micromachines

Article Ultrasonically Assisted Single Point of Optical Mold of Tungsten Carbide

Zhanjie Li 1, Gang Jin 1,*, Fengzhou Fang 2, Hu Gong 2 and Haili Jia 1 1 Tianjin Key Laboratory of High Speed Cutting and Precision , Tianjin University of Technology and Education, Tianjin 300222, China; [email protected] (Z.L.); [email protected] (H.J.) 2 State Key Laboratory of Precision Measuring Technology & Instruments, College of Precision Instrument and Opto-Electronics Engineering, Tianjin University, Tianjin 300072, China; [email protected] (F.F.); [email protected] (H.G.) * Correspondence: [email protected]

Received: 10 January 2018; Accepted: 8 February 2018; Published: 12 February 2018

Abstract: To realize high efficiency, low/no damage and high precision machining of tungsten carbide used for lens mold, a high frequency ultrasonic vibration cutting system was developed at first. Then, tungsten carbide was precisely machined with a polycrystalline diamond (PCD) tool assisted by the self-developed high frequency ultrasonic vibration cutting system. Tool wear mechanism was investigated in ductile regime machining of tungsten carbide. The cutter back-off phenomenon in the process was analyzed. The subsequent experimental results of ultra-precision machining with a single crystal diamond tool showed that: under the condition of high frequency ultrasonic vibration cutting, nano-scale surface roughness can be obtained by the diamond tool with smaller tip radius and no defects like those of ground surface were found on the machined surface. Tool wear mechanisms of the single crystal diamond tool are mainly abrasive wear and micro-chipping. To solve the problem, a method of inclined ultrasonic vibration cutting with negative rake angle was put forward according to force analysis, which can further reduce tool wear and roughness of the machined surface. The investigation was important to high efficiency and quality ultra-precision machining of tungsten carbide.

Keywords: tungsten carbide; lens mold; single point diamond turning (SPDT); ultrasonic vibration; Ductile regime; surface quality; wear

1. Introduction Today, there is an increasing demand for aspheric lenses with the rapid development of the optical industry. The precision molding technique has become an important method for making optical components because of its high efficiency and high precision [1,2]. To undergo the process environment of high temperatures (400–800 ◦C) and large forces (1–10 kN) in the precision molding technique, the mold material should be heat-resistant and hard [3]. So far, ceramics have become the most promising material for precision molding, especially superfine tungsten carbide [4–6]. The molds for precision molding are typically ultra precision ground technique with a subsequent polishing [7–9], which is a process time-consuming process with low reproducibility. On the other hand, ultra-precision diamond turning is a mechanical manufacturing process that can achieve sub-nanometer level surface finishes (below 5 nm Ra) and sub-micrometer form accuracies (below 300 nm) on complex geometries [10]. Therefore, making optical molds with high efficiency, low/no damage and high precision can be realized by ultra-precision diamond turning [11]. The ultrasonic assisted ultra-precision diamond turning has already proved its potential for machining hard-to-cut materials such as [12], Co-Cr-Mo alloy [13], single-crystal [14] and [15,16]. These publications demonstrate that ductile mode processing of tungsten carbide is possible [17–19].

Micromachines 2018, 9, 77; doi:10.3390/mi9020077 www.mdpi.com/journal/micromachines Micromachines2018, 9, x FOR PEER REVIEW 2 of 12 Micromachines2018, 9, x FOR PEER REVIEW 2 of 12 materials such as steel [12], Co-Cr-Mo alloy [13], single-crystal silicon [14] and glass [15,16]. These materialsMicromachinespublications such2018 demonstrat as, 9 ,steel 77 [12e], that Co -ductileCr-Mo modealloy [1processing3], single -ofcrystal tungsten silicon carbide [14] isand possible glass [1 [175,1–619].]. These 2 of 11 publicationsIn this paper,demonstrat tungstene that carbide ductile willmode be processing ultra-precision of tungsten machined carbide using is possible(Single Point [17–19 Diamond]. Turning) SPDT assisted by a self-developed high frequency ultrasonic vibration cutting system. In this paper, tungsten carbide will be ultra-precisionultra-precision machined using ( (SingleSingle Point Diamond Critical depth of cut and wear mechanism will be investigated in ductile regime machining of TurningTurning)) SPDTSPDT assisted assisted by by a self-developeda self-developed high high frequency frequency ultrasonic ultrasonic vibration vibration cutting cutting system. system. Critical tungsten carbide. Some phenomena and problems in the process will be analyzed, and then Criticaldepth of depth cut and of wear cut mechanismand wear mechanism will be investigated will be ininvestigated ductile regime in machiningductile regime of tungsten machining carbide. of corresponding solutions will be put forward. This work has the extensive applicability and practical tungstenSome phenomena carbide. andSome problems phenomena in the processand problems will be analyzed, in the process and then will corresponding be analyzed, solutions and then will significance for ultra-precision machining tungsten carbide and optical molding industry. correspondingbe put forward. solutions This work will has be the put extensive forward. applicability This work has and the practical extensive significance applicability for ultra-precision and practical significancemachining tungsten for ultra- carbideprecision and machining optical molding tungsten industry. carbide and optical molding industry. 2. Experimental Preparation 22.. Experimental Experimental Preparation 2.1.Ultrasonic Vibration Cutting System 2.1. Ultrasonic Vibration Cutting System 2.1.UltrasonicAs shown Vibration in Figure Cutting 1, the System ultrasonic vibration cutting system used in this experiment consists of ultrasonicAs shown generator, in Figure power11,, thethe ultrasonic ultrasonicamplifier, vibrationhorn,vibration transducer cuttingcutting systemandsystem its usedclampingused inin thisthis device, experimentexperiment cutting consists consiststool and ofintegrated ultrasonic micro generator, height power adjustment. amplifier, amplifier, A horn,digital transducer-tracking- modeand its ultrasonic clamping generatordevice, cutting with tool working and integratedintegratedfrequency micro scope heightbetween adjustment.adjustment. 20 and 100 A A kHz digital digital-tracking-mode was-tracking selected-mode in order ultrasonic ultrasonic to ensure generator stable frequency with working and frequencyfrequencyvibrating amplitudescope scope between between in the 20 20cutting and 1 100process.00 kHz was selected in order to ensure stable frequency and vibrating amplitude in the cutting process.

