Research ArticleFinite Element Analysis and Simulation aboutMicrogrinding of SiC
Shijun Ji Leilei Liu Ji Zhao and Changrui Sun
School of Mechanical Science and Engineering Jilin University Changchun 130025 China
Correspondence should be addressed to Ji Zhao jzhaojlueducn
Received 16 February 2015 Revised 18 June 2015 Accepted 29 June 2015
Academic Editor Takuya Tsuzuki
Copyright copy 2015 Shijun Ji et alThis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The application of silicon carbide (SiC) is often limited due to its low machining efficiency and unpredictability about the results ofthe grinding process The aim of this paper is to set up finite element analysis models (FEM) about microgrinding process of SiCto study the change processes about tangential and normal grinding force which can lead to stress and strain inside SiC materialunder different grinding parameters and to predict the results before the grinding process Adaptive remeshing technique is usedto minimize the computational time without sacrificing the accuracy of the results in the simulation of SiC grinding process Theresearch results can be used to choose reasonable grinding parameters based on the required surface quality
1 Introduction
Due to its high strength high hardness and chemical stabilityat high temperatures silicon carbide as an advanced mate-rial has attracted more attention and a wide range of appli-cations such as optical instrument automotive aerospaceand construction industry [1 2] In fact considering thelightweight of the spatial optical system SiC optical mirrorcan do well in spatial optical system and components [3]
As the abrasive is embedded inside the microgrindingtool abrasive belt grinding has a longer life span thanthe electroplated one In recent years studies of surfacegeneration and process optimization have been conductedabout the microgrinding of ceramic materials on account ofthe above advantages [4ndash7] The research of nanowires andbrittle single crystal materials on brittle-to-ductile transitionreceives wide concerns and it is applied into other materialsbehaving brittle and ductile properties [8ndash10] Doman Bargeand Qiuning discussed the brittle-to-ductile transition andcritical cutting depth by developing several single-gritmodelsand conducting many experiments [11ndash13] It is known thatductile-regime grinding is capable of attaining better surface
quality However due to the brittle nature and high hardnesspostmachining will be difficult and increase the cost of SiCproduct significantly in the fabrication of parts with big sizeand complex shape FurthermoreWang et al investigated thechanges of grinding force influenced by the velocity in thegrinding process [14] Arrazola et al have established severalmodels and they do some experiments of other materialsto study how the grinding geometrical shapes of tool affectthe grinding results [15ndash19] But fewer simulation models aresuccessful owing to either lack of considering the nose radiumor inability to establish steady-state models
In this paper the finite element method simulation basedon the single point diamond turning (SPDT) technology isstudied and the simple variablemethod is adopted to analyzethe effect caused by depth velocity and toolrsquos parametersin microgrinding process The main purpose is to generatethe effective grinding simulation according to the givenmicrogrinding parameters which can forecast and optimizeprocessing ahead of machining To verify the finite elementsimulation of microgrinding process experiments are con-ducted for scratching the SiC sample with different depthsand velocities This paper not only reports the performance
Hindawi Publishing CorporationJournal of NanomaterialsVolume 2015 Article ID 575398 9 pageshttpdxdoiorg1011552015575398
2 Journal of Nanomaterials
of SiC microgrinding process combined with geometricalparameters of tool but also provides a rational reference forpractical manufacturing
2 Description of Finite Element Model
21 Single Abrasive Grinding Principle In order to generateSiC chip and cutouts inmicrogrinding process it is necessaryto consider the critical grinding depth The cutting edge ofabrasive can make the material flow and bulge in front and itcan make the chips of the cut slide along the cutting edgeWhen the depth of microgrinding is less than the criticalgrinding depth the chip of silicon carbide material is formedand removed in a manner of the plastic flow Whereas themicrogrinding depth is greater than the critical grindingdepth manufacturing process is brittle grinding As shownin Figure 1 120574 is the rake angle 120572 is the clearance angle B isthe shear angle 119905 is the initial microgrinding depth Ι is theprimary deformation zone II is the second deformation zoneIII is the third deformation zone
22 Single Abrasive Finite ElementModel ofMicrogrinding Inthe study of microgrinding mechanism the grinding processof SiC mirror can be simplified to the two-dimensionalorthogonal microgrinding finite element analysis modelThehardness andmodulus of elasticity of single diamond abrasiveare far more than SiC workpiece even though the machiningprocess is elastic belt grinding Therefore abrasive grit isassumed to be analyzed rigid body during the simulation Asshown in Figure 2 the model size of SiC workpiece is 2 120583m times
15 120583m Quadrilateral element mesh is generated by linearreduced integration unit (CPE4RT) and structured meshtechnique which is stable in the meshing process Moreoveredge biased seed is applied to encrypt meshes in the regionto be manufactured In addition improved Lagrange law(ALE) is adopted so that mesh distortion would be avoided inmicrogrinding process Both accuracy of solving the premiseand operational efficiency are taken into account
221 Material Constitutive Model Drucker and Pragermodel proposed by Drucker and Prager is chosen inwhich the influence on the yield of hydrostatic pressure isconsideredThe yield function for the Drucker-Prager modelis as follows
119891(1198681 radic1198692) = radic1198692 minus1205721198681 minus 119896 = 0 (1)
where 1198681andradic1198692 are the invariant of the stress tensor 120572 and
119896 are the material constantIn Abaqus coefficient of expansion 120575 can be represented
by the expansion angle 120595
120575 = tan (120595)
120575 =tr119863119901
(21198631199011015840 1198631199011015840)12
(2)
where 119863119901 is on behalf of the plastic of the deformation ratetensor119863119863119901
1015840
represents the deviation section of119863119901
Chip Tool
Workpiece
t
r0
120572
120574
Φ
I
II
III
Figure 1 Microgrinding process of abrasive
RP
X
Y
Z
Normal direction
Tangential direction
Figure 2 Two-dimensional finite element model
In Mohr-Coulomb model the angle of internal frictioncan be obtained by single-yield tensile and compressive stress
By comparing the Mohr-Coulomb model with the linearDrucker-Prager model
tan120573 =6 sin1206013 minus sin120601
119870 =3 minus sin1206013 + sin120601
(4)
where 120573 is the slope of the linear yield surface in the 119901-119905 stressplane and is commonly referred to as the friction angle of thematerial 119870 is the ratio of the yield stress in triaxial tensionto the yield stress in triaxial compression [20] The specificparameter is shown in Table 1
Figure 4 The tangential force comparison for the different micro-grinding depths
Table 1 Constitutive model parameters of the SiC workpiecematerial
