- Email: [email protected]
Using two-dimensional vibration cutting for micro-milling
International Journal of Machine Tools & Manufacture 46 (2006) 659–666 www.elsevier.com/locate/ijmactool
Using two-dimensional vibration cutting for micro-milling Gwo-Lianq Chern*, Yuan-Chin Chang Department of Mechanical Engineering, National Yunlin University of Science and Technology, 123 University Road, Sec. 3, Touliu, Yunlin 640, Taiwan, ROC Received 10 March 2005; accepted 5 July 2005 Available online 19 August 2005
Abstract The purpose of this paper is to investigate the effects of assisted vibration cutting (VC) on the micro-milling quality of aluminum alloy Al 6061-T6. The desired vibration is proposed from the workpiece side by a two-dimensional vibrating worktable we developed. The slot produced by end milling is studied by examining its geometrical shape and machining accuracy. Through extensive experiments with end mills of diameter 1 mm, we found that slot oversize, displacement of slot center and slot surface roughness could be improved by imposing VC. The employment of VC increases the number of slots produced within the tolerance when high amplitude and proper frequency are imposed. With the help of Taguchi method and analysis of variance (ANOVA), we analyzed the effect of VC in end milling by investigating the slot-width accuracy. It is found that the use of second directional VC to minimize slot-width oversize in end milling is helpful. q 2005 Elsevier Ltd. All rights reserved. Keywords: Vibration cutting; Micro-milling; End-milling; Vibrating worktable
1. Introduction Precision machining plays an important role in manufacturing. Milling process is one of the most commonly used metal removal operations in industry. It is based on interrupted cutting which is very susceptible to vibrations. Problems associated with vibrations in machining are more serious when small-diameter end mills are employed. In that case, the tool deformation is prominent and it deteriorates the stability in a machining process. Excessive deflection of a micro end mill may cause tolerance violations and poor surface roughness [1]. Precision machining is hard to achieve in this case and hence the machining technology must be improved. Vibration cutting (VC) is a cutting method in which periodical vibration is imposed to the cutting tool or the workpiece, besides the original relative motion between these two, to obtain better cutting performance. The fundamental feature of VC is that the tool face is separated from the workpiece repeatedly. This technique had been firstly employed in the precision drilling of wood [2–3] * Corresponding author. Tel.: C886 5 5342601x4145; fax: C886 5 5312062. E-mail address: [email protected] (G.-L. Chern).
0890-6955/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2005.07.006
and low carbon steel [4]. Ultraprecision ductile cutting of glass could be obtained by applying ultrasonic vibration in the cutting direction [5]. Zhou et al. [6] pointed out that the cutting force in ultrasonic VC will be reduced due to the effect of dynamic friction and aerodynamic lubrication. The method of ultrasonic VC had also been applied to the turning of machinable glass ceramics [7], and the diamond turning of stainless steel [8]. Besides ultrasonic VC, low frequency VC has been found to prolong tool life and help reduce burr sizes in drilling [9,10]. Adachi et al. [9] developed an electrohydraulic servo system to cause VC of 100 Hz in the spindle of an NC vertical milling machine. Through their experimental studies on drilling of aluminum, they found that burr size could be reduced considerably with the assistance of VC. Chern and Lee [11] developed a vibrating worktable in drilling to create the desired vibration (of a maximum of 10 KHz) from the workpiece side. They found that hole oversize, displacement of the hole center and surface roughness of the drilled wall could be improved with the increase of vibrating frequency and amplitude. The researches mentioned above employed only onedimensional VC. Shamoto and Moriwaki [12,13] proposed an ‘elliptical vibration cutting’. Synchronized two-dimensional vibration is applied to the cutting edge in the plane containing the cutting direction and the chip flow direction in such a way that the cutting edge forms an elliptical locus
660
G.-L. Chern, Y.-C. Chang / International Journal of Machine Tools & Manufacture 46 (2006) 659–666
in each cycle of the vibration. Two piezoelectric plates with some phase shift were employed, causing an about 20 KHz vibration. Their experimental results, conducted on a turning machine, showed that the diamond cutting on hardened steel can be carried out successfully by applying elliptical VC. The effect of ultrasonic elliptical VC on machining accuracy in turning has also been analyzed theoretically [14]. It has been found that the heat generated during VC is reduced effectively [15]. Also, the friction of the tool and work material can be reduced accordingly by the formation of oxide films on the tool rake face. The decreased cutting force makes the chip thinner. Xiao et al. [16] pointed that VC has a chatter-suppressing dynamics while conventional cutting is a chatter-generating one, meaning that VC has a higher cutting stability as compared with conventional cutting. Thus, overall machining quality is improved with VC. From these researches, it can be concluded that VC is an effective method to be utilized in a machining operation. However, VC has not yet been employed in the field of micro-milling. In this paper, a two-dimensional vibrating worktable was designed and manufactured. VC is produced from the workpiece side, and no modification is needed on the machining center or the milling machine when utilizing the vibrating worktable. Micro-amplitude vibration is produced in the worktable via piezo-electrical materials in order to achieve better cutting performance. With the help of Taguchi method and analysis of variance, the effect of VC on slot-width accuracy is investigated. The experimental results and discussions are presented.
2. Experimental equipments and method Piezoelectric actuators feature the characteristics of good precision, fast response and large driving force. In this paper, VC is realized by employing piezoelectric actuators in conjunction with the relatively simple designed structure for generating the desired two-dimensional vibration. We first made a two-dimensional vibrating worktable containing two piezoelectric actuator and two linear guideways, as shown schematically in Fig. 1. The vibrating worktable serves two purposes: (1) to clamp the workpiece; and (2) to produce the desired vibration in the horizontal X and Y directions. It is composed of: (A) workpiece-holding block, (B) linear guideway, (C) piezoelectric actuator, (D) adapting plate, (E) spring, and (F) base block. The workpiece-holding block (A) is to clamp the workpiece during milling experiments. Two Physik Instrumente (PI)-made piezoelectric actuator (PI model P-244.10) and two linear guideways are employed in the worktable. P-244.10, having a maximum operating frequency of 16 KHz and a maximum traveling distance of 10 mm, is cooperated with a two-channel high power amplifier (PI model P-270.02) and a waveform generator (HP-33120A) to
Fig. 1. Schematic illustration of vibrating worktable.
produce the desired vibration. The maximum pushing force of P-244.10 is 2000 N. The output voltage of P-270.02 is from 0 to K1000 V. Its peak current is 50 mA. The linear guideway can ensure uni-axial motion of P-244.10 when VC is applied. Piezoelectric actuators are arranged perpendicularly. Two-dimensional vibration of the workpiece-holding block is realized by these two piezoelectric actuators through the adapting plate (D). The spring (E) is to provide the necessary preload for P-244.10, since the piezoelectric actuator is very brittle and can only withstand a maximum pulling force of 300 N. Photo of the vibrating worktable is shown in Fig. 2. Other experimental equipments are described as follows: 1. Machining center (MC-1050P, Mitsubishi-520AM controller). the range of the spindle speed is from 45 to 6000 rpm. 2. Laser displacement meter (Keyence LC-2430). the sampling rate of this sensor is 50 KHz; the resolution is 0.01 mm and the laser beam spot is 12 mm. Vibration amplitude of the workpiece was measured by this highaccuracy instrument. 3. Toolmakers’ microscope (Olympus, MM-11). to observe the machined surfaces. It possesses a maximum magnification of 200 times. 4. Surface roughness measuring machine (Talyround, series2). to measure the surface roughness of the workpiece after end milling.
