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The effect of tool nose radius in ultrasonic vibration cutting of hard metal
International Journal of Machine Tools & Manufacture 43 (2003) 1375–1382
The effect of tool nose radius in ultrasonic vibration cutting of hard metal M. Xiao a,∗, K. Sato a, S. Karube a, T. Soutome b a
Utsunomiya University, Department of Mechanical Systems Engineering, 7-1-2 Yoto, Utsunomiya, Tochigi, 321-8585, Japan b Pilot Corporation, 1-4-3 Nisihatiman, Hiratsuka, Kanagawa, 254-8585, Japan Received 7 December 2002; received in revised form 28 April 2003; accepted 7 May 2003
Abstract A tool edge with a small nose radius can alleviate the regenerative chatter. In general, it is important for conventional cutting to use the smallest possible tool nose radius. However, a sharp tool shape has an adverse effect on tool strength and the instability of machining process still occurs. Previous researches have shown that vibration cutting has a higher cutting stability as compared with conventional cutting. In the present paper, the influence of tool nose radius on cutting characteristics including chatter vibration, cutting force and surface roughness is investigated by theory. It is found from the theoretical investigation that a steady vibration created by motion between the tool and the workpiece is still obtained even using a large nose radius in vibration cutting. This article presents a vibration cutting method using a large nose radius in order to solve chatter vibration and tool strength problem in hard-cutting. With a suitable nose radius size, experimental results show that a stable and a precise surface finish is achieved. 2003 Elsevier Ltd. All rights reserved. Keywords: Nose radius; Chatter vibration; Steady vibration; Ultrasonic vibration cutting; Hard-cutting; Precision machining; Cutting model
1. Introduction Hardened steel, Ni-based alloys and brittle materials are very difficult to machine using conventional cutting methods. Since these materials possess high strength and low thermal conductivity, they almost always cause machining troubles such as chatter vibration and unusual tool wear. During the past three decades, the technique of vibration cutting, which is an intermittent cutting force method with ultrasonic frequency, has been successfully applied in hard-cutting [1]. Vibration cutting is a quite promising machining method for hard-cutting because of its high cutting stability [2]. However, the intermittent cutting force has a bad influence on the strength of tool edge so that instability of the machining process can still arise. Some methods such as adding a leaning tool device or using a diamond-tool have been undertaken in order to improve machining performance [3–5]. Although these efforts were designed to achieve
∗
Corresponding author. Tel. and fax: +81-28-689-6065. E-mail address: [email protected] (M. Xiao).
0890-6955/$ - see front matter 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0890-6955(03)00129-9
a mirror surface, there has been little discussion about the physical cause of machining instabilities. The major cause of machining instabilities in hardcutting are regenerate chatter and unusual tool wear such as fracturing or chipping. It is important for conventional cutting to use the smallest possible nose radius in general, because a small nose radius can alleviate the regenerative effect [6,7]. However, a tool with small nose radius still will lead to significant instabilities [6,8] due to marked decline in the strength of tool edge. Work by Liu et al. [9] indicated that it is possible to achieve high surface quality in combination with a chosen nose radius. Recent experimentation and theory by the author of this paper [2] showed that vibration cutting has a higher cutting stability as compared with conventional cutting. The research [2] presented a cutting model containing the vibration cutting process. When unstable chatter vibration is suppressed by vibration cutting, the work displacement amplitudes can be accurately predicted by the model. This chatter-suppressing dynamics of vibration cutting is called steady vibration in our research. In the present paper, the work displacements are simu-
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M. Xiao et al. / International Journal of Machine Tools & Manufacture 43 (2003) 1375–1382
Nomenclature m x 1, x 2 cl, c2 k 1, k 2 hxl, hx2 sf Fc,Ft z v a0 g0 tl,tm w y, yback y˙ f,l,kab f, a T tc r rn fd fo m Cs Kr Rth Ry
effective mass work displacement in xl and x2 direction damping coefficient in xl and x2 direction stiffness coefficient in xl and x2 direction additional damping factor in xl and x2 direction low speed stability factor cutting force and thrust force variation of the tool angle cutting speed tool rake angle tool clearance angle deformed and undeformed chip thickness width of cut work displacement in present and previous revolution velocity of the work displacement shear angle, friction angle and shear stress tool frequency and tool amplitude tool vibration period (1/f) cnet cutting time in each tool vibration period edge contact rate (tc/T) tool nose radius feed per revolution overlap-length between the previous cut and the present cut overlap factor side cutting edge angle maximum cutting edge angle theoretical surface roughness surface roughness
lated by using our cutting model, in order to have a good grasp on different vibrations such as steady vibration or chatter vibration. The influence of tool nose radius on cutting characteristics including chatter vibration, cutting force and surface roughness is investigated by theory. It is found from the theoretical investigation that steady vibration is still obtained even using a large nose radius in vibration cutting. This article presents a vibration cutting method using a large nose radius, in order to solve chatter vibration and tool strength problem in hard-cutting. Experimental results obtained with a suitable nose radius size will show that a stable and a precise surface finish is achieved.
