Handbook of Advanced Ceramics Machining Episode 2 pptx

f max ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R(d c þ y c ) Æ R(d c þ y c ) ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 À d c d c þ y c  2 s v u u t (1:8) If (d c =(d c þ y c )) 2 << 1, the equation is simplified as f max ¼ d c ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R 2(d c þ y c ) s (1:9) This model is useful since it acknowledges the occurrence of the cracks in the cutting zone or the zone to be cut and the effectiveness of reducing the machining energy. However, it is difficult to predict the crack path and to control its growth rate. In the final finishing, the available alternative for feed rate f max ¼ d c as if concerning the crack growth and its penetration depth. Eda et al. 12,13 have developed a new ultraprecision machine with an actuator capable of controlling the specific material removal within the condition, f max ¼ d c , with which the surface roughness of subnanometer was achieved for a wide range of materials. The grinding energy required for ductile mode is different from that for brittle mode. Based on the concept of the critical depth-of-cut d c , which has attracted considerable attention so far, a general description has been suc- cessfully introduced to express the brittle–ductile relationship. The total grinding energy E b required for brittle materials is the sum of the energy for brittle grinding E f and the energy for ductile grinding E p . Out of E b , E f is expressed as E f ¼ 2pC L g s þ 2C m g s þ p 4 as p d 2 p  L (1:10) where C L is the lateral crack radius, L the length of C L cylinder, g s the energy for surface generation, C m the median crack radius, s p the yield stress, d p the diameter of plastic flow zone, and a a constant, whereas E p is E p ¼ F t L (1:11) where F t is the tangential grinding force and L the grinding length. Dividing this by the removed volume V f at the brittle mode or V p at the ductile mode, the specific grinding energy m f and m p are given as m f ¼ E f =V f ¼ K f d À 4 3 þ K p ,(1:12) m p ¼ E p =V p % s Y % H ¼ K p (1:13) As grinding shifts from the brittle mode to the perfect ductile mode, the specific energy for brittle grinding m f should agree with the condition s p < s< s f shown in Figure 1.1, and the specific energy for ductile grinding m p should take a value equivalent to hardness H. If the grinding speed is as Ioan D. Marinescu/Handbook of Advanced Ceramics Machining 3837_C001 Final Proof page 16 6.10.2006 2:05am 16 Handbook of Advanced Ceramics Machining slow as scratching, m p should be equal to P tip described in Section 1.3.2. In Figure 1.15, the specific energy m p of grinding SiC produced by CVD is plotted against d À 4 3 . The line can be approximately expressed by the equation m p ¼ 535 þ53776d À 4 3 (GJ=m 3 )(1:14) Figure 1.16 summarizes the grinding results of six kinds of materials listed in Table 1.1. 14 CVD silicon carbide 6000 Ductile regime Brittle regime m = 535 + 53776 d −4/3 (R 2 = 0.974) d −4/3 (nm −4/3 ) d −4/3 (nm −4/3 ) 4000 2000 m (GJ/m 3 ) Surface fracture (%) 0 0 0.0 0.1 0.2 0.3 5 10 15 0.0 0.1 0.2 0.3 FIGURE 1.15 Specific grinding energy (top) and area percent grinding-induced surface fracture (bottom) vs. the grain depth-of-cut to the À4=3 power for CVD silicon carbide. Tomita, Y. and Eda, H., Development of new bonding materials for fixed abrasive of grinding stone instead of free abrasives processing, Bull JSPE (in Japanese), 61, 10 (1995) 1428; Lawn, B.R. and Swain, M.V., Microfracture beneath point indentations in brittle solids, J Mater Sci, 10 (1975) 113. Ioan D. Marinescu/Handbook of Advanced Ceramics Machining 3837_C001 Final Proof page 17 6.10.2006 2:05am Ductile Grinding of Ceramics: Machine Tool and Process 17 1.5 Machine Tools for Ductile Grinding of Ceramics 1.5.1 Design Criteria of