Fig. 2. Photo of vibrating worktable.
G.-L. Chern, Y.-C. Chang / International Journal of Machine Tools & Manufacture 46 (2006) 659–666
661
Table 2 Machining condition of uniaxial VC experiment Spindle speed (rpm) Frequency (Hz) Amplitude (mm) Feed (mm/tooth) Depth of cut (mm) Cutting fluid
Fig. 3. Micro-milling experiments.
5. Two-flute end mill. standard, made of high speed steel (HSS), with a diameter of 1 mm, a flute length of 5 mm, a helix angle of 308. Shank diameter is 6 mm. 6. Work material. aluminum alloy Al 6061-T6 was tested. To get reliable data, the workpieces were cut and polished to precise pieces (42 mm!20 mm!8 mm) before test. 7. Cutting fluid. mineral oil The micro-milling experiments were carried out, producing a slot on the workpiece after each cut, as shown in Fig. 3. Length of each slot is fixed at 10 mm. Each combination of machining parameters is tested four times. There are several methods to evaluate the quality of a machined workpiece after end milling. The method of analysis is stated as follows. 2.1. Tool-wear experiment The purpose of the experiment is to investigate the influence of VC on tool life in end milling. Number of slots produced by an end mill before out-of-tolerance slot is created can be regarded as a measurement of tool life. Since the diameter of the end mill is 1 mm, the threshold of the slot width determining tool life is chosen as 1 mm. The machining condition is summarized in Table 1. Vibrating frequencies chosen were 0, 500 Hz, 1 and 10 kHz. Vibrating amplitudes varied from 0, 4, 7, to 10 mm. Here, 0 Hz or 0 mm means that no vibration is imposed. Hundred slots were created for each machining condition. 2.2. Uniaxial VC experiment The purpose the uniaxial VC experiment is to investigate the influence of VC on machining accuracy in end milling. Table 1 Machining condition of tool-wear experiment Spindle speed (rpm) Frequency (Hz) Amplitude (mm) Feed (mm/tooth) Depth of cut (mm) Cutting fluid
1500 0, 500, 1 k, 10 k 0, 4, 7, 10 5 0.3 Mineral oil
1000, 2000, 3000 600 10 2.5, 5, 7.5 0.3 Mineral oil
Width of milled slot and displacement of slot center were used to represent the dimensional accuracy of end milling. Slot-width oversize due to tool runout and tool deviation from excessive cutting force should be kept at minimum. One-directional VC experiment was carried out. Vibration amplitude of 10 mm and frequency of 600 Hz were applied along the tool feed motion (Y-axis, as shown in Fig. 3) if VC was applied. The machining condition is summarized in Table 2. 2.3. Biaxial VC experiment The machining condition in the biaxial VC experiment is the same as the one shown in Table 2, except that now the VC is applied in both X and Y directions, as shown in Fig. 3. Vibration frequency in the X direction is set at 600 Hz. Since the employment of VC in the X direction directly increases the slot width produced in end milling, the vibrating amplitude is chosen as low as 1 mm to minimize the undesirable side effect. We would like to know if the use of biaxial VC is appropriate. 2.4. Biaxial VC experiment using Taguchi method There were many parameters involved in the experiments and thus in this paper we employed Taguchi method to deal with responses influenced by multi-variables. Taguchi used signal-to-noise (S/N) ratio as the quality characteristics of the choice of parameters. To obtain better machining accuracy and to minimize slot-width error, we should look for ‘smaller-the-better’ characteristic in which S/N can be expressed as S 1 X 2 ZK10 log y N n where n is the number of experiments and y is the measured data. The analysis of variance (ANOVA) is then carried out to analyze the effect of the process parameters. Based on ANOVA, the contribution ratio of each parameter can be determined and thus optimal combination of the parameters can be obtained. More detailed description about utilizing the Taguchi method for the planning of experiments can be found in the references [17,18] and is not summarized in this paper. We used the L18 orthogonal array to analyze their effects. The process parameters chosen are: (A) amplitude in X direction, (B) frequency in X direction, (C) spindle speed,
662
G.-L. Chern, Y.-C. Chang / International Journal of Machine Tools & Manufacture 46 (2006) 659–666
Table 3 Machining parameters and their levels in biaxial VC experiments Param.
1 2 3
(A) X-amplitude (mm)
(B) X-frequency (Hz)
(C) spindle speed (rpm)
(D) feed (mm/tooth)
(E) Y-frequency (Hz)
(F) Y-amplitude (mm)
0 1 –
100 1K 10 K
1000 2000 3000
2.5 5 7.5
100 1K 10 K
4 7 10
(D) feed, (E) frequency in Y direction, and (F) amplitude in Y direction, while the response function is the slot width. The range and number of levels of the parameters are selected as given in Table 3. The experimental layout for the machining parameters is shown in Table 4. It is noted that there is one parameter (A) at 2 levels and other five parameters at 3 levels. Only 18 experiments are needed to study the entire machining parameters using the L18 orthogonal array.
3. Results and discussions 3.1. Tool-wear experiment The numbers of slots produced within the threshold (1 mm) with respect to different vibrating amplitudes and frequencies are listed in Table 5. It is found that the employment of VC increases the number of slots produced within the tolerance. ‘Tool life’ is only 80 without VC. Such number increases to 98 under 500 Hz and 10 mm, an improvement of about 22%. We also note that higher frequencies have a negative effect on tool life, as found in the previous study [11]. Also, the chipping might be caused by the colliding or rubbing between the end mill and the workpiece. Thus, the number of slot that can be machined Table 4 Experimental layout showing levels of machining parameters No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
by an end mill under a certain machining condition tends to decrease when high frequency is imposed. The amplitude in VC directly influences the gap between the workpiece and the tool. The increase of the gap allows more cutting fluids to carry away the heat generated during milling. Thus tool life is enhanced at higher amplitudes, as seen in Table 5. 3.2. Uniaxial VC experiment A typical variation of slot width with respect to different spindle speeds is shown in Fig. 4. The feed is 5 mm/tooth. It can be seen that the slot width decreases when VC is applied. The slot-width oversize is improved in the experiment. The average value of slot-width oversize is 8 mm without VC, while such value drops to only 6 mm with VC. VC attributes to the rapid separation between the tool and the workpiece. This helps to reduce the heat generated during end milling, and the machining performance is improved. The runout of end mill in operation is reduced and the slot-width oversize is decreased accordingly. Fig. 5 shows the variation of slot positioning accuracy with respect to different spindle speeds when feed equals 2.5 mm/tooth. It is very clear that the use of VC decreases the positioning error (displacement of slot center) effectively. The average value of slot positioning error is 20 mm without VC, while such value drops to only 10 mm with VC. Table 5 Number of slots under different vibrating amplitudes and frequencies (feedZ5 mm/tooth, depth of cut Z0.3 mm, spindle speed Z1500 rpm)
Param. A
B
C
D
E
F
1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
1 2 3 1 2 3 2 3 1 3 1 2 2 3 1 3 1 2
1 2 3 2 3 1 1 2 3 3 1 2 3 1 2 2 3 1
1 2 3 2 3 1 3 1 2 2 3 1 1 2 3 3 1 2
1 2 3 3 1 2 2 3 1 2 3 1 3 1 2 1 2 3
Amp.
