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A novel method for determination of the subsurface damage depth in diamond turning of brittle materials
International Journal of Machine Tools & Manufacture 51 (2011) 918–927
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A novel method for determination of the subsurface damage depth in diamond turning of brittle materials De Ping Yu n, Yoke San Wong 1, Geok Soon Hong 2 National University of Singapore, Deptartment of Mechanical Engineering, Singapore 119260, Singapore
a r t i c l e i n f o
a b s t r a c t
Article history: Received 28 February 2011 Received in revised form 5 August 2011 Accepted 8 August 2011 Available online 17 August 2011
Micro-structured surfaces on brittle materials, e.g. ceramic and glass, are gaining increasing industrial applications such as optics, semiconductor and biomedical. However, these materials tend to be damaged with brittle fracture in machining. To generate crack-free surfaces, ductile-regime machining should be maintained for the entire micro-structured surface. In ductile-regime machining the material is removed by both plastic deformation and brittle fracture, but the cracks produced are prevented from extending into the finished surface. In this paper, a machining model has been developed for fast tool servo (FTS) diamond turning of micro-structured surfaces on brittle materials. Based on the model, a damaged region analysis method (DRAM) is proposed to determine the subsurface damage depth (Cm) by analyzing the surface damaged region of a machined micro-structured surface with sinusoidal wave along radial direction. Only one micro-structured surface is required to be machined to obtain Cm, which greatly reduces the effort for determination of Cm. With Cm, the maximum feedrate for machining a crack-free micro-structured surface can be determined. Machining experiments have verified the validity of DRAM. & 2011 Elsevier Ltd. All rights reserved.
Keywords: Ductile regime machining Critical depth of cut Subsurface damage Fast tool servo Diamond turning Brittle materials
1. Introduction There has been an increasing use of precision components with micro-structured surfaces, e.g. micro-lens arrays, Fresnel lenses, pyramids array, polygon mirrors, aspheric lenses, multifocal lenses, corner-cubes, two-dimensional planar encoders, and antireflective gratings or channels, on hard and brittle materials such as ceramics and glasses in a range of industries such as optics, semiconductor and biomedical [1–3]. However, it is challenging to machine micro-structured surfaces with mirror surface finish on brittle materials due to their low fracture toughness. It is widely accepted that ductile regime machining should be maintained during machining in order to achieve high quality finish. According to the hypothesis of ductile regime machining, all brittle materials will undergo a transition from brittle to ductile machining region at a critical undeformed chip thickness. Below this threshold, plastic deformation becomes energetically favorable as compared with fracture and the material will deform instead of fracture [4,5]. Liu et al. [6] observed that the ductile
n
Corresponding author. E-mail addresses: [email protected] (D.P. Yu), [email protected] (Y.S. Wong), [email protected] (G.S. Hong). 1 Tel.: þ65 6516 2221. 2 Tel.: þ65 6516 2272. 0890-6955/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2011.08.007
cutting mode can be realized when the undeformed chip thickness is smaller than the tool cutting edge radius and the tool cutting edge radius is small enough. Cai et al. [7] studied the nanoscale ductile mode cutting of monocrystalline silicon wafer by the employing molecular dynamics method. He found that the thrust force dominates the cutting force, leading to compressive stress in the cutting zone. However, as the undeformed chip thickness increases, this compressive stress decreases, giving way to crack propagation in the chip formation zone. Fang et al. [8] proposed an extrusion-based model for nanometric cutting and explained that when the undeformed chip thickness is smaller than the tool cutting edge radius, the negative effective rake angle produces necessary compressive stress in the cutting zone to enable plastic deformation. Nevertheless it does not necessarily mean that the larger the tool cutting edge radius, the better the ductile mode cutting. Arefin et al. [9] reported that there is an upper bound of the tool cutting edge radius for ductile mode cutting of brittle materials, e.g. 700–800 nm for silicon. There are two important parameters relating to ductile regime machining, i.e. critical depth of cut (tc) and subsurface damage depth (Cm), which may be experimentally or analytically obtained. Marshall and Lawn [10] performed indentation experiments on different materials and proposed Eq. (1) to tc of penetration by the indenter for crack initiation: tc ¼ CðE=HÞðKc =HÞ2 ,
ð1Þ
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where E is the elastic modulus, H is the hardness, Kc is the fracture toughness and C is a dimensionless constant dependent on indentation geometry. Bifano et al. [11] extended Eq. (1) to relate the grinding in-feed rate necessary for ductile material-removal with the properties of the brittle workpiece material and estimated C to be 0.15. However, for a specific machining process, e.g. micro-milling and diamond turning, the complex tool– workpiece interaction differs dynamically and geometrically from the deformation produced in indentation. Therefore, different experimental methods have been proposed to determine tc for different machining processes. For micro-milling, Matsumura et al. [12] related the ductile and brittle mode machining to the behavior of the cutting force and found that the ductile mode machining is characterized by a smooth force signal while that from the brittle mode machining oscillates about a constant mean value. Thus, tc can be estimated from the differences in the two types cutting force signals. For diamond turning, plunge cutting is a quite straightforward method to determine tc by observing the transition of the cutting mode from ductile to brittle [13]. In addition, Blake and Scattergood [5] proposed an interruptedcutting test to study the ductile-to-brittle transition at the shoulder region and a machining model to determine tc from the location of the ductile-to-brittle transition. As to the subsurface damage depth Cm, Marshall et al. clearly identified the various radial and lateral crack systems associated with indentation [14] and proposed models to predict the size of the radial and lateral cracks [15,16]. Arif et al. [17] claimed the milling process to be analogous to indentation and derived an analytical model to determine the critical feed per edge to achieve ductile mode machining based on Marshall et al.’s models [15]. For diamond turning, Blackley and Scattergood [18] proposed a phenomenological model of the ductile-to-brittle transition to quantitatively determine tc and Cm. Unlike conventional diamond turning the fast tool servo (FTS) diamond turning enables precision machining of complicated micro-structured surfaces, including both axisymmetric and nonaxisymmetric surfaces, which is difficult to be achieved by grinding and lapping. Most of the previous researches focused on the development of the FTS itself for higher performance, i.e. higher bandwidth, larger stroke, higher stiffness, etc. [19–23]. In addition, ductile materials, e.g. copper, brass and aluminum were machined to prove the performance of their developed FTS. However, few researches have been devoted to FTS diamond turning of microstructured surfaces on brittle materials. Therefore, in this paper, a
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machining model has been developed for FTS diamond turning of micro-structured surfaces on brittle materials. Based on the model, a damaged region analysis method (DRAM) has been proposed to determine the subsurface damage depth (Cm) by analyzing the surface damaged region of a machined microstructured surface with sinusoidal wave in the radial direction. With Cm, the maximum feedrate for machining a crack-free microstructured surface can be determined. Machining experiments have been carried out to verify the validity of DRAM.
