An experimental study on precision grinding of silicon using diamond grinding pins

Transcription

1 Int. J. Materials Engineering Innovation, Vol. 2, Nos. 3/4, An experimental study on precision grinding of silicon using diamond grinding pins Abdur-Rasheed Alao* Advanced Manufacturing and Materials Processing Technology (AMMPT) Laboratory, Department of Engineering Design and Manufacture, Faculty of Engineering Building, University of Malaya, Kuala Lumpur, Malaysia *Corresponding author Mohamed Konneh Department of Manufacturing and Materials Engineering, International Islamic University Malaysia (IIUM), P.O. Box 10, Kuala Lumpur, Malaysia Abstract: Silicon substrates are difficult to grind to good surface finishes using conventional machining. Ductile mode machining is often required to have flawless machining but this requires the use of expensive machine tools. However, precision grinding using conventional machine tools could generate large amounts of ductile streaks on ground silicon surfaces under good machining conditions. High wheel rotation, slow feed rate, small indentations and small grain sizes are the practical requirements to realise precision grinding of silicon. Therefore, this study examines the feasibility of quantitative determination of the criteria to realise precision grinding of silicon on an NC milling machine with factorial experimental design. The result shows massive ductile streaks at depth of cut, 20 μm; feed rate, 6.25 mm/min and spindle speed of 70,000 rpm with a 43 nm R a. Spindle speed affects mostly the surface finish. The combined effects of depth of cut and feed rate on R a and R t which add to the complexity in the precision grinding process are investigated. Keywords: precision grinding; silicon; factorial design; surface roughness; ductile streaks; diamond pins. Reference to this paper should be made as follows: Alao, A-R. and Konneh, M. (2011) An experimental study on precision grinding of silicon using diamond grinding pins, Int. J. Materials Engineering Innovation, Vol. 2, Nos. 3/4, pp Biographical notes: Abdur-Rasheed Alao is presently with the University of Malaya, Malaysia pursuing his PhD in Manufacturing Engineering. He received his MSc in Manufacturing Engineering from International Islamic University, Malaysia in 2007 and obtained his BE (Hons.) from University of Ilorin, Nigeria in He is interested in the following research areas: precision machining of metals and hard-brittle materials; vibration-assisted machining, precision manufacturing, MEMS; application of design of experiments (DOE) techniques and quality control; abrasive water-jet cutting; modelling of manufacturing processes and uncertainty analysis in measurements. He has a modest number of papers in international conference proceedings and journals. Copyright 2011 Inderscience Enterprises Ltd.

2 326 A-R. Alao and M. Konneh Mohamed Konneh is an Assistant Professor at the Department of Manufacturing and Materials Engineering, International Islamic University, Malaysia. He has taught numerous manufacturing and industrial related subjects. His research interests are in precision machining, brittle materials machining, high-speed machining and precision measurements. 1 Introduction Conventional grinding of silicon substrates results in brittle fracture at the surface generating severe sub-surface damage and poor surface finish. However, silicon is an important material for making devices in electronics, semi-conductor and optical industries. Fang and Venkatesh (1998) have reported that silicon constitutes 90% of all semiconductors and finds applications in micro-electro mechanical systems (MEMS), integrated circuits (IC) chips and optical components in high-resolution thermal imaging systems, etc. Because of the exacting requirements on the finishing technique for these applications, close tolerance and good surface finishes are critical. To meet the surface quality requirement, ductile mode machining is often required. The removal of materials in brittle materials in a ductile rather than brittle manner so that extensive micro-fracture can be minimised is termed ductile mode machining. Blackley and Scattergood (1991) have developed a hypothesis for ductile mode machining of brittle materials. They have stated that all materials irrespective of their hardness and brittleness will undergo a transition from brittle to ductile machining regime below a critical undeformed chip thickness. Below this critical thickness, the energy required to propagate cracks is believed to be larger than plastic deformation, so plastic deformation is the favoured material removal mechanism for these materials. This hypothesis was a direct result of indentation tests conducted on glass specimen where it was observed that a plastic strain zone was reported to have been produced before the initiation of the cracks. Another hypothesis in which plastic deformation is not solely responsible for ductile machining of advanced ceramics was suggested by Komanduri et al. (1997). According to this hypothesis, since the mode of deformation (elastic or plastic) depends on the stress state and not on the magnitude of the stress, it is hard to comprehend that the mode of deformation will change by merely changing the depth of cut, all other parameters remaining constant. Investigations made by Bridgman (1953) have revealed that in order for brittle materials to deform in a ductile manner, a considerable hydrostatic stress and/or temperature are required. Reducing the depth of cut will merely decrease the stress magnitude without changing the stress state. Therefore, according to this hypothesis, the superior quality of a surface produced at a lower depth of cut is due to the state of stress and is not necessarily due to plastic deformation. Ductile mode machining can be realised using two phenomena. These are single point diamond turning (SPDT) and ultra-precision grinding (UPG) both of which are performed on ultra-precision machine tools. Fang and Venkatesh (1998), Shibata et al. (1996) and Venkatesh et al. (1997) have applied SPDT on some brittle materials to obtain ductile surfaces on brittle materials with ultra-precision machine tools. Also, Bandyopadhyay et al. (1996), Fujihara et al. (1997) and Zhang et al. (2000), carried out UPG of brittle materials on ultra-precision grinders. Furthermore, Blackley and