Freq.
4 mm 7 mm 10 mm
500 (Hz)
1 (kHz)
10 (kHz)
95 97 98
91 94 96
87 91 90
no vibration with vibration slot width (mm)
Level
1.012 1.008 1.004 1
0
1000
2000 3000 spindle speed (rpm)
4000
Fig. 4. Variation of slot width vs. spindle speed in uniaxial VC (5 mm/tooth) .
G.-L. Chern, Y.-C. Chang / International Journal of Machine Tools & Manufacture 46 (2006) 659–666
no vibration with vibration
0.03
0.03
0.02 0.01 0
0
1000
2000 3000 spindle speed (rpm)
4000
The positioning accuracy is strongly related to the cutting force occurred in an end milling process. The reduced cutting force under the assistance of VC causes less positioning error, as can be seen in Fig. 5. 3.3. Biaxial VC experiment Fig. 6 shows the variation of slot width with respect to different spindle speeds for feed equals 5 mm/tooth. We found that the average value of slot-width oversize was 5 mm with biaxial VC, even better than 6 mm obtained in uniaxial VC. Similar results were obtained for feed equals 2.5 and 7.5 mm/tooth. In these tests, we found that the average slot-width oversize was contained within 4.5–5 mm under biaxial VC. This means that the introduction of second directional VC (of amplitude 1 mm) does slightly improve the slot-width accuracy. Fig. 7 shows the variation of slot positioning accuracy with respect to different spindle speeds when feed equals 2.5 mm/tooth. We found that the average value of positioning error to be 5 mm with biaxial VC, even better than 10 mm obtained in uniaxial VC. This suggests that the employment of biaxial VC can prevent the deviation of miniature end mill in operation due to more evenly distributed and reduced cutting forces. Fig. 8 shows two typical photos of machined specimens taken from the entrance side, without and with VC. The comparison of the milling quality is very clear. Without VC in Fig. 8(a), large cutting forces tend to bend the miniature tool and cause geometrical error in the slot shape. Burrs are prominent on the right side of slot where cutting velocity is pointed outward from the workpiece. Some burrs can also
slot width (mm)
no vibration with vibration 1.012 1.008 1.004 0
1000
2000 3000 spindle speed (rpm)
0.02 0.01 0
Fig. 5. Variation of positioning accuracy vs. spindle speed in uniaxial VC (2.5 mm/tooth).
1
accuracy (mm)
accuracy (mm)
no vibration with vibration
663
4000
Fig. 6. Variation of slot width vs. spindle speed in biaxial VC (5 mm/tooth).
0
1000
2000 3000 spindle speed (rpm)
4000
Fig. 7. Variation of ositioning accuracy vs. spindle speed in biaxial VC (2.5 mm/tooth).
be found along the bottom edge. On the contrary, when uniaxial VC was imposed, perfect rectangular shape can be obtained with the help of VC, as shown in Fig. 8(b). Burrs are less serious and more evenly distributed along the edges. Fig. 9 shows two photos of machined chips collected during the experiments, without and with VC. Even though the chip thicknesses were not measured in the experiments, due to limited available equipments and reliable measuring methods, we could still qualitatively compare their difference. For no VC in Fig. 9(a), much thicker chips can be found, suggesting that the cutting force is larger. When biaxial VC is applied, chips of thinner and segmented shape can be seen in Fig. 9(b). It is evident that cutting force is less in this case due to the assistance of VC, leading to better machining accuracy. Rapid separation between the tool and the workpiece in VC provides excellent chip-removal condition during end milling. The reduction of cutting force causes better positioning accuracy of the machined slot, as can be seen in Figs. 5 and 7. Also, the reduced cutting force becomes more stable and uniform during each revolution when chip removal is easy. As a result, the fluctuation of radial force during cutting decreases. Thus, the tool runout is also retarded and the slot width becomes more accurate, as can be seen in Figs. 4 and 6. Fig. 10 shows three photos of machined surfaces, taken by the toolmakers’ microscope. Their milling qualities are very easy to recognize. Without vibration in Fig. 10(a), large feed marks as well as some scratches and irregularities appear on the slot bottom surface. When the chips could not be carried away effectively, the highly-hardened chips could easily damage the machined surface. When uniaxial VC is applied in Fig. 10(b), the tool feed marks are leveled off since rapid vibration occurs on the plane. Even better surface finish can be obtained when biaxial VC is imposed, as shown in Fig. 10(c). The surface roughness on both vertical sides of slot is also important in end milling. To measure the surface roughness in those areas, the workpieces must be cut properly by wire-EDM first. Fig. 11 shows the measuring results, without and with VC. For no VC in Fig. 11(a), the roughness (Ra) on the slot side surface is 1.3017 mm. When
664
G.-L. Chern, Y.-C. Chang / International Journal of Machine Tools & Manufacture 46 (2006) 659–666
Fig. 8. Photos showing machined slots: (a) without, and (b) with VC (5 mm/tooth, 2000 rpm).
Fig. 9. Photos (!50) showing machined chips: (a) without, and (b) with biaxial VC.
uniaxial VC is applied, such value drops to 0.9141 mm, as shown in Fig. 11(b). The improvement ratio is about 30%. 3.4. Biaxial VC experiment using Taguchi method The objective of the experiment is to optimize the parameters to get smaller slot width in end milling with biaxial VC. The S/N ratio can be computed by the actual slot width measured after end milling. The response table for S/N ratio is shown in Table 6. We can predict the optimal
combination of machining parameters to be A2 (1 mm), B2 (1 kHz), C1 (1000 rpm), D2 (5 mm/tooth), E2 (1 kHz), and F3 (10 mm) by selecting the largest value of S/N ratio for each parameter. The results of ANOVA are given in Table 7. Contribution ratio, P, of each parameter can be determined in the table. It is found that vibrating amplitude in Y direction (F) has a dominant effect in biaxial VC, of more than 40% in contribution ratio. Vibration frequency in Y direction (E) also has some influence on the slot width, of about 21% in
Fig. 10. Photos (!20) showing machined surfaces: (a) without VC, (b) with uniaxial VC, and (c) with biaxial VC.
Fig. 11. Roughness of slot side surface: (a) without, and (b) with VC (5 mm/tooth, 2000 rpm).
G.-L. Chern, Y.-C. Chang / International Journal of Machine Tools & Manufacture 46 (2006) 659–666
B
C
D
E
F
42.62 45.59
44.52 44.72 43.07 B2
45.37 43.78 43.16 C1
43.36 45.09 43.86 D2
41.53 45.96 44.82 E2
40.22 45.81 46.29 F3
A2
Table 7 ANOVA in biaxial VC experiments Param.
