sensor(14) Workpiece(15) Cutting tool

Fig. 6. Experimental apparatus for the EVA cutting tests.

Fig. 7. Fibre fracture in (a) traditional cutting, (b) CDVA cutting, (c) NDVA cutting and (d) EVA cutting. The colours indicate the levels of Von Mises stresses during the cutting.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)



CFRP

ToolChips Chips

Feed direction

Workpiece holder

Chips

CFRP

Tool Chips

Feed direction

Workpiece holder

Chips

CFRP

ToolChips

Feed direction

Workpiece holder

Chips

CFRP

Tool Chips

Feed direction

Workpiece holder

(a) (b)

(c) (d)Fig. 8. Some snapshots in (a) traditional cutting, (b) CDVA cutting, (c) NDVA cutting and (d) EVA cutting of CFRP composites. The insert at the right bottom of each image isthe chips collected.

μ

Cutting direction

μ

Cutting direction

μ

Cutting direction

μ

Cutting direction

(a) (b)

(c) (d)Fig. 9. Surfaces of CFRP composites machined by (a) traditional cutting, (b) CDVA cutting, (c) NDVA cutting and (d) EVA cutting.



exerting an additional tensile stress to the fibre because the vibra-tion amplitude is very small; and (ii) it can cause the fibre to de-bond or crack vertically because of the compression as shown bythe upsetting phenomenon of the first fibre (from the right) be-neath the clearance surface of the tool. On the other hand, the ver-tical vibration does not change the horizontal wedging force of thetool tip. As a result, the stresses in the fibres ahead of the cuttingzone are greater than those under the CDVA mode.

When an elliptical vibration is applied (Fig. 7d), the chippingand breakage of the fibre are much more localised in comparisonwith the other cases. Due to the simultaneous motion of the tooltip in both the cutting and vertical directions, stresses are concen-trated in a very narrow region around the tip-fibre interactionzone. The fibre is fractured into much smaller pieces, which haslargely improved the surface integrity of the finished surface.Meanwhile, it can be clearly seen that the fibres that are not in di-rect contact with the tool tip have a very low stress. The fibre-bending observed in the previous three cases is avoided.

The experimental cutting processes were recorded by a highspeed camera. Fig. 8 shows some snapshots including the collectedchips for each method, which confirms the predicted results by theFE analysis. Due to the continuous ploughing motion of the cuttingedge, a large quantity of chips appeared and accumulated in frontof the cutting tip in the traditional cutting. With the application ofthe vibration, the chip size decreased and no chip accumulation oc-curred in front of the cutting tool. The EVA cutting produced thesmallest chips and they were always removed instantly. This is be-cause the elliptical vibration made the moving direction and veloc-ity of the tool tip change instantaneously (see Fig. 7d).

Fig. 9 shows the CFRP surfaces machined by the traditional andvibration-assisted cutting methods. It can be seen that the tradi-tional cutting pulled the fibres out, and generated deep damagesto the subsurface, Fig. 9a. The chips were large fibre–matrix clus-ters and the surfaces were rough (Ra = 5.18 lm). In contrast, thevibration-assisted cutting improved the machined surface quality.As shown in Fig. 9b, the CDVA cutting produced smoother surfaces(Ra = 4.25 lm). However, due to the frequent reciprocating of thetool along cutting direction, the surface fibres and matrix weredebonded. The NDVA cutting further reduced the surface rough-ness to Ra = 2.72 lm, and apparently minimised the fibre–matrixdebonding. A closer examination, nevertheless, revealed that thedebonding still took place and many fibres were broken in the deepsubsurface such that they were easy to be pulled out, Fig. 9c. Thebest results were by the EVA cutting, which not only made surfacemuch smoother (Ra = 1.32 lm), but also minimised the debonding,leading to high surface integrity. The above experimental resultsconfirm the predictions from the FE analysis discussed above.

5.2. Cutting forces

Fig. 10 shows the variation of the average cutting forces fromboth the FE predictions and experiments under the same condi-tions, where the force values were normalized by the ratio of thecutting force to the shear force of fibre rspD2/4 along a fibre–matrix cell width. The results demonstrate that the traditionalcutting required the largest cutting forces, and the EVA cuttingconsumed the smallest cutting energy. In the CDVA cutting, theconstraint conditions of the tool trajectory ensured the separateshear of the fibres and the matrix, so that both Fx and Fz becamesmaller. In the NDVA cutting, the cutting forces dropped not asmuch as that in the CDVA cutting, because the tool was alwaysin contact with the FRPs. The EVA cutting combined the merits ofthe CDVA and NDVA methods. On one hand, the vibrations in boththe cutting and vertical directions incur the instantaneous changesof the cutting angle to promote fibre fracture [27]; on the otherhand, the instant chip removal due to the vertical vibration re-duced the cutting forces further.