3 An experimental study on precision grinding of silicon 327 Scattergood (1991) developed an analytical model explaining ductile mode machining of brittle materials for SPDT. This model provided critical depth of cut below which defect-free surfaces are formed. Above this critical depth of cut fracture surfaces are generated on machined surfaces of brittle materials. They also gave the maximum feed rate that can be used to achieve fully ductile surfaces. König and Sinhoff (1992) provided theoretical requirements for the realisation of ductile regime grinding of optical glasses. The criteria for the realisation of ductile regime grinding, according to them, are that the depth of cut must not exceed certain critical depth of cut and the protruding grains in the grinding wheels must be flattened. Zhong (2003) reported that the range of the critical depth of cut for the realisation of fully ductile mode machining on hard and brittle materials to be between 50 nm to 1 μm depending on the machining directions and coolants used. However, this range can only be set on ultra-precision machine tools. It has also been demonstrated recently that micro-end milling machine can be used to determine ductile mode cutting conditions for silicon. Rusnaldy et al. (2008) used micro-end milling machine to find optimal conditions for axial depth of cut, feed rate and spindle speed for the ductile regime machining of single crystal silicon by using force ratios. When ductile mode machining of brittle materials is achieved, nanometre order surface roughness is obtained and subsurface damage may approach zero. However, because of the expensive nature of ultra-precision machine tools coupled with the requirements for the skilled manpower for the operation of these machine tools, the use of ductile mode machining concept has been limited to the production of optical lenses in the optical industry, although its application has been known by industries. Therefore, because of these reasons, research efforts have been shifted to the use of conventional machine tools to machine brittle materials using a machining phenomenon termed partial ductile mode machining. Partial ductile mode machining is a precision grinding technique where 100% ductile mode machining is not achievable. Partial ductile mode machining focuses on grinding conditions that generate large amounts of ductile surfaces followed by a polishing process. It is expected that the polishing time can be reduced greatly and the surface quality improved on ground surfaces with massive ductile-streaked surfaces. High wheel rotation, slow feed rate, very small grain size and small indentations are the practical requirements to realise precision grinding of brittle materials as demonstrated by Masuzawa and Tönshoff (1977). Zhong (2003), therefore, reported that partial ductile mode machining appears to be more attractive alternative to the optical and semi-conductor industries because the grinding wheels and the machines are reasonably priced. Several authors have generated some partial ductile surfaces on different brittle materials. To mention but a few, Ong and Venkatesh (1998) reported generating qualitatively 85% ductile surfaces on ground pyrex glass samples with a fine-grit resin-bonded diamond cup wheels on a conventional surface grinder. The surface roughness values were in the range of nm. Zhong (2003) obtained ductile or partial ductile surfaces of brittle materials with CNC machine tools. His studies concluded that ductile streaks generated would help in reducing the polishing time. Venkatesh et al. (2003) investigated the amounts of ductile streaks produced during diamond grinding of silicon and glass. In their investigation, an air-powered jig grinding unit (NSK planet 1500) was attached to the vertical spindle of a Maho CNC milling machine. This device