Figure 1. Schematic diagram of the ultrasonic vibration cutting system used in this experiment. FigureFigure 1. SchematicSchematic diagram diagram of of the the ultrasonic ultrasonic vibration cutting system used in this experiment. 2.2. Modal Analysis of the Horn Using Finite Element Method 2.2. Modal ModalIn order Analysis Analysis to avoid of the interference Horn Using withFinite tool Element setting Method gauge, ultrasonic horn made of quenched alloy steel was designed to an upward cutting end and a fixed end with vibration isolation groove. In In order to avoid interference with tool setting gauge, ultrasonic horn made of quenched alloy order to analyze natural frequencies of the horn before experiment, a finite element analysis was steel waswas designeddesigned toto an an upward upward cutting cutting end end and and a fixed a fixed end end with with vibration vibration isolation isolation groove. groove. In order In carried out. orderto analyze to analyze natural natural frequencies frequencies of the horn of the before horn experiment, before experiment, a finite element a finite analysis element was analysis carried was out. In the finite element analysis (FEA), material attributes were set as follows: young modulus carriedIn out. the finite element analysis (FEA), material attributes were set as follows: young modulus was set to be 206 GPa, poison ratio was set to be 0.27, and mass density was set to be 7900 kg/m3. was setIn the to befinite 206 element GPa, poison analysis ratio (FEA), was set material to be 0.27, attributes and mass were density set as wasfollows: set to young be 7900 modulus kg/m3. Plane 42 was chosen as the surface element and Solid 95 was chosen as the body element for the3 wasPlane set 42 to was be 206 chosen GPa, as poison the surface ratio was element set to and be Solid0.27, and 95 was mass chosen density as was the bodyset to elementbe 7900 forkg/m the. finite element model. The boundary condition was assumed to be isothermal [20]. Mesh tool was Planefinite element42 was chosen model. as The the boundary surface element condition and was Solid assumed 95 was to chosen be isothermal as the body [20]. element Mesh tool for wasthe selected to control mesh size. Grid partition of the axial section and horn model were shown in finiteselected element to control model. mesh The size. boundary Grid partitioncondition of was the assumed axial section to be and isothermal horn model [20]. wereMesh showntool was in Figures 2 and 3, respectively. selectedFigures2 toand control3, respectively. mesh size. Grid partition of the axial section and horn model were shown in Figures 2 and 3, respectively.

FigureFigure 2.2.Axial Axial sectionsection andand gridgrid partition.partition. Figure 2. Axial section and grid partition.

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Figure 3. Horn model and grid partition. Figure 3. Horn model and grid partition. Modal analysis was set for the FEA and subspace was set for the extraction method. The extractionModal scope analysisanalysis of wasfrequencieswas set set for for the w asthe FEA 30FEA and–90 subspaceandkHz subspaceand was the set modalwas for theset order extractionfor thenumber extraction method. was Thesetmethod. extractionto be The10. Displacementextscoperaction of frequencies scope constraints of frequencies was were 30–90 imposed kHzwas and30 on– 9upper0 the kHz modal-end and of order the hornmodal number spatial order was model, setnumber to as beshown was 10. Displacementinset Figure to be 4. 10. Displacementconstraints were constraints imposed were on upper-endimposed on of upper the horn-end spatialof the horn model, spatial as shown model, in as Figure shown4. in Figure 4.

