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Measurement of the Preston coefficient of resin and bronze bond tools for deterministic microgrinding of glass
Precision Engineering 30 (2006) 115–122
Measurement of the Preston coefficient of resin and bronze bond tools for deterministic microgrinding of glass Sha Tong a,b , S.M. Gracewski a,b,∗ , P.D. Funkenbusch a,b a
Department of Mechanical Engineering, University of Rochester, Rochester, NY 14627, USA b Center for Optics Manufacturing, University of Rochester, NY 14623, USA
Received 2 February 2004; received in revised form 3 March 2005; accepted 31 March 2005 Available online 21 September 2005
Abstract Deterministic microgrinding technology applies a bound diamond abrasive tool positioned by a Computer Numerically Controlled (CNC) machine to generate precision optical components. The ease of work material removal during the grinding process is often characterized by the specific energy or the Preston coefficient. For a given part and process, these two parameters also indicate the tool/abrasive performance. The Preston coefficient of a resin bond tool with 2–4 m diamond abrasives under different process parameter combinations has been measured with BK7 as the test glass. The Preston coefficient of a similar bronze bond tool was also measured for comparison. Experimental measurements show the resin tool behaves qualitatively differently than the bronze tool in a multiple pass grinding process. The measured Preston coefficient of the resin tool was two to three times smaller than that of the bronze tool and decreased rapidly as pass number increased. A plot of the Preston coefficient versus resin tool bond wear suggests that excessive tool wear reduces the tool’s cutting efficiency, resulting in a rapid decrease in the Preston coefficient. © 2005 Elsevier Inc. All rights reserved. Keywords: Optics manufacturing; Preston coefficient; Specific energy; CNC grinding; Tool wear
1. Introduction Deterministic microgrinding (DMG) has become one of the major methods used for fabrication of precision optical components [1–3]. In a DMG process, a bound diamond abrasive tool is positioned by a Computer Numerically Controlled (CNC) machine to generate plano, spherical or aspherical surfaces. By taking advantage of precise speed and positional control with a CNC machine, the DMG technique is able to achieve a very high level of form accuracy (0.5 m peak-to-valley) and surface finish (3–10 nm) with subsurface damage (SSD) under 1 m. In DMG processes, reliable tool performance is essential to achieve precise control of work material removal [4]. A useful parameter for characterizing the tool performance is the Preston coefficient, which is widely used to estimate the volumetric removal rate of work material under normal loading or predict loads/deflection in infeed controlled CNC grinding [4,5]. The ∗
Corresponding author. Tel.: +1 585 275 7853; fax: +1 585 256 2509. E-mail address: [email protected] (S.M. Gracewski).
0141-6359/$ – see front matter © 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.precisioneng.2005.03.004
Preston’s equation [6] can be written dV = Cp vs FN , dt
(1)
where dV dt is the volumetric removal rate of work material, Cp the Preston coefficient, FN the normal grinding force and vs is the surface speed between the tool and workpiece. Thus, the Preston coefficient can be obtained by dividing the volumetric removal rate by the surface speed and the normal grinding force. For grinding, this relationship is more commonly expressed in terms of the specific grinding energy, e, which is defined as the energy consumed per unit volume of material removed. The specific energy can be written dV 1 = (µFN )vs , (2) dt e where µ is the coefficient of friction between the tool and work. From Eqs. (1) and (2), the Preston coefficient and specific energy are inversely related by 1e = Cp µ. This paper focuses on the Preston coefficient because the normal grinding force FN is easier
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to measure than the tangential grinding force during contour grinding. The Preston coefficient depends on many factors such as material properties, tool condition and removal mechanism. Li et al. [7] measured Preston coefficients of fine (2–4 m) bronze tools in the range of (1 ± 0.3) × 10−13 Pa−1 for different process parameter combinations, consistent with the experimental data obtained by Takahashi and Funkenbusch [4] and Ong and Venkatesh [8]. Hwang et al. [9] measured Preston coefficients on the order of 10−8 Pa−1 for a 40–80 m resin tool in grinding silicon nitride. They also mentioned that the Preston coefficient decreases exponentially as the grit depth of cut is reduced, which is often referred to as the “size effect”. Yui and Lee [10] reported that the tendency of the Preston coefficient to decrease with a decrease of grit depth of cut is more remarkable when the grit depth of cut is less than 0.02 m. In this paper, we measured the Preston coefficient of a fine resin tool under different process parameter combinations with BK7 as the test glass. For comparison, the Preston coefficient of a fine bronze tool was also measured. Observed differences between the bronze tool and the resin tool in a multiple pass grinding process are reported and discussed. In addition, the bond wear of the resin tool was measured and correlated to the rapid decrease of the Preston coefficient during grinding.
is called the cross-feed. Motion in the Z direction controls the surface figure and depth of cut dc . At the Center for Optics Manufacturing (COM), a typical contour grinding process uses two tools. A rough tool having 10–20 m diamond grits is used to remove bulk material. Then, a fine tool having 2–4 m grits is used to remove the surface damage left by the rough tool and form the surface into its final shape. The second process often requires multiple passes because the small abrasive used limits the depth of cut. 3. Analysis The surface speed vs between the tool and workpiece in Eq. (1) can be written as vs = (2πΩt Rt )2 + (2πΩw r)2 , where Ωt is the tool rotation speed, Ωw the workpiece rotation speed, Rt the radius of the tool and r is the radial distance of the tool from the center of the workpiece. Since typically Ωt Rt Ωw r, vs can be simplified to vs ≈ 2πΩt Rt .
(3)
2. Background
The volume removal rate dV dt in Eq. (1) can be expressed as dV dt = Avg , where vg is the relative speed of the grinding zone with respect to the workpiece and A is the projected contact area between the tool and workpiece on the plane perpendicular to
Contour grinding, which can be used to generate aspherical optical surfaces [1,2,7], is one of the most important applications of DMG. Fig. 1 shows the geometry of contour grinding. Both the grinding tool and workpiece rotate. The grinding tool moves simultaneously in two orthogonal directions (X and Z in Fig. 1) with respect to the workpiece. The motion in the X direction
vg ≈ 2πΩw r.
the direction of vg . vg can be written as vg = (2πΩw r)2 + v2c , where vc is the cross-feed rate and 2πΩw r is the tangential speed due to the workpiece rotation. Typically, vc is much smaller than 2πΩw r except at locations very close to the center. As a result, vg can be simplified to (4)
The projected contact area A for successive passes in contour grinding can be determined as a function of dc (the current actual depth of cut), d0 (the actual depth of cut at one workpiece revolution earlier), cross-feed per revolution f and tool radius Rt . Fig. 2 shows the projected contact area between two successive passes. Marsh and Yantek [11] developed a formula for the above projected contact area. By defining δ = dc − d0 and expanding Marsh’s formula in a power series about the equilibrium point
Fig. 1. Contour grinding geometry.