4 328 A-R. Alao and M. Konneh which is driven by pneumatic pressure was attached to the spindle of a CNC machine to upgrade its spindle speed to 100,000 rpm. They obtained considerable amount of ductile streaks on silicon, germanium and glass. Venkatesh and Izman (2007) used a modified CNC machine to precisely grind IC chips. Izman and Venkatesh (2007) used diamond pins to produce flat surfaces on glass surfaces by vertical surface grinding. Furthermore, Venkatesh et al. (2005) reported generating spherical chips for glass by at 5 μm under wet conditions in surface grinding with diamond pins. The central hole ultrasonically drilled on the diamond pin enabled the formation of the spherical chips. Liu et al. (2007) reported that the resin-bonded grinding wheels outperformed metal- or vitrified-bonded wheels in terms of reduction in both the surface roughness and subsurface damage during grinding of ceramics. In all the works reviewed above, many efforts have been expended on the grinding conditions that could generate large amounts of ductile streaks using trial and error (traditional) method of experimentation. The traditional method of experimentation involves investigating a factor at a time which often takes a longer time to achieve results for all the factors under examination thereby making the experiments expensive. By studying the effect of a factor at a time, the researcher often ignores the interactions between factors and consequently experimental conclusions may not be reproducible and at times disappointing. Therefore, this study incorporates factorial experimental design to explore the grinding conditions that could generate large amounts of ductile streaks and to study the effects of grinding parameters and their interactions between the grinding parameters on the surface roughness parameters of ground surfaces in precision grinding of silicon. Also, Masuzawa and Tönshoff (1977) qualitatively described the requirements for the realisation of precision grinding of brittle materials in terms of high wheel rotation, slow feed rate, very small grain size and small indentations. This study therefore attempts to provide quantitative values of wheel rotation, feed rate and depth of cut during precision grinding of silicon. In addition to providing quantitative values of wheel rotation, feed rate and depth of cut in precision grinding of silicon, this study also provides the amount of contribution of each factor on the surface finish of precision grinding of silicon with diamond grinding pins. The paper therefore reports the results of experimentation on precision grinding of silicon using a modified conventional NC milling machine. 2 Experimental details In this section, the experimental designs are discussed. Selection of work and tool materials, equipment and instruments used are also outlined. 2.1 Work and tool materials The work piece materials that were precisely ground are mono-crystalline silicons which were diamond cut into dimension mm. Tool materials are Winter-made resin bonded diamond grinding wheels (also known as grinding pins since the diameter of each is 5 6 mm) with shape, 1A1W; diameter, 5 6 mm; diamond, grit size, 64 μm; and concentration, 100 (Figure 1).

5 An experimental study on precision grinding of silicon 329 Figure 1 Resin-bonded diamond mounted grinding wheel used in this experiment (see online version for colours) Note: Specifications 1A1 W-5-6 D64 K888 RY C Experimental equipment and instruments The following equipment and instruments were used for the experimental trials. They are: A five-axis DMU 35M Deckel Maho NC milling with motor power: 45 kw; work spindle speed, directly programmable; 5 6,300 rpm; linear traverse measuring system resolution, 1 μm and coolant flow rate 0 7 litre/min. Ultra-precision high speed jig grinder (NSK Planet 850), maximum speed 100,000 rpm. Mitutoyo Surftest (SV-514). Jeol (JSM-5600) scanning electron microscope (SEM). 2.3 Experimentation A general purpose NC milling machine was used to carry out experimental trials. Zhong and Venkatesh (2009) opined that general-purpose machines such as NC milling machine could give flexible outputs in terms of variety of lenses, without the need of the special-purpose machines like surface grinder. Thus, NC milling machines can be used for various machining operations like milling, grinding, drilling by utilising appropriate attachments and cutting tools. For this study, the machine was converted to a high speed machine by attaching to its spindle an ultra-precision high speed grinder to carry out precision grinding experiments. Few modifications were executed on this machine. These included the removal of the door switch to facilitate setting of depth of cut; the coolant nozzle was also modified to facilitate proper chip flushing and temperature reduction since the cutting fluids in a grinding process perform the functions of bulk cooling of the work piece; they also flush away the swarf and dislodged wheel grits. Finally, they serve as lubricants in the grinding process by reducing the friction between the wheel and the work piece materials as reported by Ebbrell et al. (2001). Figure 2 shows the modified coolant configuration. Furthermore, special fixtures were designed and fabricated to hold firmly silicon samples. Rough grinding (flattening operation) was performed on silicon samples in order to regulate the surface roughness before carrying out precision grinding trials. The pre-ground specimen was left unaltered in the fixture to ensure the maintenance of work piece flatness. The grinding pins were drilled (about 2 mm in diameter removed at

