椭圆轨迹振动切削加工

Journal of Materials Processing Technology 214(2014)2644–2659Contents lists available at ScienceDirectJournal of Materials ProcessingTechnologyj o u r n a l h o m e p a g e :w w w.e l s e v i e r.c o m /l o c a t e /j m a t p r o t ecFundamental investigation of ultra-precision ductile machining of tungsten carbide by applying elliptical vibration cutting with single crystal diamondJianguo Zhang,Norikazu Suzuki ∗,Yilong Wang,Eiji ShamotoDepartment of Mechanical Science and Engineering,Nagoya University,Furo-cho,Chikusa-ku,Nagoya 464-8603,Japana r t i c l ei n f oArticle history:Received 19November 2013Received in revised form 30April 2014Accepted 20May 2014Available online 9June 2014Keywords:Elliptical vibration cutting Ductile machining Tungsten carbideMaterial composition Tool wear Sculpturinga b s t r a c tThis paper presents essential investigations on the feasibility of ductile mode machining of sintered tungsten carbide assisted by ultrasonic elliptical vibration cutting technology.It lays out the foundations toward efficient application of elliptical vibration cutting technology on tungsten carbide.Tungsten car-bide is a crucial material for glass molding in the optics manufacturing industry.Its grain size and binder material have significant influence not only on the mechanical and chemical properties but also on the machining performance of tungsten carbide.In order to investigate the influence of material compo-sition on tungsten carbide machining,a series of grooving and planing experiments were conducted utilizing single crystal diamond tools.The experimental results indicated that as compared to ordinary cutting where finished surface deteriorates seriously,ductile mode machining can be attained success-fully by applying the elliptical vibration cutting technique.It was also clarified that the binder material,the grain size,cutting/vibration conditions as well as crystal orientation of the diamond tool have sig-nificant influence on the tool life and the machined surface quality.Based on these fundamental results,feasibility of micro/nano-scale fabrication on tungsten carbide is investigated.By applying amplitude con-trol sculpturing method,where depth of cut is arbitrary changed by controlling the vibration amplitude while machining,ultra-precision textured grooves and a dimple pattern were successfully sculptured on tungsten carbide in ductile mode.©2014Elsevier B.V.All rights reserved.1.IntroductionWith the rapidly developing optoelectronics industry,demand for advanced manufacturing technology for sophisticated micro/nano structures on optical systems is increasing drastically.For example,glass lenses with small radius and large curvature have been used in various devices to miniaturize their structures and/or to attain large storage capacity.Some micro/nano optical gratings have been used in optical communication equipments,encoders,and digital cameras.In order to realize mass production of those glass devices,tungsten carbide is heavily used in molding because of its unique mechanical,thermal and chemical properties.Ultra-precision cutting has been generally applied to fabricate sophisticated micro/nano structures,and it has been widely used∗Corresponding author.Tel.:+81527894491;fax:+81527893107.E-mail addresses:nuzhjg@upr.mech.nagoya-u.ac.jp (J.Zhang),nsuzuki@mech.nagoya-u.ac.jp (N.Suzuki),wang@upr.mech.nagoya-u.ac.jp (Y.Wang),shamoto@mech.nagoya-u.ac.jp (E.Shamoto).especially for a variety of plastic molding applications.However,application of ultra-precision cutting to brittle materials is limited.Since tungsten carbide is a typically hard and brittle material,its ductile machining is extremely difficult by the ordinary ultra-precision cutting technology due to generations of brittle fracture in the workpiece and excessive tool damage.Bulla et al.(2012)reported the feasibility of ultra-precision diamond turning in ductile mode on binderless,nano crystalline tungsten carbide.However,tool wear is not negligible and thus the cutting area is extremely restricted.In contrast to cutting,ultra-precision grind-ing is applicable to ductile mode machining of tungsten carbide,as reported by Yin et al.(2004).Suzuki et al.(2008)has applied the grinding technology successfully in particular applications.Suzuki et al.