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An investigation into parallel and cross grinding of BK7 glass
Precision Engineering 30 (2006) 145–153
An investigation into parallel and cross grinding of BK7 glass X. Sun a , D.J. Stephenson a,∗ , O. Ohnishi b , A. Baldwin a a
School of Industrial and Manufacturing Science, Building 50, Cranfield University, Cranfield, Bedford MK43 0AL, UK b Department of Intelligent Machinery and Systems, Faculty of Engineering, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan Received 5 October 2004; received in revised form 12 April 2005; accepted 6 July 2005 Available online 11 October 2005
Abstract Conventional grinding of BK7 glass will normally result in brittle fracture at the surface, generating severe sub-surface damage and poor surface finish. The precision grinding of BK7 glass in parallel and cross grinding modes has been investigated. Grinding process, maximum chip thickness, ductile/brittle regime, surface roughness and sub-surface damage have been addressed. Special attention has been given to the condition for generating a ductile mode response on the ground surface. A polishing–etching method has been used to obtain the depth of sub-surface damage. Experiments reveal that the level of surface roughness and depth of sub-surface damage vary differently for different grinding modes. This study gives an indication of the strategy to follow to achieve high quality ground surfaces on brittle materials. © 2005 Elsevier Inc. All rights reserved. Keywords: BK7 glass; Ductile/brittle grinding; Sub-surface damage
1. Introduction Precision grinding is commonly used to manufacture optical components. Optical glass is hard to machine as microcracks are normally generated on the ground surfaces. Therefore, a polishing process is generally applied to achieve the required surface integrity. Polishing processes tend to be very time consuming due to the magnitude of sub-surface damage and therefore in order to minimise polishing it is very important to reduce the grinding induced surface/subsurface damage. To this end there has been intensive previous research on the grinding of brittle materials aimed at achieving ground surfaces that are damage free and of low surface roughness. An “indentation fracture model” has been commonly used to describe the brittle fracture process of brittle materials [1,2]. How an indenter initiates median, lateral and radial cracks has been illustrated in the model to explain the surface crack state and grinding mechanism of brittle materials. The protruding abrasive grains in a ∗
Corresponding author. Tel.: +44 1234 754751; fax: +44 1234 751172. E-mail address: [email protected] (D.J. Stephenson).
0141-6359/$ – see front matter © 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.precisioneng.2005.07.001
diamond grinding wheel have been regarded as a series of closely spaced high-speed indenters sliding/scratching over the ground surface [1,3,4]. It is possible to machine or grind brittle materials in such a way that material is removed by plastic flow rather than by microfracture mechanisms, giving a fine crack free surface [5–7]. This process is often referred to as ductile regime grinding. Generally, ductile grinding can produce surfaces which exhibit little or no sub-surface damage compared to a brittle grinding mode. To achieve a high surface integrity, grinding within the ductile regime is most important. Previous research suggests that fracture damage may be avoided or minimised if the normal force per grit is kept below some critical level [5,8]. The critical load, which results in localised fracture, corresponds with a critical chip thickness since the force per grit is reduced as chip thickness is reduced [9]. Under the condition that the maximum chip thickness is less than the critical chip thickness, plastic deformation dominates. The volume of material removal per grit has also been used when considering the ductile regime grinding of brittle materials. This is based on the observation that plastic deformation dominates in brittle materials when the deformation volume of workpiece material is very small.
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To some extent, this hypothesis is in agreement with the “critical chip thickness” theory since a smaller amount of material removal is consistent with a smaller maximum chip thickness. It has been suggested that it is impossible to fracture brittle materials when the interaction volume is small, because they cannot store enough elastic energy to propagate a crack through the bulk material before plastic flow takes place [10]. The energy of plastic deformation scales with deformed volume. Therefore, plastic deformation becomes energetically
favourable as the scale of deformation decreases, and there is a volume below which material will deform and not fracture [6]. Despite various research efforts in glass grinding over the past few decades, much work is needed to understand further the material-removal mechanism. Parallel grinding and cross grinding are two typical grinding modes with distinctive feed behaviour. Either a flat or a curved surface can be generated under the two grinding modes. However, to our best knowl-
Fig. 1. Kinematical illustration of (a) parallel grinding and (b) cross grinding (also see Fig. 3).
X. Sun et al. / Precision Engineering 30 (2006) 145–153
edge, a significant investigation comparing the two grinding modes when grinding brittle materials is not available in the current literature. The objectives of this study were to (1) analyse the kinematics of the two grinding modes; (2) understand surface finish and microcrack distribution; (3) investigate the degree of sub-surface damage and the condition for generating ductile regime grinding conditions. This study has found that the ground surfaces from the two grinding modes display different characteristics when grinding BK7 glass. The issues discussed in this paper include grinding process analysis, wheel wear, critical depth of cut, maximum undeformed chip thickness, the generation of subsurface damage and control of surface roughness. This study gives an indication of the strategy to follow to achieve high quality ground surfaces on brittle materials.