Fig. 2. Projected contact area between two successive passes. The relative velocity of the grinding zone with respect to the workpiece vg is perpendicular to the projected contact area, i.e. along the Y direction.
S. Tong et al. / Precision Engineering 30 (2006) 115–122
δ = 0, we can obtain the first-order approximation A ≈ fdc ,
(5)
(6)
Ωw r Ωt Rt Cp
where R = is a nondimensional parameter that reflects the grinding process parameters. Eq. (6) represents the mean force created under stable grinding conditions. Solve for the Preston coefficient Cp from Eq. (6) to obtain Cp =
dc fΩw r . FN Ωt Rt
(7)
If used without correcting for the finite tool footprint, Eq. (7) predicts that the Preston coefficient approaches zero (Cp → 0) as the radius position approaches zero (r → 0), since the grinding force is not equal to zero (FN = 0). To compensate for the finite tool footprint, instead of using the radial position of the tool geometry center, the radial position of the middle point rm between the tool front contact point and geometry center is used to calculate the Preston coefficient. For small depths of cut, the √ relationship between r and rm is approximately rm = r + 21 2Rt dc . Eq. (7) thus can be rewritten as Cp =
dc fΩw rm . FN Ω t R t
cut for each pass, the Preston coefficient for any pass can be calculated. 4. Experiments
Eqs. (1), (3)–(5) can be combined to obtain FN = f × dc × R,
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(8)
In the above formula, the grinding force FN can be calculated by FN = km T, where km is the spindle static stiffness and T is the tool deflection. The spindle static stiffness is obtained by exciting the tool with a shaker at low frequency (∼1 Hz) and measuring the resulting tool deflection with an eddy current probe. Then, the force during grinding can be determined from an eddy current probe measurement of the tool deflection during grinding. Therefore, the Preston coefficient can be calculated using Eq. (8) if the actual depth of cut is known. However, the actual depth of cut dc differs from the programmed depth of cut dp due to the finite spindle stiffness. Li et al. [7] and Franse [12] studied the relationship between the actual depth of cut and the programmed depth of cut for multipass grinding processes. For a bronze tool grinding BK7 glass, Li et al. found as pass number increases, the actual depth of cut dc approaches a steady-state value dp . Based on this result, he ground a BK7 workpiece with five consecutive passes and used the last pass to calculate the Preston coefficient. Because the actual depth of cut did not asymptotically approach the programmed depth of cut for grinding BK7 with a resin bond tool, Li’s technique was modified so that the actual depth of cut dc was measured after each pass of a multi-pass grinding processes. For each pass, a workpiece, 40 mm in diameter, is fine ground only from the center r = 0 to the radial position r = 15 mm. Thus, the edge of the workpiece (r = 15–20 mm) serves as an absolute reference when applying a line scan across the workpiece after each pass. The actual depth of cut of the last pass is obtained from the height difference between the current scan and the previous scan using the edge as a reference. Since the above technique can be used to measure the actual depth of
4.1. Preston coefficient of bronze tool A Moore NanotechTM AG 150 contour grinding machine was used as the test machine. BK7 glass with a diameter of 40 mm was initially rough ground with a 10–20 m bronze tool to a plano surface. (Although the contour grinding process can be used to generate both spherical and aspheric surfaces, for simplicity all workpiece surfaces used in the experiments reported here were plano.) A fine bronze-bond tool (Socmac 97-14103, 38 mm in diameter, containing 2–4 m diamond abrasives, 75 concentration, N hardness) was trued to a spherical profile of 38 mm diameter (matching the tool diameter) and dressed using a 150 grit alumina dressing stick (Norton). The tool was then used to finish grind the surface from the center r = 0 to 15 mm in five consecutive passes. The process parameters were: Ωt = 12,000 rpm, Ωw = 43 rpm, dp = 5 m and vc = 6 mm/min. For all experiments, the work zone was flooded with coolant during grinding. After each pass, the workpiece surface profile was measured and the actual depth of cut during the previous pass was calculated. At the same time, an eddy current probe fixed over the tool spindle measured the tool deflection during each pass. Fig. 3 plots the actual depth of cut versus radial position of the fifth pass. The averaged actual depth of cut dc = 4.93 m is approaching a steady-state value equal to the programmed depth of cut dp = 5 m, confirming Li et al.’s [7] study on multiple grinding passes. Fig. 4 shows the tool deflection relative to the tool spindle housing measured with an eddy current probe during the same multiple pass process. The plot shows that the tool deflection increases from pass to pass, gradually reaching a steady state. Knowing the actual depth of cut and tool deflection, the Preston coefficient for each pass can be calculated using Eq. (8). In Fig. 5, the Preston coefficient is plotted versus radial position for each pass. Fig. 6 shows the averaged value (for 3 mm < r < 15 mm) of the Preston coefficient Cp for each pass for the data in Fig. 5.
Fig. 3. Actual depth of cut of a bronze tool in the fifth pass (programmed depth of cut dp = 5 m).
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S. Tong et al. / Precision Engineering 30 (2006) 115–122 Table 1 Process parameter combinations for investigating resin tool performance Combination A dp (m) 5 6 vc (mm/min) Ωw (rpm) 43 Ωt (rpm) 12000
Fig. 4. Bronze tool deflection plotted vs. tool radial position for five consecutive passes.
Combination B 10 6 43 12000
Combination C 5 6 215 12000
Combination D 5 3 43 12000
The averaged Preston coefficient of the second through fifth pass Cp = 0.95 × 10−13 Pa−1 is close to Cp = 1 × 10−13 Pa−1 , consistent with Li et al.’s [7] experimental result. 4.2. Preston coefficient of resin tool
Fig. 5. The Preston coefficient of the bronze tool plotted vs. distance from the workpiece center for the first five passes.
The Preston coefficient of the first pass is obviously larger than the successive passes. The abrupt decrease in the Preston coefficient is likely due to changes in the work material. During the first pass, the tool removes the damaged layer left by the rough grind. This damaged layer is relatively easy to remove, resulting in a high Preston coefficient. The plot also shows that after the second pass, the Preston coefficient gradually decreases as pass number increases. This may be attributed to a decreasing workpiece surface roughness as well as variations in tool cutting conditions, such as diamond sharpness and protrusion [4].
Fig. 6. The averaged Preston coefficient of the bronze tool for the first five passes. The Preston coefficient monotonically decreases with pass number.