(2010)additionally reported that following lapping and/or polishing are also effective to achieve higher quality surface finish.However it is extremely difficult to fabricate sophisticated micro/nano-scale structures especially with sharp edges by these methods.In addition,the conventional ultra-precision grinding operation is generally time-consuming as compared to cutting operation due to its complexity.These facts impose significant/10.1016/j.jmatprotec.2014.05.0240924-0136/©2014Elsevier B.V.All rights reserved.J.Zhang et al./Journal of Materials Processing Technology214(2014)2644–26592645restrictions in practical use of tungsten carbide and define the bottleneck of ultra-precision machining of tungsten carbide.In the last few decades,ultrasonic vibration cutting technology has been successfully applied to difficult-to-cut materials machin-ing,as reviewed by Brehl and Dow(2008).In particular,elliptical vibration cutting technology,which was proposed by Shamoto and Moriwaki(1994),has been the foreseen alternative to attain ultra-precision machining of hard brittle materials.Moriwaki and Shamoto(1995)developed ultrasonic elliptical vibration cutting devices,and Shamoto and Moriwaki(1999)verified the feasibil-ity of steel material machining by use of single crystal diamond (SCD)tools.Brehl and Dow(2007)challenged to create complex micro-structures by utilizing the elliptical vibration cutting tech-nology.Zhang et al.(2011)conducted further investigations on machining performance of hardened steel using polycrystalline diamond(PCD)tools.On the other hand,Suzuki et al.(2004)have applied the elliptical vibration cutting technology to machining of tungsten carbide with Cobalt binder,and its ductile machin-ing has been attained successfully by applying SCD tools.Suzuki et al.(2006)investigated the fundamental mechanism of ductile machining of tungsten carbide by applying elliptical vibration cut-ting as well.However,the tool damage has been significant unlike hardened steel machining,and thus the cutting area was restricted to be extremely small.Nath et al.(2009a)also carried out several experimental investigations on elliptical vibration cutting of sin-tered tungsten carbide,where machinability of tungsten carbide by using PCD tools was investigated.Following this,the influence of the cutting parameters and tool radius on machined surface qual-ity was further investigated by Nath et al.(2009b).Consequently, Nath et al.(2009c)concluded that restriction in the cutting area is improved successfully by using PCD tools and a surface with roughness of less than30nm Ra was attained at the beginning of cutting.However,surface roughness deteriorates significantly, which may not be acceptable in manufacturing of optical elements. This fact indicates that further research contribution to extend the tool life of SCD is necessary to realize practical machining of tungsten carbide by applying the elliptical vibration cutting tech-nology.On the other hand,tungsten carbide material has been studied and developed with better properties by modifying the material composition and the grain size.Material property affects machin-ing characteristics of tungsten carbide significantly at the same time.For instance,material strength depends on the grain size and binder material,which may have chemical affinity to diamond.The material strength and the chemical affinity have major influence on tool wear.Jia and Fischer(1996)conducted a series of scratch tests of tungsten carbide with cobalt binder by means of a modified Vickers hardness tester,where significant advantage of small-sized grain in abrasion resistance was clarified.Paul et al.(1996)reported significance of chemical aspect of tool wear in cutting with SCD tools.Saito et al.(2006)studied the influences of cobalt content and grain size on the wear resistance of tungsten carbide against carbon steel in their abrasion experiments,where the wear rate increased with cobalt content and grain size of tungsten carbide.Krakhmalev et al.(2007)also studied abrasion wear process of tungsten car-bide against silicon carbide abrasive.Ren et al.(2009)investigated influence of grain size and cobalt binder on grinding process.Zhang et al.