2. Experimental details Grinding tests were conducted on a Holroyd Edgetek SAM 5-axis surface grinder to assess parallel and cross grinding operations. The two modes, including the feed rate directions and grinding tracks/zones, are depicted in Fig. 1. Test 1 was referred to as parallel grinding, in which the side surface of the grinding wheel is positioned parallel to the circumferential direction of the workpiece. Test 2 was defined as cross grinding, in which the side surface of the wheel is positioned along the radial direction of the workpiece. The test conditions used are summarised below: • Wheel Wheel specification: 75 concentration, 7 m diamond grit resin bonded wheel. Wheel diameter: Ø 200 mm. Wheel width: 15 mm. Cutting speed: 39 m/s. • Workpiece Specification: BK7 glass. Ground surface: Ø 50 diameter. • Grinding conditions Speed of rotary worktable: 5.5 rpm. Radial feed: 0.025 mm/s. Depth of cut: 5 m. Coolant: water-based CEM 1:50. Preparation: around 80 m depth of cleaning cuts (5 m per pass) was conducted prior to each grinding trial to remove the pre-existing microcracks from the asreceived surfaces. A Talysurf was used to measure the surface roughness over a trace length of 4 mm. Measurements were taken in both the circumferential and radial directions of the workpiece. To investigate the depth of sub-surface damage a polishing method was used to remove ground material. Before each polishing step, indents were made on the ground/polished surfaces using a Vickers indenter. The depth
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of the removed material by polishing was obtained through calculation according to the change of the dimensions of the indents. Ammonium bifluoride acid was used to etch the polished surfaces to obtain a clear view of cracks on the surface. After etching, optical microscopy was used to record the state of sub-surface damage at various depths from the ground surface.
3. Discussion and results 3.1. Wheel wear and surface formations The grinding of BK7 optical glass, which has a relatively high hardness, can result in wheel wear, which could be more critical for small grit size wheels. Even a small amount of wheel wear can affect the generation of surfaces in high precision grinding. The cleaning cuts prior to the final grinding pass have been shown to result in wheel wear. During grinding the primary material-removal zone associated with the leading edge of the wheel will tend to break down more rapidly than the rest of the wheel. Theoretically, parallel grinding will have a step shape wheel wear profile near the leading edge of the wheel under the condition of a fixed feed per revolution of the workpiece. As the radial feed per revolution of the workpiece is much lower than the wheel width in the experiment, there exists a secondary grinding zone or finish zone along the grinding track shown in Fig. 1a. The uncut depth remaining on the ground surface due to the wheel wear in the primary material-removal zone will be further removed by the subsequent secondary zone, leading to some wheel wear in this section. The wheel wear, therefore, extends with time from the primary material-removal zone to the secondary zone. The scalloped type of wear shown in Fig. 2 is to be expected, in which the wheel wear in the secondary zone includes only one step for illustration. The transition edge between the steps is unstable and can easily breakdown, leading to an inclining transition from step to step. Actually, wear occurs across the whole wheel face including many worn steps, but is greatest at the leading edge. Likewise, there is non-uniform wheel wear on the wheel surface for cross grinding. The primary material-removal zone is illustrated in Fig. 3a. The primary material-removal zone width, GH, in Fig. 3a, can be expressed as GH ≈ stgϕ
(1)
f where s, which equals 2πV ωW , is the radial feed per revolution of workpiece, and ϕ is the angle of the spiral curve at point G. According to Eq. (1), GH decreases as the angle, ϕ, decreases when the wheel moves from the outer area to the central area of the workpiece. As the wheel wear was mainly generated in the primary material-removal zone, a concave wear profile is to be expected. The wheel wear will result in a convex ground profile shown in Fig. 3b. As the radial feed per workpiece revolution is much smaller than the wheel width, the wear
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Fig. 2. Proposed wheel wear for parallel grinding.
region is considered as a small length along the wheel width for both grinding modes. Wheel wear can cause the depth of cut in the primary material-removal zone to be smaller than the nominal depth of cut. The secondary zone in Figs. 1a and 3a will subsequently remove the remaining depth, and determine the final surface roughness. 3.2. Surface roughness The surface roughness of the two ground surfaces is shown in Fig. 4. It can be seen that the surface finish produced by parallel grinding displays a remarkable difference between the outer region compared to the central area of the workpiece. The trend suggests a continuous improvement in surface finish toward the centre of the workpiece. The primary material removal in parallel grinding, shown in Fig. 1a, can be considered to be a roughing process, while the secondary zone performs a final finishing process. The higher incidence of fracture caused by the roughing process at higher circumferential feed rates can only be improved to a very limited extent by the finishing process, and therefore, contributes to the high surface roughness. As the grinding changes from brittle fracture to ductile mode, the finishing process in the secondary zone has a more beneficial effect on the roughness. In cross grinding, although the central area of the workpiece shows a better surface finish than the outer area for cross grinding, the difference is not significant. The large range of axial feed rate for the cross grinding mode, which is 0–14.39 mm/s from centre to the edge of the workpiece, has not resulted in a significant change to the surface roughness. Surface roughness along the radial and circumferential directions also does not show a significant difference for a given grinding mode in Fig. 4.
