Development of the Cylindrical

Jun Qu Wire Electrical Discharge Research Assistant Machining Process, Part 2: Albert J. Shih Associate Professor Surface Integrity and Roundness Department of Mechanical and Aerospace Engineering, This study investigates the surface integrity and roundness of parts created by the cylin- North Carolina State University, drical wire EDM process. A mathematical model for the arithmetic average surface Raleigh, NC 27695 roughness on the ideal surface of a cylindrical wire EDM workpiece is first derived. Effects of wire feed rate and part rotational speed on the surface finish and roundness for brass and carbide work-materials at high material removal rates are investigated. The Ronald O. Scattergood pulse on-time and wire feed rate are varied to explore the best possible surface finish and Professor, roundness achievable by the cylindrical wire EDM process. This study has demonstrated Department of Materials Science and that, for carbide parts, an arithmetic average surface roughness and roundness as low as Engineering, 0.68 and 1.7 ␮m, respectively, can be achieved. Surfaces of the cylindrical EDM parts North Carolina State University, were examined using Scanning Electron Microscopy (SEM) to identify the macro-ridges Raleigh, NC 27695 and craters on the surface. Cross-sections of the EDM parts are examined using the SEM to quantify the sub-surface recast layers and heat-affected zones under various process parameters. This study has demonstrated that the cylindrical wire EDM process param- eters can be adjusted to achieve either high material removal rate or good surface integ- rity and roundness. [DOI: 10.1115/1.1475989]

1 Introduction Scanning Electron Microscopy ͑SEM͒ has been a common tool to examine EDM surfaces ͓4,7͔. The EDM surface consists of The wire Electrical Discharge Machining ͑EDM͒ process re- small craters created by electrical sparks ͓1͔. To improve the EDM moves the work-material by a series of electrical sparks between surface integrity, the size of craters needs to be small. This study the workpiece and wire electrode. These sparks generate craters uses the SEM to examine and estimate the sizes of craters. Sub- on the surface and the recast layer and heat-affected zone on the surface depths of the recast layer and heat-affected zone are two sub-surface of the EDM workpiece. The surface integrity de- other important characteristics of the EDM surface integrity. The scribes the mechanical, metallurgical, topological, and chemical SEM is used to examine the polished cross-section of EDM sur- conditions of the surface region. EDM surfaces are complicated. A faces to quantify and compare subsurface damage for various comprehensive description of the surface integrity on EDM sur- EDM process parameters and material removal rates. faces involves the measurement of surface roughness, depth of In this paper, a mathematical model of the arithmetic surface heat-affected zone, micro-hardness, size of surface crater, residual roughness of an ideal cylindrical wire EDM surface is introduced stresses, and endurance