2. Theory on FTS diamond turning of brittle materials 2.1. FTS diamond turning of micro-structured surfaces FTS diamond turning evolves from conventional diamond turning to ultra-precision fabrication of complicated micro-structured surfaces, including both axisymmetric and non-axisymmetric surfaces. It is realized by integrating a specially designed tool servo into conventional diamond turning machine to drive the cutting tool in and out of the workpiece when it is rotating. Depending on the bandwidth of the tool servo, it can be named as slow tool servo (STS) [24,25] or fast tool servo [19–23,26]. Fig. 1 shows a FTS diamond turning machine in which there are totally four axes: X axis—the x slide, Z axis—the z slide, C axis—the spindle and W axis—the FTS. Such a machining system is expressed in cylindrical coordinates (r, j, z), whereas, the surface model to be machined is expressed in Cartesian coordinates (X, Y, Z). For conversion between the two coordinate systems, it is convenient to assume that the Z-axis of both systems is coaxial and then the correspondence between the cylindrical coordinates (r, j) and Cartesian coordinates (x, y) is ( ( pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x ¼ r cos j r ¼ x2 þ y2 , ð2Þ 3 y ¼ r sin j j ¼ Fðtan1 ðx=yÞÞ where FðUÞis to determine the total angle rotated after start machining. Consider the micro-structured surface with sinusoidal wave along radial direction (SWR); it can be described by pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi! 2p x2 þ y2 , ð3Þ zðx,yÞ ¼ A sin
Fig. 1. Working principle of FTS diamond turning.
l
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where A is the wave amplitude and l is the wavelength. The SWR can be expressed in cylindrical coordinate by Eq. (4). 0 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 2p ðr cos jÞ2 þ ðr sin jÞ2 A, ð4Þ zðr, jÞ ¼ A sin@
l
The projection of the relative tool–workpiece movement to the XY-plane is a spiral curve (r, j), whose shape is determined by the feedrate f(mm/min) and spindle speed u (rpm), as shown in Fig. 2. As the numerical controller used in the FTS diamond turning machine can implement only a finite number of motion commands, the coordinates (r, j) need to be sampled by an important sampling parameter Nj, which divides one rotation equally into Nj divisions. The sampled spiral curve (r0, j0) can be calculated by Eq. (5), e.g. the dotted spiral curve with Nj ¼36: 8 < Rw uNfij To the center of the workpiece r0 ¼ fi : uN From the center of the workpiece j
j0 ¼
2p i, i ¼ 0,1,. . .,Rw uNj =f Nj
ð5Þ
With (r0, j0) the tool path TP(x0, y0, z0) for SWR at a particular f and u can then be calculated by Eqs. (4) and (5), e.g. the tool path in Fig. 2. With TP(x0, y0, z0), the CNC code for fabrication of CWR can be generated easily. During fabrication, the workpiece is mounted on a high-precision spindle with air–hydrostatic bearing. The cutting tool is mounted on FTS [27,28] and driven to the desired position by a piezoelectric actuator (for different performances, the piezoelectric actuator may be replaced by other actuators such as the Lorentz force actuator, magnetostriction actuator, etc. [22]). When the spindle rotates to a certain position, the cutting tool is driven to the right position as specified in the CNC code [29], as shown in Fig. 1. The micro-structured surface is formed by the complex interaction between the workpiece and tool geometry. Fig. 3(a) shows in 3D the surface formation in FTS diamond turning of SWR with A¼2 mm and l ¼0.2 mm using a cutting tool with nose radius R¼0.4 mm. Fig. 3(b) shows the formation of the sectional surface profile fj(r) as shown in Fig. 1 when the cutting tool moves along the tool path TPj generated with f¼8 mm/min, u ¼1000 rpm and nominal depth of cut D0 ¼2 mm. It is clear that the surface formation can be viewed as the intersection of the successive tool cutting edge profiles. An important property of FTS diamond turning of microstructured surfaces is shown in Fig. 3. It can be seen that the chip geometry of the current pass is different from those of the previous pass and the next pass. It is this continuous changing chip geometry that brings about difficulty to FTS diamond turning
Fig. 2. A micro-structured surface with sinusoidal wave along radial direction.
Fig. 3. Visualization for the surface formation of FTS diamond turning of SWR: (a) 3D and (b) 2D.
of micro-structured surface on brittle materials, which will be elaborated in the next section. 2.2. Machining model for FTS diamond turning of brittle materials As the brittle materials tend to crack easily during machining, it is necessary to predetermine the cutting conditions for FTS diamond turning of micro-structured surfaces on brittle materials in order to generate crack-free surface. Therefore a machining model for FTS diamond turning of micro-structured surfaces on brittle materials is proposed as shown in Fig. 4, which is evolved from the phenomenological model [5,18] for conventional diamond turning of brittle materials. For each pass i the effective chip thickness tieff varies from zero at the apex of the tool, to a maximum (tim) at the top of the previous uncut region and to zero at the top of the current uncut region. From literature review, there exists a critical depth of cut (tc) below which no crack will be generated. Therefore, there is a microfracture damage zone for each pass if tieff 4tc, e.g. the microfracture damage zone for pass 0 shown in Fig. 4(a). Fig. 4(a) and (b) shows the machining of the same microstructured surface with high and low feedrate, respectively. When
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Fig. 4. Machining model for FTS diamond turning of micro-structured surfaces on brittle materials: (a) high feedrate and (b) low feedrate.
a high feedrate is used, tc is located at low portion of the uncut region and the associated subsurface damage depth (Cm) extends into the finish surface as shown in Fig. 4(a). When a low feedrate is used, tc moves towards the high portion of the uncut region, the microfracture damage zone for each pass is removed by the next passes and the finish surface is free of crack. Therefore the occurrence of crack on the finish surface is determined by a critical feedrate (fc), which is defined as the maximum feedrate to obtain crack-free micro-structured surfaces. If the feedrate is larger than fc, cracks will be generated at some portion of the micro-structured surface. If the feedrate is smaller than fc, the whole machined surface will be free of cracks. For practical application, it is desirable to maximize the feedrate to reduce machining time. In order to determine fc, it is important to determine the length of the subsurface damage (Cm) for the combination of used cutting tool and brittle material of the workpiece. It is important to note that Cm is assumed to be the average fracture propagation depth after crack initiation. With Cm, the critical feedrate fc for machining a crack-free micro-structured surface can be determined. Fig. 5. Geometry for calculation of chip thickness.
2.3. Damaged region analysis method In order to determine Cm, a damaged region analysis method (DRAM) is proposed. In DRAM, a SWR with a certain A and l is machined for the cutting tool with nose radius R on the chosen brittle material. Then the machined SWR is observed by a microscope and the damaged region is measured. Finally, Cm can be derived from the relationship between the length of the damaged region and Cm. Due to the complex nature of the micro-structured surface, there is no simple form of relationship between the length of the damaged region and Cm. Therefore, a numerical computation method is used to simulate the formation of the surface and predict the initiation of cracks. Fig. 5 shows the geometry for the calculation of the chip thickness in FTS diamond turning of micro-structured surface. In Fig. 5, 0, 1 and –1 represents the current pass, next pass and previous pass, respectively, R is the tool nose radius and D is the nominal depth of cut for the current pass. Due to different chip shapes at [0, y1] and [y1, y2], the effective chip thickness teff is calculated differently as shown in Eq. (11):
DD0 ¼ z0 z1 d0 ¼
ð6Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi f 2 þ DD0 2
a0 ¼ p þarctan
ð7Þ
DD0 f
ð8Þ
a1 ¼ arccos
d0 2R
ð9Þ
sin b d0 d0 ¼ ) b ¼ arcsin sinða1 þ yÞ sinða1 þ yÞ R R
teff ¼
ð10Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 8 < R R2 þ d2 2Rd0 cosðpa1 ybÞ, 0
y A ½0, y1
: R
y A ½y1 , y2
RD , sinð2pya0 a1 Þ
0qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 R2 ðRðD þ DD0 Þ2 f 3 Aa0 a1 y1 ¼ p þarc tan@ 2 RD
y2 ¼ 2parc sin
RD a0 a1 R
ð11Þ
ð12Þ
ð13Þ
Fig. 6 shows the simulation of the formation of the sectional surface profile fj(r) and the initiation of the crack at each pass. For each pass, the effective chip thickness teff is firstly calculated by Eqs. (6)–(13). The z values used in Eq. (6) is obtained from TPj(r), which is the dotted curve. Then the crack initiation location where teff ¼ tc is searched and a crack with length of Cm is placed at the crack initiation location as shown in Fig. 6. Finally, the intersection between the cracks and the finish surface profile fj(r) is searched. If the cracks extend into fj(r), the used feedrate
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Fig. 6. Definition of crack ratio.
