aluminium stack materials

Accepted Manuscript Interpretation of force signals into mechanical effects in vibration-assisted drilling of carbon fibre reinforced plastic (CFRP)/aluminium stack materials Chunliang Kuo, Chihying Wang, Mengkun Liu PII: DOI: Reference:

S0263-8223(17)31101-7 http://dx.doi.org/10.1016/j.compstruct.2017.07.077 COST 8732

To appear in:

Composite Structures

Received Date: Revised Date: Accepted Date:

5 April 2017 25 June 2017 21 July 2017

Please cite this article as: Kuo, C., Wang, C., Liu, M., Interpretation of force signals into mechanical effects in vibration-assisted drilling of carbon fibre reinforced plastic (CFRP)/aluminium stack materials, Composite Structures (2017), doi: http://dx.doi.org/10.1016/j.compstruct.2017.07.077

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Interpretation of force signals into mechanical effects in vibration-assisted drilling of carbon fibre reinforced plastic (CFRP)/aluminium stack materials Chunliang Kuo*, Chihying Wang, Mengkun Liu Department of Mechanical Engineering, National Taiwan University of Science Technology, 43 Keelung Road, Sec. 4 Taipei, Taiwan, 10607 * Corresponding Author / E-mail: [email protected] TEL: +886-2-2733-3141#6448, FAX: +886-(0)2-2737-6460 Abstract: This study investigates if the vibration frequency and amplitude, coupled with cutting parameters could reduce the thrust force in the drilling of CFRP/Al stacks. In the ANOVA and main-effect plots, the contributions (PCRs) of the vibrating amplitude were high (CFRP: 80.14%, Al: 48.14%). When drilling in the steady states, the interactions between the employed vibration parameters with the machine tool and the fixation system were interpreted using the empirical mode decomposition (EMD) and Fourier spectrum with appreciable results (CFRP: R2 = 84.1%, Al: R2 = 93.9%). When drilling in the CFRP layer at the cutting onsets, the resolved spectrums perfectly matched the mechanical effects in the cutting stage (19.5–1367 Hz), with chattered-induced vibration (683.6 and 1367 Hz). When drilling of the Al layer, the damping-induced vibration led to an increase in the background noises (39.1–117.2 Hz), whereas the frequencies produced by the spindle remained largely the same.

Keywords: CFRP/Al stack; vibration drilling; thrust force; statistical analysis; empirical mode decomposition

1. Introduction Carbon fibre reinforced plastic (CFRP) bonded with a metallic alloy in a preferred configuration, such as stack materials of CFRP/Al [1-3], CFRP/Ti [4-8] and Ti/CFRP/AL [9-12], can provide high specific strength (2.5–4.5 GPa) and high modulus (400 GPa) for heavy-duty 1

applications. Compared to advanced structure materials of aluminium alloys [13], CFRP composite materials have advantages such as low weight and good machinability. However, because of the different inherent material properties in the metallic parts and CFRP composites, drilling a hole in a single shot of stack material is very challenging. Krishnaraj et al. [14] discussed the challenges of producing multi-material stacks and proposed solutions for future work. This has led to considerable research interest in developing the vibration-assisted drilling process of stack materials, which provides significant benefits in terms of not only productivity, but also accessibility for in situ measurement for a lean production. Arul et al. [15] suggested that the vibration due to drilling led to a decrease in the thrust force (up to 60%) and extended tool life (by up to 50%) in woven glass fabric reinforced plastic (GFRP) composites. They concluded that the intermittent cutting concentrated the cutting energy and eliminated chip deformation, thereby reducing the thrust force. Similarly, Wang et al. [16] studied the thrust force in the vibration drilling of fibre-reinforced plastics under low frequency (100–300 Hz) and high amplitude (2–6 µm) conditions using carbide and high–speed–steel drills. They found that the increases in the axial amplitude (6 µm) and vibration (300 Hz) would lead to a decrease in the thrust force. In the drilling of aluminium alloys, Takeyama et al. [17] investigated the effects of ultrasonic vibration on the thrust force. They concluded that when the operating vibration amplitude was larger (~13.5 µm), the thrust force could be reduced (~46%) in the drilling of aluminium alloy and GFRP. Brehl and Dow [18] presented a review work to introduce the kinetics of vibrationassisted machining (VAM) and a cutting system. They concluded that the tool life was extended because of the reduction in the cutting force owing to the VAM mechanism. Neugebauer and Stoll [19] investigated the cutting forces and edge paths of drilling via ultrasonic-assisted energy. They found that when the cutting-edge paths and alternate effective-cutting speeds overlapped with the oscillation, the force and torque could be reduced by up to 30–50% and the corresponding tool life could be increased up to 20-fold compared to conventional cutting. Jallageas et al. [20, 21]

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proposed an analytical model of a force-excited vibration system to optimise the operating oscillation frequencies in the drilling of stack materials. The design parameters of the vibrationassisted drilling system were optimised through simulation to ensure a stable cutting condition. Thereafter, a new adaptive vibration control system (MITIS system) was developed based on the various cutting strategies. The proposed vibration-assisted drilling system could be used to reduce the heat diffusion and burr height in the drilling of CFRP/Al stacks. The surface roughness of the CFRP material was improved but deep tearing of fibres was observed at specific ply orientations. To analyse the time-domain response on the vibration parameters, the Fourier transform is a conventional method used to convert a signal in time domain into its frequency counterpart. ElWardany et al. [22] applied a Fourier-based vibration-signature analysis technique on the drilling force to detect drill wear and breakage. Statistical indices such as the instantaneous ratio of the absolute mean value and kurtosis value were calculated from the vibration signals in the time and frequency domains. They showed the proposed method was effective and robust in detecting the discriminant characteristics due to tool wear and breakage. Abu-Mahfoz [23] used frequency domain characteristics such as harmonic wavelet coefficients and maximum entropy spectrum peaks to train the multi-layer feed-forward neural network. The results demonstrated the effectiveness of using the vibration signals in a supervised neural network for drill-wear detection and classification. Jallageas et al. [24] proposed an approach based on the discrete wavelet transform (DWT) to identify the specific frequency characteristics generated in multi-stacked material drilling. By comparing the magnitude of the frequencies on the Fourier spectrum, the boundaries of the composite and metallic layers were well marked, and a self-adjusting cutting parameter strategy was applied to different materials in real time. Sun et al. [25] proposed a tool wear index based on the characteristics extracted from the DWT of the drilling force vibration to represent the severity of tool wear. They found that the energy distribution of the vibration signal tends to shift towards the low frequency range when the tool wear develops. Hence, the