2. Model for machine tool chatter
duced. The equations of motion for the cutting system are as follows:
再
mx¨1 ⫹ c1hx1x˙1 ⫹ k1x1 ⫽ F1 ⫽ Fxsina1 ⫹ Fycosa1 mx¨2 ⫹ c2hx2x˙2 ⫹ k2x2 ⫽ F2 ⫽ Fxsina2 ⫹ Fycosa2 (1)
where
再
Fx ⫽ Fccosz ⫹ Ftsinz Fy ⫽ ⫺Fcsinz ⫹ Ftcosz
hxi ⫽
冦
1⫺sf
1
A dynamic cutting model containing the vibration cutting process with an arbitrarily chosen two degrees of freedom had been presented by authors [2] (see Fig. 1). The chatter model is described by the differential equations. In the case of vibration cutting process, an intermittent cutting force with ultrasonic frequency is intro-
z (for y˙ ⬍ 0) g (i ⫽ 1,2) (for y˙ⱖ0)
(2)
(3)
where z and g are given by: z ⫽ tan⫺1
冉冊
y˙ , g ⫽ g0 ⫹ z. v
(4)
M. Xiao et al. / International Journal of Machine Tools & Manufacture 43 (2003) 1375–1382
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In the case of the vibration cutting process, the intermittent cutting force with ultrasonicfrequency has the following form: R⫽
kabt1w U(t )t(t,r). sinfcos(f ⫹ l⫺a) 1
(8)
where the edge contact unit step function t(t,r) is expressed as: t(t,r) ⫽
(9)
再
1 : nTⱕt ⬍ (n ⫹ r)T
0 : (n ⫹ r)Tⱕt ⬍ (n ⫹ 1)T (n ⫽ 0,1,2,%)
where the edge contact rate r denoted as the net cutting ratio at each tool vibration period T can be obtained by using the following equation: af ⫽ v
冋
1⫺r
册
v 2sinprcos cos (⫺ )⫺pr 2paf ⫺1
(10)
(for 2paf ⬎ v).
3. Experimental procedure Fig. 1. Vibration model of chip formation with two degree of freedom.
With a thin-shear-plane model for orthogonal cutting [10], the cutting force Fc and the thrust force Ft can be calculated from:
冦
Fc ⫽ Rcos(l⫺a)
Ft ⫽ Rsin(l⫺a) kabt1w R⫽ U(t ) sinfcos(f ⫹ l⫺a) 1
where a, tl and U(t1) take the following form: a ⫽ a0⫺z, t1 ⫽ tm ⫹ (yback⫺y) and U(t1)
再
(5)
(6)
0 t1 ⬍ 0 . 1 t1ⱖ0 The cutting force components are determined by the experimental cutting database of S45C carbon steel [11]: ⫽
冦
f ⫽ exp(0.0587v ⫹ 1.0398t1 ⫹ 0.6742a⫺1.2392)
Stainless steel SUS304 and nickelbase alloy Incone1600, classified as difficult-to-cut materials, are used in this turning. The machinability and chemical composition of the two materials are listed in Table 1. Turning tests were carried out on a lathe fitted with a vibration cutting device. Fig. 2 shows the dimensions of the workpiece holder and the workpiece used in all experimental tests. Five different tool nose radii, rn = 0.02, 0.1, 0.2, 0.5, 1 mm, were investigated and all these side cutting edge angles were 45°. A tool with a rake angle of 0° and a clearance angle of 3° was used. A tool edge material with a low-cost cemented carbide K10 was chosen. The experimental conditions used in turning tests are shown in Table 2. The surface roughness was measured using a Suntronic3+ surface roughness meter (Taylor Hobson). The largest peak to valley Ry with a cut-off length of 0.8 mm was taken to represent the experimental results.
4. Theory 4.1. Influence of tool nose radius on regenerate chatter
l ⫽ exp(⫺0.0546v⫺0.8856t1 ⫹ 0.8923a⫺0.2388) kab ⫽ exp(0.0059v⫺0.4246t1 ⫹ 0.0818a ⫹ 6.3211). (7)
In the present numerical simulation, work displacements measured by an eddy current sensor were used to determine the hardware parameters [2]. The effective
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Table 1 Composition of workpiece materials Workpiece materials
C (%)
Si (%)
Mn (%)
Cr (%)
Ni (%)
Hardness (HB)
UTS (N/mm2)
SUS304 Incone1600
0.08 0.15
1.0 0.50
2.0 1.00
18–20 15.5
8–10 72.0
187 179
520 550
Fig. 2.
Dimensions of workpiece holder and workpiece.
mass, stiffness, and damping were determined to be m = 0.19 kg, k 1 = 0.70, k 2 = 1.12 MN/m, c 1 = 52, c 2 = 63 Ns/m. The cutting parameters were used based on the experimental conditions in Table 2. The cutting parameters are as follows: v = 58 m/min; R S = 460 rpm; t m = 0.05 mm; w = 0.051 mm; a 0 = 0° and g 0 = 3°. The tool vibration frequency and amplitude are f = 20 kHz and a = 15 µm respectively. From Eq. (10), the edge contact rate r is determined to be 0.48. In addition, a 1 = 20°, a 2 = 110° and s f =1 [12] are chosen. The simulation results corresponding to experimental tests are shown in Fig. 3. The work displacement obtained by conventional cutting [see Fig. 3(a)] becomes larger and larger with increasing number of revolutions and its amplitude becomes saturated with a finite value. In contrast, the simulation’s result obtained by vibration cutting [see Fig. 3(b)] shows that the growth of the work dis-
Fig. 3. Work displacement simulations. Chatter-generating dynamics for conventional cutting in (a). Chatter-suppressing dynamics for vibration cutting in (b).