Density (kgm3) 3250 Angle of friction (∘) 13Youngrsquos modulus (GPa) 205 Flow stress ratio 092Poissonrsquos ratio 016 Dilation angle (∘) minus5Thermal conductivity(JmsdotK) 185 Yield stress (MPa) 12500
Expansion coefficient alpha(120583mK) 4 Specific heat (JkgsdotK) 800
222 Chip Separation Criterion The stress-strain responseas illustrated in Figure 3 shows distinct phases The materialresponse is initially linear elastic a-b followed by plasticyielding with strain hardening b-c Beyond point c there isa marked reduction of load-carrying capacity until rupturec-d The deformation during this last phase is localized in aneck region of the specimen Point c identifies the materialstate at the onset of damage which is referred to as thedamage initiation criterion Beyond this point the stress-strain response c-d is governed by the evolution of thedegradation of the stiffness in the region of strain localization
Figure 5 The normal force comparison for different depths
15 20 25 30 35 40 45 501355
136
1365
137
1375
138
1385
Microgrinding depth (nm)
Equi
vale
nt st
ress
(MPa
)
5524
25
26
27
28
29
3
Equi
vale
nt p
lasti
c str
ain
times104
The maximum equivalent stressThe maximum equivalent plastic strain
Figure 6 Changes of the equivalent stress and the equivalent plasticstrain based on the depth
The criterion for damage initiation is met when thefollowing condition is satisfied
120596119904= int
119889120576119901119897
120576119901119897
119904
= 1 (5)
where 120596119904is a state variable that increases monotonically with
plastic deformation proportional to the incremental changein equivalent plastic strain 120576119901119897
119904is the equivalent plastic strain
and 119889120576119901119897 is the equivalent plastic strain increment
3 The Results of Finite Element Analysis
In the microgrinding progress the force of microgrindingis affected by microgrinding depth rake angle clearanceangle microgrinding velocity and the abrasive nose radius ofcutting edge to different extent and then the smooth grindingprocess changes so that rough precision of microgrindingsurface emerges Now the influence of parameters of tool insimulation is studied in microgrinding process and differentmodels in simulation are shown in Table 2
+24800e + 00+22733e + 00+20667e + 00+18600e + 00+16533e + 00+14467e + 00+12400e + 00+10333e + 00+82667e minus 01+62000e minus 01+41333e minus 01+20667e minus 01+00000e + 00
(a) Microgrinding depth 20 nm
+27300e + 00+25025e + 00+22750e + 00+20475e + 00+18200e + 00+15925e + 00+13650e + 00+11375e + 00+91000e minus 01+68250e minus 01+45500e minus 01+22750e minus 01+00000e + 00
PEEQ(avg 75)
(b) Microgrinding depth 30 nm
+27300e + 00+25025e + 00+22750e + 00+20475e + 00+18200e + 00+15925e + 00+13650e + 00+11375e + 00+91000e minus 01+68250e minus 01+45500e minus 01+22750e minus 01+00000e + 00
PEEQ(avg 75)
(c) Microgrinding depth 40 nm
+29200e + 00+26767e + 00+24333e + 00+21900e + 00+19467e + 00+17033e + 00+14600e + 00+12167e + 00+97333e minus 01+73000e minus 01+48667e minus 01+24333e minus 01+00000e + 00
PEEQ(avg 75)
(d) Microgrinding depth 50 nm
Figure 8 Comparison of the maximum equivalent plastic strain
The third generation of mirror is made from SiC andcarbon fiber reinforced SiC composites SiC mirror hasadvantage in lightweight whose radius-thickness ratio couldreach 20 1 easily The optical properties of SiC can be on apar with optical glass so that high polishing accuracy couldbe achieved [21] As rough SiC surface would be achieved inthe brittle machining process the plastic processing is mainlystudied in order to achieve higher precision SiC mirror Thecritical microgrinding depth of SiC material is 65 nm thusseveral microgrinding depths of models in simulation are20 nm 30 nm 40 nm and 50 nm As shown in Figure 4 thecorresponding tangential forces are 004428120583N 007368120583N009302120583N and 01109 120583N respectively and the homolo-gous normal forces are 002376 120583N 003765 120583N 004647 120583Nand 005758120583N respectively With the steady increase ofmicrogrinding depth the tangential force and the normalforce rise stably Due to the increase of microgrinding depthundeformed chip thickens and abrasive cutting area involvedbecomes bigger Thus the plastic deformation energy theabrasive needed to overcome and the grinding force growbigger Comparing the curve shape in Figure 4 with thosein Figure 5 the tangential force is larger than the normalforce inmicrogrinding process of identical depth At the sametime the fluctuation of grinding force of group 1-model 4whosemicrogrinding depth is 50 nmbecomes bigger than theother models in group 1 resulting from the microgrinding
depth close to critical depth The maximum equivalentstresses of group 1 are 13838MPa 13792MPa 13691MPa and13552MPa respectively and themaximum equivalent plasticstrains are 248 273 285 and 292 respectively As shownin Figure 6 with the increment of microgrinding depththe maximum equivalent stress decreases successively whilethe maximum equivalent plastic strain increases graduallyFigures 7 and 8 show that the maximum equivalent stressmainly emerges in the primary deformation zone and thesecond deformation zone while the maximum equivalentplastic strain appears in the second deformation zone
The theoretical formula of single abrasive grinding force[22]
119865119905119892=120587
41198651198751198862119892sin 120579
119865119899119892= 1198651198751198862119892sin 120579 tan 120579
(6)
where 120579 is semitip angle 80∘ le 2120579 le 140∘ 119886119892is undeformed
microgrinding depth 119865119901is unit microgrinding force
1198651199011 =
4119865119905119892
1205871198862119892sin 120579
1198651199012 =
119865119899119892
1198862119892sin 120579 tan 120579
(7)
6 Journal of Nanomaterials
0
002
004
006
008
01
012
1
2
3
4
5
6
7
FtFn
Forc
e(120583
N)
Rake angle (∘)minus30 minus20 minus10 0
Tangential forceNormal forceFtFn
Figure 9 Changes of grinding force based on rake angle
Figure 10 Changes of the strain based on rake angle
The average of 1198651199011 and 1198651199012 is adopted as 119865
119901
119865119901=1198651199011 + 1198651199012
2 (8)
Taking the efficiency and accuracy of microgrinding intoaccount 119886
119892is used as 40 nm The unit microgrinding force
can be calculated as approximate 844 times 107N according tothe simulation by Abaqus The macroscopic force could befigured out simply after that
Comparing the models in group 2 the result is shownin Figure 9 With the negative rake angle increasing steadilythe microgrinding force grows stably while the ratio of thetangential force and the normal force of microgrinding 119865
119905119865119899
monotonically decreasesThis is because the increment of thenegative rake angle makes the contact area of abrasive andworkpiece bigger so does the load of abrasive cutting edgeThe shear angles of the corresponding models are shown tobe 3289∘ 2750∘ 2337∘ and 2122∘ respectivelyThe balancedaugmenter of the negative rake angle gets the shear angledown However the cutting deformation changes converselyThus the relation between the negative rake angle and theshear angle is consistent with Lee and Shaffer shear angle
12 16 20 240
005
01
17
19
21
FtFn
Forc
e(120583
N)
Tangential forceNormal forceFtFn
Clearance angle (∘)
Figure 11 Changes based on the clearance angle
01 02 03 04 050
005
01
1
15
2
FtFn
Forc
e(120583
N)
Tangential forceNormal forceFtFn
r040
Figure 12 Changes based on the nose radium of the cutting edge