Figure 4. Imposing constraints on upper-end of the horn. Figure 4. ImposingImposing constraints constraints on upper upper-end-end of the horn. Corresponding natural frequencies of the horn between 30 kHz and 90 kHz when resonance Corresponding natural frequencies of the horn between 30 kHz and 90 kHz when resonance occurredCorresponding are shown in natural Table 1. frequencies By observing of the vibration horn between mode shapes 30 kHz of andthe horn, 90 kHz we whenknow resonancethat axial occurred are shown in Table 1. By observing vibration mode shapes of the horn, we know that axial resonanceoccurredare occurred shown at in a Table frequency1. By observingof 67.533 kHz. vibration Vibration mode mode shapes shape of the of horn, the horn we knowat frequency that axial of resonance occurred at a frequency of 67.533 kHz. Vibration mode shape of the horn at frequency of 67.533resonance kHz occurred is shown at in a frequencyFigure 5. No of 67.533axial resonance kHz. Vibration occurred mode at shapeother frequencies. of the horn at The frequency vibration of 67.533 kHz is shown in Figure 5. No axial resonance occurred at other frequencies. The vibration mode67.533 shape kHz is of shown the horn in Figure at a frequency5. No axial of resonance 38.198 kHz occurred is shown at otherin Figure frequencies. 6. The vibration mode mode shape of the horn at a frequency of 38.198 kHz is shown in Figure 6. shape of the horn at a frequency of 38.198 kHz is shown in Figure6. Table 1. Natural frequencies of the ultrasonic horn. Table 1. Natural frequencies of the ultrasonic horn. TableOrder 1. Natural frequenciesNatural Frequencies of the ultrasonic (kHz horn.) Order Natural Frequencies (kHz) 1 35.454 Order Natural Frequencies (kHz) 21 38.19835.454 32 1 35.45438.19838.198 2 38.198 43 67.55338.198 4 3 38.19867.553 5 4 67.55379.864 5 5 79.86479.864

A sandwich transducer was fabricated using PZT8 piezoelectric ceramics, and the electrode slices was fabricated using .

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Figure 5. Vibration mode shape of cylindrical horn at frequency of 67.533 kHz. Figure 5. Vibration mode shape of cylindrical horn at frequency of 67.533 kHz. Figure 5. Vibration mode shape of cylindrical horn at frequency of 67.533 kHz.

Figure 6. Vibration mode shape of cylindrical horn at frequency of 38.198 kHz. Figure 6. Vibration mode shape of cylindrical horn at frequency of 38.198 kHz. A Figuresandwich 6. Vibrationtransducer mode was fabricated shape of cylindricalusing PZT8horn piezoelectric at frequency ceramics, of 38.198 and the kHz. electrode slicesA was sandwich fabricated transducer using beryllium was fabricated copper. using PZT8 piezoelectric ceramics, and the electrode 2.3. Performanceslices was Testing fabricated of the using Ultrasonic beryllium Vibration copper. Cutting System 2.3.Performance Testing of the Ultrasonic Vibration Cutting System 2.3.Performance Testing of the Ultrasonic Vibration Cutting System The no-loadThe testno-load results test results of the of developed the developed ultrasonic ultrasonic vibration vibration cutting cutting system system showed that that the the cutting end reachedcutting resonanceThe end no -loadreached at test a frequency resonanceresults of oftheat 64.769a developed frequency kHz. ultrasof The 64.769onic experimental vibrationkHz. The cuttingexperimental result system is in good resultshowed agreementis inthat good the with the FEA result.cuttingagreement The laserend with reached interference the FEA resonance result. vibration Theat a laserfrequency measuring interference of 64.769 system vibration kHz. (SIOS, Themeasuring SP-S,experimental SP-S system 120/500, result(SIOS, isSP SIOS in-S ,good SP MeBtechnik-S GmbH, Ilmenau,agreement120/500, SIOS Germany) with MeBtechnik the FEA was result. GmbH, adopted The Ilmenau, laser to trackinterference Germany the amplitude vibration) was adopted measuring of the to cuttingtrack system theend. amplitude(SIOS, The SP-S correspondingof, SP the-S 120/500,cutting end. SIOS The MeBtechnik corresponding GmbH, amplitude Ilmenau, between Germany 1 and) was 14µm adopted was measuredto track the at theamplitude voltage ofrange the amplitude between 1 and 14µm was measured at the voltage range of 0–400 V. cuttingof 0–40 0end. V. The corresponding amplitude between 1 and 14µm was measured at the voltage range of 0–400 V. 2.4. Experimental2.4. Experimental Condition Condition and Planand Plan 2.4. Experimental Condition and Plan J05 tungstenJ05 tungsten carbide carb withide a diameterwith a diameter of 16 mm of 16 was mm used was in used this experiment.in this experiment. Material Material properties of J05 were shownpropertiesJ05 intungsten Tableof J05 2were .carb A precisionideshown with in aTable cutting diameter 2. A process precisionof 16 withmm cutting was PCD processused tool in (tipwith this radius PCDexperiment. tool 1 mm, (tip Materialradius Shenzhen 1 Yuhe Diamondpropertiesmm Tools, Shenzhen Co., of Ltd.,J05 Yuhe were Shenzhen, Diamond shown inTools China)Table Co., 2. Ltd wasA .precision, Shenzhen arranged cutting, China at firstprocess) was due arranged with to lowerPCD at firsttool surface due(tip toradius smoothnesslower 1 of mmsurface, Shenzhen smoothness Yuhe ofDiamond the specimen. Tools Co., Then, Ltd. ,a Shenzhen natural ,single China )crystal was arranged diamond at toolfirst duewas toused lower to the specimen.surfaceultra-precision Then, smoothness a cutting natural of fromthe single specimen.the operator crystal Then, diamondto the a centernatural tool of single the was workpiece usedcrystal to diamond ultra-precisionalong the tool X-axis was direction. cuttingused to from the operatorultraB tooth the -processesprecision center werecutting of the performe from workpiece thed withoperator lubrication along to the the centerofX light-axis of mineral the direction. workpiece oil (isopar Both along H). processes the X-axis direction. were performed with lubricationBoth Asprocesses shown of light werein mineralFigure performe 7, oilthed with (isoparself- developedlubrication H). highof light frequency mineral ultrasonicoil (isopar vibrationH). cutting system was amountedAs shown onin anFigure ultra 7,-precision the self- developedlathe (Nanotech high 250UPLfrequency, Moore ultrasonic Nanotechnology vibration cutting System, system LLC, wasKeene, amounted NH, USA on). an The ultra Tabletool-precision setting 2. Material andlathe cutting (Nanotech properties process 250UPL ofes tungsten were, Moore assisted carbide. Nanotechnology by a real time System, monitoring LLC, Keene,system. NH, USA). The tool setting and cutting processes were assisted by a real time monitoring system. Chemical Composition Name Hardness Grain Size (µm) Density (g/cm3) (Weight Percentage %)