3.3. Brittle/ductile transitions in the central area of the workpiece Previous research suggests the existence of a critical chip thickness. If the maximum uncut chip thickness is less than the threshold, plastic deformation dominates over fracture. The critical depth of cut to produce a ductile mode surface on hard and brittle material is expressed as [5]: 2 E Kc dc = 0.15 (2) H H where E is the elastic modulus, H the hardness and Kc is the fracture toughness. The critical depth of cut solely depends on the properties of the material to be machined. For instance, the critical depth of cut for BK7 glass is calculated as 42 nm based on the commonly used material properties of E: 81 GPa , Kc : 0.82GPa m0.5 and Hv : 5.8 GPa , which are believed to be obtained from a surface without residual stress and microcracks. In this study, experiments were conducted to obtain the exact values of Vickers hardness and fracture toughness [11] of the ground surfaces and a polished surface. The results shown in Fig. 5 indicate that the values of Vickers hardness and fracture toughness vary within certain limits corresponding to different machining conditions. Ground surfaces display higher hardness and fracture toughness than the polished surface. The grinding induced residual stress associated with localised plastic deformation and microcracks may contribute to the higher values and the variations of hardness and fracture toughness. Based on the values of Vickers hardness and fracture toughness, the critical depth of cut is within the range 40–70 nm. According to the “critical chip thickness” theory [5,12], ductile regime grinding can be
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Fig. 3. (a) Material removal and polishing for cross grinding; (b) wheel wear and the profile (wheel width GH) and (c) illustration of velocity vectors (R = OG).
achieved on BK7 when the calculated maximum undeformed chip thickness is smaller than the values of critical depth of cut. The general features of the ground surfaces for parallel and cross grinding are illustrated in Fig. 6. Both ground surfaces are dominated by localised microfracture. However, the central zones of the two ground surfaces display pure ductile behaviour. The ductile/brittle transition boundary, shown
in Fig. 6a, appears within a round region of about 18 mm diameter for the parallel grinding test. The maximum chip thickness, which depends on the cutting tool geometry, the depth of cut, cutting velocity and work speed, can be calculated by the expression [9] 4Vw ae 1/2 hmax = (3) Vc Cr dc
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the grinding process complex, and Eq. (3), which is developed from conventional surface grinding, cannot be applied to cross feed grinding. The work material was machined along the spiral grinding track in Fig. 3a. The work speed Vw and the cutting speed Vc in Eq. (3) become RωW sin ϕ + Vf cos ϕ and Vf cos ϕ, respectively (Fig. 3c) along the work feed direction, where R is the radius of the cutting point, ωW the angular velocity of the worktable, Vf the radial feed rate and ϕ can be Vf obtained from cos ϕ = Rω . By substituting the work speed W and the cutting speed into Eq. (3), the following equation is obtained Fig. 4. Roughness of parallel and cross grindings. (//)—Circumferential direction; ()—radial direction.
where Vc is the speed of the wheel, Vw the work speed, r the ratio of mean chip width to chip thickness, dc the wheel diameter, ae the depth of cut and C is the active grit concentration and is estimated as 1.0 × 108 /m2 for the wheel used in these experiments. The value of r is reported to be in the range of 10–20 [9]; r was assumed to be equal to 10 in this study. According to Eq. (3), a reduction in table speed will give a smaller maximum chip thickness. The calculation of the maximum chip thickness for parallel grinding is based on a simplified model shown in Fig. 1a. Based on the fixed depth of cut, 5 m, and wheel speed 39 m/s, the undeformed maximum chip thickness at different positions on the ground surface has been estimated as shown in Fig. 7, in which the maximum undeformed chip thickness at the brittle/ductile transition position is determined to be around 50 nm. This value is in the range of the critical depth of cut calculated above. The actual depth of cut in the primary material-removal zone is smaller than the nominal depth of cut due to wheel wear. The threshold, which determines the transition from a brittle-induced microcracked surface into a deformation controlled ductile ground surface, should be smaller than the calculated value. Cross grinding results in a relatively small central ductile zone, which appears only as a circular area of around 0.8 mm diameter shown in Fig. 6b. The axial feed of the wheel makes
Fig. 5. Vickers hardness and fracture toughness on ground and polished surfaces. Hv1 , Kc1 —parallel grinding; Hv2 , Kc2 —cross grinding; Hvp , Kcp —polished surface.