limit, etc. ͓1͔. This study investigates the in Section 2. Results of surface roughness and roundness measure- surface integrity and roundness of cylindrical wire EDM parts and ments for two sets of experiments intended to produce for high explores possible ways to adjust process parameters to achieve material removal rate and fine surface roughness, respectively, are better surface integrity and roundness. presented in Section 3. SEM micrographs of the surfaces and Investigations have been carried out to analyze and improve the cross-sections of the sub-surfaces of cylindrical wire EDM car- surface integrity of parts created by die-sinking EDM ͓2–5͔ and bide and brass parts are illustrated and discussed in Section 4. wire EDM ͓6–9͔. In representative studies, the arithmetic average surface roughness, Ra , of the wire EDM processed workpiece ␮ ͓ ͔ ␮ was about 0.2 to 0.4 m for tool steels 6 and 1.4 to 3.9 m for 2 Surface Finish Modeling metal matrix ceramic composites ͓9͔. For the die-sinking EDM process, better surface finish has been reported. The Ra values The cross-section of an ideal surface produced by the cylindri- could be achieved as low as 0.014 ␮m on silicon components ͓5͔ cal wire EDM process consists of a series of circular arcs, as and 0.6 ␮m on titanium carbide parts ͓4͔. Researchers have dem- shown in Fig. 1. The real EDM surface is the combination of this onstrated that better surface integrity can be achieved by optimiz- ideal geometry and craters generated by sparks on the surface. The ing the EDM process parameters ͓2,4,6,8,9͔. For the cylindrical radius of the circular arc in the ideal surface, re , is equal to the wire EDM process, effects of the new process parameters, such as radius of the wire, rw , plus the gap between wire and workpiece. part rotational speed, on the surface integrity and roundness are The same cross-section geometry can be found on surfaces ma- ͓ not known. A set of preliminary experiments was conducted to chined by turning with a radius tool and by ball-end milling 10– ͔ identify key process parameters that significantly affect the mate- 16 . The peak to valley surface roughness, Rt , of the ideal surface ͓ ͔ rial removal rate and surface roughness. Two sets of experiments, with circular arcs has been studied 12,13,15,16 . However, the in which these parameters are varied, were conducted to investi- closed-form analytical expression of the commonly used arith- gate their effects on material removal rate, surface integrity, and metic average surface roughness, Ra , could not be found in lit- roundness of cylindrical wire EDM carbide and brass parts. erature. Only the approximation solution, which replaced the cir- cular arc by a section of the parabolic curve, is available ͓15,16͔. The closed-form representation of the arithmetic average surface Contributed by the Manufacturing Engineering Division for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received roughness, Ra , for an ideal surface consisting of circular arcs is May 2001; revised December 2001. Associate Editor: Y. L. Yao. derived in this study.