Fig. 7. Relationship between CR and Cm.
f is too big for generation of crack-free surface. From Fig. 6, it can be seen that the crack region is located at the lower left region of the sinusoidal wave. In addition, the depth of the crack left on the finished surface is the deepest at the center of each damaged region, which is denoted as a red dot in the figure, and decreases to zero on both sides. The larger the length of the subsurface damage (Cm), the longer the length of the damaged region. Therefore, there is a relationship between the length of the damaged region and Cm. To quantitatively describe the relationship a crack ratio (CR) is defined, as shown in Eq. (14), as the length of the damaged region (Lc) within a cycle of sine wave to the wavelength (L): CR ¼
Lc L
ð14Þ
Fig. 7 shows an example of the relation between Cm and CR when machining SWR with A¼2 mm and l ¼0.2 mm using a cutting tool with R ¼0.4 mm and tc ¼0.25 mm and a feedrate f¼3 mm/rev. After machining SWR, the machined SWR is observed under the microscope and the length of the damaged region (Lc) is measured to obtain CR. The measured CR can then be used to extract the Cm from Fig. 7.
Fig. 8. Damaged region analysis for the measured CR: (a) microscopic images and (b) processed image.
2.4. Measurement of CR To obtain Cm from Fig. 7, a SWR is machined to obtain the measured CR (MCR). Fig. 8(a) shows a microscopic image of a
D.P. Yu et al. / International Journal of Machine Tools & Manufacture 51 (2011) 918–927
machined SWR (Note: the white spots scattered in the image are caused by the microscope. It can be omitted during analysis.) It can be seen that there exists a damaged region in which the largest crack is located at the center and the size of the crack decreases on both sides. Such damaged behavior is the same as that simulated in Fig. 6. In practice, there are two uncertainties in determining MCR. Firstly, it is difficult to locate the exact boundaries of the damaged region due to some small random distributed cracks. Secondly, the length of the damaged region (Lc) at different locations may be different due to varying composition of the material and machining conditions. In this paper, an image processing method and a statistical method are adopted to solve these problems, respectively. To highlight the damaged region, a thresholding method is used to set the relatively dark cracks to black color andthe background colors to white color. Fig. 8(b) shows the processed image of the microscopic images as shown in Fig. 8(a). To locate the left boundary (LB) and right boundary (RB) of the damaged region the severity of damage (SD) is calculated vertically along the processed image, which is the cutting direction. Fig. 8(b) shows the SD value for the processed image. Thus LB and RB are, respectively, defined as the leftmost and rightmost locations whose SD value is a certain percentage of the maximum SD, which is controlled by the crack percentage (CP) as shown in the figure. In this paper, CP is chosen to be 90%. Finally, LB and RB are located as shown in Fig. 8(b). To improve the credibility of the MCR, damaged regions at different locations as shown in Fig. 9 are measured and MCR is calculated by Eq. (15). There is one point worth noting. As reported in literature [30], the severity of damage is greatly influenced by the crystal orientation. Fig. 9 shows that crack occurs when the tool is cutting within a certain degree of the o1 1 0 4 direction. It means that the severity of damage is different along different directions of the machined surfaces. To make sure that the whole machined surface is free of crack, the measurement locations are chosen to be on the direction as shown in Fig. 9: PN MCR ¼
i¼1
Lci
NL
ð15Þ
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3. Experiments and discussion 3.1. Experimental apparatus FTS diamond turning of micro-structured surfaces on brittle materials was performed on the machine tool [27,28,31] as shown in Fig. 10. Two most important components of the machine are the air bearing spindle and FTS. The air bearing spindle is a brushless DC motor (Cannon SP-501HCL) with rotational speed from 10 rpm to 15,000 rpm. The FTS is specially designed for machining micro-structured surface. It consists of a piezoelectric actuator, a flexure, a capacitor sensor, a tool holder and a force transducer. The stroke of the FTS is 7 mm with positioning accuracy below 1 nm. The cutting tool was single crystal diamond (SCD) with nose radius of 0.4 mm, nominal rake angle of 01, clearance angle of 71 and cutting edge radius of about 100 nm. Fig. 11 shows the microscopic images for the SCD cutting tool used in the experiments. The rectangular shaped workpiece of MgF2 glass was attached to an aluminum block using heatsoften glue, which was then clamped by a collet on the air bearing spindle as shown in Fig. 10. The properties of MgF2 glass are listed in Table 1. In this paper, MgF2 is chosen as the brittle material to be studied because it is relatively soft when compared with to other glass such as BK7 and thus the cutting tool can last long enough for all tests without changing the critical depth of cut tc, which is important for the verification of the proposed DRAM. A constant spindle speed of 1000 rpm was used in all tests. All cuttings were performed under dry conditions. After machining, the machined micro-structured surfaces were cleaned with alcohol to remove the chips attached on the surface. An Optical microscope was used to observe and measure the machined surface for further analysis. 3.2. Determination of critical depth of cut The value for critical depth of cut tc can be estimated by Bifano’s model [11] for typical brittle materials using the values for all parameters as listed in Table 1 and C is set to be 0.15 as suggested for grinding [11]: tc ¼ 0:15ðE=HÞðKC =HÞ2 ¼ 249:6 nm As the geometry of the cutting edge of the SCD tool is different from the grains in the grinding wheel, C is difficult to be obtained for the SCD tool. Therefore, a plunge cutting experiment was carried out for the tool and workpiece combination. As shown in
Fig. 9. Influence of crystal orientation and the measurement locations.
Fig. 10. FTS diamond turning machine.
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In this experiment, l, d and the cutting velocity are set to be 4 mm, 1 mm and 20 mm/min respectively. The mark left on the surface was observed under the microscope. Due to the limited measurement range of the microscope, Fig. 12(b) shows the image corresponding to only the region I–III indicated in Fig. 12(a). As there is no clear boundary for transition from ductile to brittle, lc was found to lie within [0.945, 1.065]. Using Eq. (16) tc is found to be 236–266 nm, in which tc found by Bifano’s model lies. Therefore, tc is set to 250 nm for all the analysis. 3.3. Verification of DRAM To verify the validity of the proposed DRAM, SWR A ¼2 mm and l ¼0.2 mm is machined using the cutting tool as shown in Fig. 11 on MgF2 with f¼3 mm/min and u ¼1000 rpm. The machined surface is measured at 15 different locations as shown in Fig. 9. A typical microscopic image for the damaged region is shown in Fig. 8(a). All microscopic images were processed as explained in Section 2.4 and the MCR were obtained as shown in Fig. 13(a) with CP¼90%. The average MCR is calculated by Eq. (15) and found to be 0.36172. To obtain the subsurface damage depth Cm, the relationship between Cm and CR was simulated by DRAM
Fig. 11. Microscopic images for the SCD cutting tool: (a) clearance face and (b) rake face.
Table 1 Properties of MgF2 glass. Hardness (H: GPa) Elastic modulus (E: GPa) Fracture toughness (KC: MPa. m1/2) Density (g/cm3) Melting point (1C)
4 138.5 0.9 3.18 1255
Fig. 12. Plunge cutting for determination of tc: (a) schematic diagram and (b) microscopic images for brittle to ductile transition.