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conventional Fourier spectrum cannot be used to obtain such transitions with desirable accuracy. Huang et al. [26, 27] developed an empirical mode decomposition (EMD) to investigate the nonlinear and non-stationary time series data. The EMD method could be used to decompose the signal into multiple intrinsic mode functions (IMFs) containing the fundamental oscillation mode imbedded in the data. Each IMF was not restricted to a narrow band signal and could be both frequency and amplitude modulated. Yang and Suh [28] investigated the crack-induced vibration of the rotary system using the EMD method. They found that the instantaneous frequency retrieved from the EMD and Hilbert transform was a suitable alternative to the Fourier-based spectral analysis. Moreover, the interpretation of crack-induced nonlinearity via the instantaneous frequency was both intuitively rigorous and physically valid. Yan and Gao [29] extracted an instantaneous frequency component within the signal through the EMD process; the deterioration of a test bearing could be effectively detected through the time-dependent amplitudes and frequencies using the Hilbert–Huang transform. They demonstrated that the EMD, along with the Hilbert transform, was an adaptive signal demodulation approach to consider the varying machining conditions in practical applications. In this study, the vibration-assisted energy was introduced in the single-shot drilling of CFRP/Al stack material using CVD diamond-coated tools. The employed operating parameters with low vibration frequency and high amplitude were investigated to effectively reduce the thrust force. The effects of the cutting and vibration parameters on the thrust force are discussed; moreover, the statistical significance of the operating parameters in the hybrid drilling is presented. The EMD is applied as multiple band-pass filters to analyse the influence of the vibration parameters on the thrust force. The Fourier spectrum of the re-assembled delegate signal can be used to identify the apparent dominant frequencies corresponding to the drilling actions. The interactions of the vibration frequency with the spindle speed, tooth-passing frequency, and natural frequency of the machine are determined and discussed.

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2. Experiment procedure 2.1 Design of hybrid vibration-assisted device The hybrid energy was derived from the vibration-assisted device comprising an activated electro-magnetic vibrator and a multi-channel invertor to adjust the input frequency and resulting amplitude. The designed vibrating work was calculated to be in the range of 0.011–1.175 J based on the 300-g fixture plate driven by the operating parameters without friction work involved. In Fig. 1, fixture A depicts the vibration device, whereas in fixture B, a similar design was replicated, but a laser displacement sensor was installed to monitor the frequency and amplitude. The base plate of fixture B was mounted onto a piezoelectric dynamometer (Kistler 9272) to investigate the thrust force when the data acquisition was synchronised to the set frequencies and amplitudes.

Fig. 1. Design of (a) vibration-assisted fixtures and CFRP/Al stacks in (b) strip and (c) plate forms 2.2 Arrangements of workpiece material, machining tool, and machine set-up The stack material comprised the CFRP laminate and aluminium alloy with an overall thickness of 6.5 mm. The CFRP composite was laid up with the woven fabric prepregs (BMS 8-168 TY2 CL2 STY 3K-70-PW) for 16 plies for a thickness of 3.5 mm, an elastic modulus of 48263 MPa, 5

and a tensile strength of 517 MPa. The thickness of the Al plate (A7075T6) bonded to the CFRP laminate was 3 mm with an elastic modulus of 72 GPa and a tensile strength of 577 MPa. The cutting tools employed in the tests were coated with a CVD diamond of ultra-high hardness (~10000 HV) with an elastic modulus in the range of 600–800 GPa. The point geometry was a double point with dimensions of 120° × 20°, a helix angle of 40°, and a clearance angle of 14°. Fig. 2(a) shows the force measurement conducted using the dynamometer and analysis via the Kistler DynoWare. The thrust force was measured using the set-up of a piezoelectric dynamometer (Kistler 9272) platform, a data acquisition device (Kistler 5697), a charge amplifier (Kistler 5070), and DynoWare software for data analysis. The hybrid energy was introduced using a vibration device, which could be used to obtain low frequencies (44–96 Hz) with adjustable amplitudes (1–80 µm). The static and dynamic vibration frequencies and amplitudes were measured and validated using a laser-displacement sensor (Keyence LH-H025) for an operating range of ±3 mm and a resolution of 1 µm under a sampling rate of 10 kHz.

Fig. 2. Machining set-up for drilling of CFRP/Al stack for (a) force measurement, and (b) vibration frequency and amplitude measurements

2.3 Design of experiments In this experimental study, the workpiece and cutting materials were the fixed parameters, whereas the cutting speed (CFRP: 130–170 m/min, Al: 200 m/min), feed rate (0.04–0.08 mm/rev), vibration frequency (45–55 Hz), and amplitude (0.005–0.05 mm) were the operating parameters. 6

Each variable to be evaluated had three levels, which required a Taguchi orthogonal array (L9), as listed in Table 1. The tests were terminated based on the flank wear (VB 300 µm) defined in the ISO standard (3685), or at 200 machined holes, because of limited resources. The influence of the operating parameters on the thrust force was analysed statistically using ANOVA and was verified with the percentage contributions (PCR). The preferable combination of the operating parameters for the least thrust force was suggested and was analysed using the main effect plots.

Table 1 Taguchi (L9) test array Cutting speed in Test No. CFRP/Al (m/min) 1 130/200 2 130/200 3 130/200 4 150/200 5 150/200 6 150/200 7 170/200 8 170/200 9 170/200

Feed rate (mm/rev) 0.04 0.06 0.08 0.04 0.06 0.08 0.04 0.06 0.08

Frequency (Hz) 45 50 55 50 55 45 55 45 50

Amplitude (mm) 0.005 0.02 0.05 0.05 0.005 0.02 0.02 0.05 0.005

2.4 Analysis of time-domain response After performing the statistical analysis, the resolution of the time-domain response was developed to identify the effect of the vibration frequency on the cutting tool, workpiece, and its surroundings in the vibration-assisted drilling system. The EMD was used as a signal processing technique to decompose the signal into multiple independent IMFs in series. Each IMF is a monofrequency modulated signal with empirically decided bandwidth. The procedure was termed the shifting method. Fig. 3 shows a brief illustration. Two cubic splines were fitted through the local maxima and local minima to generate the upper and lower envelopes of the original time-series data, respectively. The average of the two envelopes was subtracted from the original signal to generate a new signal. The same procedure was then applied to the new signal until a stopping criterion was met [17]. The resultant signal could be defined as the first IMF. The remaining IMFs could be 7

generated by following the same procedure after the previous IMF was removed from the signal. The procedure was executed recursively until all the IMFs were found. Original time series data set x(t) Shifting process Define candidate IMF as IMFn

Draw upper and lower envelopes by cubic splines

Replace x(t) by x(t) - IMF

Substrate the average of the upper and lower envelopes from x(t)

Go through shifting process to find IMFn+1

Retrieve a candidate IMF

IMF oscillates? Match stopping criteria?