708 Õ Vol. 124, AUGUST 2002 Copyright © 2002 by ASME Transactions of the ASME 1 p/2 ¯yϭ ͵ ydx (4b) p Ϫp/2 Defines S(x) as follows: 1 1 x ͑ ͒ϭ ͵ ϭ Ϫ ͱ 2Ϫ 2Ϫ 2 ͩ ͪ S x ydx rex x re x re arcsin (5) 2 2 re Using S(x), ¯y can be expressed as: 2 p/2 2 p 2 p ¯yϭ ͵ ydxϭ ͫSͩ ͪ ϪS͑0͒ͬϭ Sͩ ͪ (6) p 0 p 2 p 2

Define another parameter xc as the x coordinate where y(xc) ϭ¯y. Fig. 1 Cross-section view of an ideal cylindrical wire EDM sur- ϭͱ Ϫ 2 face and the key parameters and coordinate system for math- xc 2re¯y ¯y (7) ematical modeling The analytical expression of arithmetic average roughness, Ra , can be expressed as:

2 xc p/2 ϭ ͑ Ϫ ͒ ϩ ͑ Ϫ ͒ As shown in Fig. 1, after defining an XY coordinate system, Ra ͫ ͵ ¯y y dx ͵ y ¯y dxͬ p 0 x one of the circular arcs on the surface can be expressed as: c 2ϩ͑ Ϫ ͒2ϭ 2 2 p p x y re re (1) ϭ ͫSͩ ͪ Ϫ2 S͑x ͒Ϫͩ Ϫ2x ͪ ¯yͬ (8) p 2 • c 2 c • where 3 Experiments on Surface Finish and Roundness p p Ϫ рxр (1a) Cylindrical wire EDM experiments were conducted to investi- 2 2 gate the surface finish and roundness generated under different ␯ cos ␣ process parameters and to verify the surface finish model. The ϭ f p ␻ (1b) same work-materials, brass and carbide, as in the previous paper ͓17͔ are used in this study. The pitch, p, as shown in Fig. 1, is a function of wire feed rate, Two sets of experiments, designated as Experiments I and II, ␯ ␻ ␣ f , workpiece rotation speed, , and wire traversing direction, were designed. In Experiment I, the Material Removal Rate ͓ ͔ 17 . The peak-to-valley surface roughness, Rt , of the ideal sur- ͑MRR͒ was high. The wire feed rate and part rotational speed face shown in Fig. 1 has been derived ͓15͔. were varied to achieve different levels of surface roughness to verify the proposed surface finish model. In Experiment II, the p2 R ϭr Ϫͱr2Ϫ (2) goal was to adjust EDM process parameters to achieve the best t e e 4 possible surface finish and roundness. After conducting prelimi- nary cylindrical wire EDM experiments, two process parameters, The arithmetic average surface finish, Ra , of the ideal surface is defined by the following formula: the pulse on-time and wire feed rate, were identified to have sig- nificant effects on surface finish. Also, compared to Experiment I, 1 p/2 the material removal rates were reduced significantly in Experi- ϭ ͵ ͉ Ϫ ͉ Ra y ¯y dx (3) ment II to achieve good surface finish and roundness. Key process p Ϫ p/2 parameters for Experiments I and II are listed in Table 1. The where ¯y is the least squares mean line of the ideal profile, which other process parameters remain the same as in the previous paper is the reference mean line of surface roughness as defined in ͓17͔. Table 2 summarizes the MRR under different process param- ASME B46.1-1995 ͓18͔. Based on the definition of least squares eters in Experiments I and II. mean line, In Experiment I, four part rotation speeds and three wire feed p/2 rates were tested for cylindrical wire EDM of brass and carbide. yϪ¯y ͒2dx In total, 24 experiments were conducted. The test configuration is͑ ͵ ץ Ϫp/2 illustrated in Fig. 2 with ␣ϭ0, Rϭ3.175 mm, and rϭ2.54 mm. ϭ0(4a) As shown in Table 2, the maximum MRR was 13.9 and 52.1 y¯ץ mm3/min for carbide and brass, respectively. These are about 80% Thus, of the maximum MRR observed in the previous paper ͓17͔.

Table 1 Machine setup for the Experiments I and II

Journal of Manufacturing Science and Engineering AUGUST 2002, Vol. 124 Õ 709 Table 2 Material removal rate of Experiments I and II