6 330 A-R. Alao and M. Konneh centres) using an ultrasonic technique to prevent the zero velocity and coolant flow rate fixed at 7 litre/min to remove stalling and dragging marks as demonstrated by Izman and Venkatesh (2007). Before starting a new grinding condition, the pin was dressed with alumina dressing stick (Figure 2). Figure 2 The experimental setup showing an ultra-precision high-speed jig grinder attached on NC vertical milling spindle and the Al 2 O 3 abrasive stick (grade Nr. 2) (see online version for colours) An ultra-precision high-speed jig grinder Grinding pin Adjusted coolant hose An abrasive dressing stick Silicon sample Figure 3 Microscopic picture of a precision ground silicon sample surface showing four passes with different grinding conditions (see online version for colours) 1st pass 2nd pass 3rd pass 4th pass On a sample of silicon, four passes representing four different grinding conditions were conducted on each silicon sample (Figure 3). An Al 2 O 3 abrasive stick was used for dressing the grinding pins at 10 μm in-feeds in every pass before starting each new

7 An experimental study on precision grinding of silicon 331 grinding condition as was used by Mayer and Fang (1994). The other conditions included the feed rate of 25 mm/min, spindle speed 70,000 rpm (0.3 MPa), coolant flow rate 7 lit/min, and four passes. The coolant used was Castrol Miracol 80 with a ratio of 1: 50 (Castrol Miracol to water). The same ratio was used by Matsuo et al. (1997) and Venkatesh et al. (2003). The coolant flow rate was high enough to prevent the stalling marks formation and to flush away chips on ground silicon surfaces as evidenced from the works of Izman and Venkatesh (2007). 2.4 The response variables and grinding parameters Venkatesh and Izman (2007) said that excellent surface quality was desirable for fault diagnosis by the manufacturers of the IC chips. The surface quality can be improved by the formation of large amounts of ductile streaks on ground silicon surfaces thereby reducing the polishing time. Surface roughness is a widely used index of a product s surface quality and in most cases a technical requirement for mechanical products. Among surface roughness parameters, the average surface roughness (R a ) is the most commonly used. Since surfaces generated by machining are usually characterised by the amplitude parameters, spacing parameters and hybrid parameters as demonstrated by Thomas (1999) and Routara et al. (2009), consideration of only one roughness parameter like R a is not sufficient to describe the surface quality. Hence, the surface roughness R a and R t were selected as the responses for this study. R a is the arithmetic mean of the departure of the roughness profile from the mean line while R t represents the maximumto-peak value within an evaluation length (five consecutive sampling lengths). Mathematically denoted by equation (1), R a is one of the statistical parameters for inspection and tolerancing of machined surface. These statistics are defined in Figure 4 below, where R a is the arithmetic mean deviation, L is the sampling length and y the ordinate of the of profile curve which is of x. Ra L 1 = y( x) dx L (1) 0 Figure 5 shows the statistics used to compute the maximum-to-peak height R t. It can be computed using equation (2) below. In equation (2), R pmax and R vmax are the respective maximum profile peak and valley depth from the entire evaluation length. And R = R + R (2) t pmax vmax Rmax = Ymax + Ymin (3) where Y max and Y min are the respective maximum peak and maximum valleys from the mean line within the sampling length. Since Rusnaldy et al. (2008), Venkatesh et al. (2003), Venkatesh and Izman (2007), and Routara et al. (2009) have reported surface finishes to be affected by machining variables, depths of cut, feed rates and spindle speeds; therefore, this study considered the above parameters as the controllable factors. Furthermore, these parameters were set at three levels as shown in Table 1. The levels for the spindle speed were based on the workable range 70,000 90,000 rpm as specified by the manufacturer of the NSK Planet

8 332 A-R. Alao and M. Konneh 850. In addition, Rusnaldy et al. (2007, 2008) reported generating partial ductile surfaces with spindle speeds in the range of 75,000 to 90,000 rpm. The levels for feed rates and depths of cut were selected based on the previous reported data of the work of Venkatesh et al. (2003), and Venkash and Izman (2007). Alao and Konneh (2009) used the same precision grinding conditions for developing prediction model of surface roughness R t of silicon with Box-Behken design. Figure 4 Definition of parameters used to compute R a Source: Stephenson and Agapiou (1997) Figure 5 Parameters used in computing R t Table 1 Grinding parameters and their levels Grinding parameter Symbol Levels Low Middle High Depth of cut (μm) a Feed rate (mm/min) f Spindle speed (rpm) n 70,000 80,000 90, Measurement procedure Average roughness (R a ) and maximum peak-to-valley (R t ) heights were measured using the 0.25 mm cut off length (sampling length) and 1.25 mm evaluation length on the

