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An ultrasonic elliptical vibration cutting device for micro V-groove machining: Kinematical analysis and micro V-groove machining characteristics
Journal of Materials Processing Technology 190 (2007) 181–188
An ultrasonic elliptical vibration cutting device for micro V-groove machining: Kinematical analysis and micro V-groove machining characteristics Gi Dae Kim a , Byoung Gook Loh b,∗ a
School of Mechanical and Automotive Engineering, Catholic University of Daegu, Hayang-up, Gyeongsansi, Gyeongbuk 712-702, Republic of Korea b Department of Mechanical Systems Engineering, Hansung University, Samsun-dong 389, Sungbuk-gu, Seoul 136-792, Republic of Korea Received 9 August 2005; received in revised form 20 December 2006; accepted 16 February 2007
Abstract Micro V-groove machining characteristics of an ultrasonic elliptical vibration cutting (UEVC) device have been experimentally investigated and compared with the conventional micro V-grooving. From the initial experiments performed on ductile material such as aluminum and brass with a single crystal diamond cutting tool, it was found that the cutting force was significantly decreased and the formation of burrs at the machining boundaries was greatly suppressed in the UEVC. The elliptical vibration of the cutting tool was achieved using two parallel stacked piezoelectric actuators with assembling metal structures. Kinematical analysis of the UEVC system has shown that the manipulation of the cutting tool path is possible by changing dimension of the mechanism, phase difference, and relative magnitude of the voltages applied to the piezoelectric actuators. © 2007 Elsevier B.V. All rights reserved. Keywords: Ultrasonic elliptical vibration cutting (UEVC); Single crystal diamond cutting tool; Burr; Piezoelectric actuator; Phase difference
1. Introduction The demands for precision and micro-machining technologies that enable to produce mechanical components of micrometer scale and mechanical features such as V-grooves and cavities of micrometer scale have drastically increased with the advance of semiconductor manufacturing industry, microelectro-mechanical systems (MEMS), bio-technology (BT), and nano-technology (NT). But the conventional machining technologies such as turning, milling, and drilling appear to have reached to the point where the speed at which the conventional machining technologies advances cannot keep up with the demands of industries requiring micro-machining technologies. In an effort to meet these demands, non-conventional machining technologies that include micro-electrical discharge machining, laser machining, electro chemical machining and, etc. have been proposed, but applications of these technologies have been limited because of lack of machinable workpieces, thermal distortion of machined surface, need for the pre-machining
∗
Corresponding author. Tel.: +82 2 760 5865; fax: +82 2 760 4329. E-mail address: [email protected] (B.G. Loh).
0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2007.02.047
of an electrode, high cost and high energy requirements, and so on. A new surface machining technology that is based on the conventional cutting but has advantages such as high productivity, low-cost and high degree of freedom in machining is needed. Therefore, a new machining method using ultrasonic vibration as a means for precision machining was proposed, but has primarily been applied to machining micro-holes which are created by micro-chipping caused by vibrating abrasive slurry at an ultrasonic frequency with a machining tool, and making it colliding with the workpiece [1]. Other application of the ultrasonic vibration to the precision machining includes reduction of the cutting force by vibrating a cutting tool in the cutting direction. But most of the efforts are geared toward enhancing the surface roughness, not toward the realization of a new kind of precision micro-machining [2–4]. Shamoto and Moriwaki [5] proposed a novel vibration cutting method termed as “the elliptical vibration cutting (EVC)” in which a cutting tool attached to piezoelectric actuators circles along an elliptical path and penetrates into a workpiece when the cutting tool actuated by the piezoelectric actuators is brought into contact with a workpiece. The elliptical path of the cutting tool was generated with two orthogonally assembled
182
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Fig. 1. Elliptical cutting tool path created by superposition of two spatially orthogonal bending modes (by Shamoto and Moriwaki [6,7]).