placement ceases with increasing number of revolutions and its maximum amplitude is a small value of 4.3 µm. It is shown that chatter vibration is effectively suppressed by applying vibration cutting, although a strong chatter vibration may be caused during conventional cutting. The figure also indicates that it is possible for vibration cutting to achieve a machining accuracy of 4.3 µm. In this simulated investigation, it is assumed that the same surface between the previous pass and the present pass is cut successively. However, the practical turning
Table 2 Experimental conditions Tool edge
Cuttingconditions
Nose radius Side cutting edge angle Rake angle and clearance angle Material Spindle speed Cutting speed Depth of cut Feed rate Tool frequency Tool amplitude
0.02, 0.1, 0.2, 0.5, 1 mm 45° a 0 = 0° g 0 = 3° K10 460 rpm 58 m/min 0.05 mm 0.051 mm/rev 20 kHz 15 µm
M. Xiao et al. / International Journal of Machine Tools & Manufacture 43 (2003) 1375–1382
operations are not always successive cuts. In order to take the regenerate effect into account, the overlap factor m is introduced [13,14]. The overlap factor is a constant value between zero and one, i.e. 0ⱕmⱕ1. Chatter vibration occurring in the overlap factor of 0 is designated primary chatter, otherwise chatter vibration is termed regenerate chatter [14]. In the case of our simulation, the surface of the present pass is modeled along with the surface of the previous pass and so m = 1. Experiments have shown that the overlap factor is principally affected by the tool nose radius and side cutting edge angle [7]. For the certain side cutting edge angle, the overlap factor m may be calculated from the ratio between the overlap-length of the machined surface fo and the feed rate fd [7]. An example of different tool nose radius with the same side cutting edge angle for turning process is shown in Fig. 4. It can be seen that the smaller nose radius has the smaller the overlap factor. For this reason, when the tool nose radius is kept as small as possible, the regenerative chatter effect can be alleviated. In contrast, our simulated result [see Fig. 3(b)] shows that the regenerative chatter is suppressed by vibration cutting even using the overlap factor of 1. Therefore, it is possible for vibration cutting to use a large nose radius. 4.2. Influence of tool nose radius on cutting force and unusual tool wear The changes of the cutting force on a small and a large nose radius size are shown in Fig. 4. The three force components Fz, Fd and Ff are in the tangential, radial, and axial directions respectively. In a small nose radius [see Fig. 4(a)], the maximum cutting edge angle Kr and the side cutting angle Cs are of equal value. However, in the case of a large nose radius [see Fig. 4(b)] the maximum cutting edge angle is determined by the following expression [6]:
Fig. 4.
Kr ⫽ cos⫺1
rn⫺tm . rn
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(11)
In the present experimental condition, the maximum cutting edge angle decreases from 41°25⬘to 18°12⬘when the nose radius increases from 0.2 to 1 mm. Thus, a small cutting edge angle is produced by a large nose radius and then the extent of the cutting force Fd and Ff will be altered (see Fig. 4). Experimental results have also shown that Ff will decrease whereas Fd will increase and the change in Fz will be almost negligible with increasing nose radius size [6,15,16]. Because the cutting force Fd in the radial direction quickly increases, chatter vibration may be caused by the large nose radius. On the other hand, a leading cause of unusual tool wear is deficient in the strength of tool edge. It is considered that the tool fracturing or chipping occurs when the shear stress is too large in the tangential and axial directions. Since the large nose radius decreases the cutting force Ff and increases the shear area (the increase of the length AB), the unusual tool wear can be reduced by the large nose radius. Additionally, the chamfered tool edge can prevent the temperature concentration and plastic deformation so that the machining stabilities are increased. 4.3. Influence of tool nose radius on the surface roughness In turning operations, the surface roughness Ry is principally affected by the shape of the tool edge profile and the cutting vibrations, which are created by motion between the tool and the workpiece. The error caused by the tool shape is called the theoretical surface roughness. For a given feed and tool nose radius, the theoretical surface roughness Rth can be calculated by [17] Rth⬇
f 2d . 8rn
Nose radius influence on regenerate effect and cutting force. (a) small nose radius, (b) large nose radius.
(12)
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In the case of tool nose radius 0.02 mm, the theoretical surface roughness has a value of 16.2 µm. From the preceding discussion (section 4.1), it is known that vibration cutting may gain a machining accuracy of 4.3 µm. For achieving the surface roughness, the necessary condition is larger than the tool nose radius of 0.08 mm.
5. Experimental results and discussion In order to observe the nose radius influence on the cutting characteristics, the predicted the maximum amplitude of vibration cutting (4.3 µm) and the surface roughness Ry versus the tool nose radius is shown in Fig. 5. In the case of conventional cutting, a slightly increase of the nose radius size makes the machining accuracy worse due to the occurrence of chatter vibration. Therefore, the smallest nose radius should be adopted in a chatter-generating dynamics. In contrast to vibration cutting, there exists a decrease in the surface roughness with increase in the nose radius size. When the nose radius
Fig. 5. Comparison between predicted and experiment surface roughness Ry versus nose radius, (a) for stainless steel of SUS3046, (b) for nickelbase alloy of Incone1600.
is equal to 0.2 mm, the surface roughness attains an approximate value of the steady vibration. It is experimentally verified that a suitable nose radius can achieve the machining accuracy created by steady vibration in a chatter-suppressing dynamics. To understand the influence of different nose radius on the machining accuracy in vibration cutting, the changes in surface roughness profiles and machined surfaces are shown in Fig. 6. In the case of the nose radius 0.02 mm, shown in Fig. 6(a), the surface roughness profile has a periodical peak-to valley with the feed of 0.051 mm/rev in feed direction, then the surface roughness Ry is 9.5 µm. For the machined surface, the cutting marks of clear straight line in cutting direction can be seen. The surface roughness in such a small nose radius shows the tendency to take the theoretical surface roughness. When the nose radius is 0.2 mm, shown in Fig. 6(b), the edge shape peaks disappear, then the machined surface becomes smooth. The surface roughness in such a suitable nose radius is improved, then it attains an approximate value of the steady vibration. As shown in Fig. 6(c) with the nose radius of 1 mm, the surface roughness profile has a large peak-to valley value with a longer period than the feed of 0.051 mm/rev in feed direction, and a large wave surface from the photograph of
Fig. 6. Change in surface roughness profiles and machined surfaces with varying nose radius in vibration cutting (workpiece: stainless steel of SUS304).