The two constraint conditions of the tool trajectory (v < 2pfa;D = v/f < D) play a key role in the EVA cutting. Fig. 11a shows theeffect of 2pfa/v on Fx and Fz. Under the same condition off = 17.43 kHz, w = 90� and ap = 50 lm, v changed from 0.3 to18 m/min with a = 1.76 lm, and a changed from 0.7 to 2.8 lm withv = 0.5 m/min. In both sets of the results, the forces first decreasesharply until the ratio reaches 5. It is therefore clear that the EVA

Traditional CDVA NDVA EVA0.0

0.4

0.8

1.2

1.6

2.0

Nor

mal

ized

cut

ting

forc

e

Cutting methods

Simulation: Fx

Simulation: Fz

Experiment: Fx

Experiment: Fz

Fig. 10. Cutting forces: FE predictions vs. experimentally measured results.

0

10

20

30

40

50

60

70

1

Fx: v changFx: a changFz: v changFz: a chang

Cut

ting

forc

e N

Rate: 2πfa/v

0 10 20 30 40 50

0 4 8 12 16 20

0

15

30

45

60

75

90

Cut

ting

forc

e N

Feed rate v m/min

Traditional cutting Fx

Traditional cutting Fz

EVA cutting Fx

EVA cutting Fz

0.5 1.0 1.5 2.0 2.5

2πfa=v

Rate: Δ/D=v/fD

Δ=D

(a)

(b)Fig. 11. Influence of (a) 2pfa/m and (b) D/D (feed rate) on cutting forces.



cutting is effective with small cutting forces when 2pfa/v is above5. Fig. 11b shows the influence of feed rate v to the cutting forces,where Vp = 60 V, f = 17.43 kHz, w = 90� and ap = 50 lm. All of theforce curves rise with the increase of v, and it is apparent thatthe vibration of the cutting tool reduces both Fx and Fy. This effectis significant when D/D is less than 0.8.

5.3. Tool wear

Fig. 12 shows the geometries of the cutting tool before and afterthe cutting of 3.5 h, using the traditional and EVA methods(Vp = 60 V, f = 17.43 kHz, w = 90�, ap = 80 lm, v = 2.0 m/min). Be-cause fibres were strongly abrasive, and the vertical cutting forcein vertical direction in traditional cutting was big (Fig. 10), the toolsuffered from significant crater and flank wear. With EVA, how-ever, due to the merit of small chips and cutting forces, the toolwear is greatly improved. In general, the maximum flake wear landsize, VBmax, should be below 0.2 mm (tool wear threshold) [47].Fig. 12b shows that VBmax has reached 0.22 mm after the cuttingof 3.5 h with the traditional cutting, indicating that this tool is nolonger useful. With the aid of the EVA, however, VBmax is only0.1 mm, Fig. 12c. This is a significant extension of the tool life.

6. Conclusions

This paper has explored the mechanisms of material removaland subsurface damage in FRPs using a vibration-assisted cuttingtechnique. A novel vibrator has been invented to work at theanti-resonant frequency to realize stable and high variationalvelocities. A three-dimensional microstructure-based FE analysisand a systematic EVA cutting experiment have been carried out.The investigations lead to the following conclusions:

(1) The application of vibration can significantly decrease thecutting forces and reduce the subsurface damage in a CFRPworkpiece. The vibration in the cutting direction is moreeffective in reducing the cutting force, but that normal tothe cutting direction has the advantage of chip removal.

(2) In the EVA cutting, i.e., when vibration is applied to both thecutting and vertical directions, the chipping and breakage ofthe fibres are much more localised and thus the fibre-bending is mostly avoided. An optimal cutting process canbe realised to provide much smaller cutting forces and amuch improved surface integrity.

(3) The ratio of the tool-feed-rate to the maximum vibrationvelocity in the cutting direction, and the ratio of the cuttingdistance in a single tool vibration cycle to the fibre diameter

are the key parameters. To maximise the advantage of theEVA cutting, it is necessary that these two parameters arebelow their critical values.

(4) EVA is effective to extend the cutting tool life, by reducingboth the crater and flank wear.

Acknowledgements

The authors appreciate the Australian Research Council for itsfinancial support. This work was supported by an award underthe Merit Allocation Scheme on the NCI National Facility.

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Rake face

Flank face

50μm50μm

50μm

(a) (b) (c)Fig. 12. Wear of the cutting tool. (a) before cutting; (b) after traditional cutting of 3.5 h and (c) after EVA cutting of 3.5 h.



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