9 An experimental study on precision grinding of silicon 333 Mitutoyo Surftest (SV-514) in transverse direction to the machined surface (Figure 6) on silicon samples. On each pass on the silicon sample, three readings of R a and R t were recorded and the average readings computed. Figure 6 shows the equipment and the surface roughness measurement process being executed. Figure 6 The setup for the measurement of surface roughness parameters (see online version for colours) Stylus Ground silicon sample 3 Results and discussion 3.1 Discussion of the results for three-levels factorials Table 2 shows the three-level factorials and the responses R a and R t. From this table, it can be found that the highest roughness values for this study are μm R a and μm R t, respectively (with grinding condition, depth of cut; 5 μm, feed rate; 10 mm/min and spindle speed; 80,000 rpm corresponding to trial 24). This condition also gave fully fractured surface [Figure 7(a)]. Although the condition for the ground surface in Figure 7(b) has a good surface finish with respect to surface roughness of R a and R t and μm (trial 19) but the surface is fully fractured. Setting the grinding parameters to obtain massive ductile streaks is a much better deal than good surface finish since the surfaces can be polished much easier before saturation can be reached leading to the improvement of the surface quality. This is due to the fact that saturation has taken place on the ground surface. Other reason for the fully fractured surfaces in Figure 7 is that the depths of cut are very small to remove materials already present during pre-grinding operations. Some ductile streaks were also obtained in this study. Figure 8 shows the SEM of the partial ductile surfaces (at higher magnification compared to Figure 7). It can be seen that the lowest surface roughness with 43 nm R a and 987 nm R t was found at the condition, depth of cut 20 μm, feed rate 6.25 mm/min and 70,000 rpm representing trial 9 in Table 2 [Figure 8(b)]. This condition also gave the largest amount of ductile streaks. Figure 8(a) shows the micrograph of surface with massive amount of fracture areas with ductile streaks with deep micro-cracks for the grinding conditions depth of cut 12.5 μm, feed rate 10 mm/min and spindle speed 90,000 rpm.

10 334 A-R. Alao and M. Konneh Figure 7 Representative scanning electron micrographs of silicon samples showing fully fracture areas, (a) depth of cut 5 μm, feed rate 10 mm/min, spindle speed 80,000 rpm, (b) depth of cut 12.5 μm, feed rate 2.5 mm/min, spindle speed 90,000 rpm (a) (b) Figure 8 SEM images of ground silicon samples, (a) massive ductile streaks and deep micro-cracks for the grinding conditions depth of cut 12.5 μm, feed rate 10 mm/min and speed 90,000 rpm (b) abundant ductile streaks with little micro fracture for conditions, depth of cut 20 μm, feed rate 6.25 mm/min and spindle speed 70,000 rpm (a) (b) Table 2 Three-level factorials experiments and the surface roughness parameters R a, and R t Experimental trial Grinding parameter a (μm) f (mm/min) n (rpm) R a (μm) R t (μm) , , , , , , , ,

11 An experimental study on precision grinding of silicon 335 Table 2 Three-level factorials experiments and the surface roughness parameters R a, and R t (continued) Experimental trial Grinding parameter a (μm) f (mm/min) n (rpm) R a (μm) R t (μm) , , , , , , , , , , , , , , , , , , , Main and interactive effects of grinding parameters on roughness parameters The graphs of the main effects of depth of cut, feed rate and spindle speed for the R a and R t are shown in Figures 9 and 11, respectively while those to determine the interactions among the grinding factors are shown in Figures 10 and 12. The plot data for the influence of each main factor are generated by grouping the surface roughness values for a particular factor level, taking the sum and dividing by the number of responses. For example, the data for the plot of Figure 9 are done as follows. The associated values of R a for depth of cut which would match those experimental runs at which depth of cut was set at level 1 in Figure 9(a) is calculated as in equation (4) a1 = 9 = μm Ra (4)