(2012)also addressed experimental investigation to evaluate the influence of material composition on the cutting performance with SCD tools.Nevertheless,few researchers have investigated the influence of material composition on ultra-precision machining of sintered tungsten carbide so far.Further study on tungsten carbide machining considering material technology may lead to significant machining performance increase.In order to investigate the possibility to extend tool life in the elliptical vibration cutting of tungsten carbide,comprehensive study on machinability of tungsten carbide is carried out in this paper.A series of fundamental cutting tests are conducted and the influence of material properties,cutting and vibration condi-tions and crystal orientation of single crystal diamond tools are investigated.Through analysis of experimental results,the influ-ence of the binder material composition and the grain size of tungsten carbide on the machining performance of the ellipti-cal vibration cutting with SCD tools are studied.Based on these fundamentalfindings,feasibility of ultra-precision machining of tungsten carbide with micro/nano-scale structures,i.e.,textured grooves and a dimple pattern,are explored.Henceforth,the paper is organized as follows.The elliptical vibration cutting process is explained in Section2,followed by experimental conditions in Section3,and results of fundamental grooving and planing experiments in Section4.Finally,nano-sculpturing applications are presented in the following section.The paper is concluded with a summary.2.Elliptical vibration cutting processFig.1shows a schematic illustration of the elliptical vibration cutting process.The diamond tool is fed at a nominal cutting speed, and the tool tip is generally controlled to vibrate elliptically in the plane determined by the nominal cutting direction and the depth of cut direction.In the present study,the nominal cutting speed is set to be lower than the maximum vibration speed ensuring that the tool is separated from the workpiece in each vibration cycle.As shown in Fig.1,in a cycle of the elliptical vibration,the cutting starts from point A,and then the workpiece material is removed in the form of a chip.After the tangent of the tool trajectory becomes parallel to the rake face,the cutting tool separates from the chip at point B.Because of this intermittent process,reduction in the chip thickness and cutting forces can be attained.Due to this separation in each vibration cycle,the cutting tool and the work-piece can be cooled by the surrounding air and/or the cuttingfluid. This also allows suppression of adhesion between the tool and the workpiece.As a result,the thermo-chemical wear is supressed effi-ciently.Because of these characteristics,ultra-precision machining of hardened steel can be attained,as reported in Brinksmeier and Gläbe(2001).Suzuki et al.(2007)also clarified that ultra-precision machining of tungsten alloy becomes feasible due to the same reason.Kim and Loh(2007)clarified that this process is also advan-tageous to fabricate micro structures due to small cutting force and less burr formation.Fig.2illustrates the elliptical vibrator and its control system for the elliptical vibration cutting.It was designed as a two-degree-of-freedom(2-DOF)elliptical vibrator and was developed by the authors.The vibrator can be actuated by exciting PZT actuators that are sandwiched with metal cylindrical parts.Since the vibrator is designed to have the same resonant frequencies in thesecond Fig.1.Elliptical vibration cutting process.2646J.Zhang et al./Journal of Materials Processing Technology 214(2014)2644–2659Table 1Types of tungsten carbide materials used in cutting experiments.NO.Average grain size (␮m)Binder phaseHardness (GPa)Elastic modulus (GPa)BL10.3Binderless,Co(≤0.2wt%)25.48675BL20.5Binderless,Co(≤0.2wt%)23.52680BL3 1.3–1.5Binderless,Co(≤0.2wt%)19.60650BL40.3Binderless,Co(≤0.1wt%)25.98680Co10.5Co(≤10wt%)19.60560Co2 1.3–1.5Co(≤10wt%)13.72560Co30.5Co(12wt%)17.30580Ni10.5Ni(≤10wt%)16.66510resonant mode of longitudinal vibration and the fifth resonant mode of bending vibration,it can generate large longitudinal and bending vibrations simultaneously at the same ultrasonic frequency by exciting the actuators.As a result,a 2-DOF elliptical vibration can conveniently be obtained at the diamond tool tip.Vibration amplitudes can be adjusted arbitrary within 4␮m p-p by