Resin is a soft bond that is often used when a better surface finish is required. Compared to a bronze tool, a resin tool with similar diamond sizes produces a surface with lower surface roughness. However, resin tools generally wear faster and, as this experiment shows, can be less efficient. Experiments were designed to investigate the Preston coefficient of a resin tool over a wide range of process parameters. For each process parameter combination, a BK7 glass with a diameter of 40 mm was initially rough ground with a 10–20 m bronze tool to a plano surface. Then, a fine resin tool (Norton 607C, 65 mm in diameter, containing 2–4 m diamond abrasives, 100 concentration) was used to finish grind the surface. The specific process parameters applied in the experiments are given in Table 1. The tool was freshly trued to a 65 mm spherical profile (matching the tool diameter) and dressed prior to grinding. For each process parameter combination, the workpiece was fine ground from the center r = 0 to 15 mm for four consecutive passes. After each pass, the workpiece surface profile was measured and the actual depth of cut during the previous pass was calculated. At the same time, an eddy current probe fixed over the tool spindle measured the tool deflection for each pass. The resin tool was trued and dressed between changes of process parameter combinations. During the experiments to measure the Preston coefficient of a resin tool with BK7 as the test glass, we found that the resin tool behaves qualitatively differently than the bronze tool. These differences are discussed in detail below. 4.2.1. Depth of cut of a resin tool in multiple pass process Fig. 7 shows the actual depth cut of the fourth pass with process parameter combination A as given in Table 1. The averaged actual depth of cut of the resin tool dc = 1.1 m is much less than the programmed depth of cut dp = 5 m. The larger grinding force and smaller material removal rate correspond to a smaller Preston coefficient as defined by Eq. (1). This phenomenon is observed for all process parameter combinations listed in Table 1. By observing the actual depth of cut for all four consecutive passes, we found, unlike the bronze tool, the actual depth of cut of the resin tool shows no sign of approaching a steady-state value (dp = 5 m) as pass number increased. Instead, the actual depth of cut gradually
S. Tong et al. / Precision Engineering 30 (2006) 115–122
Fig. 7. Actual depth of cut of a resin tool in the fourth pass (programmed depth of cut dp = 5 m).
decreased as pass number increased. This implies that the resin tool begins to fail before it approaches a steady-state value. Fig. 8 shows the tool deflection relative to the tool spindle housing. The plot shows that the tool deflection increased from pass to pass but never reached a steady state like that seen for the bronze tool. This indicates that the Preston coefficient for the resin tool decreased quickly as the pass number increased, since approximately the same amount of material was removed in the last few passes, even though the normal force increased with each successive pass. In further experiments conducted with a larger number of passes (10 passes with process parameter combination A), the removal rate approached zero as the grinding force increased for these additional passes, indicating failure of the tool. Because the resin tool could only remove a small percentage of programmed depth of cut dp , a figure error was introduced that increased the depth of cut for each successive pass. Consequently, the tool deflected more and more as the pass number increased. Eventually, the tool was pushed hard enough to cause tool failure. 4.2.2. Preston coefficient Fig. 9 shows the Preston coefficient plotted versus radial position for process parameter combination A for passes one to four. The averaged value (for 3 mm < r < 15 mm) of the Preston coefficient Cp for different process parameter combinations and pass numbers is shown in Fig. 10. The grinding experiment with process parameter combination A was conducted twice to check the repeatability of the measurement. The difference in the averaged
Fig. 8. Resin tool deflection plotted vs. tool radial position for four consecutive passes. [Note that the deflection for the resin bond tool was measured at a point on the shaft because the eddy current probe could not measure directly on the tool. Therefore, the magnitudes plotted here are lower than the actual tool displacements, but relative values can still be compared.]
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Fig. 9. The Preston coefficient of the resin tool plotted vs. distance from the workpiece center for the first four passes. The Preston coefficient decreases monastically with the pass number.
Preston coefficient of these two experiments was approximately 10%. These data can be used to estimate the experimental error. Three observations can be made from the above results. First, the Preston coefficient of the resin tool is about two to three times smaller than that of the bronze tool, indicating a possible difference in the material removal mechanism between the bronze and resin tools. Since the resin tool had a larger diameter than the bronze, differences in surface speed between the two tools are a possible contributor to these differences. However, Takahashi and Funkenbusch [4] found that the specific grinding energy of a bronze tool was nearly independent of the process conditions (including surface speed) for BK7 and two other optical glasses over a range of conditions similar to those investigated here. The material removal rate of the resin tool may be small enough to produce ductile grinding. It is known that a higher specific energy (lower Preston coefficient) is required in ductile grinding than in brittle grinding [13–15]. Fig. 11(a) shows a microscopic image of a workpiece surface ground by the bronze tool, where the brittle grinding mode can be clearly identified. The surface ground by the bronze tool is rough (surface finish 180 nm) and opaque, with extensive cracking as shown in the picture. Fig. 11(b) shows a microscopic image of a workpiece surface ground by the resin tool. The surface ground by the resin tool is smoother (surface finish 45 nm) and transparent with fewer cracks and a few diamond grooves in the grinding direction. These observations support the possible different material removal mechanisms between the bronze and resin tools. Second, the Preston coefficient of the resin tool decreases quickly as pass number increases. The Preston coefficient of the bronze tool also decreases as pass number increases, but much more slowly than that of the resin tool. The fast drop of the Preston coefficient is most likely caused by the rapid wear of
Fig. 10. The averaged Preston coefficient of the resin tool for successive passes with different process parameter combinations. The Preston coefficient decreases quickly with pass number.
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Fig. 11. Microscopic images of workpiece surface ground. Surface ground by the: (a) bronze tool and (b) resin tool.
the resin tool which decreases its cutting efficiency. This issue will be discussed later in this article. Third, the Preston coefficient is relatively insensitive to the process parameters in the initial (freshly dressed) state. Measured differences between the four process conditions in the as dressed condition are on the order of 10%, which is comparable to difference found during replication of combination A. Subsequent decline in the Preston coefficient does, however, seem to depend on the process conditions. The Preston coefficient of process parameter combination B shows the largest decline, and after four passes is about 30% smaller than that of process parameter combination D. The experimental data available here are not sufficient to judge these differences statistically. However, qualitatively, the results are, again, consistent with Takahashi and Funkenbusch’s [4] findings, which showed that the specific grinding energy of their optical glasses was initially nearly independent of the specific process conditions but that the process conditions could have a strong effect on the wear and evolution of the tool surface structure and thus indirectly alter the grinding energy. Removal processes occurring at the workpiece and tool surfaces are interrelated (e.g. [16]), an effect which is not yet well characterized but which needs to be further studied in order to understand and predict process parameter effects. 4.2.3. Bond wear of the resin tool In Section 4.2.2, it was shown that the Preston coefficient of the resin tool decreases quickly as pass number increases. This is most likely caused by rapid wear of the resin tool. The tool wear process is often broken into three major categories: diamond blunting, diamond pullout and bond wear [17]. Takahashi and Funkenbusch [4] noted that deterioration in diamond sharpness causes a rapid increase in the grinding energy or equivalently a decrease in the Preston coefficient. They also found for a hard glass like BK7, both abrasive wear and bond wear of the bronze tool are relatively high. This section investigates the bond wear rate of the resin tool by measuring the volume removed on both the tool and workpiece. Diamond abrasive wear was not studied in this work due to the fine sizes (2–4 m) involved. A technique to characterize bond wear for tools used in grinding optical surfaces was developed by Li et al. [18]. To measure the tool cutting profile, a plano workpiece is put on the work
spindle and locked to prevent any rotation of the workpiece. Then, the tool, rotating at the speed used in the grinding process, is fed into the workpiece until a 10 m depth of cut is reached. During this process, the tool leaves a footprint on the surface reflecting the tool cutting profile. Then, the workpiece is taken off the machine, and the footprint is measured. A BK7 glass workpiece again served as the test glass and process parameter combination A was applied in the experiment, beginning with a newly dressed and trued resin bond tool. The workpiece was ground from the center r = 0 to 15 mm for six passes. After each pass, the tool footprint was generated within the unground glass at the workpiece edge. After completion of each pass, the surface profile as well as tool footprint was measured. As before, an eddy current probe fixed over the tool spindle measured tool deflection during each pass. The measured tool cutting profile after each pass is shown in Fig. 12. Tool wear is most often expressed in terms of the G ratio, which is the workpiece volume removed divided by the tool volume removed. The tool volume removed after each pass can be calculated from Fig. 12 and the workpiece volume removed can be calculated from the actual depth of cut measurements. Thus, the G ratio for each pass can be determined. Fig. 13 shows G ratio of the resin tool versus pass number. The results show a fast initial wear (G ratio < 10) followed by a steady and slower wear (G ratio → 20). This phenomenon was
Fig. 12. Resin tool cutting profile after different pass numbers.