theory [23] Knowing the rake angle and the shear angle theshear strain 120574
0can be further computed as follows
1205740 =cos 120574
sin120601 cos (120601 minus 120574) (9)
where 120574 is the rake angle of abrasive andB is the shear angleAs shown in Figure 10 there is a rise of the maximum
equivalent plastic strain and the shear strain along with thenegative rake angle being larger Furthermore both alphabetsof lines have the same trends
With the clearance angle increasing gradually the chang-ing trends of the tangential force and the normal force areshown in Figure 11 The slight increase of the tangential forceand the normal force can be negligible What is more theratio of the tangential force and the normal force119865
119905119865119899almost
has no change In other words the changes of clearance angledo not affect the stability of the machining process of SiC
As shown in Figure 12 the elevation of the abrasivenose radium of cutting edge makes the microgrinding forcebecome larger Nevertheless the tangential force has a smallamplification and the normal force has a big one Whenthe abrasive nose radium of cutting edge is far less than themicrogrinding depth the ratio of the abrasive nose radium
Journal of Nanomaterials 7
1 5 10004
005
006
007
008
009
01
Microgrinding velocity (ms)15
136
137
138
139
14
141
142
Equi
vale
nt st
ress
(MPa
)
Tangential forceNormal forceThe maximum equivalent stress
of cutting edge and the microgrinding depth is nearly 0Certainly the changes of the abrasive nose radium of cuttingedge do not affect the machining process of SiC In otherwords once the abrasive nose radium of cutting edge is atthe same order of magnitude with the microgrinding depththe nose radium of cutting edge can be ignored In factthe ratio of the tangential force and the normal force 119865
119905119865119899
is almost determined by the geometrical parameters of theabrasive barely influenced by the microgrinding depth Dueto the rise of the nose radium of cutting edge the ratio of thenose radium of cutting edge and the reference microgrindingdepth 119903
040 ascends whereas 119865
119905119865119899comes down gradually
As shown in Figure 13 with the velocity of microgrindingprocess increasing progressively the tangential force andthe normal force improve slightly and both have weakincreasing trends The maximum equivalent stresses become13699MPa 13967MPa 14074MPa and 14117MPa respec-tively Considering the reduction of loss of machine tool andthe perspective of energy conservation 1ms is regarded as agood choice
4 Experiments
According to the present limited research condition to verifythe validity of the above theoretical simulation model for theSiC microgrinding process a series of scratch experimentshave been conducted on the nanoindentation apparatusAgilent Nano Indenter G200 shown in Figure 14 And thescratch picture is given in Figure 15
Figure 14 Agilent Nano Indenter G200
In the experiments simple variable method was adoptedto observe the variation caused by microgrinding depth andthe velocity As to every depth and velocity data of groups areobtained by the scratch experiments Thus the average loadcalculated in Table 3 could definitely give expression to therelationship between load and microgrinding depth
After SiC workpiece polished finely triangular pyramidhead loading 1mN scratched the SiC workpiece for 2mmdisplacement whose velocity is 1mms As the scratchimproves from 20 nm to 30 nm to 40 nm to 50 nm the loadof triangular pyramid head reaches 00455mN 00463mN00481mN and 00492mN as illustrated in Figure 16 Thenormal force given in Figure 5 changes from 00238 120583N to00387 120583N to 00471 120583N to 00570 120583N in simulation Althoughthe specific data is not in full consistency due to the situation
8 Journal of Nanomaterials
Table 3 Changes of load due to the depth and velocity
Simple variablemethod depth (nm) Load (mN) Average load (mN)
Simple variablemethod velocity
(mms)Load (mN) Average load (mN)
20004570045000458
00455 1004800048600476
00481
30004650046200462
00463 5004770047300466
00472
40004690049100483
00481 10004770047600472
00475
50004920049500489
00492 15004680047600478
00474
Figure 15 Scratched SiC workpiece
15 20 25 30 35 40 45 50 55004
0042
0044
0046
0048
005
Depth (nm)
Load
(mN
)
Figure 16 Load change based on the depth
difference between the scratch and the grinding both theexperiment data and the simulation data show an obviousrising trend accompanied by the increase of scratch depthIn addition a group of experiments with same triangularpyramid parameters and 40 nm microgrinding depth wereimplemented to indicate the effect of velocity the nodesvelocities in Figure 17 are 1mms 5mms 10mms and15mms respectively and the corresponding loads reach00481mN 00472mN 00475mN and 00474mN respec-tively At the same time the normal force in simulation
0 2 4 6 8 10 12 14 16004
0042
0044
0046
0048
005
Velocity (mms)
Load
(mN
)
Figure 17 Load change based on the velocity
achieves 00466 120583N 00474120583N 00483 120583N and 00491 120583Nas shown in Figure 13 The data shown in the experimentand simulation vividly mean that triangular pyramid headload hardly goes with the change of velocity Above all goodagreement is shown between the experimental results and thesimulation results by Abaqus
5 Conclusions
Based on the simulation of SiC microgrinding process pre-sented in the paper the following conclusions can be drawn
(1) The depth of microgrinding plays a great role inthe machining process The process owns a 40 nmmicrogrinding depth having both small fluctuationand superior efficiency
(2) For negative rake angle a small one is a benefit toobtain the surface of SiC optical component
(3) The clearance angle has barely an influence on themanufacturing of SiC surface in microgrinding pro-cess
(4) To obtain a high accuracy of machining process theabrasive nose radium of cutting edge needs to becompressed
Journal of Nanomaterials 9
(5) Velocity of about 1ms is a proper choice in simula-tion of microgrinding process
(6) Simulations of finite element in microgrinding pro-cess could provide a reference for the load in thecoarse and fine grinding process of SiC mirror
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by the National Key Basic Researchand Development Program (973 Program) of China (Grantno 2011CB706702) Natural Science Foundation of China(Grant nos 51305161 and 51135006) and Jilin Province Sci-ence and Technology Development Plan Item (Grant no20130101042JC)
References
[1] R Naslain ldquoDesign preparation and properties of non-oxideCMCs for application in engines and nuclear reactors anoverviewrdquo Composites Science and Technology vol 64 no 2 pp155ndash170 2004
[2] W Krenkel and F Berndt ldquoCC-SiC composites for spaceapplications and advanced friction systemsrdquo Materials Scienceand Engineering A vol 412 no 1-2 pp 177ndash181 2005
[3] Y Julong Ultraprecision Machining of Functional CeramicsHarbin Institute of Technology Press Harbin China 2000
[4] P-H Lee H Chung and S W Lee ldquoOptimization of micro-grinding process with compressed air using response surfacemethodologyrdquo Proceedings of the Institution of MechanicalEngineers Part B Journal of Engineering Manufacture vol 225no 11 pp 2040ndash2050 2011
[5] F J Chen S H Yin H Huang et al ldquoProfile error compen-sation in ultra-precision grinding of aspheric surfaces with on-machine measurementrdquo International Journal of Machine Toolsand Manufacture vol 50 no 5 pp 480ndash486 2010