WC: 90 (±0.5%) HRA:91.2–92.0 J05 0.6 14.65 Co.: 10 (±0.5%) HRC:76.4–77.2

As shown in Figure7, the self-developed high frequency ultrasonic vibration cutting system was amounted on an ultra-precision (Nanotech 250UPL, Moore Nanotechnology System, LLC, Keene, NH, USA). The tool setting and cutting processes were assisted by a real time monitoring system. Micromachines 2018, 9, 77 5 of 11

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(a) (b)

(c)

Figure 7. Schematic of the experiment system; (a) Cutting end; (b) Tool setting assisted by real time Figure 7. Schematic of the experiment system; (a) Cutting end; (b) Tool setting assisted by real time monitoring; (c) Ultrasonic generator and power amplifier. monitoring; (c) Ultrasonic generator and power amplifier. Table 2. Material properties of tungsten carbide.

2.5. Test Method Chemical Composition Name Hardness Grain Size (μm) Density (g/cm3) (Weight Percentage %) A white light interferometerWC: 90 (±0.5%) was usedHRA:91.2 to measure–92.0 the surface topography and roughness of J05 0.6 14.65 the machined workpiece. ACo.: 3D 10 digital(±0.5%) microscopeHRC:76.4– was77.2 used to observe the topography of diamond tool wear. 2.5.Test Method 3. Results andA white Analysis light interferometer was used to measure the surface topography and roughness of the machined workpiece. A 3D digital was used to observe the topography of diamond tool 3.1. Precisionwear. Machining Using PCD Tool and Results

The3. selectedResults and process Analysis parameters were as follows: the spindle rotation speed was set to be 100 rpm, the feed rate was set to be 1 mm/min, the depth of cut was set to be 3 µm, the frequency for ultrasonic vibration3.1. cutting Precision system Machining was Using set to PCD be 65Tool kHz and andResults the vibrating amplitude adjusted by power amplifier was set to beThe 2 µselectedm. process parameters were as follows: the spindle rotation speed was set to be 100 Therpm, surface the feed roughness rate was set of to the be machined1 mm/min, the workpiece depth of cut is 173.56was set to nm be and3 µm the, the surface frequency topography, for which reachedultrasonic the vibration requirement cutting forsystem ultra-precision was set to be machining,65 kHz and the is shownvibrating in amplitude Figure8. adjusted by powerMicromachines amplifier2018, 9 ,was x FOR set PEER to be REVIEW 2 µm . 6 of 12 The surface roughness of the machined workpiece is 173.56 nm and the surface topography, which reached the requirement for ultra-precision machining, is shown in Figure 8.

Figure 8. Surface topography and roughness of the workpiece machined by (polycrystalline Figure 8.diamond)Surface PCD topography tool (Ra 173. and56 n roughnessm). of the workpiece machined by (polycrystalline diamond) PCD tool (Ra 173.56 nm). 3.2.Ultra-Precision Machining Using Natural Single Crystal Diamond Tool To obtain nano-scale surface roughness, a diamond tool with a larger tip radius of 1.5 mm was adopted according to the geometrical factor. The selected process parameters were as follows: the spindle rotation speed was set to be 50 rpm, the feed rate was set to be 0.01 mm/min, the depth of cut was set to be 3 µm, the frequency for ultrasonic vibration cutting system was set to be 65 kHz and the vibrating amplitude adjusted by power amplifier was set to be 2 µm. To ensure cutting in the ductile region, the trial cutting method was adopted to decide the cutting depth. As shown in Figure 9, a continuous and ribbon-like chip appeared at the cutting depth of 200 nm. Thus, the optimal cutting depth was determined.

Figure 9. Continuous and ribbon-like chip.

A back-off phenomenon happened when displacement distance of the diamond tool is 2 mm along X-axis. The corresponding surface topography of the machined workpiece is shown in Figure 10. Figure 10 showed that surface roughness of 4.72 nm was obtained near the edge of the workpiece when the diamond tool cut into the workpiece. Then, the roughness was changed to 9.85 nm after a longer cutting distance. Subsequently, the cutting process cannot proceed after back-off phenomenon occurred, as shown in Figure 10c,d.