controlling the amplifier gains as shown in Fig.2.3.Experimental conditions to study on machinability of tungsten carbide3.1.Workpieces and diamond toolsThis section introduces the workpieces and diamond tools uti-lized in various cutting experiments to investigate the cutting performance of tungsten carbide.Eight kinds of workpieces with different binder materials and grain size are prepared for exper-imental investigations.The material properties including catalog values of hardness and elastic modulus are listed in Table 1.Before the machining experiments,all workpieces are ground to make flat surfaces.Note that the subsurface damage has significant influence on the machining performance of tungsten carbide.Therefore,lap-ping with fine abrasives is followed to make a flat mirror surface and to remove subsurface damage from the workpiece surfaces.The tool used in these experiments is a SCD tool with a nose radius of 1mm,a clearance angle of 10◦and a negative rake angle of −20◦.The crystal orientation of the flank face is set to be (100),while that of the rake face is set to be (100)or (110).These com-binations are denoted as R (100)F (100)and R (110)F (100)in this paper,where ‘R ’and ‘F ’represent the rake face and the flank face,respectively.Fig.2.2-DOF elliptical vibration tool.3.2.Experimental setup and cutting conditionsThis section presents the experimental setup used in grooving and planing.All experiments are performed on an ultra-precision machine tool,whose positioning resolution is 1nm.The 2-DOF elliptical vibrator,which can generate arbitrary elliptical vibration at a frequency of about 36.2kHz,was attached to the X axis table.Fig.3shows the experimental setup.In order to investigate the influence of the depth of cut on the machined surface quality,the cutting feed is controlled by the synchronized motion of the X axis table and the Z axis table.The depth of cut was linearly increased in grooving and planing,as illustrated in Fig.3.Experimental con-ditions are summarized in Table 2.4.Grooving and planing experimentsparison of elliptical vibration cutting with ordinary cuttingAt first,investigations are undertaken to compare elliptical vibration cutting performance with ordinary cutting.The binder-less workpiece of BL4is grooved by the ordinary cutting and the elliptical vibration cutting.Fig.4shows the scanning elec-tron microscope (SEM)images of the grooved surface on BL4at a depth of cut of 0.2␮m.In these experiments,the nominal cut-ting speed is set to 150mm/min.Amplitudes of elliptical vibration in the nominal cutting and depth of cut directions A c and A d are set to 4␮m p-p and 2␮m p-p to realize an elliptical vibration locus.As noted from Fig.4,the groove formed by the ordinary cutting is filled with numerous brittle defects.In contrast,a smooth sur-face can be obtained by the elliptical vibration cutting.As no brittle crack and asperity can be observed on the surface in the elliptical vibration cutting,ductile mode machining was attained success-fully.From this fact,it can be expected that the inside of tungsten carbide grains existing at the topmost layer of the remained surface was cut without fracture generation on the surface or pull-out of the grains,which are observed in the ordinary cutting.Next,Fig.5shows the cutting edges after grooving of the binder-containing workpiece of Co1.Considerable adhesion of the workpiece material can be observed on the rake face of the tool used in ordinary cutting,which may result in adhesion wear and/or considerable thermo-chemical reaction.The same phenomena was observed in the ordinary cutting of other binder-containingTable 2Experimental conditions for grooving and planing.Elliptical vibration conditionsFrequency [kHz]:36.2Amplitude in nominal cutting direction [␮m p-p ]:2–4Amplitude in depth of cut direction [␮m p-p ]:1–4Phase shift [◦]:90Cutting conditionsDepth of cut [␮m]:0–maximum 2Cutting speed [mm/min]:137.5–1100Pick feed for planing [␮m]:5Cutting fluid:oil moistening (Bluebe LB-10)J.Zhang et al./Journal of Materials Processing Technology 214(2014)2644–26592647Fig.3.Illustration and picture of experimentalsetup.Fig.4.SEM images of grooved surface (workpiece:BL4,depth of cut:0.2␮m,nominal cutting speed:150mm/min).materials.On the other hand,no adhesion was observed in the elliptical