Yes

No

Yes Keep finding the next IMF

Define this IMF as Residual

No Replace x(t) by x(t) – candidate IMF

Complete the decomposition m

x ( t ) = ∑ IMFn + Re sidual n =1

Fig. 3. Flowchart of empirical mode decomposition (EMD)

Each IMF fulfilled the definitions. First, the numbers of extrema and zero-crossings in the signal were either equal or differed at most by one. Second, the mean value of the upper and lower envelopes is zero at any point. As shown in Fig. 4, the EMD was analysed, and subsequently, extracted using several IMFs and remaining signal, which was the residual  without a vibrating component. The relationship between the original signal, IMFs, and residual can be represented as follows.   = ∑   + 

(1)

Because the IMFs were empirically generated without resorting to sinusoidal basis functions as those used in Fourier transform, they could not be described in an analytical form. Hence, the local resolution was excellent, and the transient response was not misinterpreted. The EMD with the 8

subsequent Hilbert transform, often termed the Hilbert–Huang transform (HHT), was used to analyse the non-stationary and non-linear signals by employing its frequency modulation.

Fig. 4. Example of empirical mode decomposition (EMD): (a) finding local maxima and local minima, (b) defining mean envelope by averaging the upper and lower envelopes, (c) subtracting the original signal from the mean envelope to retrieve IMF1, and (d) repeating procedures from (a) to (c) to retrieve IMF2 3. Results and discussion 3.1 Cutting force Fig. 5(a) shows the cutting force plots in the CFRP/Al stack workpiece from Test 9, which presented a typical thrust force in the drilling of the stack materials. In interval II, the thrust forces were measured in the drilling of the CFRP layer, whereas in intervals IV, VI, and VIII, the thrust forces were obtained from the Al layer. It was apparent that the highest thrust force of 88.8 N in the CFRP was much lower than that of 148.4 N in the Al layer, because of their inherent differences in machinability, despite the CFRP having a much higher elastic modulus than A7075T6. When drilling the Al layer, the thrust forces increased from 108.7 to 148.4 N in the two retraction intervals 9

from IV to VIII, respectively. This was because of the decreased thickness of the remaining workpiece in the Al layer, which reduced the force absorption and associated damping effects. The sample areas in A/B and C/D represent the important stages such as the cutting tool in the full engagement/onset of breaking through the machined layers in the CFRP and Al, respectively. In Fig. 5(b), when the drill advances into the CFRP layer, the fluctuation in the thrust force was stably measured (± ~2.8 N), indicating that the cutting lips were in contact with the CFRP workpiece, but still periodically relaxed, because of the axial displacement withdrawn via the predetermined vibration amplitude of 0.005 mm. In addition, the interval of the cyclic load was recorded in the period of 20 µs, which appeared to align with the operating frequency of 50 Hz in Test 9. In Fig. 5(c), when the cutting tool breaks through the CFRP layer and at the onset of retraction, the fluctuation in the thrust force increases (± ~5.5 N), indicating that the contact between the cutting tool and the workpiece was less because of the reduced feed load in the cutting action. In Fig. 5(d), when the drill enters into the Al layer, the fluctuations in the thrust force were reduced (± ~1.6 N). The minor reduction in the fluctuation in the thrust force was possibly due to interactions between the vibration frequency and the material plasticity, such as damping effects. This phenomenon was usually initiated by the high plasticity in the aluminium material, which was capable of absorbing the loads and storing the strain energy, resulting in a retarded vibration response produced via the vibration-assisted energy. In contrast, this damping effect was unclear in the CFRP layer compared to that in the Al layer. This is possibly because of the very high elastic modulus (48263 MPa) of the CFRP material. At the onset of the drill breaking through the Al layer, the fluctuation in the thrust force similarly increased to ± ~2.8 N, which indicated that the axial travelling displacement (> 0.005 µm) was significant. This phenomenon resulted from the relaxation of the thrust force in the cutting tool, because part of the feed force was reduced and not loaded into the workpiece when the cutting tool was breaking through. Consequently, the speed of the cutting edges advancing towards

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the workpiece could be increased under such a less contact, producing a relatively high impact on the workpiece, compared to that in the ramping-up stage.

Fig. 5. Measurement of cutting forces when cutting tool is in (a) sampled intervals in CFRP/Al stack workpiece, (b) full engagement, (c) breaking through the CFRP layer, (d) full engagement, and (e) breaking through the Al layer Fig. 6(a) shows the evolution of the thrust forces measured in the CFRP layer, ranging from 84.7 to 101.8 N at the last hole in the (L9) tests. It was apparent that the least thrust force (84.7 N) was recorded in Test 5 under the operating parameters of 150/200 m/min (cutting speed), 0.06 mm/rev (feed rate), 55 Hz (vibration frequency), and 0.005 mm (vibration amplitude), compared to 11