hmax
RωW tgϕ + Vf =2 Vc Cr
ae dc
1/2 (4)
Eq. (4) gives the estimated values of the maximum undeformed chip thickness for cross grinding. The estimated maximum undeformed chip thickness versus position on the ground surface is illustrated in Fig. 7. The ductile grinding zone is predicted to occur within a central region of less than 1 mm diameter for cross feed grinding, which is consistent with the result of the grinding test. The depth of sub-surface damage in the form of microcracking increases with an increase of the feed rate along the circumferential direction for both parallel and cross grinding. There is no sub-surface damage in the central purely ductile regime on both ground surfaces. Long fracture paths can be found sub-surface in areas associated with high feed rates of test 1 (parallel grinding) after the ground surface is removed to a depth of around 2 m. The lines are believed to be the median cracks generated by the grinding grits. The length of cracks in the cross grinding mode are generally shorter and align in irregular directions. The variation in subsurface damage morphology between the two tests is attributed to the different relative movement between the grinding wheel and the workpiece. In cross grinding, although the roughness of the ground surface does not display a significant difference at positions of 5 and 15 mm to the centre as shown in Fig. 4, the depth of sub-surface damage differs considerably. As the maximum undeformed chip thickness decreases with the decrease in distance to the centre of the workpiece as shown in Fig. 7, the grinding forces generated by the cutting action of individual abrasive grits will decrease, which results in a decrease in the magnitude of sub-surface damage. Fig. 6 shows that the depth of sub-surface damage at a position of 5 mm is below 4.6 m but greater than 6.8 m at a position of 15 mm from the centre of the workpiece. As there is no significant difference in the values of surface finish, as shown in Fig. 4, it can be concluded that surface finish is not necessarily a reliable indicator of the depth of subsurface damage. Both the ductile grinding regimes observed in these experiments are consistent with small volumes of material removal. The material-removal rate for the two grinding modes can be
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Fig. 6. Ground surfaces and sub-surface damage of (a) the parallel grinding and (b) cross grinding.
obtained from Eq. (5) VMMR = 2πRVf ae
(5)
Fig. 8 shows the material-removal rates at the ductile grinding boundary for the two different grinding configurations. A much higher material-removal rate in the ductile regime is
possible for parallel grinding than for cross grinding. The difference indicates that although ductile grinding is associated with small material-removal rates, the probability of fracture also depends on the precise grinding configuration due to the influence this has on chip thickness and hence grinding forces.
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Fig. 7. Estimated undeformed maximum chip thickness vs. position on the ground surface.
Fig. 8. Material-removal rates at ductile grinding boundary.
3.4. Non-uniform distribution of microcracks along the grinding tracks Fig. 9 illustrates the non-uniform microcrack distribution along the circumferential direction of the workpiece on the ground surface of test 2 (cross ground). There appears to be a larger-size, high-density microcrack zone and a smaller region exhibiting a low density of microcracks. This phenomenon can be observed particularly in the larger diameter area of the workpiece being ground. The width of the band, L, in Fig. 9, is equal to the radial feed per workpiece revolu-
Fig. 10. (a) Convex shape generated by the wheel wear in the primary material-removal zone and (b) surface after the convex region has been removed by the secondary finishing zone.
tion, 0.27 mm. As mentioned above, the wheel wear affects the actual depth of cut which will influence the brittle/ductile response of the material during grinding. A smaller depth of cut can result in a smaller undeformed maximum chip thickness, which will diminish the probability of generating microcracks on the ground surface. Because of the different actual depth of cut across the wheel width due to the concave profile shown in Fig. 10, there may be a variation in the density of microcracks across the workpiece surface. With the subsequent secondary finishing process, the convex profile of the workpiece will be gradually reduced by the secondary finishing zone. Assuming the height of the convex region in Fig. 10a is small, the subsequent secondary finishing action will remove the micro cracks on the top of the convex region to some extent without introducing more cracks as shown in Fig. 10b. This process results in the non-uniform microcrack distribution on the ground surface as indicated in Fig. 9. Thus, non-uniform levels of sub-surface damage can exist across the ground surface due to changes in the grinding wheel geometry. Such observations support the proposed changes in wheel profile during grinding and demonstrate the role that the secondary finishing zone has in improving surface finish.
Fig. 9. Crack distributions along a grinding track.
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4. Conclusions
References
(1) The establishment of ductile regime grinding conditions considered in this study is consistent with the “Critical Chip Thickness” theory. (2) Ductile regime grinding conditions do not necessarily depend on material-removal rate since chip thickness is a function of both the grinding configuration and materialremoval rate. (3) The depth of sub-surface damage increases as chip thickness and hence grinding forces increase. Below the critical chip thickness it is possible to generate a high quality surface which exhibits minimal sub-surface damage. (4) In the ductile mode grinding regime surface finish better than 5 nm Ra is possible. Surface roughness increases considerably within the brittle grinding regime. However, surface roughness is not a reliable indicator of the depth of sub-surface damage. (5) The grinding configuration influences grinding wheel wear. For different grinding configurations a primary removal zone and secondary finishing zone can be identified. Non-uniform wheel wear in the primary removal zone will influence chip thickness and may result in a non-uniform distribution of microcracks.
[1] Malkin S, Hwang TW. Grinding mechanisms for ceramics. Ann CIRP 1996;45(2):569–80. [2] Lawn BR, Swain MV. Microfracture beneath point indentations in brittle solids. J Mater Sci 1975;10:113–22. [3] Subramanian K, Ramanath S, Mechanism of material removal in the precision grinding of ceramics, In: Jouaneh M, Rangwala SS, editors. Precision machining: technology and machine development and improvement, PED-58; 1992. p. 1–19. [4] Li K, Liao W. Surface/subsurface damage and the fracture strength of ground ceramics. J Mater Process Technol 1996;57:207– 20. [5] Bifano T, Dow T, Scattergood R. Ductile-regime grinding of brittle materials: experimental results and the development of a model. SPIE 1988;966:108–15. [6] Blake PN, Scattergood RO. Ductile regime machining of germanium and silicon. J Am Ceram Soc 1990;73:949–57. [7] Golini D. Transition between brittle and ductile mode in loose abrasive grinding. SPIE 1990:80–91. [8] Hagan JT, Mickael V, Swain MV. Origin of median and lateral cracks around plastic indents in brittle materials. J Phys D 1978;11:2091–102. [9] Shaw M. Principles of abrasive processing. UK: Oxford University Press; 1996. [10] Feng Z, Field JE. Dynamic strengths of diamond grits. Ind Diamond Rev 1983;3. [11] Niihara K, Morena R, Hasselman DPH. Evaluation of KlC of brittle solids by the indentation method with low crack-to-indent ratios. J Mater Sci Lett 1982;1:13–6. [12] Bifano TG, Dow TA, Scattergood RO. Ductile-regime grinding: a new technology for machining brittle materials. ASME J Eng Ind 1991;113:184–9.