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Micromachines 2018, 9, 77 6 of 11 Figure 8. Surface topography and roughness of the workpiece machined by (polycrystalline diamond) PCD tool (Ra 173.56 nm). 3.2. Ultra-Precision Machining Using Natural Single Crystal Diamond Tool To3.2.Ultra obtain-Precision nano-scale Machining surface Using roughness, Natural Single a diamondCrystal Diamond tool Tool with a larger tip radius of 1.5 mm was adoptedTo obtain according nano-scale to the surface geometrical roughness, factor. a diamond The selected tool with process a larger parameterstip radius of were1.5 mm as was follows: the spindleadopted rotation according speed to the was geometrical set to be 50factor. rpm, The the selected feed rate process was set parameters to be 0.01 were mm/min, as follows: the depththe of cut wasspindle set torotation be 3 µ m,speed the was frequency set to be for 50 ultrasonicrpm, the feed vibration rate was cutting set to be system 0.01 m wasm/min, set tothe be depth 65 kHz of and the vibratingcut was set amplitude to be 3 µm adjusted, the frequency by power for ultrasonic amplifier vibration was set tocutting be 2 µ systemm. was set to be 65 kHz Toand ensure the vibrating cutting amplitude in the ductile adjusted region, by power the trial amplifier cutting was method set to be was 2 µm adopted. to decide the cutting To ensure cutting in the ductile region, the trial cutting method was adopted to decide the depth. As shown in Figure9, a continuous and ribbon-like chip appeared at the cutting depth of cutting depth. As shown in Figure 9, a continuous and ribbon-like chip appeared at the cutting 200 nm. Thus, the optimal cutting depth was determined. depth of 200 nm. Thus, the optimal cutting depth was determined.

Figure 9. Continuous and ribbon-like chip. Figure 9. Continuous and ribbon-like chip. A back-off phenomenon happened when displacement distance of the diamond tool is 2 mm Aalong back-off X-axis. phenomenon The corresponding happened surface whentopography displacement of the machined distance workpiece of the diamondis shown in tool Figure is 2 mm along10.X -axis. The corresponding surface topography of the machined workpiece is shown in Figure 10. MicromachinesFigure 102018 show, 9, x FORed PEERthat REVIEW surface roughness of 4.72 nm was obtained near the edge7 ofof 12 the workpiece when the diamond tool cut into the workpiece. Then, the roughness was changed to 9.85 nm after a longer cutting distance. Subsequently, the cutting process cannot proceed after back-off phenomenon occurred, as shown in Figure 10c,d.

(a) (b)

(c) (d)

Figure 10. Back-off phenomenon of diamond tool and surface topography of the machined Figure 10. Back-off phenomenon of diamond tool and surface topography of the machined workpiece; (a) Surface roughness (Ra 4.72 nm) near the edge of workpiece; (b) Surface roughness workpiece;(Ra 9.85 (a) Surfacenm) before roughness back-off (Raphenomenon; 4.72 nm) ( nearc) Surface the edge roughness of workpiece; (Ra 17.3 nm) (b) Surfaceat back- roughnessoff (Ra 9.85phenomenon; nm) before ( back-offd) Two-dimensional phenomenon; graph ( cof) Surfaceback-off phenomenon. roughness (Ra 17.3 nm) at back-off phenomenon; (d) Two-dimensional graph of back-off phenomenon. The reason for the back-off phenomenon was assumed to be the hardness of tungsten carbide and the tool tip radius. The stress put on the diamond tool was so strong that the screw was loosened due to the longer contact between tool tip and workpiece. To reduce the stress, a diamond tool with a tip radius of 0.5 mm and lower spindle rotation speed were adopted. Figure 11a showed an obvious chipping on the tool edge (in the red elliptic mark). In Figure 11b, some small grooves were found in the wear land. So, wear mechanisms of the single crystal diamond tool were mainly abrasive wear and micro-chipping according to Figure 11 as well as surface topography of the machined workpiece, as shown in Figure 12. The surface roughness of the machined workpiece was Ra 2.55 nm when diamond tool cutting in a very short distance, but gradually rose to Ra 8.85 nm due to the longer cutting distance and tool wear. Surface quality was so good that no micro crack was found in the surface topography of the machined workpiece.

(a) (b)

Figure 11. Wear of diamond tool with tip radius of 0.5 mm after cutting along X-axis with a distance of 1 mm (wear land width: 3.05 µm, wear land length: 44.61 µm); (a) Wear of rake face; (b) Wear of rear face.

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(a) (b)

Micromachines 2018, 9, 77 7 of 11 (c) (d)