S. Tong et al. / Precision Engineering 30 (2006) 115–122
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Fig. 15. Particle protrusion and diameter [20]. Fig. 13. G ratio of the resin tool at different pass numbers.
also observed by Takahashi and Funkenbusch [4] for bronze tools during their investigation of the micromechanics of tools during grinding. The G ratio of the resin tool is an order of magnitude smaller than that of the bronze tool, which usually has a G ratio over 200. In Fig. 14, the Preston coefficient versus accumulated tool wear is plotted. Again, the initial rapid drop of the Preston coefficient corresponds to the first one or two passes as shown in Fig. 10, which is most likely due to the transition of the workpiece material from the damaged layer to a more solid and smooth layer during these two passes. After that, the plot shows the Preston coefficient decreases gradually as accumulated tool wear increases. Bond wear does not have a direct relationship to the cutting efficiency, since cutting is done by the diamond abrasives. In fact, significant bond wear in grinding processes can be beneficial by removing damaged abrasive particles and exposing fresh abrasive. This effect, also known as “self-dressing”, helps to maintain tool cutting performance. However, in the experiments described above, excessive bond wear was associated with decreased tool cutting efficiency. The extremely low G ratio of the resin bond tool suggests that blunting of the diamond abrasives is not a likely cause of the poor tool performance. Hence, one possible explanation is that low cutting efficiency was caused by high diamond pullout rates as a result of excessive grinding forces. Miller and Kakumanu [17] noted that a wheel may wear so quickly that it does not efficiently remove work material. It is known that pullout of the abrasive particles is controlled by the bond strength, the forces experienced by the particles, as well as the wear of bond around each particle [19]. Given a protrusion height h and a particle size D as shown in Fig. 15, experiments show that the ratio of the critical protru-
Fig. 14. The Preston coefficient vs. accumulated tool wear. The Preston coefficient decreases monotonically with the tool wear.
sion to particle size is about 0.6 for particle pullout [20]. The fast exposure of the embedded abrasive particles and weak hold of the resin bond leads to rapid loss of abrasive particles. In other words, in grinding a hard glass like BK7, the resin bond may not be able to hold the diamond abrasives firmly enough to do efficient work. A high percentage of diamond abrasive is pulled out when sliding between the tool and the workpiece, resulting in low cutting performance. In multiple pass grinding processes, because of the accumulated figure error, the load on the tool increases as pass number increases. An increase in load per abrasive leads to an increase in pullout rate, which may explain the continuous decrease in the Preston coefficient/cutting efficiency after a relatively steady wear state has been reached. For the bronze tool, because of its high wear resistance as well as high bond strength, rapid pullout of the abrasive particles is not expected. The slow decrease of the Preston coefficient/cutting efficiency is partially caused by the blunting of sharp diamonds. Investigation of the effect of tool wear on the Preston coefficient provides an illustration of the importance of producing the right bond wear rate to maintain the tool cutting performance. Excessive tool wear and inadequate tool wear both deteriorate the tool performance. 5. Conclusions The Preston coefficient of a fine (2–4 m diamond) resin bond tool was measured under different process parameter combinations and compared to that of a similar bronze tool. In addition, the bond wear of the resin tool was measured and correlated with a rapid decrease of the Preston coefficient during the grinding: • The actual depth of cut of the resin tool did not reach a steady state (programmed depth of cut). This eventually led to tool failure. • The Preston coefficient of the resin tool was two to three times smaller than that of the bronze tool. Also, the Preston coefficient of the resin tool decreased more quickly with pass number than that of the bronze tool. This was most likely caused by the rapid wear of the resin tool, which decreased its cutting efficiency. • The resin tool wore much faster than the bronze tool. The G ratio of resin tool was approximately an order of magnitude smaller than that of the bronze tool.
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Acknowledgements This work was supported in part by the US Army Material Command through the University of Rochester Center for Optics Manufacturing. We would also like to thank Mr. Ed Fess for providing great assistance in the experimentation. References [1] Pollicove HM, Moore DT. Automation for optics manufacturing. In: Proceedings of the SPIE, vol. 1333. 1990. p. 2–6. [2] Pollicove HM, Moore DT. COM: working to move the optics industry into the 21st century. Photonics Spectra 1992;26(5):127–34. [3] Paula G. Automating lens manufacturing. Mech Eng 1997;119(3):88. [4] Takahashi T, Funkenbusch PD. Micromechanics of diamond composite tools during grinding of glass. Mater Sci Eng 2000;A285:69–79. [5] Takahashi T, Funkenbusch PD. Dynamic model for bound abrasive grinding and its application. In: Proceedings of the SPIE, vol. 3134. 1997. p. 213–22. [6] Preston FW. The theory and design of plate glass polishing machines. J Soc Glass Technol 1927;11:214–56. [7] Li Y, Gracewski SM, Funkenbusch PD, Ruckman J. Tool wear and profile development in contour grinding of optical materials. Int J Mach Tool Manuf 2004;44:427–38. [8] Ong NS, Venkatesh VC. Semi-ductile grinding and polishing of pyrex glass. J Mater Process Technol 1998;83:261–6. [9] Hwang TW, Evans CJ, Malkin S. Size effect for specific energy in grinding of silicon nitride. Wear 1999;229:862–7.