piezoelectric actuators. The experimental results indicated a significant decrease in the cutting force using the EVC compared with the conventional machining. Shamoto and co-workers [6] continued their research into increasing the excitation frequency to 20 kHz and creating an elliptical cutting tool path by attaching two pairs of piezoelectric actuators to a rectangular metal block in the orthogonal directions as in Fig. 1. In this method, the vibration amplitude of the cutting tool could be greatly amplified by selecting the excitation frequency as one of the resonance frequencies of the system, and the elliptical cutting tool path was created as superposition of two orthogonal bending modes excited by two pairs of piezoelectric actuators oriented 90◦ to each other. The generation of the elliptical cutting tool path by superimposing two orthogonal modes seems simple in principle, but it is practically challenging to have the elliptical cutting tool path coplanar with the plane containing the cutting and chip-flow direction. Furthermore, there are drawbacks in the design such as zero bandwidth, i.e. fixed excitation frequecny, difficulty in synchronizing two resonant frequencies of the spatially orthogonal bendig modes, compliance of the support, and lack of methodologies to design the optimum shape of horns [7]. Cerniway [8] proposed a device creating an elliptical tool path using two parallel stacked piezoelectric actuators with bandwidth of 4.5 kHz and investigated creating a precision surface on the diamond turning machine. The audible actuation frequency creates unpleasant noises, and the low bandwidth limits the feedrate of the workpiece, resulting in prolonged machining time. Among many potential applications of the ultrasonic elliptical vibration cutting (UEVC), the UEVC is ideal for patterning micro V-grooves that have been widely used for optical devices, because fabricating micro V-grooves free of burrs with conventional techniques, such as etching and lithography is known to be costly and time-consuming, but cutting in conjunction with ultrasonic vibration has demonstrated its effectiveness in fabricating a surface with high surface finish. Capabilities for fabricating an array of micro V-grooves on a surface are essential to manufacturing optical devices, such as a Fresnel lens and a liquid crystal display (LCD). Accordingly, an in-depth grasp of machining characteristics of micro V-groove using the UEVC would play a
critical role in establishing low-cost and reliable micro V-groove fabrication technology. Lee et al. [9] studied the characteristics of micro V-grooves produced on a planar lightwave circuit and glass by the UEVC. It is notable that feasibility of applying the UEVC to micro V-grooving has been studied, but the elliptical tool paths are generated with superposition of two orthogonal resonant modes, which puts constraints on its industrial implementation as discussed in review of Shamoto’s studies. In this study, a UEVC system, which is based on Cerniway’s design but modified to increase the operating frequency to 65 kHz and to facilitate fabrication, is presented, and its kinematical analysis is performed to investigate the formation of the elliptical cutting tool path. In addition, micro V-groove machining characteristics of the UEVC, such as the primary and thrust cutting force, surface finish, and the formation of chips and burrs are experimentally investigated. 2. Generation and analysis of the elliptical vibration of the cutting tool 2.1. Principle of the elliptical vibration cutting (EVC) In Fig. 2(a–d), the principle of the EVC is illustrated. In the EVC, the elliptically rotating speed of the cutting tool is set to be greater than the cutting speed, which allows the cutting tool to make contacts with a workpiece and to lose contacts in succession along a proceeding elliptical path in the process of cutting as shown in Fig. 2(a). Cutting is initiated bringing the cutting tool into contact with the workpiece as in Fig. 2(b), and then, the cutting tool cuts into the workpiece in a way similar to the conventional cutting process as in Fig. 2(c). What differentiates the EVC from the conventional cutting is the process illustrated in Fig. 2(d) where the cutting tool moves up along the upward elliptical path and lifts off the workpiece. This upward elliptical motion contributes to the reduction of the cutting force, because the frictional force between the rake face of the tool and the chip is reversed in contrast to the conventional cutting process, assisting in discharging of chips. The cutting tool completely looses a contact with the workpiece at lift-off and moves to a position to repeat the cutting cycle as in Fig. 2(a). 2.2. Ultrasonic elliptical vibration cutting system (UEVCS) Fig. 3 shows the picture of the piezoelectric actuator for the ultrasonic elliptical vibration cutting system (UEVCS) which consists of two parallel stacked piezoelectric actuators, a single crystal diamond cutting tool, and supporting metal structures. The stacked piezoelectric actuators which enable low voltage operation are sandwiched between the assembling structures and preloaded with a bolt. When energized with sinusoidal voltages, the stacked piezoelectric actuators periodically expand and contract, and controlling a phase between the sinusoidal voltages applied to the actuators allows for translating or rotating the cutting tool along a prescribed elliptical path.
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183
Fig. 2. Principle of elliptical vibration cutting.
2.3. Kinematical analysis of the UEVCS For kinematical analysis, the UEVCS is modeled as a simple T-shaped bar as shown in Fig. 4 where y1 and y2 are the displacements resulting from the expansion of the piezoelectric actuators, and the position P denoting the tip of the T-shaped bar represents the edge of the cutting tool. The movements of the position P on the x–y plane in response to the variation of displacements y1 and y2 represent the cutting tool path of the UEVCS and can be formulated into Eqs. (4) and (5) by substituting Eq. (3) into Eqs. (1) and (2) where xCT and yCT are the displacements of P in the x and y direction, respectively, and lx is half distance between PZTs in the x direction and ly is the distance between the cutting tool edge and the PZT in the y
Fig. 3. Picture of the UEVCS.
direction. xCT = −ly sin θ
(1)
yCT = y1 + lx sin θ + ly cos θ − ly −1 y2 − y1 θ = sin 2lx
(2)
ly (y1 − y2 ) 2lx y2 − y1 y1 + y 2 − ly = + ly cos sin−1 2 2lx
(3)
xCT =
(4)
yCT
(5)
Since the piezoelectric actuators are energized with sinusoidal voltages, y1 and y2 can be expressed as Eqs. (6) and (7). y1 = A1 sin(2πft)
(6)
y2 = A2 sin(2πft + φ)
(7)
Fig. 4. Kinematical schematic diagram for the UEVCS.
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Fig. 5. Generation of elliptical cuing tool path by exciting two parallel PZTs with 90◦ phase difference. Angular displacement: (a) 45◦ , (b) 135◦ , (c) 225◦ , and (d) 315◦ .