Ductile Microgrinding Machine Tool Generally, microgrinding is referred to as the material removal rate (MRR) ranging from 0.1 to 0.0001 mm 3 =mm sec, which includes the process 60 76 74 72 70 68 66 64 30 66 68 70 72 74 76 78 35 40 45 50 55 60 65 50 40 Brittle zone Brittle zone Brittle zone Brittle zone Brittle zone Brittle zone 30 20 10 0 0 0 0.02 0.04 0.06 0.08 0.120.1 0 0 0.02 0.02 0.04 0.04 0.06 0.06 0.08 0.08 0.12 0.12 0.1 0.1 0.02 (d) F6 (e) GOE91 0.04 0.06 0.08 0.1 0.12 m (Gj/m 3 ) m (Gj/m 3 ) m (Gj/m 3 ) d −4/3 (nm −4/3 ) d −4/3 (nm −4/3 ) d −4/3 (nm −4/3 ) d −4/3 (nm −4/3 ) 10 20 30 40 50 60 70 0 0.02 0.04 0.06 0.08 0.1 0.12 (a) TRC 5 m (Gj/m 3 ) d −4/3 (nm −4/3 ) 40 35 45 50 55 60 65 70 0 0.02 0.04 0.06 0.08 0.1 0.12 (b) KzF6 (c) BK7 (f) SK7 m (Gj/m 3 ) m (Gj/m 3 ) d −4/3 (nm −4/3 ) Ductile removal zone Ductile removal zone Ductile removal zone Ductile removal zone Ductile removal zone Ductile removal zone Brittle–ductile transition Brittle–ductile transition Brittle–ductile transition Brittle–ductile transition Brittle–ductile transition Brittle–ductile transition FIGURE 1.16 Specific grinding energy vs. d À4=3 . Ioan D. Marinescu/Handbook of Advanced Ceramics Machining 3837_C001 Final Proof page 18 6.10.2006 2:05am 18 Handbook of Advanced Ceramics Machining normally done by polishing. 17,18 Now, it is possible to reach 10 À4 mm 3 =mm sec or even smaller by using fixed abrasives with sponge bond. 15 In such cases, the in-feed (depth-of-cut) is usually about several 10 nm, the grinding area is 100 mm 2 or smaller, and the grinding force is about several 10 mN. For studying the grinding temperature, Lawn has conducted a penetra- tion test by applying a constant force against a diamond indenter with the half-nominal angle of 688. The temperature rise DT, including the heat due to plastic flow and the heat due to sliding friction between the abrasive and workpiece, is expressed as DT ¼ H cot u 2prC r (1:15) Taking Si as an example, its hardness H ¼ 10.6 GPa, density r ¼ 2325 kg f =m 3 , specific heat C r ¼ 678 Nm=kg f K, and DT is assumed to be 433 K. The temperature rises for various ceramics are summarized in Table 1.3. Going one step ahead, Blok et al. have solved the temperature at the contact area between the wheel and workpiece, by simplifying the grind- ing process into a rectangular object (wheel) sliding over the workpiece. The following equation is introduced to express the maximum surface temperature. T max ¼ 2q k a Á l V  1 2 (1:16) TABLE 1.3 The Estimated Temperature Rises in the Plastic Zone during Indentation Test of Several Brittle Materials Estimated Data Material Hardness (H) (GPa) Density (kg m À3 ) Specific Heat (C r )(jkg À1 k À1 ) Temperature Rise (T ) (K) KzF6 4.44 2550 544 190.82 BK7 5.62 2520 760 174.95 F6 4.14 3740 524 125.94 GOE91 6.71 2550 880 178.27 SK7 5.32 3510 725 124.64 Glass II; TRC 5 8.48 2980 727 233.36 AL 2 O 3 15.2 3710 1050 232.63 ZrO 2 12.8 2530 821 367.40 SiC 10.6 3100 1040 196.02 Si 3 N 4 9.2 2500 710 309.01 Ioan D. Marinescu/Handbook of Advanced Ceramics Machining 3837_C001 Final Proof page 19 6.10.2006 2:05am Ductile Grinding of Ceramics: Machine Tool and Process 19 where q is the thermal heat flux, k the thermal conductivity, a the thermal diffusivity, l the contact length, and V the grinding wheel speed. When the tangential grinding force F t 4N,V 10 m=sec and l %0.006 m, the q (¼Ft ÁV=l) 10 6 10 6 J=m 2 sec. However, the temperature DT is only 28C, which is much lower than the actual case. Subsequently, the model is rebuilt on the sliding contact by the diamond abrasive alone, excluding the effect of contact between the bond and workpiece. The results are much closer to the actual grinding process. Figure 1.17 shows the grinding tem- perature calculated using the new equation as below T max ¼ 3qd 2 N 1 2 4 ffiffiffi 2 p k (1:17) where