M. Xiao et al. / International Journal of Machine Tools & Manufacture 43 (2003) 1375–1382
machined surface can be seen in cutting direction. The experimental result indicates that a oversize nose radius causes the occurrence of chatter vibration. It is considered that a oversize nose radius results in a pronounced increase of thrust cutting force, then the chattersuppressing dynamics in vibration cutting is destroyed. With an initial nose radius of 0.02 mm and a suitable nose radius of 0.2 mm in vibration cutting, the changes of surface roughness at the cutting length are shown in Fig. 7. A stable and a precise surface finish is achieved by using the suitable nose radius, while the instability of the machining accuracy with the initial nose radius appears at a short cutting length. In regard to the two sizes of nose radius, the photographs of machined surfaces and tool edge after the experimental tests are shown in Fig. 8. In the case of the initial nose radius, the fracturing edge can be seen. Because of the worn tool, the surface roughness profile with a deep peak-to valley is produced so that the machining accuracy becomes worse. In the case of the suitable nose radius, a large cutting edge radius [15] can be seen. Also, the
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situation from the surface roughness profile and the machined surface may be identified as chatter vibration, causing the decrease of surface roughness. It is considered that a large nose radius rubbed by normal tool wear results in the occurrence of chatter vibration. As a result, a suitable tool nose radius prevents the tool fracturing occurrence so that the instability of the machining process is markedly reduced.
6. Conclusions The influence of tool nose radius on cutting characteristics including chatter vibration, cutting force and surface roughness was investigated by theory. Turning tests of two different hard metals were performed on conventional cutting and vibration cutting using five sizes of tool nose radius. The following conclusions were obtained. 1. The simulation results corresponding to the experimental conditions showed that vibration cutting has a chatter-suppressing dynamics, but conventional cutting is a chatter-generating dynamics. 2. The theoretical investigation showed that it is possible for chatter-suppressing dynamics to use a large nose radius. However, the cutting force in the radial direction quickly increases when the tool nose radius is larger than 0.2 mm so that vibration cutting’s chattersuppressing dynamics may be destroyed. 3. The experimental results showed that vibration cutting enables a larger tool nose radius to be used than conventional cutting. In the case of nickelbase alloy Incone1600, the allowable tool nose radius in vibration cutting was 0.2 mm, while one in conventional cutting was 0.02 mm. Also, it was demonstrated that chatter vibration is caused by a larger than tool nose radius of 0.2 mm in vibration cutting. 4. The simulation corresponding to the experimental conditions predicted that the best surface roughness Ry in vibration cutting is 4.3 µm. The experimental results showed that the nearest value (R y = 4.7 µm) of the predicted surface roughness is obtained when tool nose radius is 0.2 mm. The nose radius is determined as a suitable nose radius. 5. The vibration cutting’s experiment using the suitable nose radius of 0.2 mm showed that the tool fracture is prevented and the machining accuracy is improved in comparison with an initial nose radius of 0.02 mm. A stable and a precise surface finish is achieved.
Acknowledgements Fig. 7. Comparison between nose radii 0.02 and 0.2 mm surface roughness Ry versus cutting length in vibrarion cutting, (a) for stainless steel of SUS304, (b) for nickelbase alloy of Incone1600.
The authors would like to thank the Editor in Chief for his many helpful comments. This research was sup-
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Fig. 8. Surface roughness profiles, photographs of machined surfaces and tool edge in vibration cutting (a) after a cutting length of 216 m with the nose radius of 0.02 mm, (b) after a cutting length of 1080 m with the nose radius of 0.2 mm (workpiece: nickelbase alloy of Incone1600).
ported by the Grant-in-Aid for Scientific Research of Japan ((B) no. 14350116).
References [1] J. Kumabe, Vibration Cutting, Jikkyo Publisher, Japan, 1979. [2] M. Xiao, S. Karube, T. Soutome, K. Sato, Analysis of chatter suppression in vibration cutting, Int. J. Mach. Tools Manufact. 42 (2002) 1677–1685. [3] J. Kumabe, K. Fuchizawa, T. Soutome, Y. Nishimoto, Utrasonic superposition vibration cutting of ceramics, Precision Engineering 11 (1989) 71–77. [4] T. Moriwaki, E. Shamoto, Ultraprecision diamond turning of stainless steel by applying ultrasonic vibration, Annals of CIRP 40 (1991) 559–562. [5] M. Jin, M. Murakawa, Development of a practical ultrasonic vibration cutting tool system, J. Mater. Process. Technol. 113 (2001) 342–347. [6] W. Chen, Cutting forces and surface finish when machining medium hardness steel using CBN tools, Int. J. Mach. Tools Manufact. 40 (2000) 455–466. [7] T. Sugita, K. Ueda, T. Inamura, Basic Cutting Study, Kyoritsu Shuppan, Japan, 1990.