Fig. 12, the cutting tool was plunged into the workpiece with depth of cut changing from zero to d and the total length of cutting is l. There exists a brittle to ductile transition location lc where the depth of cut equals tc and the cutting changes from ductile to brittle mode. Therefore, by measuring the distance lc, the critical depth of cut can be estimated by tc ¼
lc d l
ð16Þ
Fig. 13. Determination of Cm: (a) measured CR at different locations and (b) relationship between Cm and CR with CP¼ 90%.
D.P. Yu et al. / International Journal of Machine Tools & Manufacture 51 (2011) 918–927
and obtained as shown in Fig. 13(b). It is important to note that the relationship is slightly different from the one shown in Fig. 7 as the CP is set to be 90%, which is the same as the CP used in extracting the MCR. From Fig. 13(b), Cm is found to be 0.878 mm.
Fig. 14. Relationship between CR and feedrate (f).
With the obtained Cm, the relationship between CR and f can be simulated and found as shown in Fig. 14. In order to verify reliability of the obtained Cm, SWRs were fabricated with feedrate f¼[1,1.5,2, 2.5,3.5,4,4.5,5,6] mm/min and spindle speed u¼ 1000 rpm. The corresponding MCRs were obtained as listed in Table 2. Some representative microscopic images for each feedrate are also listed in Table 2 (note: due to the limited measurement range of the microscope, two or three neighboring images were stitched together to form a large image for f¼[4.5,5,6]). From Table 2 it can be seen that larger feedrate results in wider damaged region and more severe damage, which is indicated as the size of the crack. For feedrate f of 1 and 1.5 mm/min, the machined surfaces are clear and free of cracks thus their CRs are taken as 0. For feedrate f of 5 and 6 mm/min, the whole machined surfaces are full of cracks with larger cracks located at the center portion with smaller cracks located at both sides, thus their CRs are taken as 1. For the feedrates between 1.5 and 5, the width of the damaged region increases with feedrate. For each feedrate, the captured microscopic images were processed and the MCRs were obtained as listed in Table 2. Fig. 14 shows a comparison of the predicted CRs (PCR) and MCRs. It can be seen that the MCRs correlate well with the predicted CRs. Therefore, it can be claimed that the predicted subsurface damage depth Cm is reasonable. With Cm, the maximum feedrate for generating crack-free micro-structured surfaces can be searched. Taking the SWR machined in the experiments for example, the maximum feedrate can be found from Fig. 14 to be 1.85 mm/min, where CR changes from zero to
Table 2 Experimental results. Feedrate (mm/min)
PCR
MCR
1
0
0
1.5
0
0
2
0.1137
0.0680
2.5
0.2546
0.2570
925
Representative microscopic images
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Table 2 (continued ) Feedrate (mm/min)
PCR
MCR
3
0.3617
0.3617
3.5
0.4665
0.4635
4
0.5982
0.5900
4.5
0.7329
0.7383
5
1
1
6
1
1
non-zero value. For different micro-structured surfaces, the maximum feedrate for generating crack-free surfaces can be searched based on tc found by plunge cutting and Cm found by DRAM for a given tool and workpiece combination.
4. Conclusions A novel method for determination of the subsurface damage depth in diamond turning of brittle materials has been presented.
Representative microscopic images
The following conclusions can be drawn from the development and demonstration of the method:
This method enables the machining of crack-free micro-struc
tured surfaces on brittle materials by fast tool servo (FTS) diamond turning. Using sinusoidal wave along radial direction (SWR) as a fundamental and representative type of micro-structured surfaces, a surface crack damage region is shown to exist on a particular segment of the wave. Moreover, the length of the
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damaged region is found to vary with the feedrate used in machining. To explain and predict such regional subsurface damage region phenomenon, a machining model has been proposed for FTS diamond turning of micro-structured surfaces on brittle materials. Based on the proposed machining model, a damaged region analysis method (DRAM) has been developed to determine the subsurface damage depth (Cm) for a tool–workpiece combination by analyzing the surface damaged region of a machined SWR. Through measuring the crack ratio (CR) of the machined SWR, Cm can be determined from the relationship between Cm and the measured CR (MCR), determined by DRAM. A series of experiments on machining SWR with different feedrates have been carried out. From microscopic images of the machined SWR surfaces captured and processed by image processing methods to obtain MCR it is shown that the predicted CR correlates well with MCR, demonstrating the validity of DRAM.
Using the proposed method, only one SWR is required to be machined to obtain Cm, which greatly reduces the effort for determination of Cm. In addition, the maximum feedrate for machining a crack-free micro-structured surface can be obtained before machining using the determined Cm. References [1] L. De Chiffre, H. Kunzmann, G.N. Peggs, D.A. Lucca, Surfaces in precision engineering, microengineering and nanotechnology, CIRP Annals— Manufacturing Technology 52 (2003) 561–577. [2] C.J. Evans, J.B. Bryan, Structured, textured or engineeredsurfaces, CIRP Annals—Manufacturing Technology 48 (1999) 541–556. [3] Y. Takeuchi, K. Sawada, T. Sata, Ultraprecision 3D micromachining of glass, CIRP Annals—Manufacturing Technology 45 (1996) 401–404. [4] F.Z. Fang, L.J. Chen, Ultra-precision cutting for ZKN7 glass, CIRP Annals—Manufacturing Technology 49 (2000) 17–20. [5] P.N. Blake, R.O. Scattergood, Ductile-Regime machining of germanium and silicon, Journal of the American Ceramic Society 73 (1990) 949–957. [6] K. Liu, X.P. Li, S.Y. Liang, Modeling of ductile cutting of tungsten carbide, NAMRI/SME 29 (2001) 251–258. [7] M.B. Cai, X.P. Li, M. Rahman, Study of the mechanism of nanoscale ductile mode cutting of silicon using molecular dynamics simulation, International Journal of Machine Tools and Manufacture 47 (2007) 75–80. [8] F.Z. Fang, H. Wu, Y.C. Liu, Modelling and experimental investigation on nanometric cutting of monocrystalline silicon, International Journal of Machine Tools and Manufacture 45 (2005) 1681–1686. [9] S. Arefin, X. Li, M. Rahman, K. Liu, The upper bound of tool edge radius for nanoscale ductile mode cutting of silicon wafer, The International Journal of Advanced Manufacturing Technology 31 (2007) 655–662. [10] D.B. Marshall, B.R. Lawn, Indentation of brittle materls, in: P.J. Blau, B.R. Lawn (Eds.), Microindentation Techniques in Materials Science and Engineering, American Society for Testing and Materials, pp. 26–46.