the highest force (101.8 N) in Test 3 (130/200 m/min, 0.08 mm/rev, 55 Hz, and 0.05 mm). When the drill advanced into the successive Al layers, similar results for the thrust forces were recorded in the Al layers, ranging from 137.7 to 188.2 N at the last holes (200 holes), as shown in Fig. 6(b). Among these tests, the highest increase (~23%) in the thrust force occurred in Test 3, compared to the other (L9) tests. It was clear that the run-in effect in the machining of the CFRP layer was not observed. This was because the chip-tool contact time is usually shorter when machining with brittle material (CFRP: 500 HV). Hence, the stress concentration occurred at the uneven cutting edge, thus reducing the thrust force. Conventionally, the low thrust forces are dominated by the low feed rate (0.04 mm/rev) and high cutting speed (170/200 m/min); however, with the imposed vibration-assisted amplitude (0.005–0.05 mm), the sudden increase in the uncut thickness could maximise the impact on the intermittent cutting in the shear zone and vary the thrust force. In Fig. 6(a), the two groups of thrust forces show that the lowest thrust forces in Tests 1, 5, and 9 were produced by the low cutting forces, which were similarly initiated from the lowest vibration amplitude of 0.005 mm with feed rates of 0.04, 0.06, and 0.08 mm/rev in sequence. For the thrust force in the Al layer, drastic reductions (~18%) were encountered in most of the tests after the run-in stage (40th holes) compared to the first holes. This was because of the inherent plasticity of the metallic materials, which allows them to extend the tool-chip contact time and exacerbate the effect of the stress concentration at the uneven spots, leading to effective run-in at the high spots. As soon as the high spots were reduced and made even, the increased cutting area helped in improving the cutting action, thereby reducing the thrust force. Moreover, the trend in the thrust forces, presented in two distinct groups, looked similar to the pattern in the machining of the CFRP layer. The high thrust forces produced in Tests 3, 6, 7, and 8 were observed after the 120th hole, which continuously increased until the tests were terminated. Usually, the high thrust force was produced because of the high feed rate, implying that the chip thickness was considerable. However, this phenomenon could be influenced by the imposed vibration energy, as demonstrated

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in the thrust-force plots. The interactions between the vibration amplitude and the frequency of the feed rate should be examined via statistical analysis to understand their significance, and the associated percentage contribution rate should be identified.

Fig. 6. Evolution of thrust forces in (a) CFRP layer, and (b) Al layer in Taguchi (L9) tests

3.2 Statistical analysis When the assisting energy, produced by the vibration parameters, was imposed on to the drilling action, it was aimed that the thrust force would be decreased under the coupled cutting parameters of the high cutting speed (170 m/min) with the least compromise on the feed rate (0.08 mm/rev). In Fig. 7(a), the main effect plot for the drilling of the CFRP layer shows that the 13

preferable combination to obtain a low thrust force was a cutting speed of 150 m/min, feed rate of 0.06 mm/rev, vibration frequency of 50 Hz, and an amplitude of 0.005 mm. In this combination, the vibration amplitude is the most statistically significant factor (PCR: 80.14%) compared to the cutting speed (PCR: 9.02%) and feed rate (PCR: 10.67%) when the variance produced by the vibration frequency was pooled in the residual variance. This explained that the contribution of the vibration amplitude nullified the effects produced by the cutting speed and feed rate, though the effects of both on the thrust force were significant. However, the contribution of the vibration frequency was reasonably limited. Similarly, in the main effect plot for drilling in the Al layer, the preferred combination was the same as that for the drilling in the CFRP layer. In ANOVA (Fig. 7(b)), the contributions (PCR) of the vibration amplitude to the CFRP and Al workpiece layers were 80.14% and 48.14% respectively, meaning it was the most effective parameter in the combination set. It was manifested that the imposed vibration amplitude on the feed rate increased the uncut thickness and thereby increased the shearing area, leading to the increase of the thrust force. Whereas the low vibration frequency (45-55 Hz) produced only limited effects on the thrust force in the CFRP and Al workpiece layers, due to the absorption, interruption and interaction with the workpiece materials, drilling actions such as chattering, and the fixation system, respectively. In contrast, the influences of these cutting parameters were ineffective because the F calculated values did not exceed the thresholds of the statistical significance (F0.05 2, 2 = 19). The increases in the percentage contribution rate to the feed rate (PCR: 23.58%) and frequency (PCR: 16.07%) counteracted the contribution produced by the vibration amplitude (PCR: 48.14%), despite the operating parameters being statistically insignificant. In addition, the limited contribution of the vibration frequency to the thrust force reflected that the delivered vibration energy was possibly counteracted, or it interacted with the drilling system, including the absorption of the vibration energy by the cutting tool, spindle, machining fixture, or machine tool. These would

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need further analysis in the time-domain response of the input vibration frequency, prior to conducting the final validation run, to obtain the best combination of the parameter set.

Fig. 7. (a) Main effect plots, and (b) ANOVA for thrust force in Taguchi (L9) tests 3.3 Analysis of time-domain response The time response and corresponding Fourier spectrum of the sample area A (Fig. 5) were resolved, as shown in Fig. 8. The integrated Fourier spectrum was less effective in identifying the corresponding thrust force. This was because of the produced fluctuation in the thrust force, which could be interacted or counteracted with the other vibration sources in the vibration-assisted drilling actions. Hence, the EMD is suitable in decomposing and identifying the frequency content, which was imposed by possible sources such as cutting tool, chuck, spindle, moving table, cooling system, and machine tool during the drilling.

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Fig. 8. Measurement of sample area A for (a) time domain response and (b) Fourier spectrum

When the EMD was employed to decompose the force measurement in the sample area A (Fig. 5), the fluctuation in the thrust force could be disintegrated into nine intrinsic mode functions and one residual, as shown in Fig. 9. Each intrinsic mode function (IMF1-9) represented a signal, which has a mono-frequency varying with time and amplitude with a clear separation of the frequency modulation to each class. However, the remaining residual (39–61 N) indicated that none of the vibration was involved and presented solely the feed force directly.

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Fig. 9. Intrinsic mode functions and residual of sample A

However, the physical interpretation of the IMFs of the decomposed spectrum could not be ensured without confirmation using the Fourier analysis. The mean frequency and power percentage of each IMF were calculated. Table 2 lists the same. When mapping the results in Table 2 to the Fourier spectrum as shown in Fig. 8(b), no prominent frequencies were observed between 3000 and 15000 Hz on the Fourier spectrum, as shown in Fig. 8(b), corresponding to the mean frequencies of IMF1, IMF2, and IMF3 as listed in Table 2. These resolved frequencies were clearly not in the 17

ranges produced by the machining system and possibly exist in the high orders such as part of the environmental condition or electric disturbance from the force sensor. Hence, IMF1, IMF2, and IMF3 could be assumed as background noises to be ignored.

Table 2 Mean frequency and power percentage of each IMF in Sample A Channel IMF1 IMF2 IMF3 IMF4 IMF5 IMF6 IMF7 IMF8 IMF9 Residual

Mean Freq. (Hz) 14576.69 6960.325 3373.946 1480.787 768.5098 431.1153 181.1934 62.48047 24.99219 6.248047

Power (%) 24.11225 8.537633 5.529729 6.812059 6.498698 2.116719 3.898338 23.35 19.14457 —

Hence, to filter the noises irrelevant to the drilling actions, the IMFs except IMF1, IMF2, IMF3, and residual were combined to form a delegate signal. Fig. 10 shows the results of the timedomain response and corresponding Fourier spectra in a dry run such as a base line test. When the vibration frequency of 50 Hz, labelled with A, was triggered, the resolved frequency of 49.74 Hz could be clearly identified, as shown in Fig. 10(b). It was clear that the frequencies of 686 and 1372 Hz, labelled as B and C, respectively, had already existed before starting the drilling actions. These two background signals were recorded throughout the experiment, which could be considered harmonics to be generated by the machine tool itself. Consequently, the three resolved signals were considered an initial condition with which to compare the onward drilling actions.