[8] F.C. Moon, Dynamics and Chaos in Manufacturing Processes, Wiley, New York, 1998. [9] C.R. Liu, S. Mittal, Single-step superfinish hard machining: feasibility and feasible cutting conditions, Robotics Comput.-Integr. Manufact 12 (1996) 15–27. [10] M.E. Merchant, Mechanics of the Metal Cutting Process, J. Appl. Phys 16 (1945) 267–275. [11] Y. Kashimura, Study on prediction of tool flank wear by means of cutting force ratios (1st report), J. JSPE Japan 51 (1985) 2115–2121. [12] K. Jemielniak, A. Widota, Numerical Simulation of Non-linear Chatter Vibration in Turning, Int, J. Mach Tools Manuf 29 (1989) 239–247. [13] S.A. Tobias, W. Fishwick, The chatter of lathe tools under orthogonal cutting conditions, Trans. ASME B 80 (1958) 1079–1088. [14] H.E. Merritt, Theory of self-excited machine-tool chatter, J. Engg. Ind. ASME 87 (1965) 447–454. [15] J.A. Arsecularatne, R.F. Fowle, P. Mathew, Prediction of chip flow direction, cutting forces and surface roughness in finish turning, J. Manufact. Sci. Eng. ASME 120 (1998) 1–12. [16] H.A. Kishawy, M.A. Elbestawi, Effects of process parameters on material side flow during hard turning, Int. J. Mach. Tools Manufact. 39 (1999) 1017–1030. [17] A. Vyas, M.C. Shaw, Mechanics of saw-tooth chip formation in metal cutting, J. Manufact. Sc. Eng. ASME 121 (1999) 163–172.
The effect of tool nose radius in ultrasonic vibration cutting of hard metal M. Xiao a,∗, K. Sato a, S. Karube a, T. Soutome b a
Utsunomiya University, Department of Mechanical Systems Engineering, 7-1-2 Yoto, Utsunomiya, Tochigi, 321-8585, Japan b Pilot Corporation, 1-4-3 Nisihatiman, Hiratsuka, Kanagawa, 254-8585, Japan Received 7 December 2002; received in revised form 28 April 2003; accepted 7 May 2003
Abstract A tool edge with a small nose radius can alleviate the regenerative chatter. In general, it is important for conventional cutting to use the smallest possible tool nose radius. However, a sharp tool shape has an adverse effect on tool strength and the instability of machining process still occurs. Previous researches have shown that vibration cutting has a higher cutting stability as compared with conventional cutting. In the present paper, the influence of tool nose radius on cutting characteristics including chatter vibration, cutting force and surface roughness is investigated by theory. It is found from the theoretical investigation that a steady vibration created by motion between the tool and the workpiece is still obtained even using a large nose radius in vibration cutting. This article presents a vibration cutting method using a large nose radius in order to solve chatter vibration and tool strength problem in hard-cutting. With a suitable nose radius size, experimental results show that a stable and a precise surface finish is achieved. 2003 Elsevier Ltd. All rights reserved. Keywords: Nose radius; Chatter vibration; Steady vibration; Ultrasonic vibration cutting; Hard-cutting; Precision machining; Cutting model
1. Introduction Hardened steel, Ni-based alloys and brittle materials are very difficult to machine using conventional cutting methods. Since these materials possess high strength and low thermal conductivity, they almost always cause machining troubles such as chatter vibration and unusual tool wear. During the past three decades, the technique of vibration cutting, which is an intermittent cutting force method with ultrasonic frequency, has been successfully applied in hard-cutting [1]. Vibration cutting is a quite promising machining method for hard-cutting because of its high cutting stability [2]. However, the intermittent cutting force has a bad influence on the strength of tool edge so that instability of the machining process can still arise. Some methods such as adding a leaning tool device or using a diamond-tool have been undertaken in order to improve machining performance [3–5]. Although these efforts were designed to achieve
∗
Corresponding author. Tel. and fax: +81-28-689-6065. E-mail address: [email protected] (M. Xiao).
0890-6955/$ - see front matter 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0890-6955(03)00129-9
a mirror surface, there has been little discussion about the physical cause of machining instabilities. The major cause of machining instabilities in hardcutting are regenerate chatter and unusual tool wear such as fracturing or chipping. It is important for conventional cutting to use the smallest possible nose radius in general, because a small nose radius can alleviate the regenerative effect [6,7]. However, a tool with small nose radius still will lead to significant instabilities [6,8] due to marked decline in the strength of tool edge. Work by Liu et al. [9] indicated that it is possible to achieve high surface quality in combination with a chosen nose radius. Recent experimentation and theory by the author of this paper [2] showed that vibration cutting has a higher cutting stability as compared with conventional cutting. The research [2] presented a cutting model containing the vibration cutting process. When unstable chatter vibration is suppressed by vibration cutting, the work displacement amplitudes can be accurately predicted by the model. This chatter-suppressing dynamics of vibration cutting is called steady vibration in our research. In the present paper, the work displacements are simu-
1376
M. Xiao et al. / International Journal of Machine Tools & Manufacture 43 (2003) 1375–1382
Nomenclature m x 1, x 2 cl, c2 k 1, k 2 hxl, hx2 sf Fc,Ft z v a0 g0 tl,tm w y, yback y˙ f,l,kab f, a T tc r rn fd fo m Cs Kr Rth Ry
effective mass work displacement in xl and x2 direction damping coefficient in xl and x2 direction stiffness coefficient in xl and x2 direction additional damping factor in xl and x2 direction low speed stability factor cutting force and thrust force variation of the tool angle cutting speed tool rake angle tool clearance angle deformed and undeformed chip thickness width of cut work displacement in present and previous revolution velocity of the work displacement shear angle, friction angle and shear stress tool frequency and tool amplitude tool vibration period (1/f) cnet cutting time in each tool vibration period edge contact rate (tc/T) tool nose radius feed per revolution overlap-length between the previous cut and the present cut overlap factor side cutting edge angle maximum cutting edge angle theoretical surface roughness surface roughness
lated by using our cutting model, in order to have a good grasp on different vibrations such as steady vibration or chatter vibration. The influence of tool nose radius on cutting characteristics including chatter vibration, cutting force and surface roughness is investigated by theory. It is found from the theoretical investigation that steady vibration is still obtained even using a large nose radius in vibration cutting. This article presents a vibration cutting method using a large nose radius, in order to solve chatter vibration and tool strength problem in hard-cutting. Experimental results obtained with a suitable nose radius size will show that a stable and a precise surface finish is achieved.