In Experiment II, four pulse on-times and three wire feed rates the trend suggested in the ideal surface roughness equation. The were tested for brass and carbide. Similar to Experiment I, 24 tests possible cause is the vibration at higher spindle speed affects the were conducted. The cutting configuration shown in Fig. 2 with surface roughness. ␣ϭ0, Rϭ2.59 mm, and rϭ2.54 mm was used. A thin, 50 ␮m • Combined Ideal and 2D Surface Roughness: A set of 2D wire layer of work-material was removed. This so called ‘‘skim cut’’ experiments was conducted on the same work-materials and under helps improve the surface finish. A small pitch of pϭ0.01 mm the same EDM process parameters as in Experiment I, except that was set for all tests in Experiment II to minimize surface rough- the workpiece was stationary. Table 3 shows the measured Ra and ness. To maintain the same pitch, the part rotational speeds, as Rz values of the 2D wire EDM carbide and brass parts under the ␯ shown in Table 2, were varied for different wire feed rates. same wire feed rate, f , as used in the cylindrical wire EDM experiments. The three dashed curves in Fig. 3 show results of the 3.1 Results of Experiment I. The surface finish and round- addition of the ideal and 2D surface roughness at three wire feed ness of the 24 parts machined in Experiment I are shown in Fig. 3. rates. These three curves have fairly good agreement with the The surface finish was measured using a Taylor Hobson Talysurf three measured surface roughness curves. Although simply adding stylus profiler. The cutoff was set at 0.8 mm. Five cutoff lengths two surface roughness parameters to get the combined surface or 4 mm in total measuring length was used. The surface rough- roughness lacks scientific justification, results in Fig. 3 suggest a ness parameter R ͑ISO standard͒, instead of R , was used to z t simple method to predict the roughness of cylindrical wire EDM represent the peak-to-valley of the measured trace. R is defined z surface. The SEM micrographs shown in following section reveal as the distance between the average of the top five peaks and the that cylindrical wire EDM surfaces do consist of both the ideal average of the bottom five valleys on the filtered waviness trace. arc-shape in macro-scale and the surface craters and recast layer Since the 4 mm measuring range covers a large number ͑over 30͒ in the micro-scale. of peaks and valleys across an ideal surface shown in Fig. 1, Rz is a better indication than Rt for the true peak-to-valley value on the The roundness of the machined parts was measured using the cylindrical wire EDM surface to avoid the misleading spikes of Mahr Formtester MMQ40 form measurement machine. Round- peak or valley in the measurement trace. ness results, ranging from 8 to 20 ␮m under high MRR conditions, Three sets of data are presented in the surface roughness graphs are shown in Fig. 3. The results indicate that, in general, better ␯ in Fig. 3. roundness can be achieved at lower wire feed rate f . This is possibly due to less wire vibration. The effect of part rotational • Ideal Surface Roughness: For an ideal surface, the peak-to- ͑ ͒ speed on roundness is not significant. valley surface roughness, Rt , is equal to Rz . Equations 3 and ͑ ͒ 9 are used to calculate Rz and Ra , respectively, of an ideal 3.2 Results of Experiment II. The goal of Experiment II surface consisting of circular arcs. As shown in Fig. 3, higher part was to achieve the best possible surface finish and roundness by rotational speed and slower wire feed rate generate smaller pitch adjusting two critical process parameters, the wire feed rate and and lower Ra and Rz . pulse on-time. Figure 4 shows the surface finish and roundness • Measured Surface Roughness: Results of the Ra and Rz on results for Experiment II. Much better surface finish and round- the 24 cylindrical wire EDM carbide and brass parts are shown in ness are observed in Experiment II. The shorter pulse on-time and Fig. 3. The measured values of Ra and Rz are much higher than lower feed rate, in general, created better surface finish and round- the ideal surface roughness due to the additional craters on the ness. At the shortest pulse on-time, 2 ␮s, significant decreases in EDM surface. Slightly higher values of measured Ra and Rz were the surface roughness and roundness can be observed. Shorter seen on parts machined at high rotational speeds. This contradicts pulse on-time generates smaller sparks, which, in turn, creates smaller craters and better surface finish. This can be verified in the SEM micrographs of EDM surfaces. The best Ra and roundness generated on carbide in this study are 0.68 and 1.7 ␮m, respec- tively. These values are comparable to that of rough grinding, which makes the cylindrical wire EDM process suitable for both high material removal rate and precision machining of the difficult-to-machine materials. However, this value is not as low ␮ as the 0.014 m Ra surface roughness reported in EDM of silicon ͓5͔. Better EDM machines could generate even lower surface roughness. The 1.7 ␮m roundness at 2 ␮s pulse on-time are much smaller than the 6 to 9 ␮m spindle error presented in Fig. 5 of the previ- ous paper ͓17͔. The frequency spectrum of the spindle error pre- ͓ ͔ sented in Fig. 6 of 17 is used to explain this observation. The f o , the major peak of the spindle error at the frequency that is equal to the part rotational speed, is about 2.2 ␮m in amplitude or 4.4 ␮m Fig. 2 The configuration of surface finish experiment in spindle error. This large off center error does not affect the