Sum of squares, S
Degree of freedom, f
Variance, V
Contribution ratio, P (%)
A B C D E F Total
34.544 11.921 37.277 31.406 64.575 124.364 304.087
1 2 2 2 2 2 11
34.54 5.96 18.64 15.70 32.29 62.18
11.4 3.9 12.3 10.3 21.2 40.9 100
Table 8 Machining condition of further VC experiment Spindle speed (rpm) Frequency (Hz) Amplitude (mm) Feed (mm/tooth) Depth of cut (mm) Cutting fluid
1000 X: 1 K; Y: 0, 100, 1 K, 10 K X: 1; Y: 0, 4, 7, 10 5 0.3 Mineral oil
contribution ratio. P for spindle speed (C) and feed (D) are 12.3 and 10.3%, respectively. Since A (amplitude in X direction) in the optimal combination is other than 0 mm (no vibration), it suggests that the use of second directional vibration to minimize slot-width oversize in end milling is helpful. The contribution ratio of amplitude in X direction is 11.4%, as shown in Table 7. To validate the finding of this analysis, confirming experiment was conducted with the optimal level of machining parameters: A2, B2, C1, D2, E2, and F3. The average measured slot-width oversize of this optimum combination was 3.8 mm, even lower than the smallest one (4.5 mm) in the biaxial VC experiment. It has been shown that machining parameters chosen at their optimum levels can ensure significant improvement in the slot-width accuracy in biaxial VC.
1.009 1.008 1.007 1.006 1.005 1.004 1.003 1.002 1.001 1 –0.001
0.001
0.003 0.005 0.007 amplitude (mm)
0.009
0.011
Fig. 12. Variation of slot width vs. amplitude (5 mm/tooth, 1000 rpm, Y: 1 KHz).
slot width (mm)
1 2 3 Optimal
A
slot width (mm)
Table 6 Response table for S/N ratio in biaxial VC experiments
665
1.009 1.008 1.007 1.006 1.005 1.004 1.003 1.002 1.001 1
0
100 1K frequency (Hz)
10K
Fig. 13. Variation of slot width vs. frequency (5 mm/tooth, 1000 rpm, Y: 10 mm).
amplitudes. It can be seen that larger amplitudes tend to reduce the slot-width oversize. Larger amplitudes in VC create more room for the separation between the tool and the workpiece, and more lubricant can reach the cutting edge and carry away the heat generated during machining. Thus, cutting force can be reduced and slot-width oversize can be prevented effectively. Fig. 13 shows the variation of slot width with respect to different vibrating frequencies. At first, slot width seems to be reduced with the increase of frequency. But slot widths at 10 kHz were slightly larger than those at 1 kHz and we obtained a minimum of slot-width oversize at 1 kHz. It seems that the use of vibration at high frequency, such as 10 kHz in the experiment, cannot effectively improve the machining accuracy. Similar results of the influence of vibrating frequency on machining accuracy had also been studied in micro-drilling with VC [11].
3.5. Influence of vibrating amplitude and frequency
4. Conclusions
To investigate the effects of vibrating amplitude and frequency on slot-width oversize, some further experiments were carried out. Table 8 shows the machining condition. Since vibration in the X direction would naturally increase slot width, we kept the X-directional amplitude and frequency at 1 mm and 1 kHz, respectively. Fig. 12 shows the variation of slot width with respect to different vibrating
In this paper, we developed a two-dimensional vibrating worktable with the desired vibration created from the workpiece side. Form this research, we draw three conclusions: 1. Through extensive experiments, we found that slot oversize, displacement of slot center and slot surface
666
G.-L. Chern, Y.-C. Chang / International Journal of Machine Tools & Manufacture 46 (2006) 659–666
roughness could be improved by imposing VC during end milling. 2. It is found that the employment of VC increases the number of slots produced within the tolerance when high amplitude and proper frequency are imposed. Higher frequencies have a negative effect on tool life. 3. Based on the Taguchi method and ANOVA, we found that vibrating amplitude in feed direction has a dominant effect of more than 40% in contribution ratio, while its associated frequency has some influence on slot-width accuracy of about 21% in contribution ratio. The use of second directional VC to minimize slot-width oversize in end milling is helpful. References [1] E.B. Kivanc, E. Budak, Structural modeling of end mills for form error and stability analysis, Int. J. Mach. Tools Manuf. 44 (2004) 1151–1161. [2] J. Kumabe, T. Sabuzawa, Study on the precision drilling of wood (1st report) - profile analysis of drilled hole, J. JSPE, 37 (2) (1971) 98-104 (in Japanese). [3] J. Kumabe, T. Sabuzawa, Study on the precision drilling of wood (2nd report)—drilling force and its accuracy, J. JSPE 38 (5) (1972) 456– 461 (in Japanese). [4] T. Koyama, K. Adachi, K. Murakami, Study on vibratory drilling (2nd Report)—comparison of conventional drilling with vibratory drilling, J. JSPE 43 (1) (1977) 55–60 (in Japanese). [5] T. Moriwaki, E. Shamoto, K. Inoue, Ultraprecision ductile cutting of glass by applying ultrasonic vibration, Ann. CIRP 41 (1) (1992) 141–144.
[6] M. Zhou, X.J. Wang, B.K.A. Ngoi, J.G.K. Gan, Brittle-ductile transition in the diamond cutting of glasses with the aid of ultrasonic vibration, J. Mater. Process. Technol. 121 (2002) 243–251. [7] H. Weber, J. Herberger, R. Pilz, Turning of machinable glass ceramics with an ultrasonically vibrated tool, Ann. CIRP 33 (1) (1984) 85–87. [8] T. Moriwaki, E. Shamoto, Ultraprecision diamond turning of stainless steel by applying ultrasonic vibration, Ann. CIRP 40 (1) (1991) 559– 562. [9] K. Adachi, N. Arai, S. Harada, K. Okita, S. Wakisaka, A study on burr in low frequency vibratory drilling—drilling of aluminum, Bull. JSPE 21 (4) (1987) 258–264. [10] H. Takeyama, S. Kato, Burrless drilling by means of ultrasonic vibration, Ann. CIRP 40 (1) (1991) 83–86. [11] G.L. Chern, H.J. Lee, Using workpiece vibration cutting for microdrilling, Int. J. Adv. Manuf. Tech., DOI: 10.1007/s00170-004-2255-8, to appear in 2005. [12] E. Shamoto, T. Moriwaki, T. Study, on elliptical vibration cutting, Ann. CIRP 43 (1) (1994) 35–38. [13] E. Shamoto, T. Moriwaki, Ultraprecision diamond cutting of hardened steel by applying elliptical vibration cutting, Ann. CIRP 48 (1) (1999) 441–444. [14] C.X. Ma, E. Shamoto, T. Moriwaki, L.J. Wang, Study of machining accuracy in ultrasonic elliptical vibration cutting, Int. J. Mach. Tools Manuf. 44 (2004) 1305–1310. [15] M. Jin, M. Murakawa, Development of a practical ultrasonic vibration cutting tool system, J. Mat. Process. Technol. 113 (2001) 342–347. [16] M. Xiao, K. Sato, S. Karube, T. Soutome, The effect of tool nose radius in ultrasonic vibration cutting of hard metal, Int. J. Mach. Tools Manuf. 43 (2003) 1375–1382. [17] P.M. George, B.K. Raghunath, L.M. Manocha, A.M. Warrier, E.D.M. machining, of carbon-carbon composite - a Taguchi approach, J. Mater. Process. Technol. 145 (2004) 66–71. [18] J.A. Ghani, I.A. Choudhury, H.H. Hassan, Application of Taguchi method in the optimization of end milling parameters, J. Mater. Process. Technol. 145 (2004) 84–92.