12 336 A-R. Alao and M. Konneh Other depths of cut at levels 2 and 3 in Figure 9(a) are generated similarly. Similar procedures are applied to the generation of the data in Figures (9) and (11). Interactions occur when two or more main factors acting together have different effect on the roughness parameters (R a and R t ) than the effect of each factor acting individually as demonstrated by Peace (1993). Therefore, if there is an interaction between two factors, knowledge of its existence is more useful than the knowledge of the main effect (Montgomery et al., 1998). According to Peace (1993), there exist three kinds of interaction between two factors or input parameters: strong or high; mild or weak and nil interactions. A strong or high interaction exists if there is a dramatic change in the response or output parameter (R a or R t ) as a factor (depth of cut, feed rate or spindle speed) changes at different levels of the response. Therefore, according to Montgomery et al. (1998), if a strong interaction exists between two factors (depth of cut and feed rate), the corresponding main effects have very little practical meaning. A mild interaction between these factors is feasible if the response increases or decreases at slightly different rate as the factor changes at different levels of the response. When the output increases or decreases at the same rate as the value of factor changes for different levels of input, there is no interaction. In this study, therefore, the graphs showing the influence of the interaction between depth of cut at level 1 and feed rate at level 1 are calculated as in equation (5), = = (5) 3 a1 x f1 μm R a The following sections illustrate the effects of main factors as well as their interactions on R a or R t The main effects of grinding parameters on roughness parameter R a As shown in Figure 9(a), increasing the depth of cut from 5 to 12.5 μm leads to a corresponding decrease in the value of R a but when depth of cut is increased from 12.5 to 20 μm, R a is increased. Therefore, the effect of depth of cut on the R a in precision grinding of silicon is non-linear. By increasing feed rate from 2.5 to 6.25 mm/min, there is an improvement in the value of R a. Increasing feed rate further from 6.25 to 10 mm/min leads to an increase in R a. Increasing spindle speed from 70,000 to 80,000 rpm increases the R a but by changing it from 80,000 to 90,000 rpm, the R a is improved. It can be concluded that depth of cut, feed rate and spindle speed have non-linear effects on R a indicating that their respective effect on R a is complex. Considering the grinding factors that give expected lowest R a, it is seen on Figure 9 that these correspond to a depth of cut, 12.5 μm; feed rate, 6.25 mm/min; and spindle speed, 70,000 rpm and 63 nm R a is shown in Table 2. However, 63 nm R a is not the lowest R a (43 nm) as observed in Table 2. The reason for this discrepancy is the interactive effect between depth of cut and feed rate as discussed in the following section. The interaction makes depth of cut and feed rate to have little effects on R a. Again, this is why design of experiment approach is better than the traditional method of experimentation.

13 An experimental study on precision grinding of silicon 337 Figure 9 The effects of (a) depth of cut, (b) feed rate and (c) spindle speed on the average surface roughness R a (see online version for colours) Ra (µm) DOC (µm) (a) Ra (µm) Feed rate (mm/min) (b) Ra (µm) Spindle speed (rpm) (c)

14 338 A-R. Alao and M. Konneh Figure 10 The graphs show the interactive effects on surface roughness R a between (a) depth of cut and feed rate, (b) depth of cut and spindle speed and (c) feed rate and spindle speed Ra (µm) f(2.5) f(6.25) f(10) DOC (µm) (a) Ra (µm) n (70000) n (80000) n (90000) DOC (µm) (b) Ra (µm) n (70000) n (80000) n (90000) Feed rate (mm/min) (c)

15 An experimental study on precision grinding of silicon Interactive effects of grinding parameters on roughness parameter R a Figure 10 shows various interactive effects between the grinding parameters and the R a. As can be seen on Figure 10(a) strong interaction exists between depth of cut and feed rate at spindle speed of 80,000 rpm on R a. This makes the corresponding main effects of depth of cut and feed rate to have very little or no practical effect on R a. The implication of this is that at 80,000 rpm, the effect of depth of cut on R a depends on the levels of feed rate. Therefore, depth of cut and feed rate have a combined effect on R a in precision grinding of silicon. This interdependence between depth of cut and feed rate leads to the unpredictability of the expected lowest R a in Figure 9. At the middle value of feed rate (6.25 mm/min), no interaction exists between depth of cut and spindle speed [Figure 10(b)]. This indicates that depth of cut and spindle speeds are not interdependent and each influences R a individually. Since depth of cut is interacted with feed rate, only spindle speed has direct effect on R a. From Figure 10(b), it can be observed that the expected lowest R a is obtained at depth of cut, 12.5 μm; spindle speed, 70,000 rpm at 6.25 mm/min feed rate. This corresponds to the expected lowest R a value discussed in Section if no interaction exists. Figure 10(c) also shows mild interaction between feed rate and spindle speed at the middle value of depth of cut. Again, there is no interdependence between feed rate and spindle speed. Therefore, it can be observed that expected lowest R a is obtained at feed rate, 6.25 mm/min; spindle speed, 70,000 rpm and at depth of cut, 12.5 μm. Again, the expected lowest R a corresponds to its value discussed in Section for mild or no interaction between feed rate and spindle speed at the mid-value of depth of cut. In summary, spindle speed affects R a of precision ground surfaces of silicon mostly in this study while feed rate and depth of cut combine interactively to influence the R a The main effects of grinding parameters on roughness parameter R t The individual effect of the grinding parameters, depth of cut, feed rate and spindle speed on the roughness R t is shown on Figure 11. As shown in Figures 11(a) and 11(b), increasing respectively, the values of depth of cut from 5 to 12.5 μm and feed rate from 2.5 to 6.25 mm/min, there is a corresponding improvement in R t but when depth of cut and feed rate are respectively increased from 12.5 to 20 μm and 6.25 to 10 mm/min, R t is increased. Therefore, both depth of cut and feed rate have non-linear effects on the R t in precision grinding of silicon. Increasing spindle speed from 70,000 to 80,000 rpm increases R t but by changing it from 80,000 to 90,000 rpm, the R t is improved. It can be concluded that depth of cut, feed rate and spindle speed have non-linear on R t indicating that their respective effect on R t is complex. Considering the grinding factors that give expected lowest R t, it is seen on Figure 11 that these correspond to a depth of cut, 12.5 μm; feed rate, 6.25 mm/min; and spindle speed, 70,000 rpm and 1,370 nm R t is observed in Table 2. However, 1,370 R t is higher than the lowest R t as observed in Table 2. The same reason as given in Section explains the disparity in the values of the R t in terms of the interaction effect between depth of cut and feed rate discussed in the following section.