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[11] T.G. Bifano, T.A. Dow, R.O. Scattergood, Ductile-regime grinding: a new technology for machining brittle materials, Journal of Engineering for Industry 113 (1991) 184–189. [12] T. Matsumura, T. Hiramatsu, T. Shirakashi, T. Muramatsu, A study on cutting force in the milling process of glass, Journal of Manufacturing Processes 7 (2005) 102–108. [13] K. Liu, X.P. Li, Ductile cutting of tungsten carbide, Journal of Material Processing Technology 113 (2001) 348–354. [14] B. Lawn, R. Wilshaw, Indentation fracture: principles and applications, Journal of Material Science 10 (1975) 1049–1081. [15] B.R. Lawn, A.G. Evans, D.B. Marshall, Elastic/plastic indentation damage in ceramics: the median/radial crack system, Journal of American Ceramic Society 63 (1980) 574–581. [16] D.B. Marshall, B.R. Lawn, A.G. Evans, Elastic/plastic indentation damage in ceramics: The lateral crack system, Journal of American Ceramic Society 65 (1982) 561–566. [17] M. Arif, M. Rahman, Y.S. Wong, Analytical model to determine the critical feed per edge for ductile–brittle transition in milling process of brittle materials, International Journal of Machine Tools and Manufacture 54 (2010) 170–181. [18] W.S. Blackley, R.O. Scattergood, Ductile-regime machining model for diamond turning of brittle materials, Precision Engineering 13 (1991) 95–103. [19] T.A. Dow, M.H. Miller, P.J. Falter, Application of a fast tool servo for diamond turning of nonrotationally symmetric surfaces, Precision Engineering 13 (1991) 243–250. [20] W. Gao, T. Araki, S. Kiyono, Y. Okazaki, M. Yamanaka, Precision nanofabrication and evaluation of a large area sinusoidal grid surface for a surface encoder, Precision Engineering 27 (2003) 289–298. [21] C. Brecher, S. Lange, M. Merz, F. Niehaus, C. Wenzel, M. Winterschladen, M. Weck, NURBS based ultra-precision free-form machining, CIRP Annals—Manufacturing Technology 55 (2006) 547–550. [22] D. Trumper, X.D. Lu, Fast tool servos: advances in precision, acceleration, and bandwidth, Towards Synthesis of Micro-/Nano-systems (2007) 11–19. [23] H.S. Kim, K.I. Lee, K.M. Lee, Y.B. Bang, Fabrication of free-form surfaces using a long-stroke fast tool servo and corrective figuring with on-machine measurement, International Journal of Machine Tools and Manufacture 49 (2009) 991–997. [24] A.Y. Yi, L. Li, Design and fabrication of a microlens array by use of a slow tool servo, Opt Lett 30 (2005) 1707–1709. [25] L.A. Lei, Microfabrication on a curved surface using 3D microlens array projection, Journal of Micromechanics and Microengineering 19 (2009) 105010. [26] S.R. Patterson, E.B. Magrab, Design and testing of a fast tool servo for diamond turning, Precision Engineering 7 (1985) 123–128. [27] S.W. Gan, M. Rahman, H.S. Lim, Development of a fine tool servo with force monitoring system for nanomachining applications, Journal of Vacuum Science and Technolology B 27 (2009) 1272–1277. [28] D.P. Yu, S.W. Gan, Y.S. Wong, M. Rahman, G.S. Hong, Design of a fast tool servo based diamond turning machine for fabricating micro-structured surfaces, Key Engineering Materials 443 (2010) 669–674. [29] D.P. Yu, S.W. Gan, Y.S. Wong, M. Rahman, G.S. Hong, An optimization approach for tool path generation of micro-structured surfaces in FTS-based diamond turning, In: Proceedings of the 3rd international conference of Asian Society for precision engineering and nanotechnology, Kitakyushu, Japan, 2009. [30] T. Nakasuji, S. Kodera, S. Hara, H. Matsunaga, N. Ikawa, S. Shimada, Diamond turning of brittle materials for optical components, CIRP Annals— Manufacturing Technology 39 (1990) 89–92. [31] D.P. Yu, G.S. Hong, Y.S. Wong, Integral sliding mode control for fast tool servo diamond turning of micro-structured surfaces, International Journal of Automation Technology 5 (2011) 4–10.
Contents lists available at SciVerse ScienceDirect
International Journal of Machine Tools & Manufacture journal homepage: www.elsevier.com/locate/ijmactool
A novel method for determination of the subsurface damage depth in diamond turning of brittle materials De Ping Yu n, Yoke San Wong 1, Geok Soon Hong 2 National University of Singapore, Deptartment of Mechanical Engineering, Singapore 119260, Singapore
a r t i c l e i n f o
a b s t r a c t
Article history: Received 28 February 2011 Received in revised form 5 August 2011 Accepted 8 August 2011 Available online 17 August 2011
Micro-structured surfaces on brittle materials, e.g. ceramic and glass, are gaining increasing industrial applications such as optics, semiconductor and biomedical. However, these materials tend to be damaged with brittle fracture in machining. To generate crack-free surfaces, ductile-regime machining should be maintained for the entire micro-structured surface. In ductile-regime machining the material is removed by both plastic deformation and brittle fracture, but the cracks produced are prevented from extending into the finished surface. In this paper, a machining model has been developed for fast tool servo (FTS) diamond turning of micro-structured surfaces on brittle materials. Based on the model, a damaged region analysis method (DRAM) is proposed to determine the subsurface damage depth (Cm) by analyzing the surface damaged region of a machined micro-structured surface with sinusoidal wave along radial direction. Only one micro-structured surface is required to be machined to obtain Cm, which greatly reduces the effort for determination of Cm. With Cm, the maximum feedrate for machining a crack-free micro-structured surface can be determined. Machining experiments have verified the validity of DRAM. & 2011 Elsevier Ltd. All rights reserved.
Keywords: Ductile regime machining Critical depth of cut Subsurface damage Fast tool servo Diamond turning Brittle materials
1. Introduction There has been an increasing use of precision components with micro-structured surfaces, e.g. micro-lens arrays, Fresnel lenses, pyramids array, polygon mirrors, aspheric lenses, multifocal lenses, corner-cubes, two-dimensional planar encoders, and antireflective gratings or channels, on hard and brittle materials such as ceramics and glasses in a range of industries such as optics, semiconductor and biomedical [1–3]. However, it is challenging to machine micro-structured surfaces with mirror surface finish on brittle materials due to their low fracture toughness. It is widely accepted that ductile regime machining should be maintained during machining in order to achieve high quality finish. According to the hypothesis of ductile regime machining, all brittle materials will undergo a transition from brittle to ductile machining region at a critical undeformed chip thickness. Below this threshold, plastic deformation becomes energetically favorable as compared with fracture and the material will deform instead of fracture [4,5]. Liu et al. [6] observed that the ductile
n
Corresponding author. E-mail addresses: [email protected] (D.P. Yu), [email protected] (Y.S. Wong), [email protected] (G.S. Hong). 1 Tel.: þ65 6516 2221. 2 Tel.: þ65 6516 2272. 0890-6955/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2011.08.007
cutting mode can be realized when the undeformed chip thickness is smaller than the tool cutting edge radius and the tool cutting edge radius is small enough. Cai et al. [7] studied the nanoscale ductile mode cutting of monocrystalline silicon wafer by the employing molecular dynamics method. He found that the thrust force dominates the cutting force, leading to compressive stress in the cutting zone. However, as the undeformed chip thickness increases, this compressive stress decreases, giving way to crack propagation in the chip formation zone. Fang et al. [8] proposed an extrusion-based model for nanometric cutting and explained that when the undeformed chip thickness is smaller than the tool cutting edge radius, the negative effective rake angle produces necessary compressive stress in the cutting zone to enable plastic deformation. Nevertheless it does not necessarily mean that the larger the tool cutting edge radius, the better the ductile mode cutting. Arefin et al. [9] reported that there is an upper bound of the tool cutting edge radius for ductile mode cutting of brittle materials, e.g. 700–800 nm for silicon. There are two important parameters relating to ductile regime machining, i.e. critical depth of cut (tc) and subsurface damage depth (Cm), which may be experimentally or analytically obtained. Marshall and Lawn [10] performed indentation experiments on different materials and proposed Eq. (1) to tc of penetration by the indenter for crack initiation: tc ¼ CðE=HÞðKc =HÞ2 ,