2. Model for machine tool chatter
duced. The equations of motion for the cutting system are as follows:
再
mx¨1 ⫹ c1hx1x˙1 ⫹ k1x1 ⫽ F1 ⫽ Fxsina1 ⫹ Fycosa1 mx¨2 ⫹ c2hx2x˙2 ⫹ k2x2 ⫽ F2 ⫽ Fxsina2 ⫹ Fycosa2 (1)
where
再
Fx ⫽ Fccosz ⫹ Ftsinz Fy ⫽ ⫺Fcsinz ⫹ Ftcosz
hxi ⫽
冦
1⫺sf
1
A dynamic cutting model containing the vibration cutting process with an arbitrarily chosen two degrees of freedom had been presented by authors [2] (see Fig. 1). The chatter model is described by the differential equations. In the case of vibration cutting process, an intermittent cutting force with ultrasonic frequency is intro-
z (for y˙ ⬍ 0) g (i ⫽ 1,2) (for y˙ⱖ0)
(2)
(3)
where z and g are given by: z ⫽ tan⫺1
冉冊
y˙ , g ⫽ g0 ⫹ z. v
(4)
M. Xiao et al. / International Journal of Machine Tools & Manufacture 43 (2003) 1375–1382
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In the case of the vibration cutting process, the intermittent cutting force with ultrasonicfrequency has the following form: R⫽
kabt1w U(t )t(t,r). sinfcos(f ⫹ l⫺a) 1
(8)
where the edge contact unit step function t(t,r) is expressed as: t(t,r) ⫽
(9)
再
1 : nTⱕt ⬍ (n ⫹ r)T
0 : (n ⫹ r)Tⱕt ⬍ (n ⫹ 1)T (n ⫽ 0,1,2,%)
where the edge contact rate r denoted as the net cutting ratio at each tool vibration period T can be obtained by using the following equation: af ⫽ v
冋
1⫺r
册
v 2sinprcos cos (⫺ )⫺pr 2paf ⫺1
(10)
(for 2paf ⬎ v).
3. Experimental procedure Fig. 1. Vibration model of chip formation with two degree of freedom.
With a thin-shear-plane model for orthogonal cutting [10], the cutting force Fc and the thrust force Ft can be calculated from:
冦
Fc ⫽ Rcos(l⫺a)
Ft ⫽ Rsin(l⫺a) kabt1w R⫽ U(t ) sinfcos(f ⫹ l⫺a) 1
where a, tl and U(t1) take the following form: a ⫽ a0⫺z, t1 ⫽ tm ⫹ (yback⫺y) and U(t1)
再
(5)
(6)
0 t1 ⬍ 0 . 1 t1ⱖ0 The cutting force components are determined by the experimental cutting database of S45C carbon steel [11]: ⫽
冦
f ⫽ exp(0.0587v ⫹ 1.0398t1 ⫹ 0.6742a⫺1.2392)
Stainless steel SUS304 and nickelbase alloy Incone1600, classified as difficult-to-cut materials, are used in this turning. The machinability and chemical composition of the two materials are listed in Table 1. Turning tests were carried out on a lathe fitted with a vibration cutting device. Fig. 2 shows the dimensions of the workpiece holder and the workpiece used in all experimental tests. Five different tool nose radii, rn = 0.02, 0.1, 0.2, 0.5, 1 mm, were investigated and all these side cutting edge angles were 45°. A tool with a rake angle of 0° and a clearance angle of 3° was used. A tool edge material with a low-cost cemented carbide K10 was chosen. The experimental conditions used in turning tests are shown in Table 2. The surface roughness was measured using a Suntronic3+ surface roughness meter (Taylor Hobson). The largest peak to valley Ry with a cut-off length of 0.8 mm was taken to represent the experimental results.
4. Theory 4.1. Influence of tool nose radius on regenerate chatter
l ⫽ exp(⫺0.0546v⫺0.8856t1 ⫹ 0.8923a⫺0.2388) kab ⫽ exp(0.0059v⫺0.4246t1 ⫹ 0.0818a ⫹ 6.3211). (7)
In the present numerical simulation, work displacements measured by an eddy current sensor were used to determine the hardware parameters [2]. The effective
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Table 1 Composition of workpiece materials Workpiece materials
C (%)
Si (%)
Mn (%)
Cr (%)
Ni (%)
Hardness (HB)
UTS (N/mm2)
SUS304 Incone1600
0.08 0.15
1.0 0.50
2.0 1.00
18–20 15.5
8–10 72.0
187 179
520 550
Fig. 2.