16 340 A-R. Alao and M. Konneh Figure 11 The effects of (a) depth of cut, (b) feed rate and (c) spindle speed on the peak-to-valley height R t (see online version for colours) Rt (µm) DOC (µm) (a) Rt (µm Feed rate (mm/min) (b) Rt (µm) Spindle speed (rpm) (c)

17 An experimental study on precision grinding of silicon 341 Figure 12 The graphs show the interactive effects on surface roughness R t between (a) depth of cut and feed rate, (b) depth of cut and spindle speed and (c) feed rate and spindle speed Rt (µm) f (2.5) f (6.25) f (10) DOC (µm) (a) Rt (µm) n (70000) n (80000) n (90000) DOC (µm) (b) Rt (µm) n (70000) n (80000) n (90000) feed rate (mm/min) (c)

18 342 A-R. Alao and M. Konneh Interactive effects of grinding parameters on roughness parameter R t The various interactive effects between the grinding parameters and the R t are shown in Figure 12. As can be seen in Figure 12(a), there is a strong interaction between depth of cut and feed rate at spindle speed of 80,000 rpm on R t. What this implies is that at 80,000 rpm, the effect of depth of cut on R t depends on the levels of feed rate. Therefore, the depth of cut and feed rate have a combined effect on R t in precision grinding of silicon. This interdependence between depth of cut and feed rate leads to the unpredictability of expected lowest R t from Figure 11. At the middle value of feed rate (6.25 mm/min), no interaction exists between depth of cut and spindle speed [Figure 12(b)]. This indicates that depth of cut and spindle speed are not interdependent and each affects R t separately. Since depth of cut is interacted with feed rate, only spindle speed affects R t. As can be observed in Figure 12(b), the expected lowest R t is obtained at depth of cut, 12.5 μm; spindle speed, 70,000 rpm at 6.25 mm/min feed rate. This corresponds to the R t value discussed in Section for non-existence of interaction. Figure 12(c) also shows mild interaction between feed rate and spindle speed at the middle value of depth of cut. Again there is no interdependence between feed rate and spindle speed. Therefore, it can be seen that expected lowest R t in this study is obtained at feed rate, 6.25 mm/min; spindle speed, 70,000 rpm and at 12.5 μm depth of cut. Again, the expected lowest R t corresponds to its value discussed in Section for mild or no interaction between feed rate and spindle speed at 5 μm depth of cut. In summary, spindle speed affects R t of precision ground surfaces of silicon mostly in this study while feed rate and depth of cut combine interactively to influence the R t. 3.3 The influence of grinding factors on the surface finish during precision grinding of silicon with diamond pins An attempt has been made in this study to determine quantitatively and experimentally how high a wheel should rotate; how slow the feed rate should be and how small the indentation (depth of cut) should be set according to qualitative criteria provided for the realisation of precision grinding of silicon by Masuzawa and Tönshoff (1977). These values have been established as wheel rotation, 70,000 rpm; feed rate, 6.25 mm/min; and depth of cut, 20 μm during precision grinding of silicon with diamond pins of size 64 μm. Since the interaction between depth of cut and feed rate only shows the combined effects on R a and R t but it is not a physical parameter, the quantitative influence of depth of cut, feed rate and spindle speed on R a and R t are respectively shown in Figures 13 and 14 for this study. From these figures, it is shown that spindle speed mostly affects R a and R t followed by feed rate and depth of cut. These translate to spindle speed contributing about 42.86% on R a followed by feed rate which contributes about 30% on R a and depth of cut contributes 27.14% on R a. The percentage contributions of spindle speed, feed rate and depth of cut on R t are respectively 51.76%, 33.96% and 14.28%.