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Fig. 10. (a) Time domain response, and (b) Fourier spectrum of delegate signal without drilling

3.4 Vibration-assisted drilling in the steady state Figs. 11(a) and 11(b) show the analysis results of the time-domain response and Fourier spectrum, respectively, in the drilling of the CFRP layer when the post-processing technique was applied to the case in the feeding stage and at the onset of the retraction cycle. The recorded frequencies were distributed into seven distinguished bands (αA/B – ψA/B) and perfectly mapped to the sampled intervals of A and B. The delegated signals represented the thrust forces within the sampled time intervals, as shown in Fig. 11(a), whereas the corresponding peak values in the Fourier spectra were identified, as shown in Fig. 11(b). Amongst these power spectra, α A (19.5 Hz) and γA (58.6 Hz) showed the most dominant sources, which were the background noise and the input low vibration frequency (50 Hz), respectively. It was apparent that the spectrum κA of 283.2

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Hz was mapped to the source, which was initiated from the operating cutting speed of 170 m/min for a cutting tool diameter of 6.35 mm. The calculated revolution speed was 8488.26 rpm, corresponding to the frequency of 141 Hz in the spindle, which resulted in a tool passing frequency of 282 Hz when the cutting tool had two cutting lips. Fig. 11(b) shows these results clearly, such as 146.5 Hz (spectrum ηA) and 283.2 Hz (spectrum κA) with small shifts of 3.9% and 0.35%, respectively, compared to the theoretical values. In the background, spectrums φA and ψA with frequencies of 683.6 and 1367 Hz, respectively, were perfectly mapped to the results in the dry run, as shown in Fig. 11(b), with the spectrums labelled as γA and η A, respectively. However, spectrum αA with a low frequency of 19.5 Hz was transformed to IMF9 of frequency 24.99 Hz (Fig. 9) with a shift of 21.8%. One of the ways of increasing the frequency from low to high value without inputting extra energy was initiated by the resonance; this possibly occurred because the CFRP material was relatively rigid (E = 48 GPa) and not prone to absorb or store any load in the fibre material via plastic deformation during drilling. In contrast, a real-time response, such as bouncing back of the fibre or orientation-induced vibration in the drilling, could produce sources to interact with the background frequency, thereby shifting the spectrums. These effects were similarly observed in the resolved signals of spectrums γA and ξA, which were collected with frequencies of 58.6 and 410.2 Hz, respectively. Fig. 11(b) shows that the Fourier spectrums in the feeding stage (sampled interval of A) were largely mapped to the results at the cessation of drilling (sampled interval of B), except for spectrum ψB, which had a shift of 0.01%. This phenomenon was again because of the elastic modulus of the CFRP, which was sufficiently high to produce a strong reactive force on the drill via a strong contact between the cutting lips and the CFRP laminate. Hence, each spectrum produced by the vibration frequency was easily identified.

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Fig. 11. Analysis of samples A and B for (a) time-domain response, and (b) Fourier spectrum of delegate signal in the drilling of the CFRP workpiece layer

When the drill advanced to the Al layer, the recorded frequencies were again distributed into the seven distinguished bands (βC/D – ψC/D). Fig. 12(a) shows the force measurement in the sampled intervals of C and D. Fig. 12(b) shows the corresponding Fourier spectrums. Amongst these power spetrums, γC (58.6 Hz) and γD (58.6 Hz) in the sampled intervals of C and D respectively, showed the most dominant source, which was the input low vibration frequency influencing the drilling actions in the sampled transient. When drilling in the Al workpiece layer, the cutting speed was increased to 200 m/min so that its equivalent spindle speed increased to 166 Hz with a calculated tool cutting frequency of 332 Hz for a two-cutting-lips drill. Both of their Fourier spectrums were clearly observed in the sampled interval of C, such as spectrums of θC (166 Hz) and λC (332 Hz); and similarly in the sampled interval of D, such as θD (166 Hz) and λD (332 Hz), as shown in Fig. 21

12. As discussed in the previous section, the background noise in spectrum γDry of 49.7 Hz (Fig. 10(b)) was shifted to spectrum γC of 58.6 Hz in the sampled interval of C, and confirmed with that of spectrum γD in the sampled interval of D. The resolved spectrum γC in low frequency, could usually be produced from the background noises such as imperfections in the assembly of the moving components, like servo feeding systems. Additionally, new sources of spectrums βC and εC with frequencies of 39.1 and 117.2 Hz were possibly produced by the interaction between the cutting tool and the aluminium workpiece material. For such a low vibration frequency (50 Hz), the force absorption and resulting damping effects could be interrupted and hindered by the intermittent contact during the drilling action. It is clear that the spectrum βC, with a frequency of 39.1 Hz, was produced by the intermittent contact between the cutting tool and the aluminium material; whereas the spectrum εC, with a frequency of 117.2 Hz, was initiated by the interaction between the rotation speed (166 Hz) of the spindle and aluminium material. These postulations were based on the decay of the vibration energy, which should not exceed the input vibration frequencies, despite the fact that the resonance of the mixture frequency could sporadically increase the frequency. The relatively high frequencies of 683.6 and 1357 Hz in spectrums φC and ψC were steadily mapped to the machine harmonics frequencies of 686 and 1372 Hz with minor shifting. When the drill was at the onset of breaking through the aluminium layer, the collected frequencies were reduced to five distinguished bands (γD–ψD). In the sampled interval of D, only the spectrums θD and λD with frequencies of 166 and 332 Hz, which were consistently produced by the spindle and two-cutting lip dill matched to θC and λC in sampled interval of C. The background noises and interactions between the drilling action and the surroundings were reduced; the resolved frequencies of 39.1 and 117.2 Hz, labelled with spectrum βC and εC in the sampled interval of C, were neglected in sampled interval of D. This is because the two spectrums were produced possibly by the chatter, drillingrelated vibration or the interactions between the cutting tool and the CFRP workpiece layer. This

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postulation was confirmed in the resolved Fourier spectrum of the delegated signal as shown in Fig. 12(b). These two spectrums were dismissed after the tool broke through the aluminium layer.