Acknowledgement This work was supported in part by an EC project—Nano Grind (GRD1-2001-40538).
An investigation into parallel and cross grinding of BK7 glass X. Sun a , D.J. Stephenson a,∗ , O. Ohnishi b , A. Baldwin a a
School of Industrial and Manufacturing Science, Building 50, Cranfield University, Cranfield, Bedford MK43 0AL, UK b Department of Intelligent Machinery and Systems, Faculty of Engineering, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan Received 5 October 2004; received in revised form 12 April 2005; accepted 6 July 2005 Available online 11 October 2005
Abstract Conventional grinding of BK7 glass will normally result in brittle fracture at the surface, generating severe sub-surface damage and poor surface finish. The precision grinding of BK7 glass in parallel and cross grinding modes has been investigated. Grinding process, maximum chip thickness, ductile/brittle regime, surface roughness and sub-surface damage have been addressed. Special attention has been given to the condition for generating a ductile mode response on the ground surface. A polishing–etching method has been used to obtain the depth of sub-surface damage. Experiments reveal that the level of surface roughness and depth of sub-surface damage vary differently for different grinding modes. This study gives an indication of the strategy to follow to achieve high quality ground surfaces on brittle materials. © 2005 Elsevier Inc. All rights reserved. Keywords: BK7 glass; Ductile/brittle grinding; Sub-surface damage
1. Introduction Precision grinding is commonly used to manufacture optical components. Optical glass is hard to machine as microcracks are normally generated on the ground surfaces. Therefore, a polishing process is generally applied to achieve the required surface integrity. Polishing processes tend to be very time consuming due to the magnitude of sub-surface damage and therefore in order to minimise polishing it is very important to reduce the grinding induced surface/subsurface damage. To this end there has been intensive previous research on the grinding of brittle materials aimed at achieving ground surfaces that are damage free and of low surface roughness. An “indentation fracture model” has been commonly used to describe the brittle fracture process of brittle materials [1,2]. How an indenter initiates median, lateral and radial cracks has been illustrated in the model to explain the surface crack state and grinding mechanism of brittle materials. The protruding abrasive grains in a ∗
Corresponding author. Tel.: +44 1234 754751; fax: +44 1234 751172. E-mail address: [email protected] (D.J. Stephenson).
0141-6359/$ – see front matter © 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.precisioneng.2005.07.001
diamond grinding wheel have been regarded as a series of closely spaced high-speed indenters sliding/scratching over the ground surface [1,3,4]. It is possible to machine or grind brittle materials in such a way that material is removed by plastic flow rather than by microfracture mechanisms, giving a fine crack free surface [5–7]. This process is often referred to as ductile regime grinding. Generally, ductile grinding can produce surfaces which exhibit little or no sub-surface damage compared to a brittle grinding mode. To achieve a high surface integrity, grinding within the ductile regime is most important. Previous research suggests that fracture damage may be avoided or minimised if the normal force per grit is kept below some critical level [5,8]. The critical load, which results in localised fracture, corresponds with a critical chip thickness since the force per grit is reduced as chip thickness is reduced [9]. Under the condition that the maximum chip thickness is less than the critical chip thickness, plastic deformation dominates. The volume of material removal per grit has also been used when considering the ductile regime grinding of brittle materials. This is based on the observation that plastic deformation dominates in brittle materials when the deformation volume of workpiece material is very small.
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To some extent, this hypothesis is in agreement with the “critical chip thickness” theory since a smaller amount of material removal is consistent with a smaller maximum chip thickness. It has been suggested that it is impossible to fracture brittle materials when the interaction volume is small, because they cannot store enough elastic energy to propagate a crack through the bulk material before plastic flow takes place [10]. The energy of plastic deformation scales with deformed volume. Therefore, plastic deformation becomes energetically
favourable as the scale of deformation decreases, and there is a volume below which material will deform and not fracture [6]. Despite various research efforts in glass grinding over the past few decades, much work is needed to understand further the material-removal mechanism. Parallel grinding and cross grinding are two typical grinding modes with distinctive feed behaviour. Either a flat or a curved surface can be generated under the two grinding modes. However, to our best knowl-
Fig. 1. Kinematical illustration of (a) parallel grinding and (b) cross grinding (also see Fig. 3).