710 Õ Vol. 124, AUGUST 2002 Transactions of the ASME Fig. 4 The surface finish and roundness of cylindrical wire Fig. 3 The surface finish and roundness of cylindrical wire EDM parts in Experiment II with improvements on surface fin- EDM parts in Experiment I with high material removal rate ish and roundness roundness because the distance from the rotational axis to the wire 4.1 Macro-Ridges. Although regular EDM surfaces are iso- remains constant. The second peak of the spindle error, f 1 , at the tropic and have no specific texture or pattern ͓1͔, cylindrical wire frequency that is equal to five times the part rotational speed, is EDM surfaces may have macro-ridges, or circular arcs, in the about 0.8 ␮m in amplitude or 1.6 ␮m in spindle error. This is cross-section. Figure 5 shows the surfaces of three cylindrical identified as the main cause of the 1.7 ␮m roundness error on wire EDM brass parts in Experiment I with 30 rpm rotational cylindrical wire EDM parts. The third and fourth peaks of the speed and wire feed rates of 4.57, 3.81, and 2.54 mm/min. The spindle error, f 2 and f 3 , remain at 60 and 120 Hz, respectively, corresponding pitches are 152, 127, and 84.7 ␮m. Similar macro- independent of the spindle rotational speed. Since the standard ridges exist on carbide parts. Figure 5 also shows the ideal sur- 1–50 undulation per revolution filter was used in roundness mea- faces that consist of circular arcs with the same p and re . These surement, the spindle error at these two high frequencies does not SEM micrographs also verify the surface finish model described show up in the roundness results. In summary, only the f 1 peak of in Section 2. the spindle error spectrum affects the roundness results in low MRR cylindrical wire EDM conditions. 4.2 Craters. The rough surfaces in Experiment I and fine surfaces in Experiment II are observed using the SEM machine to 4 SEM Micrographs of EDM Surface and Sub- compare the surface texture and crater size. As illustrated in the surface finish results in Fig. 4, the short, 2 ␮s, pulse on-time Surface generates fine surface finish. Under shorter pulse on-time, electri- SEM is used to examine the surface and sub-surface of cylin- cal sparks generate smaller craters on the surface. For carbide drical wire EDM carbide and brass parts in Experiments I and II. parts, as shown in Fig. 6, the rough estimate of the crater size is The cylindrical samples were sliced in the radial direction. Sur- about 50, 30, and 20 ␮m under 14, 5, and 2 ␮s pulse on-time, faces of sliced cross-sections were polished to observe the sub- respectively. As shown in Fig. 7, slightly bigger craters, estimated surface damage. The macro-ridges and craters on the surface and as 60, 40, and 25 ␮m, can be seen on the brass parts machined the recast layers and heat-affected zones in the sub-surface of the under the same pulse on-time. On carbide parts, about 1 to 2 ␮m cylindrical wire EDM parts are presented in the following three size tungsten carbide grain can be seen on the SEM micrographs sections. in Fig. 6.

Table 3 Surface finish of 2D wire EDM parts in Experiment I

Journal of Manufacturing Science and Engineering AUGUST 2002, Vol. 124 Õ 711 Fig. 5 SEM micrographs of macro-ridges and ideal arcs on surfaces of brass parts in Experi- Ä ment I „re 0.183 mm…

4.3 Sub-Surface Recast Layers and Heat-Affected Zones and recast layers of steel and tungsten carbide using the die- The recast layer is defined as the material melted by electrical sinking EDM and have summarized and explained the possible sparks and resolidified on the surface without being ejected nor causes for EDM surface defects. removed by flushing ͓2͔. Below the recast layer is the heat- SEM micrographs of the cross-section of carbide and brass affected zone. For the carbide material, the cobalt matrix melts parts machined under both high and low MRRs ͑Experiments I and resolidifies in the heat-affected zone. The molten cobalt fills and II͒ are shown in Figs. 6 and 7. On carbide parts, the ␮m size the pores in the tungsten carbide. This is observed in the SEM carbide grains can be identified. The recast layer, bubbles in the micrographs of the carbide cross-section and is used to identify recast layer, and heat affected zone of three carbide samples are the depth of heat-affected zone. Rajurkar and Pandit ͓19͔ have identified in Fig. 6. Under high MRR at 14 ␮s pulse on-time, the studied the recast layer and heat-affected zones of EDM surfaces recast layer, about 3 ␮m thick, can be clearly recognized on the and developed a thermal model to predict the thicknesses of dam- surface. Thinner recast layers, less than 2 ␮m, exist on samples aged layers. For the die-sinking EDM process, the depth of the machined using shorter pulse on-time. Bubbles can be identified damaged layer was reported to be from 30 to 100 ␮m for an AISI in the recast layers of all three carbide samples. Anon ͓2͔ has 4130 steel workpiece machined with pulse on-time of 100 to 300 proposed that these micro-bubbles were generated by thermal ␮s ͓4͔. Anon ͓2͔ has studied the sub-surface heat-affected zones stresses and tension cracking in the recast layer. As shown in Fig.