[10] Yui A, Lee HS. Surface grinding with ultra high speed CBN wheel. J Mater Process Technol 1996;62:393–6. [11] Marsh ER, Yantek DS. Simulation and measurement of chatter in diamond turning. Precision Eng 1998;22:252–7. [12] Franse J. Aspects of precision grinding. PhD thesis. Technische Universiteit Eindhoven; 1991. [13] Bifano TG, Scattergood RO. Ductile-regime grinding of brittle materials: experimental results and the development of a model. In: Proceedings of the SPIE, vol. 966. 1989. p. 108–15. [14] Brown NJ, Fuchs BA. Shear mode grinding. In: Proceedings of the Annual Frequency Control Symposium, vol. 43. 1989. p. 606–10. [15] Yan J, et al. Brittle–ductile transition behavior in diamonds turning of single crystal silicon using straight-nosed tools. In: ASPE Proceedings, vol. 18. 1998. p. 128–31. [16] Funkenbusch PD, Zhou YY, Takahashi T, Golini D. Grinding of single crystal sapphire: workpiece roughness correction. Wear 1998; 218:1–7. [17] Miller MH, Kakumanu TS. Investigation of the self-dressing of resin bound grinding wheels. ASME IMECE Manuf Sci Eng Med 1999;10:493–8. [18] Li Y, Funkenbusch PD, Gracewski SM, Ruckman J. Effect of tool wear on tool and workpiece profiles produced in contour grinding. In: Proceeding of Optical Fabrication and Testing. 2000. p. 11–3. [19] Zhou Y, Funkenbusch PD, Quesnel DJ. Stress distributions at the abrasive matrix interface during tool wear in bound abrasive grinding—a finite element analysis. Wear 1997;209:247–54. [20] Yuhta T, Igarashi S, Okuma R, Satou T. On the surface nature of diamond wheel in the process of grinding carbon steel. Ann CIRP 1996;27(1):255.
Measurement of the Preston coefficient of resin and bronze bond tools for deterministic microgrinding of glass Sha Tong a,b , S.M. Gracewski a,b,∗ , P.D. Funkenbusch a,b a
Department of Mechanical Engineering, University of Rochester, Rochester, NY 14627, USA b Center for Optics Manufacturing, University of Rochester, NY 14623, USA
Received 2 February 2004; received in revised form 3 March 2005; accepted 31 March 2005 Available online 21 September 2005
Abstract Deterministic microgrinding technology applies a bound diamond abrasive tool positioned by a Computer Numerically Controlled (CNC) machine to generate precision optical components. The ease of work material removal during the grinding process is often characterized by the specific energy or the Preston coefficient. For a given part and process, these two parameters also indicate the tool/abrasive performance. The Preston coefficient of a resin bond tool with 2–4 m diamond abrasives under different process parameter combinations has been measured with BK7 as the test glass. The Preston coefficient of a similar bronze bond tool was also measured for comparison. Experimental measurements show the resin tool behaves qualitatively differently than the bronze tool in a multiple pass grinding process. The measured Preston coefficient of the resin tool was two to three times smaller than that of the bronze tool and decreased rapidly as pass number increased. A plot of the Preston coefficient versus resin tool bond wear suggests that excessive tool wear reduces the tool’s cutting efficiency, resulting in a rapid decrease in the Preston coefficient. © 2005 Elsevier Inc. All rights reserved. Keywords: Optics manufacturing; Preston coefficient; Specific energy; CNC grinding; Tool wear
1. Introduction Deterministic microgrinding (DMG) has become one of the major methods used for fabrication of precision optical components [1–3]. In a DMG process, a bound diamond abrasive tool is positioned by a Computer Numerically Controlled (CNC) machine to generate plano, spherical or aspherical surfaces. By taking advantage of precise speed and positional control with a CNC machine, the DMG technique is able to achieve a very high level of form accuracy (0.5 m peak-to-valley) and surface finish (3–10 nm) with subsurface damage (SSD) under 1 m. In DMG processes, reliable tool performance is essential to achieve precise control of work material removal [4]. A useful parameter for characterizing the tool performance is the Preston coefficient, which is widely used to estimate the volumetric removal rate of work material under normal loading or predict loads/deflection in infeed controlled CNC grinding [4,5]. The ∗
Corresponding author. Tel.: +1 585 275 7853; fax: +1 585 256 2509. E-mail address: [email protected] (S.M. Gracewski).
0141-6359/$ – see front matter © 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.precisioneng.2005.03.004
Preston’s equation [6] can be written dV = Cp vs FN , dt
(1)
where dV dt is the volumetric removal rate of work material, Cp the Preston coefficient, FN the normal grinding force and vs is the surface speed between the tool and workpiece. Thus, the Preston coefficient can be obtained by dividing the volumetric removal rate by the surface speed and the normal grinding force. For grinding, this relationship is more commonly expressed in terms of the specific grinding energy, e, which is defined as the energy consumed per unit volume of material removed. The specific energy can be written dV 1 = (µFN )vs , (2) dt e where µ is the coefficient of friction between the tool and work. From Eqs. (1) and (2), the Preston coefficient and specific energy are inversely related by 1e = Cp µ. This paper focuses on the Preston coefficient because the normal grinding force FN is easier
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to measure than the tangential grinding force during contour grinding. The Preston coefficient depends on many factors such as material properties, tool condition and removal mechanism. Li et al. [7] measured Preston coefficients of fine (2–4 m) bronze tools in the range of (1 ± 0.3) × 10−13 Pa−1 for different process parameter combinations, consistent with the experimental data obtained by Takahashi and Funkenbusch [4] and Ong and Venkatesh [8]. Hwang et al. [9] measured Preston coefficients on the order of 10−8 Pa−1 for a 40–80 m resin tool in grinding silicon nitride. They also mentioned that the Preston coefficient decreases exponentially as the grit depth of cut is reduced, which is often referred to as the “size effect”. Yui and Lee [10] reported that the tendency of the Preston coefficient to decrease with a decrease of grit depth of cut is more remarkable when the grit depth of cut is less than 0.02 m. In this paper, we measured the Preston coefficient of a fine resin tool under different process parameter combinations with BK7 as the test glass. For comparison, the Preston coefficient of a fine bronze tool was also measured. Observed differences between the bronze tool and the resin tool in a multiple pass grinding process are reported and discussed. In addition, the bond wear of the resin tool was measured and correlated to the rapid decrease of the Preston coefficient during grinding.
is called the cross-feed. Motion in the Z direction controls the surface figure and depth of cut dc . At the Center for Optics Manufacturing (COM), a typical contour grinding process uses two tools. A rough tool having 10–20 m diamond grits is used to remove bulk material. Then, a fine tool having 2–4 m grits is used to remove the surface damage left by the rough tool and form the surface into its final shape. The second process often requires multiple passes because the small abrasive used limits the depth of cut. 3. Analysis The surface speed vs between the tool and workpiece in Eq. (1) can be written as vs = (2πΩt Rt )2 + (2πΩw r)2 , where Ωt is the tool rotation speed, Ωw the workpiece rotation speed, Rt the radius of the tool and r is the radial distance of the tool from the center of the workpiece. Since typically Ωt Rt Ωw r, vs can be simplified to vs ≈ 2πΩt Rt .