Figure 10. Back-off phenomenon of diamond tool and surface topography of the machined Figure 10 showed that surface roughness of 4.72 nm was obtained near the edge of the workpiece workpiece; (a) Surface roughness (Ra 4.72 nm) near the edge of workpiece; (b) Surface roughness when the diamond tool cut into the workpiece. Then, the roughness was changed to 9.85 nm after (Ra 9.85 nm) before back-off phenomenon; (c) Surface roughness (Ra 17.3 nm) at back-off a longer cutting distance. Subsequently, the cutting process cannot proceed after back-off phenomenon phenomenon; (d) Two-dimensional graph of back-off phenomenon. occurred, as shown in Figure 10c,d. TheThe reason for the back back-off-off phenomenon was was assumed to to be the hardness of tungsten carbide andand thethe tooltool tip tip radius. radius. The The stress stress put put on theon diamondthe diamond tool wastool so was strong so thatstrong the that screw the was screw loosened was looseneddue to the due longer to the contact longer between contact toolbetween tip and tool workpiece. tip and workpiece. To reduce To the reduce stress, the a diamond stress, a diamond tool with toola tip with radius a tip of 0.5radius mm of and 0.5 lower mm and spindle lower rotation spindle speed rotation were speed adopted. were Figure adopted. 11a showedFigure 11a an showed obvious anchipping obvious on chipping the tool edgeon the (in tool the rededge elliptic (in the mark). red elliptic In Figure mark). 11b, In some Figure small 11b grooves, some small were foundgroove ins werethe wear found land. in the So, wear wear land mechanisms. So, wear of mechanisms the single crystal of the diamondsingle crystal tool werediamond mainly tool abrasive were mainly wear abrasiveand micro-chipping wear and accordingmicro-chipping to Figure according 11 as well to asFigure surface 11 topographyas well as s ofurface the machined topography workpiece, of the machinedas shown workpiec in Figuree 12, a.s shown The surface in Figure roughness 12. The ofsurface the machined roughness workpiece of the machined was Ra workpiece 2.55 nm when was Radiamond 2.55 nm tool when cutting diamond in a very tool shortcutting distance, in a very but short gradually distance, rose but to Ragradually 8.85 nm rose due to to Ra the 8.8 longer5 nm duecutting to the distance longer and cutting tool distance wear. Surface and tool quality wear. was Surface so good qua thatlity was no micro so good crack that was no foundmicro incrack the wassurface found topography in the surface of the topography machined workpiece.of the machined workpiece.

(a) (b)

Figure 11. Wear of diamond tool with tip radius of 0.5 mm after cutting along X-axis with a distance Figure 11. Wear of diamond tool with tip radius of 0.5 mm after cutting along X-axis with a distance of 1 mm (wear land width: 3.05 µm, wear land length: 44.61 µm); (a) Wear of rake face; (b) Wear of of 1 mm (wear land width: 3.05 µm, wear land length: 44.61 µm); (a) Wear of rake face; (b) Wear of rear face. rear face. Micromachines2018, 9, x FOR PEER REVIEW 8 of 12

(a) (b)

Figure 12. Surface topography of the machined workpiece after cutting along X-axis with a distance Figure 12. Surface topography of the machined workpiece after cutting along X-axis with a distance of of 1 mm by a diamond tool with tip radius of 0.5 mm; (a) Ra 2.55 nm when diamond tool cutting in 1 mm by a diamond tool with tip radius of 0.5 mm; (a) Ra 2.55 nm when diamond tool cutting in a very ashort very distance; short distance; (b) Ra 8.85(b) Ra nm 8.85 when nm diamondwhen diamond tool cutting tool cutting in a distance in a distance of 1 mm. of 1 mm.

3.3. Discussion 3.3. Discussion From the above experimental results, the strong stress and friction between tool tip and From the above experimental results, the strong stress and friction between tool tip and workpiece workpiece easily gave rise to an inclined angle δ of ultrasonic horn, which changed 0° of rake angle easily gave rise to an inclined angle δ of ultrasonic horn, which changed 0◦ of rake angle to a positive to a positive rake angle, as shown in Figure 13. In the cutting direction, cutting force F1 and friction rake angle, as shown in Figure 13. In the cutting direction, cutting force F1 and friction force f 1 existed force f1 existed between flank surface of diamond tool and machined surface of workpiece at the stage of withdraw of the diamond tool from the chip. At the same time, in the feed direction, cuttingforceF2 and friction forcef2 existed between the flank surface of the diamond tool and the transitional surface of the workpiece when the diamond tool left the chip (Figure 14). Therefore, diamond tool micro-chipping happened very easily due to the impact and alternating stress between the diamond tool and the workpiece [21].

(a) (b)

Figure 13. Force analysis of ultrasonic horn; (a) Schematic diagram of force analysis; (b) Finite element analysis of the force on horn.

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(a) (b)

Figure 12. Surface topography of the machined workpiece after cutting along X-axis with a distance of 1 mm by a diamond tool with tip radius of 0.5 mm; (a) Ra 2.55 nm when diamond tool cutting in a very short distance; (b) Ra 8.85 nm when diamond tool cutting in a distance of 1 mm.

3.3. Discussion

MicromachinesFrom the2018 above, 9, 77 experimental results, the strong stress and friction between tool tip 8and of 11 workpiece easily gave rise to an inclined angle δ of ultrasonic horn, which changed 0° of rake angle to a positive rake angle, as shown in Figure 13. In the cutting direction, cutting force F1 and friction between flank surface of diamond tool and machined surface of workpiece at the stage of withdraw of force f1 existed between flank surface of diamond tool and machined surface of workpiece at the stagethe diamond of withdraw tool from of the the diamond chip. At thetool same from time, the inchip. the feedAt the direction, same time, cuttingforce in the feedF2 and direction, friction f cuttingforceforce 2 existedF2 and between friction the force flankf2 existed surface between of the diamond the flank tool surface and theof t transitionalhe diamond surfacetool and of the the transitionalworkpiecewhen surface the of diamond the workpiece tool left when the chip the (Figure diamond 14). tool Therefore, left the diamond chip (Figure tool micro-chipping14). Therefore, diamondhappened tool very micro easily-chipping due to the happened impact and very alternating easily due stress to the between impact the and diamond alternating tool and stress the betweenworkpiece the [21 diamond]. tool and the workpiece [21].