ð1Þ
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where E is the elastic modulus, H is the hardness, Kc is the fracture toughness and C is a dimensionless constant dependent on indentation geometry. Bifano et al. [11] extended Eq. (1) to relate the grinding in-feed rate necessary for ductile material-removal with the properties of the brittle workpiece material and estimated C to be 0.15. However, for a specific machining process, e.g. micro-milling and diamond turning, the complex tool– workpiece interaction differs dynamically and geometrically from the deformation produced in indentation. Therefore, different experimental methods have been proposed to determine tc for different machining processes. For micro-milling, Matsumura et al. [12] related the ductile and brittle mode machining to the behavior of the cutting force and found that the ductile mode machining is characterized by a smooth force signal while that from the brittle mode machining oscillates about a constant mean value. Thus, tc can be estimated from the differences in the two types cutting force signals. For diamond turning, plunge cutting is a quite straightforward method to determine tc by observing the transition of the cutting mode from ductile to brittle [13]. In addition, Blake and Scattergood [5] proposed an interruptedcutting test to study the ductile-to-brittle transition at the shoulder region and a machining model to determine tc from the location of the ductile-to-brittle transition. As to the subsurface damage depth Cm, Marshall et al. clearly identified the various radial and lateral crack systems associated with indentation [14] and proposed models to predict the size of the radial and lateral cracks [15,16]. Arif et al. [17] claimed the milling process to be analogous to indentation and derived an analytical model to determine the critical feed per edge to achieve ductile mode machining based on Marshall et al.’s models [15]. For diamond turning, Blackley and Scattergood [18] proposed a phenomenological model of the ductile-to-brittle transition to quantitatively determine tc and Cm. Unlike conventional diamond turning the fast tool servo (FTS) diamond turning enables precision machining of complicated micro-structured surfaces, including both axisymmetric and nonaxisymmetric surfaces, which is difficult to be achieved by grinding and lapping. Most of the previous researches focused on the development of the FTS itself for higher performance, i.e. higher bandwidth, larger stroke, higher stiffness, etc. [19–23]. In addition, ductile materials, e.g. copper, brass and aluminum were machined to prove the performance of their developed FTS. However, few researches have been devoted to FTS diamond turning of microstructured surfaces on brittle materials. Therefore, in this paper, a
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machining model has been developed for FTS diamond turning of micro-structured surfaces on brittle materials. Based on the model, a damaged region analysis method (DRAM) has been proposed to determine the subsurface damage depth (Cm) by analyzing the surface damaged region of a machined microstructured surface with sinusoidal wave in the radial direction. With Cm, the maximum feedrate for machining a crack-free microstructured surface can be determined. Machining experiments have been carried out to verify the validity of DRAM.
2. Theory on FTS diamond turning of brittle materials 2.1. FTS diamond turning of micro-structured surfaces FTS diamond turning evolves from conventional diamond turning to ultra-precision fabrication of complicated micro-structured surfaces, including both axisymmetric and non-axisymmetric surfaces. It is realized by integrating a specially designed tool servo into conventional diamond turning machine to drive the cutting tool in and out of the workpiece when it is rotating. Depending on the bandwidth of the tool servo, it can be named as slow tool servo (STS) [24,25] or fast tool servo [19–23,26]. Fig. 1 shows a FTS diamond turning machine in which there are totally four axes: X axis—the x slide, Z axis—the z slide, C axis—the spindle and W axis—the FTS. Such a machining system is expressed in cylindrical coordinates (r, j, z), whereas, the surface model to be machined is expressed in Cartesian coordinates (X, Y, Z). For conversion between the two coordinate systems, it is convenient to assume that the Z-axis of both systems is coaxial and then the correspondence between the cylindrical coordinates (r, j) and Cartesian coordinates (x, y) is ( ( pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x ¼ r cos j r ¼ x2 þ y2 , ð2Þ 3 y ¼ r sin j j ¼ Fðtan1 ðx=yÞÞ where FðUÞis to determine the total angle rotated after start machining. Consider the micro-structured surface with sinusoidal wave along radial direction (SWR); it can be described by pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi! 2p x2 þ y2 , ð3Þ zðx,yÞ ¼ A sin
Fig. 1. Working principle of FTS diamond turning.
l
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where A is the wave amplitude and l is the wavelength. The SWR can be expressed in cylindrical coordinate by Eq. (4). 0 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 2p ðr cos jÞ2 þ ðr sin jÞ2 A, ð4Þ zðr, jÞ ¼ A sin@
l
The projection of the relative tool–workpiece movement to the XY-plane is a spiral curve (r, j), whose shape is determined by the feedrate f(mm/min) and spindle speed u (rpm), as shown in Fig. 2. As the numerical controller used in the FTS diamond turning machine can implement only a finite number of motion commands, the coordinates (r, j) need to be sampled by an important sampling parameter Nj, which divides one rotation equally into Nj divisions. The sampled spiral curve (r0, j0) can be calculated by Eq. (5), e.g. the dotted spiral curve with Nj ¼36: 8 < Rw uNfij To the center of the workpiece r0 ¼ fi : uN From the center of the workpiece j
j0 ¼
2p i, i ¼ 0,1,. . .,Rw uNj =f Nj
ð5Þ
With (r0, j0) the tool path TP(x0, y0, z0) for SWR at a particular f and u can then be calculated by Eqs. (4) and (5), e.g. the tool path in Fig. 2. With TP(x0, y0, z0), the CNC code for fabrication of CWR can be generated easily. During fabrication, the workpiece is mounted on a high-precision spindle with air–hydrostatic bearing. The cutting tool is mounted on FTS [27,28] and driven to the desired position by a piezoelectric actuator (for different performances, the piezoelectric actuator may be replaced by other actuators such as the Lorentz force actuator, magnetostriction actuator, etc. [22]). When the spindle rotates to a certain position, the cutting tool is driven to the right position as specified in the CNC code [29], as shown in Fig. 1. The micro-structured surface is formed by the complex interaction between the workpiece and tool geometry. Fig. 3(a) shows in 3D the surface formation in FTS diamond turning of SWR with A¼2 mm and l ¼0.2 mm using a cutting tool with nose radius R¼0.4 mm. Fig. 3(b) shows the formation of the sectional surface profile fj(r) as shown in Fig. 1 when the cutting tool moves along the tool path TPj generated with f¼8 mm/min, u ¼1000 rpm and nominal depth of cut D0 ¼2 mm. It is clear that the surface formation can be viewed as the intersection of the successive tool cutting edge profiles. An important property of FTS diamond turning of microstructured surfaces is shown in Fig. 3. It can be seen that the chip geometry of the current pass is different from those of the previous pass and the next pass. It is this continuous changing chip geometry that brings about difficulty to FTS diamond turning
Fig. 2. A micro-structured surface with sinusoidal wave along radial direction.