Dimensions of workpiece holder and workpiece.
mass, stiffness, and damping were determined to be m = 0.19 kg, k 1 = 0.70, k 2 = 1.12 MN/m, c 1 = 52, c 2 = 63 Ns/m. The cutting parameters were used based on the experimental conditions in Table 2. The cutting parameters are as follows: v = 58 m/min; R S = 460 rpm; t m = 0.05 mm; w = 0.051 mm; a 0 = 0° and g 0 = 3°. The tool vibration frequency and amplitude are f = 20 kHz and a = 15 µm respectively. From Eq. (10), the edge contact rate r is determined to be 0.48. In addition, a 1 = 20°, a 2 = 110° and s f =1 [12] are chosen. The simulation results corresponding to experimental tests are shown in Fig. 3. The work displacement obtained by conventional cutting [see Fig. 3(a)] becomes larger and larger with increasing number of revolutions and its amplitude becomes saturated with a finite value. In contrast, the simulation’s result obtained by vibration cutting [see Fig. 3(b)] shows that the growth of the work dis-
Fig. 3. Work displacement simulations. Chatter-generating dynamics for conventional cutting in (a). Chatter-suppressing dynamics for vibration cutting in (b).
placement ceases with increasing number of revolutions and its maximum amplitude is a small value of 4.3 µm. It is shown that chatter vibration is effectively suppressed by applying vibration cutting, although a strong chatter vibration may be caused during conventional cutting. The figure also indicates that it is possible for vibration cutting to achieve a machining accuracy of 4.3 µm. In this simulated investigation, it is assumed that the same surface between the previous pass and the present pass is cut successively. However, the practical turning
Table 2 Experimental conditions Tool edge
Cuttingconditions
Nose radius Side cutting edge angle Rake angle and clearance angle Material Spindle speed Cutting speed Depth of cut Feed rate Tool frequency Tool amplitude
0.02, 0.1, 0.2, 0.5, 1 mm 45° a 0 = 0° g 0 = 3° K10 460 rpm 58 m/min 0.05 mm 0.051 mm/rev 20 kHz 15 µm
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operations are not always successive cuts. In order to take the regenerate effect into account, the overlap factor m is introduced [13,14]. The overlap factor is a constant value between zero and one, i.e. 0ⱕmⱕ1. Chatter vibration occurring in the overlap factor of 0 is designated primary chatter, otherwise chatter vibration is termed regenerate chatter [14]. In the case of our simulation, the surface of the present pass is modeled along with the surface of the previous pass and so m = 1. Experiments have shown that the overlap factor is principally affected by the tool nose radius and side cutting edge angle [7]. For the certain side cutting edge angle, the overlap factor m may be calculated from the ratio between the overlap-length of the machined surface fo and the feed rate fd [7]. An example of different tool nose radius with the same side cutting edge angle for turning process is shown in Fig. 4. It can be seen that the smaller nose radius has the smaller the overlap factor. For this reason, when the tool nose radius is kept as small as possible, the regenerative chatter effect can be alleviated. In contrast, our simulated result [see Fig. 3(b)] shows that the regenerative chatter is suppressed by vibration cutting even using the overlap factor of 1. Therefore, it is possible for vibration cutting to use a large nose radius. 4.2. Influence of tool nose radius on cutting force and unusual tool wear The changes of the cutting force on a small and a large nose radius size are shown in Fig. 4. The three force components Fz, Fd and Ff are in the tangential, radial, and axial directions respectively. In a small nose radius [see Fig. 4(a)], the maximum cutting edge angle Kr and the side cutting angle Cs are of equal value. However, in the case of a large nose radius [see Fig. 4(b)] the maximum cutting edge angle is determined by the following expression [6]:
Fig. 4.
Kr ⫽ cos⫺1
rn⫺tm . rn
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(11)
In the present experimental condition, the maximum cutting edge angle decreases from 41°25⬘to 18°12⬘when the nose radius increases from 0.2 to 1 mm. Thus, a small cutting edge angle is produced by a large nose radius and then the extent of the cutting force Fd and Ff will be altered (see Fig. 4). Experimental results have also shown that Ff will decrease whereas Fd will increase and the change in Fz will be almost negligible with increasing nose radius size [6,15,16]. Because the cutting force Fd in the radial direction quickly increases, chatter vibration may be caused by the large nose radius. On the other hand, a leading cause of unusual tool wear is deficient in the strength of tool edge. It is considered that the tool fracturing or chipping occurs when the shear stress is too large in the tangential and axial directions. Since the large nose radius decreases the cutting force Ff and increases the shear area (the increase of the length AB), the unusual tool wear can be reduced by the large nose radius. Additionally, the chamfered tool edge can prevent the temperature concentration and plastic deformation so that the machining stabilities are increased. 4.3. Influence of tool nose radius on the surface roughness In turning operations, the surface roughness Ry is principally affected by the shape of the tool edge profile and the cutting vibrations, which are created by motion between the tool and the workpiece. The error caused by the tool shape is called the theoretical surface roughness. For a given feed and tool nose radius, the theoretical surface roughness Rth can be calculated by [17] Rth⬇
f 2d . 8rn
Nose radius influence on regenerate effect and cutting force. (a) small nose radius, (b) large nose radius.
(12)
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In the case of tool nose radius 0.02 mm, the theoretical surface roughness has a value of 16.2 µm. From the preceding discussion (section 4.1), it is known that vibration cutting may gain a machining accuracy of 4.3 µm. For achieving the surface roughness, the necessary condition is larger than the tool nose radius of 0.08 mm.