(a) (b)

Figure 13. Force analysis of ultrasonic horn; (a) Schematic diagram of force analysis; (b) Finite Figure 13. Force analysis of ultrasonic horn; (a) Schematic diagram of force analysis; (b) Finite element element analysis of the force on horn. analysis of the force on horn. Micromachines2018, 9, x FOR PEER REVIEW 9 of 12

(a) (b)

Figure 14. Schematic diagram of force analysis at the stage of diamond tool withdrawing; (a) Front Figure 14. Schematic diagram of force analysis at the stage of diamond tool withdrawing; (a) Front view; (b) Top view. view; (b) Top view.

In the inclined ultrasonic vibration cutting with negative rake angle, the diamond tool vibrated In the inclined ultrasonic vibration cutting with negative rake angle, the diamond tool vibrated along the direction, as shown in Figure 15. On one hand, not only inclined cutting can decrease the along the direction, as shown in Figure 15. On one hand, not only inclined cutting can decrease the impact force between diamond tool and workpiece, but also cutting with negative rake angle can impact force between diamond tool and workpiece, but also cutting with negative rake angle can enhance the strength of diamond tool. On the other hand, inclined cutting can avoid the contact and enhance the strength of diamond tool. On the other hand, inclined cutting can avoid the contact and friction between the rear face of the diamond tool. At the same time, the separation between the friction between the rear face of the diamond tool. At the same time, the separation between the diamond tool and the workpiece can help the cutting fluid reach the tool tip region, which can cool diamondand lubricate tool the and diamond the workpiece tool completely. can help the In cuttingthis method, fluid reachthe size the of tool both tip negative region, whichrake angle can cooland andincluded lubricate angle the between diamond vibrating tool completely. directionIn and this cutting method, direction the size had of both a great negative influence rake on angle surface and includedroughness angle and tool between wear. vibrating direction and cutting direction had a great influence on surface roughness and tool wear.

(a) (b)

Figure 15. Schematic diagram of inclined ultrasonic vibration cutting with negative rake angle; (a) Front view; (b) Top view.

To validate the proposed method and raise machining efficiency, an experiment was conducted under the following conditions: tip radius was 0.5 mm, light mineral oil (isopar H) was selected as lubrication, the spindle rotation speed was set to be 400 rpm, the feed rate was set to be 1 mm/min, the depth of cut was set to be 3 µm, the frequency for ultrasonic vibration cutting system was set to be 65 kHz and the vibrating amplitude adjusted by power amplifier was set to be 2 µm, inclination between rake face and XOZ plane was set to be about −5°, inclination between the center line of diamond tool and Z-axis was set to be about 5°.

Micromachines2018, 9, x FOR PEER REVIEW 9 of 12

(a) (b)

Figure 14. Schematic diagram of force analysis at the stage of diamond tool withdrawing; (a) Front view; (b) Top view.

In the inclined ultrasonic vibration cutting with negative rake angle, the diamond tool vibrated along the direction, as shown in Figure 15. On one hand, not only inclined cutting can decrease the impact force between diamond tool and workpiece, but also cutting with negative rake angle can enhance the strength of diamond tool. On the other hand, inclined cutting can avoid the contact and friction between the rear face of the diamond tool. At the same time, the separation between the diamond tool and the workpiece can help the cutting fluid reach the tool tip region, which can cool and lubricate the diamond tool completely. In this method, the size of both negative rake angle and Micromachinesincluded2018, 9 ,angle 77 between vibrating direction and cutting direction had a great influence on surface 9 of 11 roughness and tool wear.

(a) (b)

Figure 15. Schematic diagram of inclined ultrasonic vibration cutting with negative rake angle; Figure 15.(aSchematic) Front view; diagram (b) Top view. of inclined ultrasonic vibration cutting with negative rake angle; (a) Front view; (b) Top view. To validate the proposed method and raise machining efficiency, an experiment was conducted under the following conditions: tip radius was 0.5 mm, light mineral oil (isopar H) was To validateselected theas lubrication proposed, the method spindle rotation and raise speed machining was set to be efficiency, 400 rpm, the an feed experiment rate was set to was be 1 conducted under them followingm/min, the depth conditions: of cut was tip set radius to be 3 wasµm, the 0.5 frequency mm, light for ultrasonic mineral vibration oil (isopar cutting H) system was selected as lubrication,was the set spindleto be 65 kHz rotation and the speed vibrating was amplitude set to be adjust 400ed rpm, by power the feedamplifier rate was was set set to be to 2 be µm 1, mm/min, inclination between rake face and XOZ plane was set to be about −5°, inclination between the center the depthMicromachines of cut was2018, set 9, x FOR to be PEER 3 µREVIEWm, the frequency for ultrasonic vibration cutting system10 of 12 was set to line of diamond tool and Z-axis was set to be about 5°. be 65 kHz and the vibrating amplitude adjusted by power amplifier was set to be 2 µm, inclination Figure 16 showed surface topography of the machined workpiece◦ using the proposed method. betweenSurface rake face roughness and XOZ of theplane machined was workpiece set to be has about been −improved5 , inclination (Ra 1.82–6. between2 nm) compared the center to line of diamond tool and Z-axis was set to be about 5◦. that of conventional ultrasonic vibration cutting (Ra 2.55–8.85 nm, within a distance of 1 mm). Figure 16Figure showed 17 showed surface wear topography of the diamond of the tool machined using the workpieceproposed m usingethod. W theear proposed has been method. Surface roughnessimproved (wear of the land machined width 0.78 workpiece µm, wear land has leng beenth 41.47 improved µm) compared (Ra 1.82–6.2 to that of nm) conventional compared to that ultrasonic vibration cutting (wear land width 3.05 µm, wear land length 44.61 µm). Tool wear land of conventional ultrasonic vibration cutting (Ra 2.55–8.85 nm, within a distance of 1 mm). of single crystal diamond tool was smaller and no obvious chipping was found on the tool edge.