Fig. 6 SEM micrographs of surfaces and cross-sections of carbide parts

712 Õ Vol. 124, AUGUST 2002 Transactions of the ASME Fig. 7 SEM micrographs of surfaces and cross-sections of brass samples

6, the depth of the heat-affected zone is estimated to be about 4, 3, Concepts presented in this study, including the quantification of and 2 ␮m on the three carbide samples with 14, 5, and 2 ␮s pulse maximum material removal rate, key process parameters to on-time, respectively. achieve fine surface finish and roundness, and thickness of recast As shown in Fig. 7, very thin recast layers, about 1 ␮m, can be layers and heat-affected zones, etc., can be applied for cylindrical observed on the cross-section of three brass samples. No heat- wire EDM using other wire EDM machines on different types of affected zone can be recognized on brass samples, possibly due to work-materials. the good thermal conductivity of brass. The heat-affected zone may exist but cannot be identified in brass samples. For carbide, the contrast of porosity filled by the molten cobalt makes the 6 Acknowledgments identification of the heat-affected zone easier. For brass material, The authors gratefully acknowledge the support by National such phenomenon does not exist. This has made the heat-affect Science Foundation Grant #9983582 ͑Dr. K. P. Rajurkar, Program zone difficult to be identified. Director͒. Portion of this research was sponsored by the User program in the High Temperature Material Lab, Oak Ridge Na- 5 Concluding Remarks tional Lab and the Heavy Vehicle Propulsion Systems Materials The surface integrity and roundness of cylindrical wire EDM Program, Office of Transportation Technologies, US Department carbide and brass parts were investigated. A model with the of Energy. closed-form solution of the arithmetic average surface roughness of the ideal surface generated by the cylindrical wire EDM pro- References cess was derived. Two sets of experiments, Experiments I and II, ͓ ͔ were conducted to identify the effects of the part rotational speed, 1 Rajurkar, K. P., and Pandit, S. M., 1988, ‘‘Recent Progress in Electrical Dis- charge Machine Technology and Research,’’ Proceedings of Manufacturing wire feed rate, and pulse on-time on the surface finish and round- International ’88, Atlanta, GA, 1, pp. 219–226. ness. Experiment I verified the surface finish model and found that ͓2͔ Anon, 1987, ‘‘Controlling EDM Surface Integrity,’’ American Machinist & simply adding the roughnesses of 2D wire EDM surfaces and Automated Manufacturing, 131 ͑11͒, pp. 80–83. ͓ ͔ ideal surfaces provided a good estimate of the surface roughness 3 Rajurkar, K. P., and Royo, G. F., 1988, ‘‘Improvement in EDM performance by R. F. Control and Orbital Motion,’’ ASME Symposium Volume on Research and of cylindrical wire EDM parts. Experiment II demonstrated that Technological Developments in Non-traditional Machining, PED-Vol. 34, pp. good surface finish and roundness could be achieved in the cylin- 51–62. drical wire EDM process. The macro-ridges, surface craters, re- ͓4͔ Rajurkar, K. P., and Royo, G. F., 1989, ‘‘Effect of R. F. Control and Orbital cast layers, and heat-affected zones were observed, and their sizes Motion on Surface Integrity of EDM Components,’’ J. Mech. Work. Technol., 20, pp. 341–352. were estimated using the SEM. ͓5͔ Reynaerts, D., Meeusen, W., and Brussel, H. V., 1998, ‘‘Machining of Three- In the study, all EDM experiments were conducted on a Brother Dimensional Microstructures in Silicon by Electro-discharge Machining,’’ HS-5100 wire EDM machine. Experimental results, such as ma- Sensors and Actuators, A67, pp. 159–165. ͓ ͔ terial removal rate, surface roughness, and roundness, presented in 6 Liao, Y. S., and Woo, J. C., 1997, ‘‘The Effects of Machining Settings on the Behavior of Pulse Trains in the WEDM Process,’’ J. Mater. Process. Technol., this study may not be directly transferable to other wire EDM 71, pp. 433–439. machines using different EDM power supply, wire, and tooling. ͓7͔ Williams, R. E., and Rajurkar, K. P., 1991, ‘‘Study of Wire Electrical Dis-