[6] J Feng B S Kim A Shih and J Ni ldquoTool wear monitoring formicro-end grinding of ceramic materialsrdquo Journal of MaterialsProcessing Technology vol 209 no 11 pp 5110ndash5116 2009
[7] J Feng P Chen and J Ni ldquoPrediction of surface generation inmicrogrinding of ceramic materials by coupled trajectory andfinite element analysisrdquo Finite Elements in Analysis and Designvol 57 pp 67ndash80 2012
[8] Z Yuan K-I Nomura and A Nakano ldquoA coreshell mecha-nism for stacking-fault generation in GaAs nanowiresrdquo AppliedPhysics Letters vol 100 no 16 Article ID 163103 2012
[9] B K Tanner M C Fossati J Garagorri et al ldquoPrediction ofthe propagation probability of individual cracks in brittle singlecrystal materialsrdquo Applied Physics Letters vol 101 no 4 ArticleID 041903 2012
[10] S Goel X Luo P Comley R L Reuben and A Cox ldquoBrittle-ductile transition during diamond turning of single crystalsilicon carbiderdquo International Journal of Machine Tools andManufacture vol 65 pp 15ndash21 2013
[11] D A Doman Rubbing and Plowing Phases in Single GrainGrinding Dalhousie University Halifax Canada 2006
[12] M Barge J Rech H Hamdi and J-M Bergheau ldquoExperimen-tal study of abrasive processrdquo Wear vol 264 no 5-6 pp 382ndash388 2008
[13] W Qiuning Experimental study on single diamond graingrinding of silicon wafers [MS thesis] Dalian University ofTechnology Dalian China 2006
[14] J Wang R Ye and Y Tang ldquo3D dynamic finite elementsimulation analysis of single abrasive grain during surfacegrindingrdquo Diamond amp Abrasive Engineering vol 173 no 5 pp41ndash45 2009
[15] P J Arrazola and T Ozel ldquoNumerical modelling of 3D hardturning using arbitrary Lagrangian Eulerian finite elementmethodrdquo International Journal of Machining and Machinabilityof Materials vol 4 no 1 pp 14ndash25 2008
[16] M Gunay I Korkut E Aslan and U Seker ldquoExperimentalinvestigation of the effect of cutting tool rake angle on maincutting forcerdquo Journal of Materials Processing Technology vol166 no 1 pp 44ndash49 2005
[17] Y-C Yen A Jain and T Altan ldquoA finite element analysis oforthogonal machining using different tool edge geometriesrdquoJournal of Materials Processing Technology vol 146 no 1 pp72ndash81 2004
[18] H Saglam F Unsacar and S Yaldiz ldquoInvestigation of the effectof rake angle and approaching angle on main cutting force andtool tip temperaturerdquo International Journal ofMachine Tools andManufacture vol 46 no 2 pp 132ndash141 2006
[19] J A Badger and A A Torrance ldquoComparison of two modelsto predict grinding forces from wheel surface topographyrdquoInternational Journal ofMachine Tools andManufacture vol 40no 8 pp 1099ndash1120 2000
[20] ABAQUS Userrsquos Manual Version 66 Hibbitt Karlsson andSorensen Inc Proxidence RI USA 2006
[21] J S Johnson K D Grobsky and D Bray ldquoRapid fabricationof lightweight silicon-carbide mirrorsrdquo in Proceedings of theInternational Symposium on Optical Science and Technology pp243ndash253 International Society for Optics and Photonics 2002
[22] B Li and B Zhao Modern Grinding Technology CMP BeijingChina 2003
[23] E H Lee and B W Shaffer ldquoThe theory of plasticity applied toa problem of machiningrdquo Journal of Applied Mechanics vol 18pp 405ndash413 1951
of SiC microgrinding process combined with geometricalparameters of tool but also provides a rational reference forpractical manufacturing
2 Description of Finite Element Model
21 Single Abrasive Grinding Principle In order to generateSiC chip and cutouts inmicrogrinding process it is necessaryto consider the critical grinding depth The cutting edge ofabrasive can make the material flow and bulge in front and itcan make the chips of the cut slide along the cutting edgeWhen the depth of microgrinding is less than the criticalgrinding depth the chip of silicon carbide material is formedand removed in a manner of the plastic flow Whereas themicrogrinding depth is greater than the critical grindingdepth manufacturing process is brittle grinding As shownin Figure 1 120574 is the rake angle 120572 is the clearance angle B isthe shear angle 119905 is the initial microgrinding depth Ι is theprimary deformation zone II is the second deformation zoneIII is the third deformation zone
22 Single Abrasive Finite ElementModel ofMicrogrinding Inthe study of microgrinding mechanism the grinding processof SiC mirror can be simplified to the two-dimensionalorthogonal microgrinding finite element analysis modelThehardness andmodulus of elasticity of single diamond abrasiveare far more than SiC workpiece even though the machiningprocess is elastic belt grinding Therefore abrasive grit isassumed to be analyzed rigid body during the simulation Asshown in Figure 2 the model size of SiC workpiece is 2 120583m times
15 120583m Quadrilateral element mesh is generated by linearreduced integration unit (CPE4RT) and structured meshtechnique which is stable in the meshing process Moreoveredge biased seed is applied to encrypt meshes in the regionto be manufactured In addition improved Lagrange law(ALE) is adopted so that mesh distortion would be avoided inmicrogrinding process Both accuracy of solving the premiseand operational efficiency are taken into account
221 Material Constitutive Model Drucker and Pragermodel proposed by Drucker and Prager is chosen inwhich the influence on the yield of hydrostatic pressure isconsideredThe yield function for the Drucker-Prager modelis as follows
119891(1198681 radic1198692) = radic1198692 minus1205721198681 minus 119896 = 0 (1)
where 1198681andradic1198692 are the invariant of the stress tensor 120572 and
119896 are the material constantIn Abaqus coefficient of expansion 120575 can be represented
by the expansion angle 120595
120575 = tan (120595)
120575 =tr119863119901
(21198631199011015840 1198631199011015840)12
(2)
where 119863119901 is on behalf of the plastic of the deformation ratetensor119863119863119901
1015840
represents the deviation section of119863119901
Chip Tool
Workpiece
t
r0
120572
120574
Φ
I
II
III
Figure 1 Microgrinding process of abrasive
RP
X
Y
Z
Normal direction
Tangential direction
Figure 2 Two-dimensional finite element model
In Mohr-Coulomb model the angle of internal frictioncan be obtained by single-yield tensile and compressive stress
By comparing the Mohr-Coulomb model with the linearDrucker-Prager model
tan120573 =6 sin1206013 minus sin120601
119870 =3 minus sin1206013 + sin120601
(4)
where 120573 is the slope of the linear yield surface in the 119901-119905 stressplane and is commonly referred to as the friction angle of thematerial 119870 is the ratio of the yield stress in triaxial tensionto the yield stress in triaxial compression [20] The specificparameter is shown in Table 1
Figure 4 The tangential force comparison for the different micro-grinding depths
Table 1 Constitutive model parameters of the SiC workpiecematerial
Density (kgm3) 3250 Angle of friction (∘) 13Youngrsquos modulus (GPa) 205 Flow stress ratio 092Poissonrsquos ratio 016 Dilation angle (∘) minus5Thermal conductivity(JmsdotK) 185 Yield stress (MPa) 12500
Expansion coefficient alpha(120583mK) 4 Specific heat (JkgsdotK) 800
222 Chip Separation Criterion The stress-strain responseas illustrated in Figure 3 shows distinct phases The materialresponse is initially linear elastic a-b followed by plasticyielding with strain hardening b-c Beyond point c there isa marked reduction of load-carrying capacity until rupturec-d The deformation during this last phase is localized in aneck region of the specimen Point c identifies the materialstate at the onset of damage which is referred to as thedamage initiation criterion Beyond this point the stress-strain response c-d is governed by the evolution of thedegradation of the stiffness in the region of strain localization