Fig. 3. Visualization for the surface formation of FTS diamond turning of SWR: (a) 3D and (b) 2D.
of micro-structured surface on brittle materials, which will be elaborated in the next section. 2.2. Machining model for FTS diamond turning of brittle materials As the brittle materials tend to crack easily during machining, it is necessary to predetermine the cutting conditions for FTS diamond turning of micro-structured surfaces on brittle materials in order to generate crack-free surface. Therefore a machining model for FTS diamond turning of micro-structured surfaces on brittle materials is proposed as shown in Fig. 4, which is evolved from the phenomenological model [5,18] for conventional diamond turning of brittle materials. For each pass i the effective chip thickness tieff varies from zero at the apex of the tool, to a maximum (tim) at the top of the previous uncut region and to zero at the top of the current uncut region. From literature review, there exists a critical depth of cut (tc) below which no crack will be generated. Therefore, there is a microfracture damage zone for each pass if tieff 4tc, e.g. the microfracture damage zone for pass 0 shown in Fig. 4(a). Fig. 4(a) and (b) shows the machining of the same microstructured surface with high and low feedrate, respectively. When
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Fig. 4. Machining model for FTS diamond turning of micro-structured surfaces on brittle materials: (a) high feedrate and (b) low feedrate.
a high feedrate is used, tc is located at low portion of the uncut region and the associated subsurface damage depth (Cm) extends into the finish surface as shown in Fig. 4(a). When a low feedrate is used, tc moves towards the high portion of the uncut region, the microfracture damage zone for each pass is removed by the next passes and the finish surface is free of crack. Therefore the occurrence of crack on the finish surface is determined by a critical feedrate (fc), which is defined as the maximum feedrate to obtain crack-free micro-structured surfaces. If the feedrate is larger than fc, cracks will be generated at some portion of the micro-structured surface. If the feedrate is smaller than fc, the whole machined surface will be free of cracks. For practical application, it is desirable to maximize the feedrate to reduce machining time. In order to determine fc, it is important to determine the length of the subsurface damage (Cm) for the combination of used cutting tool and brittle material of the workpiece. It is important to note that Cm is assumed to be the average fracture propagation depth after crack initiation. With Cm, the critical feedrate fc for machining a crack-free micro-structured surface can be determined. Fig. 5. Geometry for calculation of chip thickness.
2.3. Damaged region analysis method In order to determine Cm, a damaged region analysis method (DRAM) is proposed. In DRAM, a SWR with a certain A and l is machined for the cutting tool with nose radius R on the chosen brittle material. Then the machined SWR is observed by a microscope and the damaged region is measured. Finally, Cm can be derived from the relationship between the length of the damaged region and Cm. Due to the complex nature of the micro-structured surface, there is no simple form of relationship between the length of the damaged region and Cm. Therefore, a numerical computation method is used to simulate the formation of the surface and predict the initiation of cracks. Fig. 5 shows the geometry for the calculation of the chip thickness in FTS diamond turning of micro-structured surface. In Fig. 5, 0, 1 and –1 represents the current pass, next pass and previous pass, respectively, R is the tool nose radius and D is the nominal depth of cut for the current pass. Due to different chip shapes at [0, y1] and [y1, y2], the effective chip thickness teff is calculated differently as shown in Eq. (11):
DD0 ¼ z0 z1 d0 ¼
ð6Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi f 2 þ DD0 2
a0 ¼ p þarctan
ð7Þ
DD0 f
ð8Þ
a1 ¼ arccos
d0 2R
ð9Þ
sin b d0 d0 ¼ ) b ¼ arcsin sinða1 þ yÞ sinða1 þ yÞ R R
teff ¼
ð10Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 8 < R R2 þ d2 2Rd0 cosðpa1 ybÞ, 0
y A ½0, y1
: R
y A ½y1 , y2
RD , sinð2pya0 a1 Þ
0qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 R2 ðRðD þ DD0 Þ2 f 3 Aa0 a1 y1 ¼ p þarc tan@ 2 RD
y2 ¼ 2parc sin
RD a0 a1 R
ð11Þ
ð12Þ
ð13Þ
Fig. 6 shows the simulation of the formation of the sectional surface profile fj(r) and the initiation of the crack at each pass. For each pass, the effective chip thickness teff is firstly calculated by Eqs. (6)–(13). The z values used in Eq. (6) is obtained from TPj(r), which is the dotted curve. Then the crack initiation location where teff ¼ tc is searched and a crack with length of Cm is placed at the crack initiation location as shown in Fig. 6. Finally, the intersection between the cracks and the finish surface profile fj(r) is searched. If the cracks extend into fj(r), the used feedrate
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Fig. 6. Definition of crack ratio.
Fig. 7. Relationship between CR and Cm.
f is too big for generation of crack-free surface. From Fig. 6, it can be seen that the crack region is located at the lower left region of the sinusoidal wave. In addition, the depth of the crack left on the finished surface is the deepest at the center of each damaged region, which is denoted as a red dot in the figure, and decreases to zero on both sides. The larger the length of the subsurface damage (Cm), the longer the length of the damaged region. Therefore, there is a relationship between the length of the damaged region and Cm. To quantitatively describe the relationship a crack ratio (CR) is defined, as shown in Eq. (14), as the length of the damaged region (Lc) within a cycle of sine wave to the wavelength (L): CR ¼
Lc L
ð14Þ
Fig. 7 shows an example of the relation between Cm and CR when machining SWR with A¼2 mm and l ¼0.2 mm using a cutting tool with R ¼0.4 mm and tc ¼0.25 mm and a feedrate f¼3 mm/rev. After machining SWR, the machined SWR is observed under the microscope and the length of the damaged region (Lc) is measured to obtain CR. The measured CR can then be used to extract the Cm from Fig. 7.
Fig. 8. Damaged region analysis for the measured CR: (a) microscopic images and (b) processed image.
2.4. Measurement of CR To obtain Cm from Fig. 7, a SWR is machined to obtain the measured CR (MCR). Fig. 8(a) shows a microscopic image of a
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machined SWR (Note: the white spots scattered in the image are caused by the microscope. It can be omitted during analysis.) It can be seen that there exists a damaged region in which the largest crack is located at the center and the size of the crack decreases on both sides. Such damaged behavior is the same as that simulated in Fig. 6. In practice, there are two uncertainties in determining MCR. Firstly, it is difficult to locate the exact boundaries of the damaged region due to some small random distributed cracks. Secondly, the length of the damaged region (Lc) at different locations may be different due to varying composition of the material and machining conditions. In this paper, an image processing method and a statistical method are adopted to solve these problems, respectively. To highlight the damaged region, a thresholding method is used to set the relatively dark cracks to black color andthe background colors to white color. Fig. 8(b) shows the processed image of the microscopic images as shown in Fig. 8(a). To locate the left boundary (LB) and right boundary (RB) of the damaged region the severity of damage (SD) is calculated vertically along the processed image, which is the cutting direction. Fig. 8(b) shows the SD value for the processed image. Thus LB and RB are, respectively, defined as the leftmost and rightmost locations whose SD value is a certain percentage of the maximum SD, which is controlled by the crack percentage (CP) as shown in the figure. In this paper, CP is chosen to be 90%. Finally, LB and RB are located as shown in Fig. 8(b). To improve the credibility of the MCR, damaged regions at different locations as shown in Fig. 9 are measured and MCR is calculated by Eq. (15). There is one point worth noting. As reported in literature [30], the severity of damage is greatly influenced by the crystal orientation. Fig. 9 shows that crack occurs when the tool is cutting within a certain degree of the o1 1 0 4 direction. It means that the severity of damage is different along different directions of the machined surfaces. To make sure that the whole machined surface is free of crack, the measurement locations are chosen to be on the direction as shown in Fig. 9: PN MCR ¼
i¼1
Lci
NL
ð15Þ
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3. Experiments and discussion 3.1. Experimental apparatus FTS diamond turning of micro-structured surfaces on brittle materials was performed on the machine tool [27,28,31] as shown in Fig. 10. Two most important components of the machine are the air bearing spindle and FTS. The air bearing spindle is a brushless DC motor (Cannon SP-501HCL) with rotational speed from 10 rpm to 15,000 rpm. The FTS is specially designed for machining micro-structured surface. It consists of a piezoelectric actuator, a flexure, a capacitor sensor, a tool holder and a force transducer. The stroke of the FTS is 7 mm with positioning accuracy below 1 nm. The cutting tool was single crystal diamond (SCD) with nose radius of 0.4 mm, nominal rake angle of 01, clearance angle of 71 and cutting edge radius of about 100 nm. Fig. 11 shows the microscopic images for the SCD cutting tool used in the experiments. The rectangular shaped workpiece of MgF2 glass was attached to an aluminum block using heatsoften glue, which was then clamped by a collet on the air bearing spindle as shown in Fig. 10. The properties of MgF2 glass are listed in Table 1. In this paper, MgF2 is chosen as the brittle material to be studied because it is relatively soft when compared with to other glass such as BK7 and thus the cutting tool can last long enough for all tests without changing the critical depth of cut tc, which is important for the verification of the proposed DRAM. A constant spindle speed of 1000 rpm was used in all tests. All cuttings were performed under dry conditions. After machining, the machined micro-structured surfaces were cleaned with alcohol to remove the chips attached on the surface. An Optical microscope was used to observe and measure the machined surface for further analysis. 3.2. Determination of critical depth of cut The value for critical depth of cut tc can be estimated by Bifano’s model [11] for typical brittle materials using the values for all parameters as listed in Table 1 and C is set to be 0.15 as suggested for grinding [11]: tc ¼ 0:15ðE=HÞðKC =HÞ2 ¼ 249:6 nm As the geometry of the cutting edge of the SCD tool is different from the grains in the grinding wheel, C is difficult to be obtained for the SCD tool. Therefore, a plunge cutting experiment was carried out for the tool and workpiece combination. As shown in
Fig. 9. Influence of crystal orientation and the measurement locations.