vibration cutting.This fact indicates that the ellipti-cal vibration cutting may be effective to suppress tool wear progress and to attain better surface quality in machining of binder-containing tungsten carbide as well as steel materials.Mechanism of the ductile mode machining shown in Fig.4is considered as follows.In elliptical vibration cutting,the toolcutsFig.5.Cutting edges after grooving (workpiece:Co1).the surface that is finished in the previous vibration cycle.Thus,the actual uncut chip,i.e.,instantaneous uncut chip thickness shown in Fig.1,becomes extremely thin.Note that this uncut chip thickness becomes generally smaller as compared with the nominal depth of cut.The instantaneous uncut chip thickness in each vibration cycle becomes significantly small especially when the tool cuts the finished surface around the bottom of the elliptical vibration.Because of this process,the actual depth of cut becomes smaller than the critical value for ductile machining due to the size effect in fracture toughness,resulting in significant improvement of nominal critical depth of cut for ductile machining of tungsten carbide.The process is similar to that in milling,and Arif et al.(2012)clarified similar improvement in milling process through experiments with the PCD tool.4.2.Influence of cutting parameters on surface qualityIn this section,the influence of several cutting parameters,i.e.,vibration amplitudes,depth of cut,and nominal cutting speed,on the surface quality is investigated in an empirical manner.Firstly,fundamental micro grooving experiments were carried out under several conditions.Fig.6demonstrates the surface quality of micro grooves machined on Co1where the nominal cutting speed and vibration amplitudes in the nominal cutting and depth of cut direc-tions,A c and A d ,are changed.The speed ratio,i.e.,the ratio of the maximum vibration speeds in the nominal cutting direction to the nominal cutting speed,is kept to be a constant value of 25.The grooved surfaces at the vibration amplitudes A c –A d of 4–4␮m p-p and 2–2␮m p-p are filled with micrometer-scale brittle defects,as shown in Fig.6.The defect size is several times larger than the single grain size of 0.5␮m.Thus,these defects are con-sidered to be due to the pull-out of agglomerated tungsten carbide2648J.Zhang et al./Journal of Materials Processing Technology 214(2014)2644–2659Fig.6.Influence of vibration amplitude on surface quality (workpiece:Co1,depth of cut:0.9␮m,amplitudes in nominal cutting and depth of cut directions:A c –A d ␮m p-p ,nominal cutting speed:v c mm/min).grains from the workpiece surface.On the other hand,similar large defects do not generate at vibration amplitudes of 4–2and 2–1␮m p-p .Similar experimental results were also observed in case of other binder-containing and binderless materials and hence it can be concluded that the influence of vibration amplitudes on ductile machining is not negligible.The influence of the depth of cut on the surface quality was also investigated.Fig.7demonstrates a groove surface of BL4,which was machined with a circular vibration (2␮m p-p )at a nominal cutting speed of 150mm/min.The depth of cut is gradually increased from 0␮m to 2␮m.Surface quality changes depending on the depth of cut,where brittle cracks can generate at a large depth of cut even in the elliptical vibration cutting.Transition border from ductile to brittle modes are observed at the depth of cut of about 1.5␮m.Agglomerated grains seem to be pulled out at one time from the surface,and this feature of the defects is the same as that shown in Fig.6.This kind of defect characterized by their size is definedas “multi-grain-size defect”in this paper.Note that similar surface deterioration with large defects is not observed in ordinary cut-ting.Hence,this is considered to be a specific problem in elliptical vibration cutting.These amplitude and depth of cut dependencies are considered to be related to the chip pulling-up-motion in the elliptical vibra-tion cutting.Fig.8shows schematic illustrations of the elliptical vibration cutting process.When the vibration amplitude is larger in the depth of cut direction,chip pulling-up-distance in this direction becomes longer.In addition,the chip pulling-up-distance increases up to about half the amplitude when the depth of cut