Figure 5 The normal force comparison for different depths
15 20 25 30 35 40 45 501355
136
1365
137
1375
138
1385
Microgrinding depth (nm)
Equi
vale
nt st
ress
(MPa
)
5524
25
26
27
28
29
3
Equi
vale
nt p
lasti
c str
ain
times104
The maximum equivalent stressThe maximum equivalent plastic strain
Figure 6 Changes of the equivalent stress and the equivalent plasticstrain based on the depth
The criterion for damage initiation is met when thefollowing condition is satisfied
120596119904= int
119889120576119901119897
120576119901119897
119904
= 1 (5)
where 120596119904is a state variable that increases monotonically with
plastic deformation proportional to the incremental changein equivalent plastic strain 120576119901119897
119904is the equivalent plastic strain
and 119889120576119901119897 is the equivalent plastic strain increment
3 The Results of Finite Element Analysis
In the microgrinding progress the force of microgrindingis affected by microgrinding depth rake angle clearanceangle microgrinding velocity and the abrasive nose radius ofcutting edge to different extent and then the smooth grindingprocess changes so that rough precision of microgrindingsurface emerges Now the influence of parameters of tool insimulation is studied in microgrinding process and differentmodels in simulation are shown in Table 2
+24800e + 00+22733e + 00+20667e + 00+18600e + 00+16533e + 00+14467e + 00+12400e + 00+10333e + 00+82667e minus 01+62000e minus 01+41333e minus 01+20667e minus 01+00000e + 00
(a) Microgrinding depth 20 nm
+27300e + 00+25025e + 00+22750e + 00+20475e + 00+18200e + 00+15925e + 00+13650e + 00+11375e + 00+91000e minus 01+68250e minus 01+45500e minus 01+22750e minus 01+00000e + 00
PEEQ(avg 75)
(b) Microgrinding depth 30 nm
+27300e + 00+25025e + 00+22750e + 00+20475e + 00+18200e + 00+15925e + 00+13650e + 00+11375e + 00+91000e minus 01+68250e minus 01+45500e minus 01+22750e minus 01+00000e + 00
PEEQ(avg 75)
(c) Microgrinding depth 40 nm
+29200e + 00+26767e + 00+24333e + 00+21900e + 00+19467e + 00+17033e + 00+14600e + 00+12167e + 00+97333e minus 01+73000e minus 01+48667e minus 01+24333e minus 01+00000e + 00
PEEQ(avg 75)
(d) Microgrinding depth 50 nm
Figure 8 Comparison of the maximum equivalent plastic strain
The third generation of mirror is made from SiC andcarbon fiber reinforced SiC composites SiC mirror hasadvantage in lightweight whose radius-thickness ratio couldreach 20 1 easily The optical properties of SiC can be on apar with optical glass so that high polishing accuracy couldbe achieved [21] As rough SiC surface would be achieved inthe brittle machining process the plastic processing is mainlystudied in order to achieve higher precision SiC mirror Thecritical microgrinding depth of SiC material is 65 nm thusseveral microgrinding depths of models in simulation are20 nm 30 nm 40 nm and 50 nm As shown in Figure 4 thecorresponding tangential forces are 004428120583N 007368120583N009302120583N and 01109 120583N respectively and the homolo-gous normal forces are 002376 120583N 003765 120583N 004647 120583Nand 005758120583N respectively With the steady increase ofmicrogrinding depth the tangential force and the normalforce rise stably Due to the increase of microgrinding depthundeformed chip thickens and abrasive cutting area involvedbecomes bigger Thus the plastic deformation energy theabrasive needed to overcome and the grinding force growbigger Comparing the curve shape in Figure 4 with thosein Figure 5 the tangential force is larger than the normalforce inmicrogrinding process of identical depth At the sametime the fluctuation of grinding force of group 1-model 4whosemicrogrinding depth is 50 nmbecomes bigger than theother models in group 1 resulting from the microgrinding
depth close to critical depth The maximum equivalentstresses of group 1 are 13838MPa 13792MPa 13691MPa and13552MPa respectively and themaximum equivalent plasticstrains are 248 273 285 and 292 respectively As shownin Figure 6 with the increment of microgrinding depththe maximum equivalent stress decreases successively whilethe maximum equivalent plastic strain increases graduallyFigures 7 and 8 show that the maximum equivalent stressmainly emerges in the primary deformation zone and thesecond deformation zone while the maximum equivalentplastic strain appears in the second deformation zone
The theoretical formula of single abrasive grinding force[22]
119865119905119892=120587
41198651198751198862119892sin 120579
119865119899119892= 1198651198751198862119892sin 120579 tan 120579
(6)
where 120579 is semitip angle 80∘ le 2120579 le 140∘ 119886119892is undeformed
microgrinding depth 119865119901is unit microgrinding force
1198651199011 =
4119865119905119892
1205871198862119892sin 120579
1198651199012 =
119865119899119892
1198862119892sin 120579 tan 120579
(7)
6 Journal of Nanomaterials
0
002
004
006
008
01
012
1
2
3
4
5
6
7
FtFn
Forc
e(120583
N)
Rake angle (∘)minus30 minus20 minus10 0
Tangential forceNormal forceFtFn
Figure 9 Changes of grinding force based on rake angle
Figure 10 Changes of the strain based on rake angle
The average of 1198651199011 and 1198651199012 is adopted as 119865
119901
119865119901=1198651199011 + 1198651199012
2 (8)
Taking the efficiency and accuracy of microgrinding intoaccount 119886
119892is used as 40 nm The unit microgrinding force
can be calculated as approximate 844 times 107N according tothe simulation by Abaqus The macroscopic force could befigured out simply after that
Comparing the models in group 2 the result is shownin Figure 9 With the negative rake angle increasing steadilythe microgrinding force grows stably while the ratio of thetangential force and the normal force of microgrinding 119865
119905119865119899
monotonically decreasesThis is because the increment of thenegative rake angle makes the contact area of abrasive andworkpiece bigger so does the load of abrasive cutting edgeThe shear angles of the corresponding models are shown tobe 3289∘ 2750∘ 2337∘ and 2122∘ respectivelyThe balancedaugmenter of the negative rake angle gets the shear angledown However the cutting deformation changes converselyThus the relation between the negative rake angle and theshear angle is consistent with Lee and Shaffer shear angle
12 16 20 240
005
01
17
19
21
FtFn
Forc
e(120583
N)
Tangential forceNormal forceFtFn
Clearance angle (∘)
Figure 11 Changes based on the clearance angle
01 02 03 04 050
005
01
1
15
2
FtFn
Forc
e(120583
N)
Tangential forceNormal forceFtFn
r040
Figure 12 Changes based on the nose radium of the cutting edge
theory [23] Knowing the rake angle and the shear angle theshear strain 120574
0can be further computed as follows
1205740 =cos 120574
sin120601 cos (120601 minus 120574) (9)
where 120574 is the rake angle of abrasive andB is the shear angleAs shown in Figure 10 there is a rise of the maximum
equivalent plastic strain and the shear strain along with thenegative rake angle being larger Furthermore both alphabetsof lines have the same trends
With the clearance angle increasing gradually the chang-ing trends of the tangential force and the normal force areshown in Figure 11 The slight increase of the tangential forceand the normal force can be negligible What is more theratio of the tangential force and the normal force119865