Journal of Manufacturing Science and Engineering AUGUST 2002, Vol. 124 Õ 713 charge Machined Surface Characteristics,’’ J. Mater. Process. Technol. 28, pp. ͓14͔ El-wardany, T., Elbestawi, M. A., Attia, M. H., and Mohamed, E., 1992, ‘‘Sur- 127–138. face Finish in Turning of Hardened Steel,’’ Engineered Surfaces, American ͓8͔ Ramulu, M., Jenkins, M. G., and Daigneanult, J. A., 1997, ‘‘Spark-Erosion Society of Mechanical Engineers, Production Engineering Division, 62, pp. Process Effects on the Properties and Performance of a Tib2 Particulate- 141–159. ͑ ͒ Reinforced/Sic Matrix Ceramic Composite,’’ Ceram. Eng. Sci. Proc., 18 3 , ͓15͔ Whitehouse, D. J., 1994, Handbook of Surface Metrology, Institute of Physics, pp. 227–238. Bristol, Philadephia. ͓ ͔ 9 Gatto, A., and Iuliano, L., 1997, ‘‘Cutting Mechanisms and Surface Features of ͓16͔ Cheung, C. F., and Lee, W. B., 2001, ‘‘Characterization of Nanosurface Gen- WED Machined Metal Matrix Composites,’’ J. Mater. Process. Technol., 65, eration in Single-Point Diamond Turning,’’ Int. J. Mach. Tools Manuf., 41͑6͒, pp. 209–214. pp. 851–875. ͓10͔ Shaw, M. C., and Crowell, J. A., 1965, ‘‘Finishing Machining,’’ CIRP Ann., ͓17͔ Qu, J., Shih, A. J., and Scattergood, R., 2002, ‘‘Development of the Cylindrical 13, pp. 5–22. ͓11͔ Nassirpour, F., and Wu, S. M., 1977, ‘‘Statistical Evaluation of Surface Finish Wire Electrical Discharge Machining Process, Part I: Concept, Design, and and its Relationship to Cutting Parameters in Turning,’’ Int. J. Mach. Tool Des. Material Removal Rate,’’ ASME J. Manuf. Sci. Eng., 124, pp. 702–707. ͓ ͔ Res., 17, pp. 197–208. 18 ASME B46.1-1995, Surface Texture-Surface Roughness, Waviness, and Lay, ͓12͔ Vajpayee, S., 1981, ‘‘Analytical Study of Surface Roughness in Turning,’’ 1995. Wear, 70, pp. 165–175. ͓19͔ Rajurkar, K. P., and Pandit, S. M., 1984, ‘‘Quantitative Expressions for Some ͓13͔ Shiraishi, M., and Sato, S., 1990, ‘‘Dimensional and Surface Roughness Con- Aspects of Surface Integrity of Electro-Discharge Machined Components,’’ trols in a Turning Operation,’’ ASME J. Eng. Ind., 112͑1͒, pp. 78–83. ASME J. Eng. Ind., 106͑2͒, pp. 171–177.

714 Õ Vol. 124, AUGUST 2002 Transactions of the ASME