(a) (b)

(c)

Figure 16. Surface topography of the machined workpiece using the proposed method; (a)Photo of Figure 16.theSurface machined topography workpiece; ( ofb) theRa 1. machined82 nm when workpiece diamond tool using cutting the in proposed a very short method; distance;( (ac)Photo) Ra of the machined6. workpiece;2 nm when diamond (b) Ra tool 1.82 cutting nm when near the diamond center of toolworkpiece cutting. in a very short distance; (c) Ra 6.2 nm when diamond tool cutting near the center of workpiece.

Figure 17. Wear of diamond tool with tip radius of 0.5 mm after cutting along X-axis with negative rake angle (wear land width: 0.78 µm, wear land length: 41.47 µm).

Micromachines2018, 9, x FOR PEER REVIEW 10 of 12

Figure 16 showed surface topography of the machined workpiece using the proposed method. Surface roughness of the machined workpiece has been improved (Ra 1.82–6.2 nm) compared to that of conventional ultrasonic vibration cutting (Ra 2.55–8.85 nm, within a distance of 1 mm). Figure 17 showed wear of the diamond tool using the proposed method. Wear has been improved (wear land width 0.78 µm, wear land length 41.47 µm) compared to that of conventional ultrasonic vibration cutting (wear land width 3.05 µm, wear land length 44.61 µm). Tool wear land of single crystal diamond tool was smaller and no obvious chipping was found on the tool edge.

(a) (b)

Micromachines 2018, 9, 77 10 of 11

Figure 17 showed wear of the diamond tool using(c) the proposed method. Wear has been improved (wear land width 0.78 µm, wear land length 41.47 µm) compared to that of conventional ultrasonic Figure 16. Surface topography of the machined workpiece using the proposed method; (a)Photo of µ µ vibrationthe machined cutting workpiece; (wear land (b width) Ra 1.8 3.052 nm whenm, wear diamond land tool length cutting 44.61 in am). very Tool short wear distance; land (c of) Ra single crystal6.2 diamondnm when tooldiamond was tool smaller cutting and near no the obvious center chippingof workpiece was. found on the tool edge.

Figure 17. Wear of diamond tool with tip radius of 0.5 mm after cutting along X-axis with negative Figure 17. Wear of diamond tool with tip radius of 0.5 mm after cutting along X-axis with negative rake angle (wear land width: 0.78 µm, wear land length: 41.47 µm). rake angle (wear land width: 0.78 µm, wear land length: 41.47 µm).

4. Conclusions

(1) A high frequency ultrasonic vibration cutting system was developed, and a tungsten carbide was precisely machined with a PCD tool assisted by the cutting system. Tool wear mechanism was investigated in ductile regime machining of tungsten carbide. The cutter back-off phenomenon in the process was analyzed. (2) Tool wear mechanisms of both PCD and single crystal diamond tool were mainly abrasive wear and micro-chipping under the condition of high frequency ultrasonic vibration. The surface roughness of the machined workpiece gradually increased with the increased diamond tool wear. The size of tip radius had a great influence on diamond machinability of tungsten carbide. A nano-scale surface roughness can be obtained by using diamond tool with smaller tip radius and no defects were found on the machined surface. (3) A method of inclined ultrasonic vibration cutting with negative rake angle was put forward according to force analysis, which can further reduce tool wear and roughness of machined surface. The above investigation is important to high efficiency and quality ultra-precision machining of tungsten carbide.

Acknowledgments: This work was supported by the National Natural Science Foundation of China (Grant No. 51320105009, 51305369, 51505336), the Tianjin City High School Science & Technology Fund Planning Project (Grant No. 2017KJ107) and the Tianjin Research Program of Application Foundation and Advanced Technology (Grant No. 15JCQNJC05200) and the Tianjin intelligent manufacturing major special project (Grant No. 15ZXZNGX00220 and 17ZXZNGX0080). Author Contributions: Zhanjie Li and Fengzhou Fang conceived and designed the experiments; Zhanjie Li and Gang Jin performed the experiments; Gang Jin and Hu Gong analyzed the data; HailiJia contributed reagents/materials/analysis tools; Jin Gang and Zhanjie Li wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.

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