Fig. 12. Analysis of samples C and D for (a) time-domain response, and (b) Fourier spectrum of delegate signal in the drilling of the Al workpiece layer

3.5Vibration-assisted drilling at the cutting onsets Recalling the sampled intervals (E, F, G and H) of interest presented in Fig. 5(a), the analysis results of the Fourier spectrums in the drilling of the CFRP layer with the EMD technique are shown in Fig. 13. The recorded frequencies were distributed into representative bands of α–χ and matched to the possible mechanical effects. In Fig. 13(a), the most dominant spectrum in the sampled interval of E from the dry run, was the γE band of 58.6 Hz, which reflected a minor shift (17.2%) compared to the input low vibrating frequency (50 Hz). Whereas the signals in the bands of ξE and χE appeared as 390.6 and 791 Hz, which reflected the magnified responses from the spindle

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(390.6 Hz) and the two-cutting-lips drill (791 Hz) under the set revolution of 8488.26 rpm, before engaging with the CFRP workpiece layer. In Fig. 13(b), the sampled interval of F at the cutting onset indicated that all Fourier spectrums of the delegate signal remained the same as those in the interval of E, except the αF band of 19.5 Hz. In comparison with the recorded signals for the spindle and cutting edges in the bands of 400.4 and 800.8 Hz, this spectrum of 19.5 Hz had a relatively high-power intensity which reflected a major drilling action, possibly produced by the chisel edge in the drill point when engaging with the CFRP workpiece material. This assumption was proven in Fig. 13(c), which showed that the responsible spectrum of the chisel edge in the drill point shifted doubly from 19.5 to 39.1 Hz. This phenomenon explained that the initial extrusion action produced by the chisel edge diverted to the actions driven by its two peripheral corners, possibly due to intermittent contacts at the onset of breaking through the CFRP workpiece layer. In addition, the delegate signals for the mechanical actions such as vibrating frequency (γG: 58.6 Hz), responses from the spindle (ξG: 410.2 Hz) and cutting tools (χG: 810.5 Hz), showed very minor shifts of 0, ~5.1 and ~2.4% respectively. In contrast, the recorded spectrums (δG: 87.9 Hz, ζG: 136.7 Hz, and νG: 371.1 Hz) reflected the inconsistent background noises, which were possibly produced by the interactions between the cutting tool, CFRP workpiece and the fixture. This postulation was proven in the next sampled interval of H (Fig. 13(d)); which showed the consistent spectrums connecting to the apparent mechanical effects, such as the effects from the vibration energy, spindle and the cutting tool, but dismissed the background noises of 87.9 to 371.1 Hz. It was obvious that the new recorded bandwidth of 498 Hz (ςH) could accommodate the interactions between the CFRP workpiece layer and the machining fixture, without the cutting tool being involved. It was again identified that the Fourier spectrums were mapped to the mechanical effects on the low vibration frequency (γH: 58.6 Hz); on the initial signals from the spindle and the coupled cutting drill (ξH: 390.6 Hz and χH: 791 Hz); and on the new increased revolution in the spindle (θH: 166 Hz) with the coupled cutting tool (λH: 332 Hz).

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Fig. 13. Analysis of power spectrums for the states of (a) dry run, (b) onset of cutting, (c) onset of breaking-through and (d) retraction of cutting tool in the drilling of the CFRP layer When the drill advanced into the Al workpiece layer, the delegate signals of interest in Fig. 5(a) were those connecting to the mechanical actions at the onset of the changing cutting speed, cutting into the Al workpiece layer, breaking through the Al workpiece layer and retraction of the cutting tool to the dry run state from the sampled intervals of H, I, J and K respectively. Fig. 14 indicates that the mechanical signals were distributed into six distinguished bands (α–χ), with a mixture of cutting actions, since the cutting edges were simultaneously engaged with both workpiece layers. Following the discussion of the power spectrums in the interval of H, Fig. 14(b) shows the decomposed power spectrums in the interval of I, which reflected the mechanical actions at the cutting onset. It was apparent that the repeated dominant spectrums of 19.5 and 58.6 Hz were consistently identified as the background noise (αI) and the low vibration frequency (γI) respectively, which were in line with the results in the interval of A when drilling the CFRP workpiece layer.

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Whereas the power spectrums representing the mechanical actions in the spindle (ξI) and the associated two-lip drill (χI) greatly shifted to 410.2 and 820.3 Hz respectively, compared to the expected spectrums of 141 and 282 Hz. This phenomenon was attributed to the inclined cutting edges simultaneously engaging with the CFRP and Al workpiece layers within the sampled transient. As a result, the produced thrust force signals were derived from a mixture of two distinguished cutting actions; whereby the power spectrums were reassembled to reflect the interaction and interruption amongst the driven cutting tool, the CFRP/Al workpiece layers and the machining fixture. In this case, the spectrum of 107.4 Hz was the one and the only band (εI) accommodated into the interaction/interruption, since it did not consistently match to those bandwidths recorded from each individual layer under steady states. Fig. 14(c) indicates the decomposed six power spectrums (β–χ) when the drill was at the onset of retraction from the CFRP/Al stacks. It was obvious that the dominant power spectrums of 39.1 and 58.6 Hz repeatedly matched to the actions of the intermittent contacts (βJ) at the chisel edge and the applied low vibration frequency (γJ). Whereas the bandwidths of 166 and 664.1 Hz consistently represented the mechanical actions for the spindle (θJ) and the cutting tool (φJ), despite the coupled spectrum (λH) of 332 Hz being dismissed and replaced by the high order bandwidth (φJ: 664.1 Hz). When the drill completely returned to the dry run position, the decomposed power spectrums of the delegate force signals in Fig. 14(d) perfectly matched to the mechanical actions in the interval of the retraction onset. Amongst these delegate signals, the low frequency vibration (γK: 58.6 Hz), spindle driven frequency (θ K: 166 Hz, ξK: 410.2 Hz) and the coupled frequencies (φK: 664.1 Hz, χK: 820.3 Hz) in the cutting tool were perfectly identified. The bands for the interactions amongst the input vibrating energy, cutting tool and workpiece materials were all dismissed.