where f is the frequency of the sinusoidal voltage, t the time, φ the phase difference between y1 and y2 , and A1 and A2 are the vibration amplitudes. To illustrate the generation of an elliptical cutting tool path, it is assumed that the amplitudes, A1 and A2 are 1 m and a phase difference, φ is 90◦ . The displacements y1 and y2 are significantly smaller than the dimension of the T-shaped bar. As a result, θ in Eq. (3) can be assumed to be very small, permitting the application of small angle assumption (sin θ ≈ θ, cos θ ≈ 1), which simplifies Eqs. (4) and (5) as in Eqs. (8) and (9). xCT = (sin 2πft − cos 2πft) (8) (ly /2lx ) yCT = (sin 2πft + cos 2πft) (1/2)
(9)
Squaring Eqs. (8) and (9), respectively, and summing give Eq. (10) which is clearly the equation √ of an ellipse with the length of the semi-major axis being (ly / 2lx ) m and the length of the √ semi-minor axis being (1/ 2) m. 2 xCT
2 yCT
+ √ √ 2 =1 2 (ly / 2lx ) (1/ 2)
(10)
A graphical illustration of generation of the elliptical tool path is shown in Figs. 5 and 6. The position of the cutting tool is at the peak of the ellipse when the angular displacement of Eqs. (6) and (7) are 45◦ . The cutting tool follows through the elliptical path as the angular displacements of PZT1 and PZT2 increase and reach to the farthest right of the ellipse at an angular displacement of 135◦ , to the bottom at 225◦ , and to the farthest left at 315◦ . The cutting tool path completes one cycle at an angular displacement of 360◦ , and this process is repeated at a prescribed frequency, f, generating a continuous elliptical motion of the cutting tool. Fig. 7 shows the variation of the elliptical cutting tool path simulated with MATLAB based on Eqs. (4) and (5) as a function of the phase difference between the PZT1 and PZT2 and dimensional parameters of T-shaped bar, lx and ly , respectively. For the case of lx = ly , the cutting tool path becomes a circular trajectory with a phase difference of 90◦ , a linear trajectory in the thrust direction with a phase difference of 0◦ , and quasi-linear trajectory in the cutting direction with a phase difference of 180◦ as shown in Fig. 7(a). The simulated results indicate that the ratio of the length of the major axis to the minor axis of the ellipti-
cal cutting tool path can be readily manipulated by varying the phase difference. The ratio of ly to lx determines the degree of the leverage effect of the T-shaped bar. As the ratio of ly to lx grows, the length of the major axis of the elliptical cutting tool path becomes greater than that of the minor axis due to the leverage effect. Thus, larger ratio of ly to lx produces larger displacement in the cutting direction than the thrust direction. Fig. 7(b) shows the elliptical cutting tool paths simulated for the case of lx = 7 mm and ly = 30 mm, respectively, under which cutting experiments presented in Chapter 4 were performed. In this case, a circular cutting tool path is obtained at a phase difference of 28.1◦ . Through the simulation, it was found that the relative magnitude difference between the amplitudes of the piezoelectric actuators also affects the shape of the elliptical cutting tool path by changing the angle of axes of the ellipse. 3. Experimental setup The UEVCS that includes a single crystal diamond cutting tool, stacked piezoelectric actuators, and assembling metal structures is mounted on the 3axis precision motorized stage and placed on the air-vibration-isolation-table as shown in Fig. 8. A jig on which the workpiece is attached is bolted down to the 3-axis tool dynamometer (Kistler 9257B) which measures the cutting forces. The measured cutting forces are amplified and sent to the PC for analysis. The
Fig. 6. Sinusoidal amplitude variations of PZT1 and PZT2 (in case of A1 = A2 = 1 m, φ = 90◦ ).
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Table 1 Specifications of a single crystal diamond cutting tool Nose radius Rake angle Clearance angle Nose angle
600 nm 0◦ 6◦ 80◦
Fig. 9. SEM picture of a single crystal diamond cutting tool nose.
specifications of the single crystal diamond cutting tool are detailed in Table 1, and its picture taken using scanning electron microscopy (SEM) is shown in Fig. 9. The stacked piezoelectric actuators are energized by sinusoidal voltages with a frequency of 65 kHz. The measured vibration amplitude of the piezoelectric actuator in the cutting direction is approximately 0.8 m. The phase difference between supplied sinusoidal voltages is set to 90◦ . Workpieces tested are made of aluminum(Al5052), copper(C1100), and brass(C2801, Cu: 60%, Zn: 40%).
4. Experimental results Fig. 7. Simulation results of elliptical cutting tool path with variation of phase. (a) lx = 10 mm, ly = 10 mm and (b) lx = 7 mm, ly = 30 mm.
To investigate characteristics of the UEVC, micro V-grooves are machined by the UEVC and the conventional cutting as illustrated in Fig. 10, and the pictures of micro V-grooves taken from the top of the workpiece using the SEM are shown in Fig. 11. The workpiece tested is made of Al5052, and the cutting speed is 5 mm/s, and the cutting depth is 15 m.
Fig. 8. Photograph of experimental setup.
Fig. 10. Graphical illustration of conventional cutting vs. the UEVC.