d is the diameter of contact diamond and N the number of diamond abrasive in the contact zone. The result shows that the temperature at ceramic grinding is much lower than the melting point of the material, and the temperature for diamond oxidation is even lower than 7008C. It is important to note the role played by 0 0 50 100 150 Maximum temperature T max (°C) 200 250 300 SiC O 510 Tangential force F t (mN) SK7 KzF6 GOE91 F6 BK7 TRC 5 AI 2 0 3 O O O O O O O 15 20 25 FIGURE 1.17 The estimated maximum surface temperature rise vs. the tangential grinding force for fixed experimental conditions. Ioan D. Marinescu/Handbook of Advanced Ceramics Machining 3837_C001 Final Proof page 20 6.10.2006 2:05am 20 Handbook of Advanced Ceramics Machining trueing. To achieve nanometer accuracy, the grinding wheel must be pre- cisely trued below 0.1 mm runout and 10 nm repeatability or better. The above conditions for ductile grinding of ceramics can be summarized as: the grinding force less than several 10 mN (per 100 mm 2 ) and the grinding temperature less than 4008C, which is equivalent to 1=100 of the force and 1=(4–5) of the temperature observable in a conventional grinding process. This is to say that the criteria for the machine tool to achieve ductile grinding of ceramics is accurate positioning capability and high repeatabil- ity to constantly control the grinding condition within s p s < s f and d d c (Figure 1.1). 1.5.2 Key Technologies of a Ductile Microgrinding Machine Tool As described in several publications, 17 the ultraprecision machine tool must have a structure of high thermal rigidity (or low thermal expansion), at least one digit better than conventional machine tools. However, the dynamic rigidity is less important and still acceptable even if it is one digit lower. For example, the compliances of C r ¼ 0.1 mm=kg f in radius direction, C a ¼ 0.03 mm=kg f in axial direction, and C c ¼ 0.1 mrad=kg m in rotational direction are sufficient for the main spindle whereas the error motions of 50 nm in both radius and axial directions and 0.2 mrad in rotational direction or better are expected. As for X–Y table, the dynamic rigidity should be k x %0.1 kg f =mm (traverse direction) and k y %0.05 kg f =mm whereas the thermal rigidity should be as good as that of the main spindle. The temperature of the environment is normally maintained at room temperature +0.18C. Between the wheel and workpiece, the contact rigidity k v % 5kg f =mm with a standard deviation of 0.5 kg f =mm in the normal direction (perpendicular to the grinding direction) and the dynamic rigidity k vd %10 kg f =mm with a standard deviation of 2 kg f =mm. These values indicate that the rigidity is one digit smaller than that of conventional machine tools. Futhermore, the tangential dynamic rigidity is about k dt %10 kg f =mm (standard deviation 0.2 kg f =mm) and k w %2kg f =mm is quite standard for the workpiece mounting table. The value listed above is designed for the aerostatic bearing and the table guideway. An aerostatic system fulfills the design criteria for the ductile microgrinding machine. In the subsequent sections, the actuators and sensors are exemplified as the key technology to realize the ductile microgrinding. [Example I] Figure 1.18 is the state-of-art machine tool newly developed for microgrind- ing. The key technology used in the system is Giant Magnetostrictive Actu- ator (GMA) for a wide range positioning of 100 mm–10 nm that is hybridized with a PZT actuator. The advantages of GMA include large displacement Ioan D. Marinescu/Handbook of Advanced Ceramics Machining 3837_C001 Final Proof page 21 6.10.2006 2:05am Ductile Grinding of Ceramics: Machine Tool and Process 21 AC servo- control system Air to sliding table sliding bed and to the air spindle GMP Diamond grinding cup wheel or single diamond tool