X. Sun et al. / Precision Engineering 30 (2006) 145–153
edge, a significant investigation comparing the two grinding modes when grinding brittle materials is not available in the current literature. The objectives of this study were to (1) analyse the kinematics of the two grinding modes; (2) understand surface finish and microcrack distribution; (3) investigate the degree of sub-surface damage and the condition for generating ductile regime grinding conditions. This study has found that the ground surfaces from the two grinding modes display different characteristics when grinding BK7 glass. The issues discussed in this paper include grinding process analysis, wheel wear, critical depth of cut, maximum undeformed chip thickness, the generation of subsurface damage and control of surface roughness. This study gives an indication of the strategy to follow to achieve high quality ground surfaces on brittle materials.
2. Experimental details Grinding tests were conducted on a Holroyd Edgetek SAM 5-axis surface grinder to assess parallel and cross grinding operations. The two modes, including the feed rate directions and grinding tracks/zones, are depicted in Fig. 1. Test 1 was referred to as parallel grinding, in which the side surface of the grinding wheel is positioned parallel to the circumferential direction of the workpiece. Test 2 was defined as cross grinding, in which the side surface of the wheel is positioned along the radial direction of the workpiece. The test conditions used are summarised below: • Wheel Wheel specification: 75 concentration, 7 m diamond grit resin bonded wheel. Wheel diameter: Ø 200 mm. Wheel width: 15 mm. Cutting speed: 39 m/s. • Workpiece Specification: BK7 glass. Ground surface: Ø 50 diameter. • Grinding conditions Speed of rotary worktable: 5.5 rpm. Radial feed: 0.025 mm/s. Depth of cut: 5 m. Coolant: water-based CEM 1:50. Preparation: around 80 m depth of cleaning cuts (5 m per pass) was conducted prior to each grinding trial to remove the pre-existing microcracks from the asreceived surfaces. A Talysurf was used to measure the surface roughness over a trace length of 4 mm. Measurements were taken in both the circumferential and radial directions of the workpiece. To investigate the depth of sub-surface damage a polishing method was used to remove ground material. Before each polishing step, indents were made on the ground/polished surfaces using a Vickers indenter. The depth
147
of the removed material by polishing was obtained through calculation according to the change of the dimensions of the indents. Ammonium bifluoride acid was used to etch the polished surfaces to obtain a clear view of cracks on the surface. After etching, optical microscopy was used to record the state of sub-surface damage at various depths from the ground surface.
3. Discussion and results 3.1. Wheel wear and surface formations The grinding of BK7 optical glass, which has a relatively high hardness, can result in wheel wear, which could be more critical for small grit size wheels. Even a small amount of wheel wear can affect the generation of surfaces in high precision grinding. The cleaning cuts prior to the final grinding pass have been shown to result in wheel wear. During grinding the primary material-removal zone associated with the leading edge of the wheel will tend to break down more rapidly than the rest of the wheel. Theoretically, parallel grinding will have a step shape wheel wear profile near the leading edge of the wheel under the condition of a fixed feed per revolution of the workpiece. As the radial feed per revolution of the workpiece is much lower than the wheel width in the experiment, there exists a secondary grinding zone or finish zone along the grinding track shown in Fig. 1a. The uncut depth remaining on the ground surface due to the wheel wear in the primary material-removal zone will be further removed by the subsequent secondary zone, leading to some wheel wear in this section. The wheel wear, therefore, extends with time from the primary material-removal zone to the secondary zone. The scalloped type of wear shown in Fig. 2 is to be expected, in which the wheel wear in the secondary zone includes only one step for illustration. The transition edge between the steps is unstable and can easily breakdown, leading to an inclining transition from step to step. Actually, wear occurs across the whole wheel face including many worn steps, but is greatest at the leading edge. Likewise, there is non-uniform wheel wear on the wheel surface for cross grinding. The primary material-removal zone is illustrated in Fig. 3a. The primary material-removal zone width, GH, in Fig. 3a, can be expressed as GH ≈ stgϕ
(1)
f where s, which equals 2πV ωW , is the radial feed per revolution of workpiece, and ϕ is the angle of the spiral curve at point G. According to Eq. (1), GH decreases as the angle, ϕ, decreases when the wheel moves from the outer area to the central area of the workpiece. As the wheel wear was mainly generated in the primary material-removal zone, a concave wear profile is to be expected. The wheel wear will result in a convex ground profile shown in Fig. 3b. As the radial feed per workpiece revolution is much smaller than the wheel width, the wear
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Fig. 2. Proposed wheel wear for parallel grinding.
region is considered as a small length along the wheel width for both grinding modes. Wheel wear can cause the depth of cut in the primary material-removal zone to be smaller than the nominal depth of cut. The secondary zone in Figs. 1a and 3a will subsequently remove the remaining depth, and determine the final surface roughness. 3.2. Surface roughness The surface roughness of the two ground surfaces is shown in Fig. 4. It can be seen that the surface finish produced by parallel grinding displays a remarkable difference between the outer region compared to the central area of the workpiece. The trend suggests a continuous improvement in surface finish toward the centre of the workpiece. The primary material removal in parallel grinding, shown in Fig. 1a, can be considered to be a roughing process, while the secondary zone performs a final finishing process. The higher incidence of fracture caused by the roughing process at higher circumferential feed rates can only be improved to a very limited extent by the finishing process, and therefore, contributes to the high surface roughness. As the grinding changes from brittle fracture to ductile mode, the finishing process in the secondary zone has a more beneficial effect on the roughness. In cross grinding, although the central area of the workpiece shows a better surface finish than the outer area for cross grinding, the difference is not significant. The large range of axial feed rate for the cross grinding mode, which is 0–14.39 mm/s from centre to the edge of the workpiece, has not resulted in a significant change to the surface roughness. Surface roughness along the radial and circumferential directions also does not show a significant difference for a given grinding mode in Fig. 4.