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Fig. 11. Micro V-groove machined by conventional cutting and the UEVC (material of workpiece: Al5052; cutting depth = 15 m; cutting speed = 5 mm/s). (a) Micro V-groove machined by the conventional cutting and (b) micro V-groove machined by the UEVC. Small cutting depth causes the specific cutting energy to increase due to the size effect, resulting plastic deformations in workpiece and creating burrs at the cutting boundaries. This phenomenon can be observed in the conventional micro V-grooving as in Fig. 11(a) but cannot be observed in the micro V-groove created with the UEVC as in Fig. 11(b). It can be, therefore, inferred that the UEVC significantly reduces the frictional force occurring between the cutting tool and chip resulting in a decline in the specific cutting energy. The inference can be verified by measuring the primary cutting forces for the conventional micro Vgrooving and the micro V-grooving with the UEVC. The measurement of the cutting forces are shown in Fig. 12 which indicates the average cutting force for the UEVC is decreased by approximately 80% compared with the conventional micro V-grooving. For the surface finish of the inside of the micro V-groove, it is observed that the conventional micro V-grooving creates a smoother surface than the micro Vgrooving with the UEVC. The superficial deterioration in surface finish inside the micro V-groove is attributable to wave-like machining marks left on the machined surface as a result of the proceeding elliptical motion of the cutting tool as investigated in previous research of Moriwaki and Shamoto [7]. To investigate the formation of the exit burrs, the cutting experiment for the copper is performed with the cutting depth of 20 m and cutting speed of 5 mm/s. The pictures of micro V-groove after the cutting experiment taken by SEM are shown in Fig. 13. It is observed that the exit burr is not created from the UEVC, but that the conventional micro V-grooving produces the exit burr as the cutting tool moves away from the workpiece. Micro V-grooving experiments are performed with the workpiece made of brass for the case of the cutting depth of 30 m, and the cutting speed of 1 mm/s. And the primary cutting force, the thrust force, and the surface finish are observed. As in Fig. 14, it is observed that both the primary and thrust force are decreased by approximately 50% in micro V-grooving using the UEVC
Fig. 12. Comparison of primary cutting force: conventional cutting vs. the UEVC (material of workpiece: Al5052; cutting depth = 15 m; cutting speed = 5 mm/s).
compared with the conventional micro V-grooving. It is also observed that as in Fig. 15 micro V-grooving with the UEVC significantly reduces the formation of burr but produces the surface finish inside the micro V-groove inferior to the conventional micro V-grooving, which is consistent with the micro V-grooving experiments with aluminum.
Fig. 13. Comparison of exit burr formation: conventional cutting vs. UEVC (material of workpiece: C1100, cutting depth = 20 m, cutting speed = 5mm/s) (a) Micro V-groove by conventional cutting and (b) micro V-groove by the UEVC.
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187
Fig. 14. Comparison of primary and thrust cutting forces between the conventional cutting and the UEVC (material of workpiece: brass; depth of cut = 30 m; cutting speed = 1 mm/s). (a) Primary cutting force (Fx ) and (b) thrust force (Fz ).
Fig. 15. Micro V-groove machined by the conventional cutting and the UEVC (material of workpiece: brass; depth of cut = 30 m; cutting speed = 1mm/s). (a) Micro V-groove by the conventional cutting and (b) micro V-groove by the UEVC. From the experimental results presented in Figs. 12 and 14, it is noticeable that the extent by which the cutting force is decreased when the UEVC is applied to micro V-grooving appears to depend upon the cutting parameters. To delve into this observation, an experiment in which the cutting depth is linearly increased while cutting is performed. The cutting speed is set to 5 mm/s, and the initial cutting depth is set to 5 m, linearly increasing to 25 m until the cutting tool travels 30 mm. The results are shown in Fig. 16. Due to the geometrical feature of a V-groove that the machined areas are proportional to the square of the cutting depth, the cutting force grows with the square of the depth of cut. At the entry cutting, the cutting depth is 5 m, and the measured cutting force for the conventional micro V-grooving is approximately 0.2 N while the measured cutting force for the UEVC is 0.05 N, a quarter of
Fig. 16. Comparison of cutting force: conventional cutting vs. the UEVC (material of workpiece: brass; depth of cut = 5 m → 25 m; cutting speed = 5 mm/s).
that for the conventional cutting. But at the exit cutting where the cutting depth reaches 25 m, the cutting force for the conventional cutting is approximately 1.6 and 0.8 N for the UEVC which is one half of that for the conventional cutting. In other words, when the cutting depth is relatively small, a decrease in the cutting force for the UEVC is more pronounced. This confirms that the decline of the specific cutting energy stemming from the reduction of frictional force between the cutting tool, chip, and workpiece is contributable to a decrease in the cutting force for the UEVC.
5. Conclusions It is experimentally shown that the ultrasonic elliptical vibration cutting can be used for machining micro V-grooves with advantages over the conventional non-vibratory V-grooving method. The advantages of micro V-grooving with the UEVC are summarized as follows. First, the cutting force is significantly reduced. Specifically reduction is more pronounced for the small cutting depths, which is attributed to the reduction of frictional force between the tool, chip and workpiece. Secondly, the UEVC suppresses the formation of the burrs at the boundaries of machining, resulting in better shape accuracy. However, the inside surface of the micro V-groove with the UEVC is observed rougher than with the conventional cutting, because cyclic vibrating waves are left on the machined surface. In addition, the kinematical analysis of the UEVC system actuated by two parallel stacked piezoelectric actuators has found that the cutting tool path can be readily manipulated by changing design parameters of the system, such as dimensions
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of the mechanism, phase difference, and relative magnitude of the sinusoidal excitation voltages. References [1] B. Thoe, K. Aspinwall, H. Wise, Review on ultrasonic machining, Int. J. Mach. Tools Manuf. 38 (4) (1998) 239–255. [2] T. Moriwaki, E. Shamoto, Ultraprecision ductile cutting of glass by applying ultrasonic vibration, Ann. CIRP 41 (1994) 141–144. [3] Z. Pei, P. Ferreira, An experimental investigation of rotary ultrasonic face milling, Int. J. Mach. Tools Manuf. 39 (1999) 1327–1344. [4] M. Wiercigroch, R. Neilson, M. Player, Material removal rate prediction for ultrasonic drilling of hard materials using an impact oscillator approach, Phys. Lett. A 259 (1999) 91–96.