(3)
2. Background
The volume removal rate dV dt in Eq. (1) can be expressed as dV dt = Avg , where vg is the relative speed of the grinding zone with respect to the workpiece and A is the projected contact area between the tool and workpiece on the plane perpendicular to
Contour grinding, which can be used to generate aspherical optical surfaces [1,2,7], is one of the most important applications of DMG. Fig. 1 shows the geometry of contour grinding. Both the grinding tool and workpiece rotate. The grinding tool moves simultaneously in two orthogonal directions (X and Z in Fig. 1) with respect to the workpiece. The motion in the X direction
vg ≈ 2πΩw r.
the direction of vg . vg can be written as vg = (2πΩw r)2 + v2c , where vc is the cross-feed rate and 2πΩw r is the tangential speed due to the workpiece rotation. Typically, vc is much smaller than 2πΩw r except at locations very close to the center. As a result, vg can be simplified to (4)
The projected contact area A for successive passes in contour grinding can be determined as a function of dc (the current actual depth of cut), d0 (the actual depth of cut at one workpiece revolution earlier), cross-feed per revolution f and tool radius Rt . Fig. 2 shows the projected contact area between two successive passes. Marsh and Yantek [11] developed a formula for the above projected contact area. By defining δ = dc − d0 and expanding Marsh’s formula in a power series about the equilibrium point
Fig. 1. Contour grinding geometry.
Fig. 2. Projected contact area between two successive passes. The relative velocity of the grinding zone with respect to the workpiece vg is perpendicular to the projected contact area, i.e. along the Y direction.
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δ = 0, we can obtain the first-order approximation A ≈ fdc ,
(5)
(6)
Ωw r Ωt Rt Cp
where R = is a nondimensional parameter that reflects the grinding process parameters. Eq. (6) represents the mean force created under stable grinding conditions. Solve for the Preston coefficient Cp from Eq. (6) to obtain Cp =
dc fΩw r . FN Ωt Rt
(7)
If used without correcting for the finite tool footprint, Eq. (7) predicts that the Preston coefficient approaches zero (Cp → 0) as the radius position approaches zero (r → 0), since the grinding force is not equal to zero (FN = 0). To compensate for the finite tool footprint, instead of using the radial position of the tool geometry center, the radial position of the middle point rm between the tool front contact point and geometry center is used to calculate the Preston coefficient. For small depths of cut, the √ relationship between r and rm is approximately rm = r + 21 2Rt dc . Eq. (7) thus can be rewritten as Cp =
dc fΩw rm . FN Ω t R t
cut for each pass, the Preston coefficient for any pass can be calculated. 4. Experiments
Eqs. (1), (3)–(5) can be combined to obtain FN = f × dc × R,
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(8)
In the above formula, the grinding force FN can be calculated by FN = km T, where km is the spindle static stiffness and T is the tool deflection. The spindle static stiffness is obtained by exciting the tool with a shaker at low frequency (∼1 Hz) and measuring the resulting tool deflection with an eddy current probe. Then, the force during grinding can be determined from an eddy current probe measurement of the tool deflection during grinding. Therefore, the Preston coefficient can be calculated using Eq. (8) if the actual depth of cut is known. However, the actual depth of cut dc differs from the programmed depth of cut dp due to the finite spindle stiffness. Li et al. [7] and Franse [12] studied the relationship between the actual depth of cut and the programmed depth of cut for multipass grinding processes. For a bronze tool grinding BK7 glass, Li et al. found as pass number increases, the actual depth of cut dc approaches a steady-state value dp . Based on this result, he ground a BK7 workpiece with five consecutive passes and used the last pass to calculate the Preston coefficient. Because the actual depth of cut did not asymptotically approach the programmed depth of cut for grinding BK7 with a resin bond tool, Li’s technique was modified so that the actual depth of cut dc was measured after each pass of a multi-pass grinding processes. For each pass, a workpiece, 40 mm in diameter, is fine ground only from the center r = 0 to the radial position r = 15 mm. Thus, the edge of the workpiece (r = 15–20 mm) serves as an absolute reference when applying a line scan across the workpiece after each pass. The actual depth of cut of the last pass is obtained from the height difference between the current scan and the previous scan using the edge as a reference. Since the above technique can be used to measure the actual depth of
4.1. Preston coefficient of bronze tool A Moore NanotechTM AG 150 contour grinding machine was used as the test machine. BK7 glass with a diameter of 40 mm was initially rough ground with a 10–20 m bronze tool to a plano surface. (Although the contour grinding process can be used to generate both spherical and aspheric surfaces, for simplicity all workpiece surfaces used in the experiments reported here were plano.) A fine bronze-bond tool (Socmac 97-14103, 38 mm in diameter, containing 2–4 m diamond abrasives, 75 concentration, N hardness) was trued to a spherical profile of 38 mm diameter (matching the tool diameter) and dressed using a 150 grit alumina dressing stick (Norton). The tool was then used to finish grind the surface from the center r = 0 to 15 mm in five consecutive passes. The process parameters were: Ωt = 12,000 rpm, Ωw = 43 rpm, dp = 5 m and vc = 6 mm/min. For all experiments, the work zone was flooded with coolant during grinding. After each pass, the workpiece surface profile was measured and the actual depth of cut during the previous pass was calculated. At the same time, an eddy current probe fixed over the tool spindle measured the tool deflection during each pass. Fig. 3 plots the actual depth of cut versus radial position of the fifth pass. The averaged actual depth of cut dc = 4.93 m is approaching a steady-state value equal to the programmed depth of cut dp = 5 m, confirming Li et al.’s [7] study on multiple grinding passes. Fig. 4 shows the tool deflection relative to the tool spindle housing measured with an eddy current probe during the same multiple pass process. The plot shows that the tool deflection increases from pass to pass, gradually reaching a steady state. Knowing the actual depth of cut and tool deflection, the Preston coefficient for each pass can be calculated using Eq. (8). In Fig. 5, the Preston coefficient is plotted versus radial position for each pass. Fig. 6 shows the averaged value (for 3 mm < r < 15 mm) of the Preston coefficient Cp for each pass for the data in Fig. 5.
Fig. 3. Actual depth of cut of a bronze tool in the fifth pass (programmed depth of cut dp = 5 m).
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S. Tong et al. / Precision Engineering 30 (2006) 115–122 Table 1 Process parameter combinations for investigating resin tool performance Combination A dp (m) 5 6 vc (mm/min) Ωw (rpm) 43 Ωt (rpm) 12000
Fig. 4. Bronze tool deflection plotted vs. tool radial position for five consecutive passes.