3.3. Brittle/ductile transitions in the central area of the workpiece Previous research suggests the existence of a critical chip thickness. If the maximum uncut chip thickness is less than the threshold, plastic deformation dominates over fracture. The critical depth of cut to produce a ductile mode surface on hard and brittle material is expressed as [5]: 2 E Kc dc = 0.15 (2) H H where E is the elastic modulus, H the hardness and Kc is the fracture toughness. The critical depth of cut solely depends on the properties of the material to be machined. For instance, the critical depth of cut for BK7 glass is calculated as 42 nm based on the commonly used material properties of E: 81 GPa , Kc : 0.82GPa m0.5 and Hv : 5.8 GPa , which are believed to be obtained from a surface without residual stress and microcracks. In this study, experiments were conducted to obtain the exact values of Vickers hardness and fracture toughness [11] of the ground surfaces and a polished surface. The results shown in Fig. 5 indicate that the values of Vickers hardness and fracture toughness vary within certain limits corresponding to different machining conditions. Ground surfaces display higher hardness and fracture toughness than the polished surface. The grinding induced residual stress associated with localised plastic deformation and microcracks may contribute to the higher values and the variations of hardness and fracture toughness. Based on the values of Vickers hardness and fracture toughness, the critical depth of cut is within the range 40–70 nm. According to the “critical chip thickness” theory [5,12], ductile regime grinding can be
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Fig. 3. (a) Material removal and polishing for cross grinding; (b) wheel wear and the profile (wheel width GH) and (c) illustration of velocity vectors (R = OG).
achieved on BK7 when the calculated maximum undeformed chip thickness is smaller than the values of critical depth of cut. The general features of the ground surfaces for parallel and cross grinding are illustrated in Fig. 6. Both ground surfaces are dominated by localised microfracture. However, the central zones of the two ground surfaces display pure ductile behaviour. The ductile/brittle transition boundary, shown
in Fig. 6a, appears within a round region of about 18 mm diameter for the parallel grinding test. The maximum chip thickness, which depends on the cutting tool geometry, the depth of cut, cutting velocity and work speed, can be calculated by the expression [9] 4Vw ae 1/2 hmax = (3) Vc Cr dc
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the grinding process complex, and Eq. (3), which is developed from conventional surface grinding, cannot be applied to cross feed grinding. The work material was machined along the spiral grinding track in Fig. 3a. The work speed Vw and the cutting speed Vc in Eq. (3) become RωW sin ϕ + Vf cos ϕ and Vf cos ϕ, respectively (Fig. 3c) along the work feed direction, where R is the radius of the cutting point, ωW the angular velocity of the worktable, Vf the radial feed rate and ϕ can be Vf obtained from cos ϕ = Rω . By substituting the work speed W and the cutting speed into Eq. (3), the following equation is obtained Fig. 4. Roughness of parallel and cross grindings. (//)—Circumferential direction; ()—radial direction.
where Vc is the speed of the wheel, Vw the work speed, r the ratio of mean chip width to chip thickness, dc the wheel diameter, ae the depth of cut and C is the active grit concentration and is estimated as 1.0 × 108 /m2 for the wheel used in these experiments. The value of r is reported to be in the range of 10–20 [9]; r was assumed to be equal to 10 in this study. According to Eq. (3), a reduction in table speed will give a smaller maximum chip thickness. The calculation of the maximum chip thickness for parallel grinding is based on a simplified model shown in Fig. 1a. Based on the fixed depth of cut, 5 m, and wheel speed 39 m/s, the undeformed maximum chip thickness at different positions on the ground surface has been estimated as shown in Fig. 7, in which the maximum undeformed chip thickness at the brittle/ductile transition position is determined to be around 50 nm. This value is in the range of the critical depth of cut calculated above. The actual depth of cut in the primary material-removal zone is smaller than the nominal depth of cut due to wheel wear. The threshold, which determines the transition from a brittle-induced microcracked surface into a deformation controlled ductile ground surface, should be smaller than the calculated value. Cross grinding results in a relatively small central ductile zone, which appears only as a circular area of around 0.8 mm diameter shown in Fig. 6b. The axial feed of the wheel makes
Fig. 5. Vickers hardness and fracture toughness on ground and polished surfaces. Hv1 , Kc1 —parallel grinding; Hv2 , Kc2 —cross grinding; Hvp , Kcp —polished surface.