[5] E. Shamoto, T. Moriwaki, Study on elliptical vibration cutting, Ann. CIRP 43 (1994) 35–38. [6] C. Ma, E. Shamoto, T. Moriwaki, L. Wang, Study of machining accuracy in ultrasonic elliptical vibration cutting, Int. J. Mach. Tools Manuf. 44 (2004) 1305–1310. [7] T. Moriwaki, E. Shamoto, Ultrasonic elliptical vibration cutting, Ann. CIRP 44 (1995) 31–34. [8] M.A. Cerniway, Elliptical diamond milling: kinematics, force, and tool wear, M.S. Thesis, North Carolina State University (2001). [9] J. Lee, D. Lee, Y. Jung, W. Chung, A Study on micro-grooving characteristics of planar lightwave circuit and glass using ultrasonic vibration cutting, J. Mater. Process. Technol. 130–131 (2002) 396–400.
An ultrasonic elliptical vibration cutting device for micro V-groove machining: Kinematical analysis and micro V-groove machining characteristics Gi Dae Kim a , Byoung Gook Loh b,∗ a
School of Mechanical and Automotive Engineering, Catholic University of Daegu, Hayang-up, Gyeongsansi, Gyeongbuk 712-702, Republic of Korea b Department of Mechanical Systems Engineering, Hansung University, Samsun-dong 389, Sungbuk-gu, Seoul 136-792, Republic of Korea Received 9 August 2005; received in revised form 20 December 2006; accepted 16 February 2007
Abstract Micro V-groove machining characteristics of an ultrasonic elliptical vibration cutting (UEVC) device have been experimentally investigated and compared with the conventional micro V-grooving. From the initial experiments performed on ductile material such as aluminum and brass with a single crystal diamond cutting tool, it was found that the cutting force was significantly decreased and the formation of burrs at the machining boundaries was greatly suppressed in the UEVC. The elliptical vibration of the cutting tool was achieved using two parallel stacked piezoelectric actuators with assembling metal structures. Kinematical analysis of the UEVC system has shown that the manipulation of the cutting tool path is possible by changing dimension of the mechanism, phase difference, and relative magnitude of the voltages applied to the piezoelectric actuators. © 2007 Elsevier B.V. All rights reserved. Keywords: Ultrasonic elliptical vibration cutting (UEVC); Single crystal diamond cutting tool; Burr; Piezoelectric actuator; Phase difference
1. Introduction The demands for precision and micro-machining technologies that enable to produce mechanical components of micrometer scale and mechanical features such as V-grooves and cavities of micrometer scale have drastically increased with the advance of semiconductor manufacturing industry, microelectro-mechanical systems (MEMS), bio-technology (BT), and nano-technology (NT). But the conventional machining technologies such as turning, milling, and drilling appear to have reached to the point where the speed at which the conventional machining technologies advances cannot keep up with the demands of industries requiring micro-machining technologies. In an effort to meet these demands, non-conventional machining technologies that include micro-electrical discharge machining, laser machining, electro chemical machining and, etc. have been proposed, but applications of these technologies have been limited because of lack of machinable workpieces, thermal distortion of machined surface, need for the pre-machining
∗
Corresponding author. Tel.: +82 2 760 5865; fax: +82 2 760 4329. E-mail address: [email protected] (B.G. Loh).
0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2007.02.047
of an electrode, high cost and high energy requirements, and so on. A new surface machining technology that is based on the conventional cutting but has advantages such as high productivity, low-cost and high degree of freedom in machining is needed. Therefore, a new machining method using ultrasonic vibration as a means for precision machining was proposed, but has primarily been applied to machining micro-holes which are created by micro-chipping caused by vibrating abrasive slurry at an ultrasonic frequency with a machining tool, and making it colliding with the workpiece [1]. Other application of the ultrasonic vibration to the precision machining includes reduction of the cutting force by vibrating a cutting tool in the cutting direction. But most of the efforts are geared toward enhancing the surface roughness, not toward the realization of a new kind of precision micro-machining [2–4]. Shamoto and Moriwaki [5] proposed a novel vibration cutting method termed as “the elliptical vibration cutting (EVC)” in which a cutting tool attached to piezoelectric actuators circles along an elliptical path and penetrates into a workpiece when the cutting tool actuated by the piezoelectric actuators is brought into contact with a workpiece. The elliptical path of the cutting tool was generated with two orthogonally assembled
182
G.D. Kim, B.G. Loh / Journal of Materials Processing Technology 190 (2007) 181–188
Fig. 1. Elliptical cutting tool path created by superposition of two spatially orthogonal bending modes (by Shamoto and Moriwaki [6,7]).