is large.Sintered materials are not tough against tensile stress.Because of this nature,massive grains may be pulled out from the workpiece surface by the pulling-up-motion especially when upward motion distance in the depth of cut direction is longer than the grain size.When the ratio of amplitude in the depth of cut direction to that in nominal cutting direction is large,the slope of the cutting edge trajectory becomes steep while pulling up the chip.This steep tra-jectory is also considered to enhance the above-mentioned pull-out phenomena.Hence,the vibration amplitudes and the depth of cut need to be selected properly to avoid the “multi-grain-size defect”occurrence due to the pull-out of massive grains.The influence of the nominal cutting speed on the surface quality is also examined by conducting several grooving experiments.SEM images of the machined surfaces of BL1at a depth of cut of 0.5␮m are shown in Fig.9.It is confirmed that higher quality surfaces in the ductile mode can be attained at lower nominal cutting speed.On the contrary,poor surfaces with a number of defects were observed distinctively at higher nominal cutting speed.The defect size is less than several hundred nanometers,which is almost identical to the grain size.Experiments performed on other workpieces indicated a similar tendency.To differentiate from “multi-grain-size defect”,this kind of defect is defined as “single-grain-size defect”in the present research.This cutting-speed dependency of surface quality is considered to be associated with the cut volume in each vibra-tion cycle.It should be noted that the instantaneous uncut chip thickness is almost proportional to the nominal cutting speed.Thus,the cutting forces decrease and the strain energy at the deformed zone is reduced when the nominal cutting speed decreases.Small force and strain energy are beneficial to suppress crack propaga-tions while machining.Hence,the selection of the cutting speed condition is significantly important to suppress “single-grain-size defect”occurrence.Fig.7.Machined groove with the increasing of depth of cut (workpiece:BL4,amplitudes:2–2␮m p-p ,nominal cutting speed:150mm/min).J.Zhang et al./Journal of Materials Processing Technology 214(2014)2644–26592649Fig.8.Pull up motion with different vibrationamplitudes.Fig.9.Effect of nominal cutting speed on surface quality (workpiece:BL1,amplitudes:4–2␮m p-p ,depth of cut:0.5␮m).Fig.10.SEM micrographs of machined groove surface (depth of cut:0.9␮m,vibration amplitudes:2–1␮m p-p ,nominal cutting speed:137.5mm/min).4.3.Influence of binder material and grain size on cutting performancesGrooving experiments are also conducted on tungsten carbide with different binder content and grain sizes,such as BL1,Co1,BL2,BL3and Co2.SEM images of grooved surfaces of BL1and Co1are shown in Fig.10.As noted,brittle cracks are not observed from themachined surfaces.This also indicates that ductile mode machin-ing is realized at a large depth of cut of 0.9␮m.However,ductile machining was not realized by the same cutting conditions in BL2,BL3and Co2even when the depth of cut is smaller.This can be validated from Fig.11.Their surfaces are filled with the single-grain-size defects due to brittle fracture,which were observed in the high-cutting-speed machiningexperiment.Fig.11.Brittle fracture of machined groove surface (depth of cut:0.2␮m,vibration amplitudes:2–1␮m p-p ,nominal cutting speed:137.5mm/min).2650J.Zhang et al./Journal of Materials Processing Technology214(2014)2644–2659Comparing the grooving results of BL1,BL2and BL3,the dif-ference in surface integrity indicates that smaller grain size is advantageous to attain ductile mode machining.It is known that sintered materials consisting of smaller particles generally have better toughness due to smaller initial defect size inside the mate-rial,as reported by Fang and Eason(1995).Because of this nature,finer grain is advantageous not only to increase the toughness of the material but also to realize ductile mode paring the grooving results of Co1and BL2,it is apparent that the binder phase is also advantageous to suppress the generation of brittle fracture.The defect size is,therefore,smaller in Co2than that in BL3,where the grain sizes are the same.The same advantage in fracture suppression was confirmed in