5. Experimental results and discussion In order to observe the nose radius influence on the cutting characteristics, the predicted the maximum amplitude of vibration cutting (4.3 µm) and the surface roughness Ry versus the tool nose radius is shown in Fig. 5. In the case of conventional cutting, a slightly increase of the nose radius size makes the machining accuracy worse due to the occurrence of chatter vibration. Therefore, the smallest nose radius should be adopted in a chatter-generating dynamics. In contrast to vibration cutting, there exists a decrease in the surface roughness with increase in the nose radius size. When the nose radius
Fig. 5. Comparison between predicted and experiment surface roughness Ry versus nose radius, (a) for stainless steel of SUS3046, (b) for nickelbase alloy of Incone1600.
is equal to 0.2 mm, the surface roughness attains an approximate value of the steady vibration. It is experimentally verified that a suitable nose radius can achieve the machining accuracy created by steady vibration in a chatter-suppressing dynamics. To understand the influence of different nose radius on the machining accuracy in vibration cutting, the changes in surface roughness profiles and machined surfaces are shown in Fig. 6. In the case of the nose radius 0.02 mm, shown in Fig. 6(a), the surface roughness profile has a periodical peak-to valley with the feed of 0.051 mm/rev in feed direction, then the surface roughness Ry is 9.5 µm. For the machined surface, the cutting marks of clear straight line in cutting direction can be seen. The surface roughness in such a small nose radius shows the tendency to take the theoretical surface roughness. When the nose radius is 0.2 mm, shown in Fig. 6(b), the edge shape peaks disappear, then the machined surface becomes smooth. The surface roughness in such a suitable nose radius is improved, then it attains an approximate value of the steady vibration. As shown in Fig. 6(c) with the nose radius of 1 mm, the surface roughness profile has a large peak-to valley value with a longer period than the feed of 0.051 mm/rev in feed direction, and a large wave surface from the photograph of
Fig. 6. Change in surface roughness profiles and machined surfaces with varying nose radius in vibration cutting (workpiece: stainless steel of SUS304).
M. Xiao et al. / International Journal of Machine Tools & Manufacture 43 (2003) 1375–1382
machined surface can be seen in cutting direction. The experimental result indicates that a oversize nose radius causes the occurrence of chatter vibration. It is considered that a oversize nose radius results in a pronounced increase of thrust cutting force, then the chattersuppressing dynamics in vibration cutting is destroyed. With an initial nose radius of 0.02 mm and a suitable nose radius of 0.2 mm in vibration cutting, the changes of surface roughness at the cutting length are shown in Fig. 7. A stable and a precise surface finish is achieved by using the suitable nose radius, while the instability of the machining accuracy with the initial nose radius appears at a short cutting length. In regard to the two sizes of nose radius, the photographs of machined surfaces and tool edge after the experimental tests are shown in Fig. 8. In the case of the initial nose radius, the fracturing edge can be seen. Because of the worn tool, the surface roughness profile with a deep peak-to valley is produced so that the machining accuracy becomes worse. In the case of the suitable nose radius, a large cutting edge radius [15] can be seen. Also, the
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situation from the surface roughness profile and the machined surface may be identified as chatter vibration, causing the decrease of surface roughness. It is considered that a large nose radius rubbed by normal tool wear results in the occurrence of chatter vibration. As a result, a suitable tool nose radius prevents the tool fracturing occurrence so that the instability of the machining process is markedly reduced.
6. Conclusions The influence of tool nose radius on cutting characteristics including chatter vibration, cutting force and surface roughness was investigated by theory. Turning tests of two different hard metals were performed on conventional cutting and vibration cutting using five sizes of tool nose radius. The following conclusions were obtained. 1. The simulation results corresponding to the experimental conditions showed that vibration cutting has a chatter-suppressing dynamics, but conventional cutting is a chatter-generating dynamics. 2. The theoretical investigation showed that it is possible for chatter-suppressing dynamics to use a large nose radius. However, the cutting force in the radial direction quickly increases when the tool nose radius is larger than 0.2 mm so that vibration cutting’s chattersuppressing dynamics may be destroyed. 3. The experimental results showed that vibration cutting enables a larger tool nose radius to be used than conventional cutting. In the case of nickelbase alloy Incone1600, the allowable tool nose radius in vibration cutting was 0.2 mm, while one in conventional cutting was 0.02 mm. Also, it was demonstrated that chatter vibration is caused by a larger than tool nose radius of 0.2 mm in vibration cutting. 4. The simulation corresponding to the experimental conditions predicted that the best surface roughness Ry in vibration cutting is 4.3 µm. The experimental results showed that the nearest value (R y = 4.7 µm) of the predicted surface roughness is obtained when tool nose radius is 0.2 mm. The nose radius is determined as a suitable nose radius. 5. The vibration cutting’s experiment using the suitable nose radius of 0.2 mm showed that the tool fracture is prevented and the machining accuracy is improved in comparison with an initial nose radius of 0.02 mm. A stable and a precise surface finish is achieved.
Acknowledgements Fig. 7. Comparison between nose radii 0.02 and 0.2 mm surface roughness Ry versus cutting length in vibrarion cutting, (a) for stainless steel of SUS304, (b) for nickelbase alloy of Incone1600.
The authors would like to thank the Editor in Chief for his many helpful comments. This research was sup-
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Fig. 8. Surface roughness profiles, photographs of machined surfaces and tool edge in vibration cutting (a) after a cutting length of 216 m with the nose radius of 0.02 mm, (b) after a cutting length of 1080 m with the nose radius of 0.2 mm (workpiece: nickelbase alloy of Incone1600).
ported by the Grant-in-Aid for Scientific Research of Japan ((B) no. 14350116).
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