119905119865119899almost
has no change In other words the changes of clearance angledo not affect the stability of the machining process of SiC
As shown in Figure 12 the elevation of the abrasivenose radium of cutting edge makes the microgrinding forcebecome larger Nevertheless the tangential force has a smallamplification and the normal force has a big one Whenthe abrasive nose radium of cutting edge is far less than themicrogrinding depth the ratio of the abrasive nose radium
Journal of Nanomaterials 7
1 5 10004
005
006
007
008
009
01
Microgrinding velocity (ms)15
136
137
138
139
14
141
142
Equi
vale
nt st
ress
(MPa
)
Tangential forceNormal forceThe maximum equivalent stress
of cutting edge and the microgrinding depth is nearly 0Certainly the changes of the abrasive nose radium of cuttingedge do not affect the machining process of SiC In otherwords once the abrasive nose radium of cutting edge is atthe same order of magnitude with the microgrinding depththe nose radium of cutting edge can be ignored In factthe ratio of the tangential force and the normal force 119865
119905119865119899
is almost determined by the geometrical parameters of theabrasive barely influenced by the microgrinding depth Dueto the rise of the nose radium of cutting edge the ratio of thenose radium of cutting edge and the reference microgrindingdepth 119903
040 ascends whereas 119865
119905119865119899comes down gradually
As shown in Figure 13 with the velocity of microgrindingprocess increasing progressively the tangential force andthe normal force improve slightly and both have weakincreasing trends The maximum equivalent stresses become13699MPa 13967MPa 14074MPa and 14117MPa respec-tively Considering the reduction of loss of machine tool andthe perspective of energy conservation 1ms is regarded as agood choice
4 Experiments
According to the present limited research condition to verifythe validity of the above theoretical simulation model for theSiC microgrinding process a series of scratch experimentshave been conducted on the nanoindentation apparatusAgilent Nano Indenter G200 shown in Figure 14 And thescratch picture is given in Figure 15
Figure 14 Agilent Nano Indenter G200
In the experiments simple variable method was adoptedto observe the variation caused by microgrinding depth andthe velocity As to every depth and velocity data of groups areobtained by the scratch experiments Thus the average loadcalculated in Table 3 could definitely give expression to therelationship between load and microgrinding depth
After SiC workpiece polished finely triangular pyramidhead loading 1mN scratched the SiC workpiece for 2mmdisplacement whose velocity is 1mms As the scratchimproves from 20 nm to 30 nm to 40 nm to 50 nm the loadof triangular pyramid head reaches 00455mN 00463mN00481mN and 00492mN as illustrated in Figure 16 Thenormal force given in Figure 5 changes from 00238 120583N to00387 120583N to 00471 120583N to 00570 120583N in simulation Althoughthe specific data is not in full consistency due to the situation
8 Journal of Nanomaterials
Table 3 Changes of load due to the depth and velocity
Simple variablemethod depth (nm) Load (mN) Average load (mN)
Simple variablemethod velocity
(mms)Load (mN) Average load (mN)
20004570045000458
00455 1004800048600476
00481
30004650046200462
00463 5004770047300466
00472
40004690049100483
00481 10004770047600472
00475
50004920049500489
00492 15004680047600478
00474
Figure 15 Scratched SiC workpiece
15 20 25 30 35 40 45 50 55004
0042
0044
0046
0048
005
Depth (nm)
Load
(mN
)
Figure 16 Load change based on the depth
difference between the scratch and the grinding both theexperiment data and the simulation data show an obviousrising trend accompanied by the increase of scratch depthIn addition a group of experiments with same triangularpyramid parameters and 40 nm microgrinding depth wereimplemented to indicate the effect of velocity the nodesvelocities in Figure 17 are 1mms 5mms 10mms and15mms respectively and the corresponding loads reach00481mN 00472mN 00475mN and 00474mN respec-tively At the same time the normal force in simulation
0 2 4 6 8 10 12 14 16004
0042
0044
0046
0048
005
Velocity (mms)
Load
(mN
)
Figure 17 Load change based on the velocity
achieves 00466 120583N 00474120583N 00483 120583N and 00491 120583Nas shown in Figure 13 The data shown in the experimentand simulation vividly mean that triangular pyramid headload hardly goes with the change of velocity Above all goodagreement is shown between the experimental results and thesimulation results by Abaqus
5 Conclusions
Based on the simulation of SiC microgrinding process pre-sented in the paper the following conclusions can be drawn
(1) The depth of microgrinding plays a great role inthe machining process The process owns a 40 nmmicrogrinding depth having both small fluctuationand superior efficiency
(2) For negative rake angle a small one is a benefit toobtain the surface of SiC optical component
(3) The clearance angle has barely an influence on themanufacturing of SiC surface in microgrinding pro-cess
(4) To obtain a high accuracy of machining process theabrasive nose radium of cutting edge needs to becompressed
Journal of Nanomaterials 9
(5) Velocity of about 1ms is a proper choice in simula-tion of microgrinding process
(6) Simulations of finite element in microgrinding pro-cess could provide a reference for the load in thecoarse and fine grinding process of SiC mirror
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by the National Key Basic Researchand Development Program (973 Program) of China (Grantno 2011CB706702) Natural Science Foundation of China(Grant nos 51305161 and 51135006) and Jilin Province Sci-ence and Technology Development Plan Item (Grant no20130101042JC)
References
[1] R Naslain ldquoDesign preparation and properties of non-oxideCMCs for application in engines and nuclear reactors anoverviewrdquo Composites Science and Technology vol 64 no 2 pp155ndash170 2004
[2] W Krenkel and F Berndt ldquoCC-SiC composites for spaceapplications and advanced friction systemsrdquo Materials Scienceand Engineering A vol 412 no 1-2 pp 177ndash181 2005
[3] Y Julong Ultraprecision Machining of Functional CeramicsHarbin Institute of Technology Press Harbin China 2000
[4] P-H Lee H Chung and S W Lee ldquoOptimization of micro-grinding process with compressed air using response surfacemethodologyrdquo Proceedings of the Institution of MechanicalEngineers Part B Journal of Engineering Manufacture vol 225no 11 pp 2040ndash2050 2011
[5] F J Chen S H Yin H Huang et al ldquoProfile error compen-sation in ultra-precision grinding of aspheric surfaces with on-machine measurementrdquo International Journal of Machine Toolsand Manufacture vol 50 no 5 pp 480ndash486 2010
[6] J Feng B S Kim A Shih and J Ni ldquoTool wear monitoring formicro-end grinding of ceramic materialsrdquo Journal of MaterialsProcessing Technology vol 209 no 11 pp 5110ndash5116 2009
[7] J Feng P Chen and J Ni ldquoPrediction of surface generation inmicrogrinding of ceramic materials by coupled trajectory andfinite element analysisrdquo Finite Elements in Analysis and Designvol 57 pp 67ndash80 2012
[8] Z Yuan K-I Nomura and A Nakano ldquoA coreshell mecha-nism for stacking-fault generation in GaAs nanowiresrdquo AppliedPhysics Letters vol 100 no 16 Article ID 163103 2012