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Fig. 14. Analysis of power spectrums for the (a) dry run, (b) onset of cutting, (c) onset of retraction and (d) return positions in the drilling of the Al workpiece layer

3.6 Confirmation tests According to the compared results in the EMD, it was apparent that the background noise interacted with the operating parameters, workpiece materials, and machine tool, and then reacted on the recorded cutting forces. Moreover, resolutions of the background noises could fit separately in each material layer because the output responses were influenced by the coupled operating parameters and the associated cutting conditions. In summary, Table 3 presents the decomposed spectra and the associated possible mechanical effects which could suggest the dominant parameters for monitoring the in situ machining quality.

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Table 3 Power spectra and the corresponding mechanical actions Bands of Mean power frequency Delegate mechanical actions spectra (Hz) α 19.5 Single point cutting in the chisel edge of the drill Cutting actions with two peripheral corners in the chisel β 39.1 edge γ 49.7, 58.6 Input vibration frequency of 50 Hz Background noises from the interactions amongst the δ 87.9 cutting tool, CFRP workpiece and the machining fixture Interaction between Al workpiece layer and the cutting ε 107.4, 117.2 tool Background noises from the interactions amongst the ζ 136.7 cutting tool, CFRP workpiece and the machining fixture Revolution (8488.26 rpm) in the spindle when drilling the η 146.5 CFRP workpiece layer Revolution (10,030 rpm) in the spindle when drilling the θ 166 Al workpiece layer Coupled response with the spindle, acting on the cutting κ 283.2 tool when drilling the CFRP workpiece layer Cutting, with the coupled response from the spindle when λ 332 drilling the Al workpiece layer Background noises from the interactions amongst the ν 371.1 cutting tool, CFRP workpiece and the machining fixture 390.6, 400.4, ξ Revolution (8488.26 rpm) in the spindle 410.2, 419.9 Background noises from the interactions between the ς 498 cutting tool and CFRP workpiece layer, without cutting tool being involved. Harmonic vibration, or chattering with the coupled 664, 683.6, φ response from the spindle, acting on the cutting tool when 686 drillingthe Al workpiece layer 791, 810.5, χ 820.3, Cutting, with the coupled response from the spindle 800.8, 839.8 Harmonic vibration, or chattering with the coupled 1357, 1367, ψ response from the spindle, acting on the cutting tool when 1372, 1377 drillingthe CFRP/Al stacks

For the optimisation for the process parameters, a validation test needed to be carried out. Table 4 lists the results obtained in the Taguchi (L9) tests to confirm the findings of the vibration

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parameters and cutting conditions. The recorded thrust forces in the CFRP and Al layers were 74.4 and 133.9 N, respectively, resulting in reductions in the thrust forces by 26.9 and 28.9%, compared to the highest forces in the L9 tests. It is clear that the best combination of parameters was very close to the Test 5 parameter set, with the only difference being in the vibration frequency, which was 55 Hz. In Test 5, the measured thrust forces were 84.7 and 137.7 N in the CFRP and Al layers, respectively; whereas in the confirmation run, the recorded thrust forces were 74.4 and 133.9 N, respectively. The results from the confirmation run proved that when the vibration frequency was reduced from 55 to 50 Hz, the thrust forces were slightly reduced (CFRP: 12.2%; Al: 2.8%), as shown in Fig. 15. The results suggested that the reduction of the assisting energy in terms of vibration frequency was from 55 to 50 Hz, which could reduce the thrust forces in the CFRP layer from 84.7 to 74.4 N, and in the Al layer from 137.7 to 133.9 N. The reduction rates in CFRP and AL layers were 12.2% and 2.8% respectively, which meant that the absorption of the vibration in the Al layer was higher than that in CFRP layer.

Fig. 15. Evolution of thrust forces in Test 5 and confirmation test

Table 4 Results obtained in Taguchi (L9) confirmation run Preferred combination Optimum result Observation of v f z t Estimated Confirmation thrust force (N) C.I. (m/min) (mm/rev) (Hz) (mm) optimum result CFRP layer 150 0.06 50 0.005 88.56 4.68 74.4 (R2: 84.1%) Al layer 200 0.06 50 0.005 142.7 24.68 133.9 (R2: 93.9%) v: cutting speed; f: feed rate; z: frequency; t: amplitude 29

4. Conclusions In this study, an integrated statistical-empirical method is proposed to identify and interpret the force signals into mechanical effects and their interactions with the machine tool and fixation systems. Using the developed analysis method coupled with the designed vibration platform in drilling actions, the collected force signals could be statistically and empirically analysed to identify their effects on the system. This paper reports a novel approach of translating the force signals into mechanical responses. The major analytical and experimental findings are summarised as follows:
The vibration amplitude (PCR: 80.14%) is the most statistically significant factor to obtain the thrust force of the CFRP layer. The best combination of the operating parameter suggested for the thrust forces in the CFRP and aluminium layers yield 26.9% and 28.9% reductions respectively, compared to that in the Taguchi (L9) test array, despite the operating parameters being insignificant in the Al layer.
In the drilling of the CFRP workpiece layer, the re-assembled, delegated signal indicated clear dominant frequencies for the responses (146.5 Hz) of the rotation spindle in the machine tool, cutting tool (283.2 Hz), surrounding noises (683.6/1367 Hz), decay (21.8%) of frequency, and shift (~21.8%) in frequency, reflecting the interactions between the cutting tool and the CFRP composite materials. The background noises (19.5 and 58.6 Hz) showed the most dominant sources with high-power intensities which could interact with the input vibration frequency, drilling actions and the CFRP workpiece material.
When drilling the Al workpiece layer, the decomposed dominant frequencies (166 and 332 Hz) of the rotation spindle and two-cutting-lips drill, surrounding noises (685/1357 Hz), a spectrum shift of ~17.8% from the background noise (58.6 Hz). Similarly, the background noises (39.1 and 58.6 Hz) contributed as the main part of the power intensity, which could trigger chattering and drilling-related vibration in the drilling transient.

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By following the mapping of the Fourier spectrums in the feeding stage (sample area A), to that at the onset of retraction (sample area B), with a perfect match in the drilling of the CFRP layer, the input low vibration frequency (50 Hz) was largely consumed in the cutting action, instead of being absorbed in the CFRP laminate. In the confirmation test, the minor reduction in the vibration frequency (5 Hz) could help in decreasing the reduction (12.2%) in the thrust force.
In the drilling of the Al layer with a low vibration frequency (50 Hz), the force absorption and resulting damping effects could be interrupted and impeded by the intermittent contact, because of the high plasticity in the aluminium material. When the drill was at the onset of breaking through the aluminium layer, the collected frequencies were reduced because the interactions were disregarded between the cutting tool and the workpiece, such as chattering or drillingrelated vibration.