Dryer Air compressor Digital storage oscilloscope Ethanol Workpiece Air spindle Air spindle Dynamometer Displacement sensor Digital multimeter Schematic of the MUPMT (Multipurpose Ultraprecision Machine Tool) Power PC Data recorder Probe PZT GMA Sliding table Sliding bed DC supply The feed can be set by PZT or GMA netualors FIGURE 1.18 Whole view of the MUPMT. Ioan D. Marinescu/Handbook of Advanced Ceramics Machining 3837_C001 Final Proof page 22 6.10.2006 2:05am 22 Handbook of Advanced Ceramics Machining (upto 2000 ppm), big power output (elastic energy 14 MJ=m 3 , several ten times bigger than PZT) and high response speed (msec–nsec). Making a full use of these advantages, GMA is able to execute from roughing (mm order) to finishing (several nm order). For more precise finishing at subnanometer scale, the PZT actuator is the alternative. In the range where the grinding force is relatively bigger, GMA can provide a better performance in rigidity because it requires no magnifier element to get necessary displacement or power. Contrary to GMA, PZT actuator normally demands a power supply with high voltage and a mag- nifier element to enlarge the displacement. This hybrid actuator proposes a solution to use two different kinds of actuators fully. It does not, however, mean that the GMA is unable to achieve nm positioning without the assist- ance of PZT. Figure 1.19 shows the grinding force and the relative displacement between the wheel and workpiece, by the grinding wheel of SD12000R100B at wet grinding with the conditions of 10 nm depth-of-cut, 1550 m=min grinding speed and 100 nm=rev feed rate. The results show that both the normal and tangential grinding forces are constantly below 10 mN. The surface roughness measured by Zygo is R a ¼ 0.32 nm and R y ¼ 2.42 nm (0.2 Â0.2 mm 2 )whereas R a ¼ 1.28 nm and R y ¼ 1.59 nm (0.363Â0.363 mm 2 )byAFM. The key component, as shown in Figure 1.20, has a GMA structure. 19 The position is constantly monitored by an electrostatic gap sensor. The feed- back control selectively drives the AC servomotor for a large infeed or the GMA for a fine infeed. [Example II] The key technologies for microgrinding machine tools also include rapid response speed and extremely smooth movements in the X–Y–Z axis, the main spindle, and the fine infeed. Therefore, the driving resistance and the intermittent motion such as stick-slip must be avoided. As shown in Figure 1.21, the current trend in movements for X–Y–Z axis and the main spindle is to replace the friction of solid–solid contact with pneumatic or hydraulic friction. 20–22 Since the convention ball screws possess a large spring constant, the energy generated by the rotational movement is often converted into the vibration circuit of the feed elements, resulting in an error motion. In microgrinding, the vibration induced by the disturbance from the feed device is much bigger than that granted by the grinding process itself. Instead of increasing the rigidity of the whole machine tool, therefore, efforts are made to shut noises out from the tool holder and workpiece- mounting table by using media that has a small spring constant. The feed device developed from such a viewpoint is a built-in unit comprising of an aerostatic ball screw, a rotary encoder, and a backlash-free aerostatic bear- ing connected to a servomotor. As the solid friction is free, it is able to Ioan D. Marinescu/Handbook of Advanced Ceramics Machining 3837_C001 Final Proof page 23 6.10.2006 2:05am Ductile Grinding of Ceramics: Machine Tool and Process 23 achieve the power consumption <0.5 W, the temperature rise <0.18C, the encoder resolution of 64 million pulse=rev and the infeed of 1 nm=step. Figure 1.22 shows the workpiece-mounting table B and the feed unit for Y-axis. These two units can be incorporated together or used separately. The