Combination B 10 6 43 12000
Combination C 5 6 215 12000
Combination D 5 3 43 12000
The averaged Preston coefficient of the second through fifth pass Cp = 0.95 × 10−13 Pa−1 is close to Cp = 1 × 10−13 Pa−1 , consistent with Li et al.’s [7] experimental result. 4.2. Preston coefficient of resin tool
Fig. 5. The Preston coefficient of the bronze tool plotted vs. distance from the workpiece center for the first five passes.
The Preston coefficient of the first pass is obviously larger than the successive passes. The abrupt decrease in the Preston coefficient is likely due to changes in the work material. During the first pass, the tool removes the damaged layer left by the rough grind. This damaged layer is relatively easy to remove, resulting in a high Preston coefficient. The plot also shows that after the second pass, the Preston coefficient gradually decreases as pass number increases. This may be attributed to a decreasing workpiece surface roughness as well as variations in tool cutting conditions, such as diamond sharpness and protrusion [4].
Fig. 6. The averaged Preston coefficient of the bronze tool for the first five passes. The Preston coefficient monotonically decreases with pass number.
Resin is a soft bond that is often used when a better surface finish is required. Compared to a bronze tool, a resin tool with similar diamond sizes produces a surface with lower surface roughness. However, resin tools generally wear faster and, as this experiment shows, can be less efficient. Experiments were designed to investigate the Preston coefficient of a resin tool over a wide range of process parameters. For each process parameter combination, a BK7 glass with a diameter of 40 mm was initially rough ground with a 10–20 m bronze tool to a plano surface. Then, a fine resin tool (Norton 607C, 65 mm in diameter, containing 2–4 m diamond abrasives, 100 concentration) was used to finish grind the surface. The specific process parameters applied in the experiments are given in Table 1. The tool was freshly trued to a 65 mm spherical profile (matching the tool diameter) and dressed prior to grinding. For each process parameter combination, the workpiece was fine ground from the center r = 0 to 15 mm for four consecutive passes. After each pass, the workpiece surface profile was measured and the actual depth of cut during the previous pass was calculated. At the same time, an eddy current probe fixed over the tool spindle measured the tool deflection for each pass. The resin tool was trued and dressed between changes of process parameter combinations. During the experiments to measure the Preston coefficient of a resin tool with BK7 as the test glass, we found that the resin tool behaves qualitatively differently than the bronze tool. These differences are discussed in detail below. 4.2.1. Depth of cut of a resin tool in multiple pass process Fig. 7 shows the actual depth cut of the fourth pass with process parameter combination A as given in Table 1. The averaged actual depth of cut of the resin tool dc = 1.1 m is much less than the programmed depth of cut dp = 5 m. The larger grinding force and smaller material removal rate correspond to a smaller Preston coefficient as defined by Eq. (1). This phenomenon is observed for all process parameter combinations listed in Table 1. By observing the actual depth of cut for all four consecutive passes, we found, unlike the bronze tool, the actual depth of cut of the resin tool shows no sign of approaching a steady-state value (dp = 5 m) as pass number increased. Instead, the actual depth of cut gradually
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Fig. 7. Actual depth of cut of a resin tool in the fourth pass (programmed depth of cut dp = 5 m).
decreased as pass number increased. This implies that the resin tool begins to fail before it approaches a steady-state value. Fig. 8 shows the tool deflection relative to the tool spindle housing. The plot shows that the tool deflection increased from pass to pass but never reached a steady state like that seen for the bronze tool. This indicates that the Preston coefficient for the resin tool decreased quickly as the pass number increased, since approximately the same amount of material was removed in the last few passes, even though the normal force increased with each successive pass. In further experiments conducted with a larger number of passes (10 passes with process parameter combination A), the removal rate approached zero as the grinding force increased for these additional passes, indicating failure of the tool. Because the resin tool could only remove a small percentage of programmed depth of cut dp , a figure error was introduced that increased the depth of cut for each successive pass. Consequently, the tool deflected more and more as the pass number increased. Eventually, the tool was pushed hard enough to cause tool failure. 4.2.2. Preston coefficient Fig. 9 shows the Preston coefficient plotted versus radial position for process parameter combination A for passes one to four. The averaged value (for 3 mm < r < 15 mm) of the Preston coefficient Cp for different process parameter combinations and pass numbers is shown in Fig. 10. The grinding experiment with process parameter combination A was conducted twice to check the repeatability of the measurement. The difference in the averaged
Fig. 8. Resin tool deflection plotted vs. tool radial position for four consecutive passes. [Note that the deflection for the resin bond tool was measured at a point on the shaft because the eddy current probe could not measure directly on the tool. Therefore, the magnitudes plotted here are lower than the actual tool displacements, but relative values can still be compared.]
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Fig. 9. The Preston coefficient of the resin tool plotted vs. distance from the workpiece center for the first four passes. The Preston coefficient decreases monastically with the pass number.
Preston coefficient of these two experiments was approximately 10%. These data can be used to estimate the experimental error. Three observations can be made from the above results. First, the Preston coefficient of the resin tool is about two to three times smaller than that of the bronze tool, indicating a possible difference in the material removal mechanism between the bronze and resin tools. Since the resin tool had a larger diameter than the bronze, differences in surface speed between the two tools are a possible contributor to these differences. However, Takahashi and Funkenbusch [4] found that the specific grinding energy of a bronze tool was nearly independent of the process conditions (including surface speed) for BK7 and two other optical glasses over a range of conditions similar to those investigated here. The material removal rate of the resin tool may be small enough to produce ductile grinding. It is known that a higher specific energy (lower Preston coefficient) is required in ductile grinding than in brittle grinding [13–15]. Fig. 11(a) shows a microscopic image of a workpiece surface ground by the bronze tool, where the brittle grinding mode can be clearly identified. The surface ground by the bronze tool is rough (surface finish 180 nm) and opaque, with extensive cracking as shown in the picture. Fig. 11(b) shows a microscopic image of a workpiece surface ground by the resin tool. The surface ground by the resin tool is smoother (surface finish 45 nm) and transparent with fewer cracks and a few diamond grooves in the grinding direction. These observations support the possible different material removal mechanisms between the bronze and resin tools. Second, the Preston coefficient of the resin tool decreases quickly as pass number increases. The Preston coefficient of the bronze tool also decreases as pass number increases, but much more slowly than that of the resin tool. The fast drop of the Preston coefficient is most likely caused by the rapid wear of
Fig. 10. The averaged Preston coefficient of the resin tool for successive passes with different process parameter combinations. The Preston coefficient decreases quickly with pass number.