Ni1.4.4.Analysis of fundamental grooving experimentsThrough the grooving experiments,we found that single-grain-size defects can be generated much more easily as compared to multi-grain-size defects.Therefore,it is important to select appropriate process conditions focusing upon suppression of the single-grain-size defect generation.In order to evaluate the rel-ative difference in surface deterioration due to single-grain-size defects,the machined surface quality was classified into nine lev-els and a scale from0to8are provided by the authors based on optical microscope observation.0represents the best surface with minimal defects and8is associated with the worst surfacefinish. Yan et al.(2009)developed a similar method to evaluate surface integrity of silicon carbide machined by SCD tools.Unlike the SEM observation,single-grain-size defects are simply observed as asperities or hazes by means of an optical microscope due to insufficient resolution.However,it is considered to be avail-able to evaluate an extent of single-grain-size defects from the observed optical images.In the present study,machined surfaces are observed by an optical microscope.Then,optical micrographs of the machined surfaces with a size of250×250pixels were processed using the data processing software,MATLAB.One pixel size is0.18␮m×0.18␮m.As the defect area becomes darker than the smooth area without defects,the darker portion is identi-fied as the defect surface.By counting the total number of pixels identified as a defect,the scores of the machined surfaces are eval-uated.For instance,high quality surfaces of BL1and Co1shown in Fig.10are indexed as0and1where no single-grain-size defect is observed.As compared with Co1,the score of the machined surface of BL1is judged as0because of the smoother surface.Scores of the machined surfaces of BL2,BL3and Co2in Fig.11are evaluated as 5,8,and6due to the single-grain-size defect.This quantification process might be influenced by the threshold in data processing, but relative difference in the evaluation results seem to be mostly reliable.As mentioned above,surface deterioration due to single-grain-size defects may depend on the instantaneous uncut chip thickness in elliptical vibration cutting process.In particular,the maximum instantaneous uncut chip thickness while cutting thefinished surface is considered to be directly associated with surface dete-rioration.Fig.12illustrates the tool trajectory around the bottom and the theoretical maximum instantaneous uncut chipthickness Fig.12.Maximum instantaneous uncut chip thickness while cuttingfinished sur-face.Fig.13.Influence of maximum instantaneous uncut chip thickness on surface qual-ity(evaluated at a depth of cut of about1␮m).at the i-th cycle.By considering the kinematic model of ellipti-cal vibration cutting,Table3summarizes the calculated values of the maximum instantaneous uncut chip thickness in the grooving experiments.Fig.13indicates relations of surface quality score and maxi-mum instantaneous uncut chip thickness for all evaluated materials in grooving.The values of surface quality index increase with an increase of maximum instantaneous uncut chip thickness regard-less of the workpiece material.Hence,the maximum instantaneous uncut chip thickness needs to be decreased to achieve better sur-face quality.High quality surfaces in ductile mode,whose score is0or1,are obtained when the maximum instantaneous uncut chip thickness is less than or equal to4nm and the workpieces are BL1,BL4,Co1,Co3,and Ni1.In other words,ductile machin-ing cannot be attained for Co2,BL2and BL3under all evaluated conditions.These facts indicate that appropriate vibration ampli-tude and cutting speed conditions need to be selected to satisfy a small maximum instantaneous uncut chip thickness,which is less than or equal to4nm.The grain size also needs to be less than or equal to0.5␮m and binder material is helpful to attain ductile mode machining.The feature of multi-grain-size defect occurrence is almost the same as that of the single-grain-size defect occurrence.Table3Values of maximum instantaneous uncut chip thickness in grooving experiments[nm].Vibration amplitudes in nominal cutting/depth of cut directions␮m p-p4/44/24/12/22/1Nominal cutting speed [mm/min]137.5210.542 275842168 550321686231 11001246231––。