piezoelectric actuators. The experimental results indicated a significant decrease in the cutting force using the EVC compared with the conventional machining. Shamoto and co-workers [6] continued their research into increasing the excitation frequency to 20 kHz and creating an elliptical cutting tool path by attaching two pairs of piezoelectric actuators to a rectangular metal block in the orthogonal directions as in Fig. 1. In this method, the vibration amplitude of the cutting tool could be greatly amplified by selecting the excitation frequency as one of the resonance frequencies of the system, and the elliptical cutting tool path was created as superposition of two orthogonal bending modes excited by two pairs of piezoelectric actuators oriented 90◦ to each other. The generation of the elliptical cutting tool path by superimposing two orthogonal modes seems simple in principle, but it is practically challenging to have the elliptical cutting tool path coplanar with the plane containing the cutting and chip-flow direction. Furthermore, there are drawbacks in the design such as zero bandwidth, i.e. fixed excitation frequecny, difficulty in synchronizing two resonant frequencies of the spatially orthogonal bendig modes, compliance of the support, and lack of methodologies to design the optimum shape of horns [7]. Cerniway [8] proposed a device creating an elliptical tool path using two parallel stacked piezoelectric actuators with bandwidth of 4.5 kHz and investigated creating a precision surface on the diamond turning machine. The audible actuation frequency creates unpleasant noises, and the low bandwidth limits the feedrate of the workpiece, resulting in prolonged machining time. Among many potential applications of the ultrasonic elliptical vibration cutting (UEVC), the UEVC is ideal for patterning micro V-grooves that have been widely used for optical devices, because fabricating micro V-grooves free of burrs with conventional techniques, such as etching and lithography is known to be costly and time-consuming, but cutting in conjunction with ultrasonic vibration has demonstrated its effectiveness in fabricating a surface with high surface finish. Capabilities for fabricating an array of micro V-grooves on a surface are essential to manufacturing optical devices, such as a Fresnel lens and a liquid crystal display (LCD). Accordingly, an in-depth grasp of machining characteristics of micro V-groove using the UEVC would play a
critical role in establishing low-cost and reliable micro V-groove fabrication technology. Lee et al. [9] studied the characteristics of micro V-grooves produced on a planar lightwave circuit and glass by the UEVC. It is notable that feasibility of applying the UEVC to micro V-grooving has been studied, but the elliptical tool paths are generated with superposition of two orthogonal resonant modes, which puts constraints on its industrial implementation as discussed in review of Shamoto’s studies. In this study, a UEVC system, which is based on Cerniway’s design but modified to increase the operating frequency to 65 kHz and to facilitate fabrication, is presented, and its kinematical analysis is performed to investigate the formation of the elliptical cutting tool path. In addition, micro V-groove machining characteristics of the UEVC, such as the primary and thrust cutting force, surface finish, and the formation of chips and burrs are experimentally investigated. 2. Generation and analysis of the elliptical vibration of the cutting tool 2.1. Principle of the elliptical vibration cutting (EVC) In Fig. 2(a–d), the principle of the EVC is illustrated. In the EVC, the elliptically rotating speed of the cutting tool is set to be greater than the cutting speed, which allows the cutting tool to make contacts with a workpiece and to lose contacts in succession along a proceeding elliptical path in the process of cutting as shown in Fig. 2(a). Cutting is initiated bringing the cutting tool into contact with the workpiece as in Fig. 2(b), and then, the cutting tool cuts into the workpiece in a way similar to the conventional cutting process as in Fig. 2(c). What differentiates the EVC from the conventional cutting is the process illustrated in Fig. 2(d) where the cutting tool moves up along the upward elliptical path and lifts off the workpiece. This upward elliptical motion contributes to the reduction of the cutting force, because the frictional force between the rake face of the tool and the chip is reversed in contrast to the conventional cutting process, assisting in discharging of chips. The cutting tool completely looses a contact with the workpiece at lift-off and moves to a position to repeat the cutting cycle as in Fig. 2(a). 2.2. Ultrasonic elliptical vibration cutting system (UEVCS) Fig. 3 shows the picture of the piezoelectric actuator for the ultrasonic elliptical vibration cutting system (UEVCS) which consists of two parallel stacked piezoelectric actuators, a single crystal diamond cutting tool, and supporting metal structures. The stacked piezoelectric actuators which enable low voltage operation are sandwiched between the assembling structures and preloaded with a bolt. When energized with sinusoidal voltages, the stacked piezoelectric actuators periodically expand and contract, and controlling a phase between the sinusoidal voltages applied to the actuators allows for translating or rotating the cutting tool along a prescribed elliptical path.
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183
Fig. 2. Principle of elliptical vibration cutting.
2.3. Kinematical analysis of the UEVCS For kinematical analysis, the UEVCS is modeled as a simple T-shaped bar as shown in Fig. 4 where y1 and y2 are the displacements resulting from the expansion of the piezoelectric actuators, and the position P denoting the tip of the T-shaped bar represents the edge of the cutting tool. The movements of the position P on the x–y plane in response to the variation of displacements y1 and y2 represent the cutting tool path of the UEVCS and can be formulated into Eqs. (4) and (5) by substituting Eq. (3) into Eqs. (1) and (2) where xCT and yCT are the displacements of P in the x and y direction, respectively, and lx is half distance between PZTs in the x direction and ly is the distance between the cutting tool edge and the PZT in the y
Fig. 3. Picture of the UEVCS.
direction. xCT = −ly sin θ
(1)
yCT = y1 + lx sin θ + ly cos θ − ly −1 y2 − y1 θ = sin 2lx
(2)
ly (y1 − y2 ) 2lx y2 − y1 y1 + y 2 − ly = + ly cos sin−1 2 2lx
(3)
xCT =
(4)
yCT
(5)
Since the piezoelectric actuators are energized with sinusoidal voltages, y1 and y2 can be expressed as Eqs. (6) and (7). y1 = A1 sin(2πft)
(6)
y2 = A2 sin(2πft + φ)
(7)
Fig. 4. Kinematical schematic diagram for the UEVCS.