Acknowledgements The authors would like to thank the Ministry of Science and Technology for providing the government funds (MOST-104-2218-E-011-008) throughout this work. In particular, they would like to express their gratitude to the research assistants in the Advanced Composite Manufacturing Research Group for their support in the experimental works.

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Fig. 1. Design of (a) vibration-assisted fixtures and CFRP/Al stacks in (b) strip and (c) plate forms

Fig. 2. Machining set-up for drilling of CFRP/Al stack for (a) force measurement, and (b) vibration frequency and amplitude measurements

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Original time series data set x(t) Shifting process

Define candidate IMF as IMFn

Draw upper and lower envelopes by cubic splines

Replace x(t) by x(t) - IMF

Substrate the average of the upper and lower envelopes from x(t)

Go through shifting process to find IMFn+1

Retrieve a candidate IMF

IMF oscillates? Match stopping criteria ?

Yes

No

Yes Keep finding the next IMF

Define this IMF as Residual

No

Replace x(t) by x(t) – candidate IMF

Complete the decomposition m

x ( t ) = ∑ IMFn + Re sidual n =1

Fig. 3. Flowchart of empirical mode decomposition (EMD)

Fig. 4. Example of empirical mode decomposition (EMD): (a) finding local maxima and local minima, (b) defining mean envelope by averaging the upper and lower envelopes, (c) subtracting the original signal from the mean envelope to retrieve IMF1, and (d) repeating procedures from (a) to (c) to retrieve IMF2 35

Fig. 5. Measurement of cutting forces when cutting tool is in (a) sampled intervals in CFRP/Al stack workpiece, (b) full engagement, (c) breaking through the CFRP layer, (d) full engagement, and (e) breaking through the Al layer

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Fig. 6. Evolution of thrust forces in (a) CFRP layer, and (b) Al layer in Taguchi (L9) tests

Fig. 7. (a) Main effect plots, and (b) ANOVA for thrust force in Taguchi (L9) tests 37

Fig. 8. Measurement of sample area A for (a) time domain response and (b) Fourier spectrum

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Fig. 9. Intrinsic mode functions and residual of sample A

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Fig. 10. (a) Time domain response, and (b) Fourier spectrum of delegate signal without drilling

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Fig. 11. Analysis of samples A and B for (a) time-domain response, and (b) Fourier spectrum of delegate signal in the drilling of the CFRP workpiece layer

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Fig. 12. Analysis of samples C and D for (a) time-domain response, and (b) Fourier spectrum of delegate signal in the drilling of the Al workpiece layer

Fig. 13. Analysis of power spectrums for the states of (a) dry run, (b) onset of cutting, (c) onset of breaking-through and (d) retraction of cutting tool in the drilling of the CFRP layer

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Fig. 14. Analysis of power spectrums for the (a) dry run, (b) onset of cutting, (c) onset of retraction and (d) return positions in the drilling of the Al workpiece layer

Fig. 15. Evolution of thrust forces in Test 5 and confirmation test

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Table 1 Taguchi (L9) test array Cutting speed in Test No. CFRP/Al (m/min) 1 130/200 2 130/200 3 130/200 4 150/200 5 150/200 6 150/200 7 170/200 8 170/200 9 170/200

Feed rate (mm/rev) 0.04 0.06 0.08 0.04 0.06 0.08 0.04 0.06 0.08

Frequency (Hz) 45 50 55 50 55 45 55 45 50

Amplitude (mm) 0.005 0.02 0.05 0.05 0.005 0.02 0.02 0.05 0.005

Table 2 Mean frequency and power percentage of each IMF in Sample A Channel IMF1 IMF2 IMF3 IMF4 IMF5 IMF6 IMF7 IMF8 IMF9 Residual

Mean Freq. (Hz) 14576.69 6960.325 3373.946 1480.787 768.5098 431.1153 181.1934 62.48047 24.99219 6.248047

Power (%) 24.11225 8.537633 5.529729 6.812059 6.498698 2.116719 3.898338 23.35 19.14457 —

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Table 3 Power spectra and the corresponding mechanical actions Bands of Mean power frequency Delegate mechanical actions spectra (Hz) α 19.5 Single point cutting in the chisel edge of the drill Cutting actions with two peripheral corners in the chisel β 39.1 edge γ 49.7, 58.6 Input vibration frequency of 50 Hz Background noises from the interactions amongst the δ 87.9 cutting tool, CFRP workpiece and the machining fixture Interaction between Al workpiece layer and the cutting ε 107.4, 117.2 tool Background noises from the interactions amongst the ζ 136.7 cutting tool, CFRP workpiece and the machining fixture Revolution (8488.26 rpm) in the spindle when drilling the η 146.5 CFRP workpiece layer Revolution (10,030 rpm) in the spindle when drilling the θ 166 Al workpiece layer Coupled response with the spindle, acting on the cutting κ 283.2 tool when drilling the CFRP workpiece layer Cutting, with the coupled response from the spindle when λ 332 drilling the Al workpiece layer Background noises from the interactions amongst the ν 371.1 cutting tool, CFRP workpiece and the machining fixture 390.6, 400.4, ξ Revolution (8488.26 rpm) in the spindle 410.2, 419.9 Background noises from the interactions between the ς 498 cutting tool and CFRP workpiece layer, without cutting tool being involved. Harmonic vibration, or chattering with the coupled 664, 683.6, φ response from the spindle, acting on the cutting tool when 686 drillingthe Al workpiece layer 791, 810.5, χ 820.3, Cutting, with the coupled response from the spindle 800.8, 839.8 Harmonic vibration, or chattering with the coupled 1357, 1367, ψ response from the spindle, acting on the cutting tool when 1372, 1377 drillingthe CFRP/Al stacks

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Table 4 Results obtained in Taguchi (L9) confirmation run Preferred combination Optimum result Observation of v f z t Estimated Confirmation thrust force (N) C.I. (m/min) (mm/rev) (Hz) (mm) optimum result CFRP layer 150 0.06 50 0.005 88.56 4.68 74.4 (R2: 84.1%) Al layer 200 0.06 50 0.005 142.7 24.68 133.9 (R2: 93.9%) v: cutting speed; f: feed rate; z: frequency; t: amplitude

46