19 An experimental study on precision grinding of silicon 343 Figure 13 Graphical representation of the contribution of grinding parameters on R a (see online version for colours) Figure 14 Graphical representation of the contribution of grinding parameters on R t (see online version for colours) 4 Conclusions This study investigates precision grinding of silicon with diamond pins. Three-level full factorials design was used to study the conditions that favoured massive ductile surfaces and to determine the influence of the grinding parameters, depth of cut, feed rate and spindle speed on the surface parameters R a and R t. The strong interaction between depth of cut and feed rate on R a and R t whose effects are to nullify the main effects of the individual on R a and R t has been established in this study. From the data observed in this study, the following conclusions can be drawn: 1 In this investigation surface roughness as low as 43 nm has been established with condition, depth of cut 20 μm; feed rate 6.25 mm/min and spindle speed 70,000 rpm. Other condition capable of giving ductile streaks is depth of cut 12.5 μm, feed rate 10 mm/min and spindle speed 90,000 rpm.

20 344 A-R. Alao and M. Konneh 2 An attempt has been made to determine quantitatively and experimentally how high a wheel should rotate; how slow the feed rate should be and how small the indentations (depth of cut) should be set according to qualitative criteria provided for precision grinding by Masuzawa and Tönshoff (1977). These values have been established as wheel rotation, 70,000 rpm; feed rate, 6.25 mm/min; and depth of cut, 20 μm during precision grinding of silicon with diamond pins of size 64 μm. 3 It has been established in this study that by proper setting of the grinding conditions massive ductile streaks can be realised on precision ground surfaces of brittle materials. Obtaining massive ductile surfaces is more desirable than having good surface finish (where saturation has been reached) since the former can be polished more easily than the latter leading to a reduction in the polishing time and an improvement in the surface quality. 4 Strong interaction has been found to exist between the depth of cut and feed rate for both the R a and R t in three-level factorials. Therefore, surface parameters (R a and R t ) in precision grinding of silicon are functions of both the depth of cut and feed rate. The interdependence of depth of cut and feed rate is one of the key factors influencing the unpredictability of the precision grinding process making it to be complex or to have an unsteady process behaviour. These complex characteristics determine the surface quality of the precision grinding process. 5 Spindle speed affects the surface finish of precision ground silicon mostly followed by feed rate and depth of cut. 6 It has also been established that spindle speed contributes about 42.86% on R a followed by feed rate which contributes about 30% on R a and depth of cut contributes 27.14% on R a. The percentage contributions of spindle speed, feed rate and depth of cut on R t are respectively 51.76, and 14.28%. References Alao, A-R. and Konneh, M. (2009) A response surface methodology based approach to machining processes: modelling and quality of the models, International Journal of Experimental Design and Process Optimization, Vol. 1, Nos. 2/3, pp Bandyopadhyay, B.P., Ohmori, H. and Takahashi, L. (1996) Ductile regime finish grinding of ceramics with electrolytic in-process dressing (ELID) grinding, Materials Manufacturing Processes, Vol. 11, No. 5, pp Blackley, W.S. and Scattergood, R.O. (1991) Ductile-regime machining model for diamond turning of brittle materials, Precision Engineering, Vol. 13, No. 2, pp Bridgman, P.W. (1953) Effects of very high-pressure on glass, Journal of Applied Physics, Vol. 24, No. 4, pp Ebbrell, S., Woolley, N.H., Tridimas, Y.D., Allanson, D.R. and Rowe, W.B. (2001) The effects of cutting fluid application methods on the grinding process, International Journal of Machine Tools & Manufacture, Vol. 40, No. 2, pp Fang, F.Z. and Venkatesh, V.C. (1998) Diamond cutting of silicon with nanometric finish, Annals of the CIRP, Vol. 47, No. 1, pp Fujihara, K., Ohshiba, K., Komatsu, T., Ueno, M., Ohmori, H. and Bandyopadhyay, B.P. (1997) Precision surface grinding characteristics of ceramic matrix composites and structural ceramics with ELID, Machining Science and Technology, Vol. 1, No. 1, pp

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