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Fig. 5. Generation of elliptical cuing tool path by exciting two parallel PZTs with 90◦ phase difference. Angular displacement: (a) 45◦ , (b) 135◦ , (c) 225◦ , and (d) 315◦ .
where f is the frequency of the sinusoidal voltage, t the time, φ the phase difference between y1 and y2 , and A1 and A2 are the vibration amplitudes. To illustrate the generation of an elliptical cutting tool path, it is assumed that the amplitudes, A1 and A2 are 1 m and a phase difference, φ is 90◦ . The displacements y1 and y2 are significantly smaller than the dimension of the T-shaped bar. As a result, θ in Eq. (3) can be assumed to be very small, permitting the application of small angle assumption (sin θ ≈ θ, cos θ ≈ 1), which simplifies Eqs. (4) and (5) as in Eqs. (8) and (9). xCT = (sin 2πft − cos 2πft) (8) (ly /2lx ) yCT = (sin 2πft + cos 2πft) (1/2)
(9)
Squaring Eqs. (8) and (9), respectively, and summing give Eq. (10) which is clearly the equation √ of an ellipse with the length of the semi-major axis being (ly / 2lx ) m and the length of the √ semi-minor axis being (1/ 2) m. 2 xCT
2 yCT
+ √ √ 2 =1 2 (ly / 2lx ) (1/ 2)
(10)
A graphical illustration of generation of the elliptical tool path is shown in Figs. 5 and 6. The position of the cutting tool is at the peak of the ellipse when the angular displacement of Eqs. (6) and (7) are 45◦ . The cutting tool follows through the elliptical path as the angular displacements of PZT1 and PZT2 increase and reach to the farthest right of the ellipse at an angular displacement of 135◦ , to the bottom at 225◦ , and to the farthest left at 315◦ . The cutting tool path completes one cycle at an angular displacement of 360◦ , and this process is repeated at a prescribed frequency, f, generating a continuous elliptical motion of the cutting tool. Fig. 7 shows the variation of the elliptical cutting tool path simulated with MATLAB based on Eqs. (4) and (5) as a function of the phase difference between the PZT1 and PZT2 and dimensional parameters of T-shaped bar, lx and ly , respectively. For the case of lx = ly , the cutting tool path becomes a circular trajectory with a phase difference of 90◦ , a linear trajectory in the thrust direction with a phase difference of 0◦ , and quasi-linear trajectory in the cutting direction with a phase difference of 180◦ as shown in Fig. 7(a). The simulated results indicate that the ratio of the length of the major axis to the minor axis of the ellipti-
cal cutting tool path can be readily manipulated by varying the phase difference. The ratio of ly to lx determines the degree of the leverage effect of the T-shaped bar. As the ratio of ly to lx grows, the length of the major axis of the elliptical cutting tool path becomes greater than that of the minor axis due to the leverage effect. Thus, larger ratio of ly to lx produces larger displacement in the cutting direction than the thrust direction. Fig. 7(b) shows the elliptical cutting tool paths simulated for the case of lx = 7 mm and ly = 30 mm, respectively, under which cutting experiments presented in Chapter 4 were performed. In this case, a circular cutting tool path is obtained at a phase difference of 28.1◦ . Through the simulation, it was found that the relative magnitude difference between the amplitudes of the piezoelectric actuators also affects the shape of the elliptical cutting tool path by changing the angle of axes of the ellipse. 3. Experimental setup The UEVCS that includes a single crystal diamond cutting tool, stacked piezoelectric actuators, and assembling metal structures is mounted on the 3axis precision motorized stage and placed on the air-vibration-isolation-table as shown in Fig. 8. A jig on which the workpiece is attached is bolted down to the 3-axis tool dynamometer (Kistler 9257B) which measures the cutting forces. The measured cutting forces are amplified and sent to the PC for analysis. The
Fig. 6. Sinusoidal amplitude variations of PZT1 and PZT2 (in case of A1 = A2 = 1 m, φ = 90◦ ).
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Table 1 Specifications of a single crystal diamond cutting tool Nose radius Rake angle Clearance angle Nose angle
600 nm 0◦ 6◦ 80◦
Fig. 9. SEM picture of a single crystal diamond cutting tool nose.
specifications of the single crystal diamond cutting tool are detailed in Table 1, and its picture taken using scanning electron microscopy (SEM) is shown in Fig. 9. The stacked piezoelectric actuators are energized by sinusoidal voltages with a frequency of 65 kHz. The measured vibration amplitude of the piezoelectric actuator in the cutting direction is approximately 0.8 m. The phase difference between supplied sinusoidal voltages is set to 90◦ . Workpieces tested are made of aluminum(Al5052), copper(C1100), and brass(C2801, Cu: 60%, Zn: 40%).
4. Experimental results Fig. 7. Simulation results of elliptical cutting tool path with variation of phase. (a) lx = 10 mm, ly = 10 mm and (b) lx = 7 mm, ly = 30 mm.
To investigate characteristics of the UEVC, micro V-grooves are machined by the UEVC and the conventional cutting as illustrated in Fig. 10, and the pictures of micro V-grooves taken from the top of the workpiece using the SEM are shown in Fig. 11. The workpiece tested is made of Al5052, and the cutting speed is 5 mm/s, and the cutting depth is 15 m.
Fig. 8. Photograph of experimental setup.
Fig. 10. Graphical illustration of conventional cutting vs. the UEVC.