Fig. 10. FTS diamond turning machine.
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In this experiment, l, d and the cutting velocity are set to be 4 mm, 1 mm and 20 mm/min respectively. The mark left on the surface was observed under the microscope. Due to the limited measurement range of the microscope, Fig. 12(b) shows the image corresponding to only the region I–III indicated in Fig. 12(a). As there is no clear boundary for transition from ductile to brittle, lc was found to lie within [0.945, 1.065]. Using Eq. (16) tc is found to be 236–266 nm, in which tc found by Bifano’s model lies. Therefore, tc is set to 250 nm for all the analysis. 3.3. Verification of DRAM To verify the validity of the proposed DRAM, SWR A ¼2 mm and l ¼0.2 mm is machined using the cutting tool as shown in Fig. 11 on MgF2 with f¼3 mm/min and u ¼1000 rpm. The machined surface is measured at 15 different locations as shown in Fig. 9. A typical microscopic image for the damaged region is shown in Fig. 8(a). All microscopic images were processed as explained in Section 2.4 and the MCR were obtained as shown in Fig. 13(a) with CP¼90%. The average MCR is calculated by Eq. (15) and found to be 0.36172. To obtain the subsurface damage depth Cm, the relationship between Cm and CR was simulated by DRAM
Fig. 11. Microscopic images for the SCD cutting tool: (a) clearance face and (b) rake face.
Table 1 Properties of MgF2 glass. Hardness (H: GPa) Elastic modulus (E: GPa) Fracture toughness (KC: MPa. m1/2) Density (g/cm3) Melting point (1C)
4 138.5 0.9 3.18 1255
Fig. 12. Plunge cutting for determination of tc: (a) schematic diagram and (b) microscopic images for brittle to ductile transition.
Fig. 12, the cutting tool was plunged into the workpiece with depth of cut changing from zero to d and the total length of cutting is l. There exists a brittle to ductile transition location lc where the depth of cut equals tc and the cutting changes from ductile to brittle mode. Therefore, by measuring the distance lc, the critical depth of cut can be estimated by tc ¼
lc d l
ð16Þ
Fig. 13. Determination of Cm: (a) measured CR at different locations and (b) relationship between Cm and CR with CP¼ 90%.
D.P. Yu et al. / International Journal of Machine Tools & Manufacture 51 (2011) 918–927
and obtained as shown in Fig. 13(b). It is important to note that the relationship is slightly different from the one shown in Fig. 7 as the CP is set to be 90%, which is the same as the CP used in extracting the MCR. From Fig. 13(b), Cm is found to be 0.878 mm.
Fig. 14. Relationship between CR and feedrate (f).
With the obtained Cm, the relationship between CR and f can be simulated and found as shown in Fig. 14. In order to verify reliability of the obtained Cm, SWRs were fabricated with feedrate f¼[1,1.5,2, 2.5,3.5,4,4.5,5,6] mm/min and spindle speed u¼ 1000 rpm. The corresponding MCRs were obtained as listed in Table 2. Some representative microscopic images for each feedrate are also listed in Table 2 (note: due to the limited measurement range of the microscope, two or three neighboring images were stitched together to form a large image for f¼[4.5,5,6]). From Table 2 it can be seen that larger feedrate results in wider damaged region and more severe damage, which is indicated as the size of the crack. For feedrate f of 1 and 1.5 mm/min, the machined surfaces are clear and free of cracks thus their CRs are taken as 0. For feedrate f of 5 and 6 mm/min, the whole machined surfaces are full of cracks with larger cracks located at the center portion with smaller cracks located at both sides, thus their CRs are taken as 1. For the feedrates between 1.5 and 5, the width of the damaged region increases with feedrate. For each feedrate, the captured microscopic images were processed and the MCRs were obtained as listed in Table 2. Fig. 14 shows a comparison of the predicted CRs (PCR) and MCRs. It can be seen that the MCRs correlate well with the predicted CRs. Therefore, it can be claimed that the predicted subsurface damage depth Cm is reasonable. With Cm, the maximum feedrate for generating crack-free micro-structured surfaces can be searched. Taking the SWR machined in the experiments for example, the maximum feedrate can be found from Fig. 14 to be 1.85 mm/min, where CR changes from zero to
Table 2 Experimental results. Feedrate (mm/min)
PCR
MCR
1
0
0
1.5
0
0
2
0.1137
0.0680
2.5
0.2546
0.2570
925
Representative microscopic images
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Table 2 (continued ) Feedrate (mm/min)
PCR
MCR
3
0.3617
0.3617
3.5
0.4665
0.4635
4
0.5982
0.5900
4.5
0.7329
0.7383
5
1
1
6
1
1
non-zero value. For different micro-structured surfaces, the maximum feedrate for generating crack-free surfaces can be searched based on tc found by plunge cutting and Cm found by DRAM for a given tool and workpiece combination.
4. Conclusions A novel method for determination of the subsurface damage depth in diamond turning of brittle materials has been presented.
Representative microscopic images
The following conclusions can be drawn from the development and demonstration of the method:
This method enables the machining of crack-free micro-struc
tured surfaces on brittle materials by fast tool servo (FTS) diamond turning. Using sinusoidal wave along radial direction (SWR) as a fundamental and representative type of micro-structured surfaces, a surface crack damage region is shown to exist on a particular segment of the wave. Moreover, the length of the
D.P. Yu et al. / International Journal of Machine Tools & Manufacture 51 (2011) 918–927
damaged region is found to vary with the feedrate used in machining. To explain and predict such regional subsurface damage region phenomenon, a machining model has been proposed for FTS diamond turning of micro-structured surfaces on brittle materials. Based on the proposed machining model, a damaged region analysis method (DRAM) has been developed to determine the subsurface damage depth (Cm) for a tool–workpiece combination by analyzing the surface damaged region of a machined SWR. Through measuring the crack ratio (CR) of the machined SWR, Cm can be determined from the relationship between Cm and the measured CR (MCR), determined by DRAM. A series of experiments on machining SWR with different feedrates have been carried out. From microscopic images of the machined SWR surfaces captured and processed by image processing methods to obtain MCR it is shown that the predicted CR correlates well with MCR, demonstrating the validity of DRAM.
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