hmax
RωW tgϕ + Vf =2 Vc Cr
ae dc
1/2 (4)
Eq. (4) gives the estimated values of the maximum undeformed chip thickness for cross grinding. The estimated maximum undeformed chip thickness versus position on the ground surface is illustrated in Fig. 7. The ductile grinding zone is predicted to occur within a central region of less than 1 mm diameter for cross feed grinding, which is consistent with the result of the grinding test. The depth of sub-surface damage in the form of microcracking increases with an increase of the feed rate along the circumferential direction for both parallel and cross grinding. There is no sub-surface damage in the central purely ductile regime on both ground surfaces. Long fracture paths can be found sub-surface in areas associated with high feed rates of test 1 (parallel grinding) after the ground surface is removed to a depth of around 2 m. The lines are believed to be the median cracks generated by the grinding grits. The length of cracks in the cross grinding mode are generally shorter and align in irregular directions. The variation in subsurface damage morphology between the two tests is attributed to the different relative movement between the grinding wheel and the workpiece. In cross grinding, although the roughness of the ground surface does not display a significant difference at positions of 5 and 15 mm to the centre as shown in Fig. 4, the depth of sub-surface damage differs considerably. As the maximum undeformed chip thickness decreases with the decrease in distance to the centre of the workpiece as shown in Fig. 7, the grinding forces generated by the cutting action of individual abrasive grits will decrease, which results in a decrease in the magnitude of sub-surface damage. Fig. 6 shows that the depth of sub-surface damage at a position of 5 mm is below 4.6 m but greater than 6.8 m at a position of 15 mm from the centre of the workpiece. As there is no significant difference in the values of surface finish, as shown in Fig. 4, it can be concluded that surface finish is not necessarily a reliable indicator of the depth of subsurface damage. Both the ductile grinding regimes observed in these experiments are consistent with small volumes of material removal. The material-removal rate for the two grinding modes can be
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Fig. 6. Ground surfaces and sub-surface damage of (a) the parallel grinding and (b) cross grinding.
obtained from Eq. (5) VMMR = 2πRVf ae
(5)
Fig. 8 shows the material-removal rates at the ductile grinding boundary for the two different grinding configurations. A much higher material-removal rate in the ductile regime is
possible for parallel grinding than for cross grinding. The difference indicates that although ductile grinding is associated with small material-removal rates, the probability of fracture also depends on the precise grinding configuration due to the influence this has on chip thickness and hence grinding forces.
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Fig. 7. Estimated undeformed maximum chip thickness vs. position on the ground surface.
Fig. 8. Material-removal rates at ductile grinding boundary.
3.4. Non-uniform distribution of microcracks along the grinding tracks Fig. 9 illustrates the non-uniform microcrack distribution along the circumferential direction of the workpiece on the ground surface of test 2 (cross ground). There appears to be a larger-size, high-density microcrack zone and a smaller region exhibiting a low density of microcracks. This phenomenon can be observed particularly in the larger diameter area of the workpiece being ground. The width of the band, L, in Fig. 9, is equal to the radial feed per workpiece revolu-
Fig. 10. (a) Convex shape generated by the wheel wear in the primary material-removal zone and (b) surface after the convex region has been removed by the secondary finishing zone.
tion, 0.27 mm. As mentioned above, the wheel wear affects the actual depth of cut which will influence the brittle/ductile response of the material during grinding. A smaller depth of cut can result in a smaller undeformed maximum chip thickness, which will diminish the probability of generating microcracks on the ground surface. Because of the different actual depth of cut across the wheel width due to the concave profile shown in Fig. 10, there may be a variation in the density of microcracks across the workpiece surface. With the subsequent secondary finishing process, the convex profile of the workpiece will be gradually reduced by the secondary finishing zone. Assuming the height of the convex region in Fig. 10a is small, the subsequent secondary finishing action will remove the micro cracks on the top of the convex region to some extent without introducing more cracks as shown in Fig. 10b. This process results in the non-uniform microcrack distribution on the ground surface as indicated in Fig. 9. Thus, non-uniform levels of sub-surface damage can exist across the ground surface due to changes in the grinding wheel geometry. Such observations support the proposed changes in wheel profile during grinding and demonstrate the role that the secondary finishing zone has in improving surface finish.
Fig. 9. Crack distributions along a grinding track.
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4. Conclusions
References
(1) The establishment of ductile regime grinding conditions considered in this study is consistent with the “Critical Chip Thickness” theory. (2) Ductile regime grinding conditions do not necessarily depend on material-removal rate since chip thickness is a function of both the grinding configuration and materialremoval rate. (3) The depth of sub-surface damage increases as chip thickness and hence grinding forces increase. Below the critical chip thickness it is possible to generate a high quality surface which exhibits minimal sub-surface damage. (4) In the ductile mode grinding regime surface finish better than 5 nm Ra is possible. Surface roughness increases considerably within the brittle grinding regime. However, surface roughness is not a reliable indicator of the depth of sub-surface damage. (5) The grinding configuration influences grinding wheel wear. For different grinding configurations a primary removal zone and secondary finishing zone can be identified. Non-uniform wheel wear in the primary removal zone will influence chip thickness and may result in a non-uniform distribution of microcracks.
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Acknowledgement This work was supported in part by an EC project—Nano Grind (GRD1-2001-40538).