Using two-dimensional vibration cutting for micro-milling Gwo-Lianq Chern*, Yuan-Chin Chang Department of Mechanical Engineering, National Yunlin University of Science and Technology, 123 University Road, Sec. 3, Touliu, Yunlin 640, Taiwan, ROC Received 10 March 2005; accepted 5 July 2005 Available online 19 August 2005
Abstract The purpose of this paper is to investigate the effects of assisted vibration cutting (VC) on the micro-milling quality of aluminum alloy Al 6061-T6. The desired vibration is proposed from the workpiece side by a two-dimensional vibrating worktable we developed. The slot produced by end milling is studied by examining its geometrical shape and machining accuracy. Through extensive experiments with end mills of diameter 1 mm, we found that slot oversize, displacement of slot center and slot surface roughness could be improved by imposing VC. The employment of VC increases the number of slots produced within the tolerance when high amplitude and proper frequency are imposed. With the help of Taguchi method and analysis of variance (ANOVA), we analyzed the effect of VC in end milling by investigating the slot-width accuracy. It is found that the use of second directional VC to minimize slot-width oversize in end milling is helpful. q 2005 Elsevier Ltd. All rights reserved. Keywords: Vibration cutting; Micro-milling; End-milling; Vibrating worktable
1. Introduction Precision machining plays an important role in manufacturing. Milling process is one of the most commonly used metal removal operations in industry. It is based on interrupted cutting which is very susceptible to vibrations. Problems associated with vibrations in machining are more serious when small-diameter end mills are employed. In that case, the tool deformation is prominent and it deteriorates the stability in a machining process. Excessive deflection of a micro end mill may cause tolerance violations and poor surface roughness [1]. Precision machining is hard to achieve in this case and hence the machining technology must be improved. Vibration cutting (VC) is a cutting method in which periodical vibration is imposed to the cutting tool or the workpiece, besides the original relative motion between these two, to obtain better cutting performance. The fundamental feature of VC is that the tool face is separated from the workpiece repeatedly. This technique had been firstly employed in the precision drilling of wood [2–3] * Corresponding author. Tel.: C886 5 5342601x4145; fax: C886 5 5312062. E-mail address: [email protected] (G.-L. Chern).
0890-6955/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2005.07.006
and low carbon steel [4]. Ultraprecision ductile cutting of glass could be obtained by applying ultrasonic vibration in the cutting direction [5]. Zhou et al. [6] pointed out that the cutting force in ultrasonic VC will be reduced due to the effect of dynamic friction and aerodynamic lubrication. The method of ultrasonic VC had also been applied to the turning of machinable glass ceramics [7], and the diamond turning of stainless steel [8]. Besides ultrasonic VC, low frequency VC has been found to prolong tool life and help reduce burr sizes in drilling [9,10]. Adachi et al. [9] developed an electrohydraulic servo system to cause VC of 100 Hz in the spindle of an NC vertical milling machine. Through their experimental studies on drilling of aluminum, they found that burr size could be reduced considerably with the assistance of VC. Chern and Lee [11] developed a vibrating worktable in drilling to create the desired vibration (of a maximum of 10 KHz) from the workpiece side. They found that hole oversize, displacement of the hole center and surface roughness of the drilled wall could be improved with the increase of vibrating frequency and amplitude. The researches mentioned above employed only onedimensional VC. Shamoto and Moriwaki [12,13] proposed an ‘elliptical vibration cutting’. Synchronized two-dimensional vibration is applied to the cutting edge in the plane containing the cutting direction and the chip flow direction in such a way that the cutting edge forms an elliptical locus
660
G.-L. Chern, Y.-C. Chang / International Journal of Machine Tools & Manufacture 46 (2006) 659–666
in each cycle of the vibration. Two piezoelectric plates with some phase shift were employed, causing an about 20 KHz vibration. Their experimental results, conducted on a turning machine, showed that the diamond cutting on hardened steel can be carried out successfully by applying elliptical VC. The effect of ultrasonic elliptical VC on machining accuracy in turning has also been analyzed theoretically [14]. It has been found that the heat generated during VC is reduced effectively [15]. Also, the friction of the tool and work material can be reduced accordingly by the formation of oxide films on the tool rake face. The decreased cutting force makes the chip thinner. Xiao et al. [16] pointed that VC has a chatter-suppressing dynamics while conventional cutting is a chatter-generating one, meaning that VC has a higher cutting stability as compared with conventional cutting. Thus, overall machining quality is improved with VC. From these researches, it can be concluded that VC is an effective method to be utilized in a machining operation. However, VC has not yet been employed in the field of micro-milling. In this paper, a two-dimensional vibrating worktable was designed and manufactured. VC is produced from the workpiece side, and no modification is needed on the machining center or the milling machine when utilizing the vibrating worktable. Micro-amplitude vibration is produced in the worktable via piezo-electrical materials in order to achieve better cutting performance. With the help of Taguchi method and analysis of variance, the effect of VC on slot-width accuracy is investigated. The experimental results and discussions are presented.
2. Experimental equipments and method Piezoelectric actuators feature the characteristics of good precision, fast response and large driving force. In this paper, VC is realized by employing piezoelectric actuators in conjunction with the relatively simple designed structure for generating the desired two-dimensional vibration. We first made a two-dimensional vibrating worktable containing two piezoelectric actuator and two linear guideways, as shown schematically in Fig. 1. The vibrating worktable serves two purposes: (1) to clamp the workpiece; and (2) to produce the desired vibration in the horizontal X and Y directions. It is composed of: (A) workpiece-holding block, (B) linear guideway, (C) piezoelectric actuator, (D) adapting plate, (E) spring, and (F) base block. The workpiece-holding block (A) is to clamp the workpiece during milling experiments. Two Physik Instrumente (PI)-made piezoelectric actuator (PI model P-244.10) and two linear guideways are employed in the worktable. P-244.10, having a maximum operating frequency of 16 KHz and a maximum traveling distance of 10 mm, is cooperated with a two-channel high power amplifier (PI model P-270.02) and a waveform generator (HP-33120A) to
Fig. 1. Schematic illustration of vibrating worktable.
produce the desired vibration. The maximum pushing force of P-244.10 is 2000 N. The output voltage of P-270.02 is from 0 to K1000 V. Its peak current is 50 mA. The linear guideway can ensure uni-axial motion of P-244.10 when VC is applied. Piezoelectric actuators are arranged perpendicularly. Two-dimensional vibration of the workpiece-holding block is realized by these two piezoelectric actuators through the adapting plate (D). The spring (E) is to provide the necessary preload for P-244.10, since the piezoelectric actuator is very brittle and can only withstand a maximum pulling force of 300 N. Photo of the vibrating worktable is shown in Fig. 2. Other experimental equipments are described as follows: 1. Machining center (MC-1050P, Mitsubishi-520AM controller). the range of the spindle speed is from 45 to 6000 rpm. 2. Laser displacement meter (Keyence LC-2430). the sampling rate of this sensor is 50 KHz; the resolution is 0.01 mm and the laser beam spot is 12 mm. Vibration amplitude of the workpiece was measured by this highaccuracy instrument. 3. Toolmakers’ microscope (Olympus, MM-11). to observe the machined surfaces. It possesses a maximum magnification of 200 times. 4. Surface roughness measuring machine (Talyround, series2). to measure the surface roughness of the workpiece after end milling.