built-in friction free air balance in the Y-axis guarantees the level of B table to be +0.04 mm=f200 mm, as the Y-axis moves up and down. The accuracy has currently been improved upto nanometers. Unground shoulder Ground SEM micrograph of ductile grinding on glass BK7 Displacement Tangential force Normal force 0 Z force (mN) −5 0 5 10 20 30 Time (sec) 40 50 60 0 X force (mN) −50 0 50 10 20 30 40 50 60 0 Plunge (nm) −40 −20 20 0 40 10 20 30 40 50 60 FIGURE 1.19 Experimentally measured normal and tangential force during grinding test on glass BK7. Ioan D. Marinescu/Handbook of Advanced Ceramics Machining 3837_C001 Final Proof page 24 6.10.2006 2:05am 24 Handbook of Advanced Ceramics Machining External view of the GMA Cooling water Permanent magnet Driving coil In Out Magnetostrictive rod Displacement FIGURE 1.20 Schematic of the GMA. Ioan D. Marinescu/Handbook of Advanced Ceramics Machining 3837_C001 Final Proof page 25 6.10.2006 2:05am Ductile Grinding of Ceramics: Machine Tool and Process 25 [...]... mm=f200 mm) and up-down feed Y-axis unit 360° f 22 0 mm Ioan D Marinescu /Handbook of Advanced Ceramics Machining 3837_C001 Final Proof page 27 6.10 .20 06 2: 05am Ductile Grinding of Ceramics: Machine Tool and Process 27 Ioan D Marinescu /Handbook of Advanced Ceramics Machining 3837_C001 Final Proof 28 page 28 6.10 .20 06 2: 05am Handbook of Advanced Ceramics Machining References 1 Eda, H et al., Principle of. .. TABLE 2. 1 Experimental Conditions Wheel Workpiece Wheel speed Table speed Depth of cut Coolant SD140Q50M SD800Q50M SSN (HV:1600) HIPSN (HV :24 00) HPSC (HV:3300) SSC (HV :25 00) Vg ¼ 20 –85 m=sec vw ¼ 0.05–150 mm=sec tt ¼ 5 mm Soluble (1=50) Flow rate: 12 L=min Ioan D Marinescu /Handbook of Advanced Ceramics Machining 3837_C0 02 Final Proof page 32 2.10 .20 06 10:33am Handbook of Advanced Ceramics Machining 32. .. Grinding of Fine Ceramics with Coarse-Grain-Size Diamond Wheels H Yasui CONTENTS 2. 1 Introduction 29 2. 2 Ductile-Mode Grinding with #140 Mesh Wheel 30 2. 2.1 Experimental Procedure 30 2. 2 .2 Influence of the Table Speed 32 2 .2. 3 Influence of the Wheel Speed 39 2. 2.4 Influence of the Workpiece Material 43 2. 3 Ultra-smoothness Grinding 46 2. 3.1 Ultra-smoothness... #140-mesh wheel 2. 2.3 Influence of the Wheel Speed The HPSC surfaces ground at four kinds of table speeds of vw ¼ 0.05 mm=sec, 0.5 mm=sec, 5 mm=sec, and 50 mm=sec for the wheel speed of Vg ¼ 20 m=sec and 85 m=sec are compared photographically in Figure 2. 12 It is clear from Ioan D Marinescu /Handbook of Advanced Ceramics Machining 3837_C0 02 Final Proof page 40 Handbook of Advanced Ceramics Machining 40... one of the most effective methods used for high smoothness machining of fine ceramics It is difficult, however, to achieve crack-free high smoothness surfaces by ductile-mode grinding because of their mechanical properties of high brittleness [1] Therefore, it is necessary 29 Ioan D Marinescu /Handbook of Advanced Ceramics Machining 3837_C0 02 Final Proof page 30 2. 10 .20 06 10:33am Handbook of Advanced Ceramics. .. Ioan D Marinescu /Handbook of Advanced Ceramics Machining 3837_C001 Final Proof page 26 6.10 .20 06 2: 05am Handbook of Advanced Ceramics Machining 20 mm B Y Air balance 180 . 4.44 25 50 544 190. 82 BK7 5. 62 2 520 760 174.95 F6 4.14 3740 524 125 .94 GOE91 6.71 25 50 880 178 .27 SK7 5. 32 3510 725 124 .64 Glass II; TRC 5 8.48 29 80 727 23 3.36 AL 2 O 3 15 .2 3710 1050 23 2.63 ZrO 2 12. 8. 1.18 Whole view of the MUPMT. Ioan D. Marinescu /Handbook of Advanced Ceramics Machining 3837_C001 Final Proof page 22 6.10 .20 06 2: 05am 22 Handbook of Advanced Ceramics Machining (upto 20 00 ppm), big. Marinescu /Handbook of Advanced Ceramics Machining 3837_C001 Final Proof page 28 6.10 .20 06 2: 05am 28 Handbook of Advanced Ceramics Machining 2 Ductile-Mode Ultra-Smoothness Grinding of Fine Ceramics