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Fig. 11. Micro V-groove machined by conventional cutting and the UEVC (material of workpiece: Al5052; cutting depth = 15 m; cutting speed = 5 mm/s). (a) Micro V-groove machined by the conventional cutting and (b) micro V-groove machined by the UEVC. Small cutting depth causes the specific cutting energy to increase due to the size effect, resulting plastic deformations in workpiece and creating burrs at the cutting boundaries. This phenomenon can be observed in the conventional micro V-grooving as in Fig. 11(a) but cannot be observed in the micro V-groove created with the UEVC as in Fig. 11(b). It can be, therefore, inferred that the UEVC significantly reduces the frictional force occurring between the cutting tool and chip resulting in a decline in the specific cutting energy. The inference can be verified by measuring the primary cutting forces for the conventional micro Vgrooving and the micro V-grooving with the UEVC. The measurement of the cutting forces are shown in Fig. 12 which indicates the average cutting force for the UEVC is decreased by approximately 80% compared with the conventional micro V-grooving. For the surface finish of the inside of the micro V-groove, it is observed that the conventional micro V-grooving creates a smoother surface than the micro Vgrooving with the UEVC. The superficial deterioration in surface finish inside the micro V-groove is attributable to wave-like machining marks left on the machined surface as a result of the proceeding elliptical motion of the cutting tool as investigated in previous research of Moriwaki and Shamoto [7]. To investigate the formation of the exit burrs, the cutting experiment for the copper is performed with the cutting depth of 20 m and cutting speed of 5 mm/s. The pictures of micro V-groove after the cutting experiment taken by SEM are shown in Fig. 13. It is observed that the exit burr is not created from the UEVC, but that the conventional micro V-grooving produces the exit burr as the cutting tool moves away from the workpiece. Micro V-grooving experiments are performed with the workpiece made of brass for the case of the cutting depth of 30 m, and the cutting speed of 1 mm/s. And the primary cutting force, the thrust force, and the surface finish are observed. As in Fig. 14, it is observed that both the primary and thrust force are decreased by approximately 50% in micro V-grooving using the UEVC
Fig. 12. Comparison of primary cutting force: conventional cutting vs. the UEVC (material of workpiece: Al5052; cutting depth = 15 m; cutting speed = 5 mm/s).
compared with the conventional micro V-grooving. It is also observed that as in Fig. 15 micro V-grooving with the UEVC significantly reduces the formation of burr but produces the surface finish inside the micro V-groove inferior to the conventional micro V-grooving, which is consistent with the micro V-grooving experiments with aluminum.
Fig. 13. Comparison of exit burr formation: conventional cutting vs. UEVC (material of workpiece: C1100, cutting depth = 20 m, cutting speed = 5mm/s) (a) Micro V-groove by conventional cutting and (b) micro V-groove by the UEVC.
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Fig. 14. Comparison of primary and thrust cutting forces between the conventional cutting and the UEVC (material of workpiece: brass; depth of cut = 30 m; cutting speed = 1 mm/s). (a) Primary cutting force (Fx ) and (b) thrust force (Fz ).
Fig. 15. Micro V-groove machined by the conventional cutting and the UEVC (material of workpiece: brass; depth of cut = 30 m; cutting speed = 1mm/s). (a) Micro V-groove by the conventional cutting and (b) micro V-groove by the UEVC. From the experimental results presented in Figs. 12 and 14, it is noticeable that the extent by which the cutting force is decreased when the UEVC is applied to micro V-grooving appears to depend upon the cutting parameters. To delve into this observation, an experiment in which the cutting depth is linearly increased while cutting is performed. The cutting speed is set to 5 mm/s, and the initial cutting depth is set to 5 m, linearly increasing to 25 m until the cutting tool travels 30 mm. The results are shown in Fig. 16. Due to the geometrical feature of a V-groove that the machined areas are proportional to the square of the cutting depth, the cutting force grows with the square of the depth of cut. At the entry cutting, the cutting depth is 5 m, and the measured cutting force for the conventional micro V-grooving is approximately 0.2 N while the measured cutting force for the UEVC is 0.05 N, a quarter of
Fig. 16. Comparison of cutting force: conventional cutting vs. the UEVC (material of workpiece: brass; depth of cut = 5 m → 25 m; cutting speed = 5 mm/s).
that for the conventional cutting. But at the exit cutting where the cutting depth reaches 25 m, the cutting force for the conventional cutting is approximately 1.6 and 0.8 N for the UEVC which is one half of that for the conventional cutting. In other words, when the cutting depth is relatively small, a decrease in the cutting force for the UEVC is more pronounced. This confirms that the decline of the specific cutting energy stemming from the reduction of frictional force between the cutting tool, chip, and workpiece is contributable to a decrease in the cutting force for the UEVC.
5. Conclusions It is experimentally shown that the ultrasonic elliptical vibration cutting can be used for machining micro V-grooves with advantages over the conventional non-vibratory V-grooving method. The advantages of micro V-grooving with the UEVC are summarized as follows. First, the cutting force is significantly reduced. Specifically reduction is more pronounced for the small cutting depths, which is attributed to the reduction of frictional force between the tool, chip and workpiece. Secondly, the UEVC suppresses the formation of the burrs at the boundaries of machining, resulting in better shape accuracy. However, the inside surface of the micro V-groove with the UEVC is observed rougher than with the conventional cutting, because cyclic vibrating waves are left on the machined surface. In addition, the kinematical analysis of the UEVC system actuated by two parallel stacked piezoelectric actuators has found that the cutting tool path can be readily manipulated by changing design parameters of the system, such as dimensions
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