Fig. 2. Photo of vibrating worktable.
G.-L. Chern, Y.-C. Chang / International Journal of Machine Tools & Manufacture 46 (2006) 659–666
661
Table 2 Machining condition of uniaxial VC experiment Spindle speed (rpm) Frequency (Hz) Amplitude (mm) Feed (mm/tooth) Depth of cut (mm) Cutting fluid
Fig. 3. Micro-milling experiments.
5. Two-flute end mill. standard, made of high speed steel (HSS), with a diameter of 1 mm, a flute length of 5 mm, a helix angle of 308. Shank diameter is 6 mm. 6. Work material. aluminum alloy Al 6061-T6 was tested. To get reliable data, the workpieces were cut and polished to precise pieces (42 mm!20 mm!8 mm) before test. 7. Cutting fluid. mineral oil The micro-milling experiments were carried out, producing a slot on the workpiece after each cut, as shown in Fig. 3. Length of each slot is fixed at 10 mm. Each combination of machining parameters is tested four times. There are several methods to evaluate the quality of a machined workpiece after end milling. The method of analysis is stated as follows. 2.1. Tool-wear experiment The purpose of the experiment is to investigate the influence of VC on tool life in end milling. Number of slots produced by an end mill before out-of-tolerance slot is created can be regarded as a measurement of tool life. Since the diameter of the end mill is 1 mm, the threshold of the slot width determining tool life is chosen as 1 mm. The machining condition is summarized in Table 1. Vibrating frequencies chosen were 0, 500 Hz, 1 and 10 kHz. Vibrating amplitudes varied from 0, 4, 7, to 10 mm. Here, 0 Hz or 0 mm means that no vibration is imposed. Hundred slots were created for each machining condition. 2.2. Uniaxial VC experiment The purpose the uniaxial VC experiment is to investigate the influence of VC on machining accuracy in end milling. Table 1 Machining condition of tool-wear experiment Spindle speed (rpm) Frequency (Hz) Amplitude (mm) Feed (mm/tooth) Depth of cut (mm) Cutting fluid
1500 0, 500, 1 k, 10 k 0, 4, 7, 10 5 0.3 Mineral oil
1000, 2000, 3000 600 10 2.5, 5, 7.5 0.3 Mineral oil
Width of milled slot and displacement of slot center were used to represent the dimensional accuracy of end milling. Slot-width oversize due to tool runout and tool deviation from excessive cutting force should be kept at minimum. One-directional VC experiment was carried out. Vibration amplitude of 10 mm and frequency of 600 Hz were applied along the tool feed motion (Y-axis, as shown in Fig. 3) if VC was applied. The machining condition is summarized in Table 2. 2.3. Biaxial VC experiment The machining condition in the biaxial VC experiment is the same as the one shown in Table 2, except that now the VC is applied in both X and Y directions, as shown in Fig. 3. Vibration frequency in the X direction is set at 600 Hz. Since the employment of VC in the X direction directly increases the slot width produced in end milling, the vibrating amplitude is chosen as low as 1 mm to minimize the undesirable side effect. We would like to know if the use of biaxial VC is appropriate. 2.4. Biaxial VC experiment using Taguchi method There were many parameters involved in the experiments and thus in this paper we employed Taguchi method to deal with responses influenced by multi-variables. Taguchi used signal-to-noise (S/N) ratio as the quality characteristics of the choice of parameters. To obtain better machining accuracy and to minimize slot-width error, we should look for ‘smaller-the-better’ characteristic in which S/N can be expressed as S 1 X 2 ZK10 log y N n where n is the number of experiments and y is the measured data. The analysis of variance (ANOVA) is then carried out to analyze the effect of the process parameters. Based on ANOVA, the contribution ratio of each parameter can be determined and thus optimal combination of the parameters can be obtained. More detailed description about utilizing the Taguchi method for the planning of experiments can be found in the references [17,18] and is not summarized in this paper. We used the L18 orthogonal array to analyze their effects. The process parameters chosen are: (A) amplitude in X direction, (B) frequency in X direction, (C) spindle speed,
662
G.-L. Chern, Y.-C. Chang / International Journal of Machine Tools & Manufacture 46 (2006) 659–666
Table 3 Machining parameters and their levels in biaxial VC experiments Param.
1 2 3
(A) X-amplitude (mm)
(B) X-frequency (Hz)
(C) spindle speed (rpm)
(D) feed (mm/tooth)
(E) Y-frequency (Hz)
(F) Y-amplitude (mm)
0 1 –
100 1K 10 K
1000 2000 3000
2.5 5 7.5
100 1K 10 K
4 7 10
(D) feed, (E) frequency in Y direction, and (F) amplitude in Y direction, while the response function is the slot width. The range and number of levels of the parameters are selected as given in Table 3. The experimental layout for the machining parameters is shown in Table 4. It is noted that there is one parameter (A) at 2 levels and other five parameters at 3 levels. Only 18 experiments are needed to study the entire machining parameters using the L18 orthogonal array.
3. Results and discussions 3.1. Tool-wear experiment The numbers of slots produced within the threshold (1 mm) with respect to different vibrating amplitudes and frequencies are listed in Table 5. It is found that the employment of VC increases the number of slots produced within the tolerance. ‘Tool life’ is only 80 without VC. Such number increases to 98 under 500 Hz and 10 mm, an improvement of about 22%. We also note that higher frequencies have a negative effect on tool life, as found in the previous study [11]. Also, the chipping might be caused by the colliding or rubbing between the end mill and the workpiece. Thus, the number of slot that can be machined Table 4 Experimental layout showing levels of machining parameters No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
by an end mill under a certain machining condition tends to decrease when high frequency is imposed. The amplitude in VC directly influences the gap between the workpiece and the tool. The increase of the gap allows more cutting fluids to carry away the heat generated during milling. Thus tool life is enhanced at higher amplitudes, as seen in Table 5. 3.2. Uniaxial VC experiment A typical variation of slot width with respect to different spindle speeds is shown in Fig. 4. The feed is 5 mm/tooth. It can be seen that the slot width decreases when VC is applied. The slot-width oversize is improved in the experiment. The average value of slot-width oversize is 8 mm without VC, while such value drops to only 6 mm with VC. VC attributes to the rapid separation between the tool and the workpiece. This helps to reduce the heat generated during end milling, and the machining performance is improved. The runout of end mill in operation is reduced and the slot-width oversize is decreased accordingly. Fig. 5 shows the variation of slot positioning accuracy with respect to different spindle speeds when feed equals 2.5 mm/tooth. It is very clear that the use of VC decreases the positioning error (displacement of slot center) effectively. The average value of slot positioning error is 20 mm without VC, while such value drops to only 10 mm with VC. Table 5 Number of slots under different vibrating amplitudes and frequencies (feedZ5 mm/tooth, depth of cut Z0.3 mm, spindle speed Z1500 rpm)
Param. A
B
C
D
E
F
1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
1 2 3 1 2 3 2 3 1 3 1 2 2 3 1 3 1 2
1 2 3 2 3 1 1 2 3 3 1 2 3 1 2 2 3 1
1 2 3 2 3 1 3 1 2 2 3 1 1 2 3 3 1 2
1 2 3 3 1 2 2 3 1 2 3 1 3 1 2 1 2 3
Amp.