[9] B K Tanner M C Fossati J Garagorri et al ldquoPrediction ofthe propagation probability of individual cracks in brittle singlecrystal materialsrdquo Applied Physics Letters vol 101 no 4 ArticleID 041903 2012
[10] S Goel X Luo P Comley R L Reuben and A Cox ldquoBrittle-ductile transition during diamond turning of single crystalsilicon carbiderdquo International Journal of Machine Tools andManufacture vol 65 pp 15ndash21 2013
[11] D A Doman Rubbing and Plowing Phases in Single GrainGrinding Dalhousie University Halifax Canada 2006
[12] M Barge J Rech H Hamdi and J-M Bergheau ldquoExperimen-tal study of abrasive processrdquo Wear vol 264 no 5-6 pp 382ndash388 2008
[13] W Qiuning Experimental study on single diamond graingrinding of silicon wafers [MS thesis] Dalian University ofTechnology Dalian China 2006
[14] J Wang R Ye and Y Tang ldquo3D dynamic finite elementsimulation analysis of single abrasive grain during surfacegrindingrdquo Diamond amp Abrasive Engineering vol 173 no 5 pp41ndash45 2009
[15] P J Arrazola and T Ozel ldquoNumerical modelling of 3D hardturning using arbitrary Lagrangian Eulerian finite elementmethodrdquo International Journal of Machining and Machinabilityof Materials vol 4 no 1 pp 14ndash25 2008
[16] M Gunay I Korkut E Aslan and U Seker ldquoExperimentalinvestigation of the effect of cutting tool rake angle on maincutting forcerdquo Journal of Materials Processing Technology vol166 no 1 pp 44ndash49 2005
[17] Y-C Yen A Jain and T Altan ldquoA finite element analysis oforthogonal machining using different tool edge geometriesrdquoJournal of Materials Processing Technology vol 146 no 1 pp72ndash81 2004
[18] H Saglam F Unsacar and S Yaldiz ldquoInvestigation of the effectof rake angle and approaching angle on main cutting force andtool tip temperaturerdquo International Journal ofMachine Tools andManufacture vol 46 no 2 pp 132ndash141 2006
[19] J A Badger and A A Torrance ldquoComparison of two modelsto predict grinding forces from wheel surface topographyrdquoInternational Journal ofMachine Tools andManufacture vol 40no 8 pp 1099ndash1120 2000
[20] ABAQUS Userrsquos Manual Version 66 Hibbitt Karlsson andSorensen Inc Proxidence RI USA 2006
[21] J S Johnson K D Grobsky and D Bray ldquoRapid fabricationof lightweight silicon-carbide mirrorsrdquo in Proceedings of theInternational Symposium on Optical Science and Technology pp243ndash253 International Society for Optics and Photonics 2002
[22] B Li and B Zhao Modern Grinding Technology CMP BeijingChina 2003
[23] E H Lee and B W Shaffer ldquoThe theory of plasticity applied toa problem of machiningrdquo Journal of Applied Mechanics vol 18pp 405ndash413 1951
Figure 4 The tangential force comparison for the different micro-grinding depths
Table 1 Constitutive model parameters of the SiC workpiecematerial
Density (kgm3) 3250 Angle of friction (∘) 13Youngrsquos modulus (GPa) 205 Flow stress ratio 092Poissonrsquos ratio 016 Dilation angle (∘) minus5Thermal conductivity(JmsdotK) 185 Yield stress (MPa) 12500
Expansion coefficient alpha(120583mK) 4 Specific heat (JkgsdotK) 800
222 Chip Separation Criterion The stress-strain responseas illustrated in Figure 3 shows distinct phases The materialresponse is initially linear elastic a-b followed by plasticyielding with strain hardening b-c Beyond point c there isa marked reduction of load-carrying capacity until rupturec-d The deformation during this last phase is localized in aneck region of the specimen Point c identifies the materialstate at the onset of damage which is referred to as thedamage initiation criterion Beyond this point the stress-strain response c-d is governed by the evolution of thedegradation of the stiffness in the region of strain localization
Figure 5 The normal force comparison for different depths
15 20 25 30 35 40 45 501355
136
1365
137
1375
138
1385
Microgrinding depth (nm)
Equi
vale
nt st
ress
(MPa
)
5524
25
26
27
28
29
3
Equi
vale
nt p
lasti
c str
ain
times104
The maximum equivalent stressThe maximum equivalent plastic strain
Figure 6 Changes of the equivalent stress and the equivalent plasticstrain based on the depth
The criterion for damage initiation is met when thefollowing condition is satisfied
120596119904= int
119889120576119901119897
120576119901119897
119904
= 1 (5)
where 120596119904is a state variable that increases monotonically with
plastic deformation proportional to the incremental changein equivalent plastic strain 120576119901119897
119904is the equivalent plastic strain
and 119889120576119901119897 is the equivalent plastic strain increment
3 The Results of Finite Element Analysis
In the microgrinding progress the force of microgrindingis affected by microgrinding depth rake angle clearanceangle microgrinding velocity and the abrasive nose radius ofcutting edge to different extent and then the smooth grindingprocess changes so that rough precision of microgrindingsurface emerges Now the influence of parameters of tool insimulation is studied in microgrinding process and differentmodels in simulation are shown in Table 2
+24800e + 00+22733e + 00+20667e + 00+18600e + 00+16533e + 00+14467e + 00+12400e + 00+10333e + 00+82667e minus 01+62000e minus 01+41333e minus 01+20667e minus 01+00000e + 00
(a) Microgrinding depth 20 nm
+27300e + 00+25025e + 00+22750e + 00+20475e + 00+18200e + 00+15925e + 00+13650e + 00+11375e + 00+91000e minus 01+68250e minus 01+45500e minus 01+22750e minus 01+00000e + 00
PEEQ(avg 75)
(b) Microgrinding depth 30 nm
+27300e + 00+25025e + 00+22750e + 00+20475e + 00+18200e + 00+15925e + 00+13650e + 00+11375e + 00+91000e minus 01+68250e minus 01+45500e minus 01+22750e minus 01+00000e + 00
PEEQ(avg 75)
(c) Microgrinding depth 40 nm
+29200e + 00+26767e + 00+24333e + 00+21900e + 00+19467e + 00+17033e + 00+14600e + 00+12167e + 00+97333e minus 01+73000e minus 01+48667e minus 01+24333e minus 01+00000e + 00
PEEQ(avg 75)
(d) Microgrinding depth 50 nm
Figure 8 Comparison of the maximum equivalent plastic strain
The third generation of mirror is made from SiC andcarbon fiber reinforced SiC composites SiC mirror hasadvantage in lightweight whose radius-thickness ratio couldreach 20 1 easily The optical properties of SiC can be on apar with optical glass so that high polishing accuracy couldbe achieved [21] As rough SiC surface would be achieved inthe brittle machining process the plastic processing is mainlystudied in order to achieve higher precision SiC mirror Thecritical microgrinding depth of SiC material is 65 nm thusseveral microgrinding depths of models in simulation are20 nm 30 nm 40 nm and 50 nm As shown in Figure 4 thecorresponding tangential forces are 004428120583N 007368120583N009302120583N and 01109 120583N respectively and the homolo-gous normal forces are 002376 120583N 003765 120583N 004647 120583Nand 005758120583N respectively With the steady increase ofmicrogrinding depth the tangential force and the normalforce rise stably Due to the increase of microgrinding depthundeformed chip thickens and abrasive cutting area involvedbecomes bigger Thus the plastic deformation energy theabrasive needed to overcome and the grinding force growbigger Comparing the curve shape in Figure 4 with thosein Figure 5 the tangential force is larger than the normalforce inmicrogrinding process of identical depth At the sametime the fluctuation of grinding force of group 1-model 4whosemicrogrinding depth is 50 nmbecomes bigger than theother models in group 1 resulting from the microgrinding