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Fig. 11. Microscopic images of workpiece surface ground. Surface ground by the: (a) bronze tool and (b) resin tool.
the resin tool which decreases its cutting efficiency. This issue will be discussed later in this article. Third, the Preston coefficient is relatively insensitive to the process parameters in the initial (freshly dressed) state. Measured differences between the four process conditions in the as dressed condition are on the order of 10%, which is comparable to difference found during replication of combination A. Subsequent decline in the Preston coefficient does, however, seem to depend on the process conditions. The Preston coefficient of process parameter combination B shows the largest decline, and after four passes is about 30% smaller than that of process parameter combination D. The experimental data available here are not sufficient to judge these differences statistically. However, qualitatively, the results are, again, consistent with Takahashi and Funkenbusch’s [4] findings, which showed that the specific grinding energy of their optical glasses was initially nearly independent of the specific process conditions but that the process conditions could have a strong effect on the wear and evolution of the tool surface structure and thus indirectly alter the grinding energy. Removal processes occurring at the workpiece and tool surfaces are interrelated (e.g. [16]), an effect which is not yet well characterized but which needs to be further studied in order to understand and predict process parameter effects. 4.2.3. Bond wear of the resin tool In Section 4.2.2, it was shown that the Preston coefficient of the resin tool decreases quickly as pass number increases. This is most likely caused by rapid wear of the resin tool. The tool wear process is often broken into three major categories: diamond blunting, diamond pullout and bond wear [17]. Takahashi and Funkenbusch [4] noted that deterioration in diamond sharpness causes a rapid increase in the grinding energy or equivalently a decrease in the Preston coefficient. They also found for a hard glass like BK7, both abrasive wear and bond wear of the bronze tool are relatively high. This section investigates the bond wear rate of the resin tool by measuring the volume removed on both the tool and workpiece. Diamond abrasive wear was not studied in this work due to the fine sizes (2–4 m) involved. A technique to characterize bond wear for tools used in grinding optical surfaces was developed by Li et al. [18]. To measure the tool cutting profile, a plano workpiece is put on the work
spindle and locked to prevent any rotation of the workpiece. Then, the tool, rotating at the speed used in the grinding process, is fed into the workpiece until a 10 m depth of cut is reached. During this process, the tool leaves a footprint on the surface reflecting the tool cutting profile. Then, the workpiece is taken off the machine, and the footprint is measured. A BK7 glass workpiece again served as the test glass and process parameter combination A was applied in the experiment, beginning with a newly dressed and trued resin bond tool. The workpiece was ground from the center r = 0 to 15 mm for six passes. After each pass, the tool footprint was generated within the unground glass at the workpiece edge. After completion of each pass, the surface profile as well as tool footprint was measured. As before, an eddy current probe fixed over the tool spindle measured tool deflection during each pass. The measured tool cutting profile after each pass is shown in Fig. 12. Tool wear is most often expressed in terms of the G ratio, which is the workpiece volume removed divided by the tool volume removed. The tool volume removed after each pass can be calculated from Fig. 12 and the workpiece volume removed can be calculated from the actual depth of cut measurements. Thus, the G ratio for each pass can be determined. Fig. 13 shows G ratio of the resin tool versus pass number. The results show a fast initial wear (G ratio < 10) followed by a steady and slower wear (G ratio → 20). This phenomenon was
Fig. 12. Resin tool cutting profile after different pass numbers.
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Fig. 15. Particle protrusion and diameter [20]. Fig. 13. G ratio of the resin tool at different pass numbers.
also observed by Takahashi and Funkenbusch [4] for bronze tools during their investigation of the micromechanics of tools during grinding. The G ratio of the resin tool is an order of magnitude smaller than that of the bronze tool, which usually has a G ratio over 200. In Fig. 14, the Preston coefficient versus accumulated tool wear is plotted. Again, the initial rapid drop of the Preston coefficient corresponds to the first one or two passes as shown in Fig. 10, which is most likely due to the transition of the workpiece material from the damaged layer to a more solid and smooth layer during these two passes. After that, the plot shows the Preston coefficient decreases gradually as accumulated tool wear increases. Bond wear does not have a direct relationship to the cutting efficiency, since cutting is done by the diamond abrasives. In fact, significant bond wear in grinding processes can be beneficial by removing damaged abrasive particles and exposing fresh abrasive. This effect, also known as “self-dressing”, helps to maintain tool cutting performance. However, in the experiments described above, excessive bond wear was associated with decreased tool cutting efficiency. The extremely low G ratio of the resin bond tool suggests that blunting of the diamond abrasives is not a likely cause of the poor tool performance. Hence, one possible explanation is that low cutting efficiency was caused by high diamond pullout rates as a result of excessive grinding forces. Miller and Kakumanu [17] noted that a wheel may wear so quickly that it does not efficiently remove work material. It is known that pullout of the abrasive particles is controlled by the bond strength, the forces experienced by the particles, as well as the wear of bond around each particle [19]. Given a protrusion height h and a particle size D as shown in Fig. 15, experiments show that the ratio of the critical protru-
Fig. 14. The Preston coefficient vs. accumulated tool wear. The Preston coefficient decreases monotonically with the tool wear.
sion to particle size is about 0.6 for particle pullout [20]. The fast exposure of the embedded abrasive particles and weak hold of the resin bond leads to rapid loss of abrasive particles. In other words, in grinding a hard glass like BK7, the resin bond may not be able to hold the diamond abrasives firmly enough to do efficient work. A high percentage of diamond abrasive is pulled out when sliding between the tool and the workpiece, resulting in low cutting performance. In multiple pass grinding processes, because of the accumulated figure error, the load on the tool increases as pass number increases. An increase in load per abrasive leads to an increase in pullout rate, which may explain the continuous decrease in the Preston coefficient/cutting efficiency after a relatively steady wear state has been reached. For the bronze tool, because of its high wear resistance as well as high bond strength, rapid pullout of the abrasive particles is not expected. The slow decrease of the Preston coefficient/cutting efficiency is partially caused by the blunting of sharp diamonds. Investigation of the effect of tool wear on the Preston coefficient provides an illustration of the importance of producing the right bond wear rate to maintain the tool cutting performance. Excessive tool wear and inadequate tool wear both deteriorate the tool performance. 5. Conclusions The Preston coefficient of a fine (2–4 m diamond) resin bond tool was measured under different process parameter combinations and compared to that of a similar bronze tool. In addition, the bond wear of the resin tool was measured and correlated with a rapid decrease of the Preston coefficient during the grinding: • The actual depth of cut of the resin tool did not reach a steady state (programmed depth of cut). This eventually led to tool failure. • The Preston coefficient of the resin tool was two to three times smaller than that of the bronze tool. Also, the Preston coefficient of the resin tool decreased more quickly with pass number than that of the bronze tool. This was most likely caused by the rapid wear of the resin tool, which decreased its cutting efficiency. • The resin tool wore much faster than the bronze tool. The G ratio of resin tool was approximately an order of magnitude smaller than that of the bronze tool.
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