Freq.
4 mm 7 mm 10 mm
500 (Hz)
1 (kHz)
10 (kHz)
95 97 98
91 94 96
87 91 90
no vibration with vibration slot width (mm)
Level
1.012 1.008 1.004 1
0
1000
2000 3000 spindle speed (rpm)
4000
Fig. 4. Variation of slot width vs. spindle speed in uniaxial VC (5 mm/tooth) .
G.-L. Chern, Y.-C. Chang / International Journal of Machine Tools & Manufacture 46 (2006) 659–666
no vibration with vibration
0.03
0.03
0.02 0.01 0
0
1000
2000 3000 spindle speed (rpm)
4000
The positioning accuracy is strongly related to the cutting force occurred in an end milling process. The reduced cutting force under the assistance of VC causes less positioning error, as can be seen in Fig. 5. 3.3. Biaxial VC experiment Fig. 6 shows the variation of slot width with respect to different spindle speeds for feed equals 5 mm/tooth. We found that the average value of slot-width oversize was 5 mm with biaxial VC, even better than 6 mm obtained in uniaxial VC. Similar results were obtained for feed equals 2.5 and 7.5 mm/tooth. In these tests, we found that the average slot-width oversize was contained within 4.5–5 mm under biaxial VC. This means that the introduction of second directional VC (of amplitude 1 mm) does slightly improve the slot-width accuracy. Fig. 7 shows the variation of slot positioning accuracy with respect to different spindle speeds when feed equals 2.5 mm/tooth. We found that the average value of positioning error to be 5 mm with biaxial VC, even better than 10 mm obtained in uniaxial VC. This suggests that the employment of biaxial VC can prevent the deviation of miniature end mill in operation due to more evenly distributed and reduced cutting forces. Fig. 8 shows two typical photos of machined specimens taken from the entrance side, without and with VC. The comparison of the milling quality is very clear. Without VC in Fig. 8(a), large cutting forces tend to bend the miniature tool and cause geometrical error in the slot shape. Burrs are prominent on the right side of slot where cutting velocity is pointed outward from the workpiece. Some burrs can also
slot width (mm)
no vibration with vibration 1.012 1.008 1.004 0
1000
2000 3000 spindle speed (rpm)
0.02 0.01 0
Fig. 5. Variation of positioning accuracy vs. spindle speed in uniaxial VC (2.5 mm/tooth).
1
accuracy (mm)
accuracy (mm)
no vibration with vibration
663
4000
Fig. 6. Variation of slot width vs. spindle speed in biaxial VC (5 mm/tooth).
0
1000
2000 3000 spindle speed (rpm)
4000
Fig. 7. Variation of ositioning accuracy vs. spindle speed in biaxial VC (2.5 mm/tooth).
be found along the bottom edge. On the contrary, when uniaxial VC was imposed, perfect rectangular shape can be obtained with the help of VC, as shown in Fig. 8(b). Burrs are less serious and more evenly distributed along the edges. Fig. 9 shows two photos of machined chips collected during the experiments, without and with VC. Even though the chip thicknesses were not measured in the experiments, due to limited available equipments and reliable measuring methods, we could still qualitatively compare their difference. For no VC in Fig. 9(a), much thicker chips can be found, suggesting that the cutting force is larger. When biaxial VC is applied, chips of thinner and segmented shape can be seen in Fig. 9(b). It is evident that cutting force is less in this case due to the assistance of VC, leading to better machining accuracy. Rapid separation between the tool and the workpiece in VC provides excellent chip-removal condition during end milling. The reduction of cutting force causes better positioning accuracy of the machined slot, as can be seen in Figs. 5 and 7. Also, the reduced cutting force becomes more stable and uniform during each revolution when chip removal is easy. As a result, the fluctuation of radial force during cutting decreases. Thus, the tool runout is also retarded and the slot width becomes more accurate, as can be seen in Figs. 4 and 6. Fig. 10 shows three photos of machined surfaces, taken by the toolmakers’ microscope. Their milling qualities are very easy to recognize. Without vibration in Fig. 10(a), large feed marks as well as some scratches and irregularities appear on the slot bottom surface. When the chips could not be carried away effectively, the highly-hardened chips could easily damage the machined surface. When uniaxial VC is applied in Fig. 10(b), the tool feed marks are leveled off since rapid vibration occurs on the plane. Even better surface finish can be obtained when biaxial VC is imposed, as shown in Fig. 10(c). The surface roughness on both vertical sides of slot is also important in end milling. To measure the surface roughness in those areas, the workpieces must be cut properly by wire-EDM first. Fig. 11 shows the measuring results, without and with VC. For no VC in Fig. 11(a), the roughness (Ra) on the slot side surface is 1.3017 mm. When
664
G.-L. Chern, Y.-C. Chang / International Journal of Machine Tools & Manufacture 46 (2006) 659–666
Fig. 8. Photos showing machined slots: (a) without, and (b) with VC (5 mm/tooth, 2000 rpm).
Fig. 9. Photos (!50) showing machined chips: (a) without, and (b) with biaxial VC.
uniaxial VC is applied, such value drops to 0.9141 mm, as shown in Fig. 11(b). The improvement ratio is about 30%. 3.4. Biaxial VC experiment using Taguchi method The objective of the experiment is to optimize the parameters to get smaller slot width in end milling with biaxial VC. The S/N ratio can be computed by the actual slot width measured after end milling. The response table for S/N ratio is shown in Table 6. We can predict the optimal
combination of machining parameters to be A2 (1 mm), B2 (1 kHz), C1 (1000 rpm), D2 (5 mm/tooth), E2 (1 kHz), and F3 (10 mm) by selecting the largest value of S/N ratio for each parameter. The results of ANOVA are given in Table 7. Contribution ratio, P, of each parameter can be determined in the table. It is found that vibrating amplitude in Y direction (F) has a dominant effect in biaxial VC, of more than 40% in contribution ratio. Vibration frequency in Y direction (E) also has some influence on the slot width, of about 21% in
Fig. 10. Photos (!20) showing machined surfaces: (a) without VC, (b) with uniaxial VC, and (c) with biaxial VC.
Fig. 11. Roughness of slot side surface: (a) without, and (b) with VC (5 mm/tooth, 2000 rpm).
G.-L. Chern, Y.-C. Chang / International Journal of Machine Tools & Manufacture 46 (2006) 659–666
B
C
D
E
F
42.62 45.59
44.52 44.72 43.07 B2
45.37 43.78 43.16 C1
43.36 45.09 43.86 D2
41.53 45.96 44.82 E2
40.22 45.81 46.29 F3
A2
Table 7 ANOVA in biaxial VC experiments Param.
Sum of squares, S
Degree of freedom, f
Variance, V
Contribution ratio, P (%)
A B C D E F Total
34.544 11.921 37.277 31.406 64.575 124.364 304.087
1 2 2 2 2 2 11
34.54 5.96 18.64 15.70 32.29 62.18
11.4 3.9 12.3 10.3 21.2 40.9 100
Table 8 Machining condition of further VC experiment Spindle speed (rpm) Frequency (Hz) Amplitude (mm) Feed (mm/tooth) Depth of cut (mm) Cutting fluid
1000 X: 1 K; Y: 0, 100, 1 K, 10 K X: 1; Y: 0, 4, 7, 10 5 0.3 Mineral oil
contribution ratio. P for spindle speed (C) and feed (D) are 12.3 and 10.3%, respectively. Since A (amplitude in X direction) in the optimal combination is other than 0 mm (no vibration), it suggests that the use of second directional vibration to minimize slot-width oversize in end milling is helpful. The contribution ratio of amplitude in X direction is 11.4%, as shown in Table 7. To validate the finding of this analysis, confirming experiment was conducted with the optimal level of machining parameters: A2, B2, C1, D2, E2, and F3. The average measured slot-width oversize of this optimum combination was 3.8 mm, even lower than the smallest one (4.5 mm) in the biaxial VC experiment. It has been shown that machining parameters chosen at their optimum levels can ensure significant improvement in the slot-width accuracy in biaxial VC.
1.009 1.008 1.007 1.006 1.005 1.004 1.003 1.002 1.001 1 –0.001
0.001
0.003 0.005 0.007 amplitude (mm)
0.009
0.011
Fig. 12. Variation of slot width vs. amplitude (5 mm/tooth, 1000 rpm, Y: 1 KHz).
slot width (mm)
1 2 3 Optimal
A
slot width (mm)
Table 6 Response table for S/N ratio in biaxial VC experiments
665
1.009 1.008 1.007 1.006 1.005 1.004 1.003 1.002 1.001 1
0
100 1K frequency (Hz)
10K
Fig. 13. Variation of slot width vs. frequency (5 mm/tooth, 1000 rpm, Y: 10 mm).
amplitudes. It can be seen that larger amplitudes tend to reduce the slot-width oversize. Larger amplitudes in VC create more room for the separation between the tool and the workpiece, and more lubricant can reach the cutting edge and carry away the heat generated during machining. Thus, cutting force can be reduced and slot-width oversize can be prevented effectively. Fig. 13 shows the variation of slot width with respect to different vibrating frequencies. At first, slot width seems to be reduced with the increase of frequency. But slot widths at 10 kHz were slightly larger than those at 1 kHz and we obtained a minimum of slot-width oversize at 1 kHz. It seems that the use of vibration at high frequency, such as 10 kHz in the experiment, cannot effectively improve the machining accuracy. Similar results of the influence of vibrating frequency on machining accuracy had also been studied in micro-drilling with VC [11].
3.5. Influence of vibrating amplitude and frequency
4. Conclusions
To investigate the effects of vibrating amplitude and frequency on slot-width oversize, some further experiments were carried out. Table 8 shows the machining condition. Since vibration in the X direction would naturally increase slot width, we kept the X-directional amplitude and frequency at 1 mm and 1 kHz, respectively. Fig. 12 shows the variation of slot width with respect to different vibrating
In this paper, we developed a two-dimensional vibrating worktable with the desired vibration created from the workpiece side. Form this research, we draw three conclusions: 1. Through extensive experiments, we found that slot oversize, displacement of slot center and slot surface
666
G.-L. Chern, Y.-C. Chang / International Journal of Machine Tools & Manufacture 46 (2006) 659–666
roughness could be improved by imposing VC during end milling. 2. It is found that the employment of VC increases the number of slots produced within the tolerance when high amplitude and proper frequency are imposed. Higher frequencies have a negative effect on tool life. 3. Based on the Taguchi method and ANOVA, we found that vibrating amplitude in feed direction has a dominant effect of more than 40% in contribution ratio, while its associated frequency has some influence on slot-width accuracy of about 21% in contribution ratio. The use of second directional VC to minimize slot-width oversize in end milling is helpful. References [1] E.B. Kivanc, E. Budak, Structural modeling of end mills for form error and stability analysis, Int. J. Mach. Tools Manuf. 44 (2004) 1151–1161. [2] J. Kumabe, T. Sabuzawa, Study on the precision drilling of wood (1st report) - profile analysis of drilled hole, J. JSPE, 37 (2) (1971) 98-104 (in Japanese). [3] J. Kumabe, T. Sabuzawa, Study on the precision drilling of wood (2nd report)—drilling force and its accuracy, J. JSPE 38 (5) (1972) 456– 461 (in Japanese). [4] T. Koyama, K. Adachi, K. Murakami, Study on vibratory drilling (2nd Report)—comparison of conventional drilling with vibratory drilling, J. JSPE 43 (1) (1977) 55–60 (in Japanese). [5] T. Moriwaki, E. Shamoto, K. Inoue, Ultraprecision ductile cutting of glass by applying ultrasonic vibration, Ann. CIRP 41 (1) (1992) 141–144.
[6] M. Zhou, X.J. Wang, B.K.A. Ngoi, J.G.K. Gan, Brittle-ductile transition in the diamond cutting of glasses with the aid of ultrasonic vibration, J. Mater. Process. Technol. 121 (2002) 243–251. [7] H. Weber, J. Herberger, R. Pilz, Turning of machinable glass ceramics with an ultrasonically vibrated tool, Ann. CIRP 33 (1) (1984) 85–87. [8] T. Moriwaki, E. Shamoto, Ultraprecision diamond turning of stainless steel by applying ultrasonic vibration, Ann. CIRP 40 (1) (1991) 559– 562. [9] K. Adachi, N. Arai, S. Harada, K. Okita, S. Wakisaka, A study on burr in low frequency vibratory drilling—drilling of aluminum, Bull. JSPE 21 (4) (1987) 258–264. [10] H. Takeyama, S. Kato, Burrless drilling by means of ultrasonic vibration, Ann. CIRP 40 (1) (1991) 83–86. [11] G.L. Chern, H.J. Lee, Using workpiece vibration cutting for microdrilling, Int. J. Adv. Manuf. Tech., DOI: 10.1007/s00170-004-2255-8, to appear in 2005. [12] E. Shamoto, T. Moriwaki, T. Study, on elliptical vibration cutting, Ann. CIRP 43 (1) (1994) 35–38. [13] E. Shamoto, T. Moriwaki, Ultraprecision diamond cutting of hardened steel by applying elliptical vibration cutting, Ann. CIRP 48 (1) (1999) 441–444. [14] C.X. Ma, E. Shamoto, T. Moriwaki, L.J. Wang, Study of machining accuracy in ultrasonic elliptical vibration cutting, Int. J. Mach. Tools Manuf. 44 (2004) 1305–1310. [15] M. Jin, M. Murakawa, Development of a practical ultrasonic vibration cutting tool system, J. Mat. Process. Technol. 113 (2001) 342–347. [16] M. Xiao, K. Sato, S. Karube, T. Soutome, The effect of tool nose radius in ultrasonic vibration cutting of hard metal, Int. J. Mach. Tools Manuf. 43 (2003) 1375–1382. [17] P.M. George, B.K. Raghunath, L.M. Manocha, A.M. Warrier, E.D.M. machining, of carbon-carbon composite - a Taguchi approach, J. Mater. Process. Technol. 145 (2004) 66–71. [18] J.A. Ghani, I.A. Choudhury, H.H. Hassan, Application of Taguchi method in the optimization of end milling parameters, J. Mater. Process. Technol. 145 (2004) 84–92.