depth close to critical depth The maximum equivalentstresses of group 1 are 13838MPa 13792MPa 13691MPa and13552MPa respectively and themaximum equivalent plasticstrains are 248 273 285 and 292 respectively As shownin Figure 6 with the increment of microgrinding depththe maximum equivalent stress decreases successively whilethe maximum equivalent plastic strain increases graduallyFigures 7 and 8 show that the maximum equivalent stressmainly emerges in the primary deformation zone and thesecond deformation zone while the maximum equivalentplastic strain appears in the second deformation zone
The theoretical formula of single abrasive grinding force[22]
119865119905119892=120587
41198651198751198862119892sin 120579
119865119899119892= 1198651198751198862119892sin 120579 tan 120579
(6)
where 120579 is semitip angle 80∘ le 2120579 le 140∘ 119886119892is undeformed
microgrinding depth 119865119901is unit microgrinding force
1198651199011 =
4119865119905119892
1205871198862119892sin 120579
1198651199012 =
119865119899119892
1198862119892sin 120579 tan 120579
(7)
6 Journal of Nanomaterials
0
002
004
006
008
01
012
1
2
3
4
5
6
7
FtFn
Forc
e(120583
N)
Rake angle (∘)minus30 minus20 minus10 0
Tangential forceNormal forceFtFn
Figure 9 Changes of grinding force based on rake angle
Figure 10 Changes of the strain based on rake angle
The average of 1198651199011 and 1198651199012 is adopted as 119865
119901
119865119901=1198651199011 + 1198651199012
2 (8)
Taking the efficiency and accuracy of microgrinding intoaccount 119886
119892is used as 40 nm The unit microgrinding force
can be calculated as approximate 844 times 107N according tothe simulation by Abaqus The macroscopic force could befigured out simply after that
Comparing the models in group 2 the result is shownin Figure 9 With the negative rake angle increasing steadilythe microgrinding force grows stably while the ratio of thetangential force and the normal force of microgrinding 119865
119905119865119899
monotonically decreasesThis is because the increment of thenegative rake angle makes the contact area of abrasive andworkpiece bigger so does the load of abrasive cutting edgeThe shear angles of the corresponding models are shown tobe 3289∘ 2750∘ 2337∘ and 2122∘ respectivelyThe balancedaugmenter of the negative rake angle gets the shear angledown However the cutting deformation changes converselyThus the relation between the negative rake angle and theshear angle is consistent with Lee and Shaffer shear angle
12 16 20 240
005
01
17
19
21
FtFn
Forc
e(120583
N)
Tangential forceNormal forceFtFn
Clearance angle (∘)
Figure 11 Changes based on the clearance angle
01 02 03 04 050
005
01
1
15
2
FtFn
Forc
e(120583
N)
Tangential forceNormal forceFtFn
r040
Figure 12 Changes based on the nose radium of the cutting edge
theory [23] Knowing the rake angle and the shear angle theshear strain 120574
0can be further computed as follows
1205740 =cos 120574
sin120601 cos (120601 minus 120574) (9)
where 120574 is the rake angle of abrasive andB is the shear angleAs shown in Figure 10 there is a rise of the maximum
equivalent plastic strain and the shear strain along with thenegative rake angle being larger Furthermore both alphabetsof lines have the same trends
With the clearance angle increasing gradually the chang-ing trends of the tangential force and the normal force areshown in Figure 11 The slight increase of the tangential forceand the normal force can be negligible What is more theratio of the tangential force and the normal force119865
119905119865119899almost
has no change In other words the changes of clearance angledo not affect the stability of the machining process of SiC
As shown in Figure 12 the elevation of the abrasivenose radium of cutting edge makes the microgrinding forcebecome larger Nevertheless the tangential force has a smallamplification and the normal force has a big one Whenthe abrasive nose radium of cutting edge is far less than themicrogrinding depth the ratio of the abrasive nose radium
Journal of Nanomaterials 7
1 5 10004
005
006
007
008
009
01
Microgrinding velocity (ms)15
136
137
138
139
14
141
142
Equi
vale
nt st
ress
(MPa
)
Tangential forceNormal forceThe maximum equivalent stress
of cutting edge and the microgrinding depth is nearly 0Certainly the changes of the abrasive nose radium of cuttingedge do not affect the machining process of SiC In otherwords once the abrasive nose radium of cutting edge is atthe same order of magnitude with the microgrinding depththe nose radium of cutting edge can be ignored In factthe ratio of the tangential force and the normal force 119865
119905119865119899
is almost determined by the geometrical parameters of theabrasive barely influenced by the microgrinding depth Dueto the rise of the nose radium of cutting edge the ratio of thenose radium of cutting edge and the reference microgrindingdepth 119903
040 ascends whereas 119865
119905119865119899comes down gradually
As shown in Figure 13 with the velocity of microgrindingprocess increasing progressively the tangential force andthe normal force improve slightly and both have weakincreasing trends The maximum equivalent stresses become13699MPa 13967MPa 14074MPa and 14117MPa respec-tively Considering the reduction of loss of machine tool andthe perspective of energy conservation 1ms is regarded as agood choice
4 Experiments
According to the present limited research condition to verifythe validity of the above theoretical simulation model for theSiC microgrinding process a series of scratch experimentshave been conducted on the nanoindentation apparatusAgilent Nano Indenter G200 shown in Figure 14 And thescratch picture is given in Figure 15
Figure 14 Agilent Nano Indenter G200
In the experiments simple variable method was adoptedto observe the variation caused by microgrinding depth andthe velocity As to every depth and velocity data of groups areobtained by the scratch experiments Thus the average loadcalculated in Table 3 could definitely give expression to therelationship between load and microgrinding depth
After SiC workpiece polished finely triangular pyramidhead loading 1mN scratched the SiC workpiece for 2mmdisplacement whose velocity is 1mms As the scratchimproves from 20 nm to 30 nm to 40 nm to 50 nm the loadof triangular pyramid head reaches 00455mN 00463mN00481mN and 00492mN as illustrated in Figure 16 Thenormal force given in Figure 5 changes from 00238 120583N to00387 120583N to 00471 120583N to 00570 120583N in simulation Althoughthe specific data is not in full consistency due to the situation
8 Journal of Nanomaterials
Table 3 Changes of load due to the depth and velocity
Simple variablemethod depth (nm) Load (mN) Average load (mN)
Simple variablemethod velocity
(mms)Load (mN) Average load (mN)
20004570045000458
00455 1004800048600476
00481
30004650046200462
00463 5004770047300466
00472
40004690049100483
00481 10004770047600472
00475
50004920049500489
00492 15004680047600478
00474
Figure 15 Scratched SiC workpiece
15 20 25 30 35 40 45 50 55004
0042
0044
0046
0048
005
Depth (nm)
Load
(mN
)
Figure 16 Load change based on the depth
difference between the scratch and the grinding both theexperiment data and the simulation data show an obviousrising trend accompanied by the increase of scratch depthIn addition a group of experiments with same triangularpyramid parameters and 40 nm microgrinding depth wereimplemented to indicate the effect of velocity the nodesvelocities in Figure 17 are 1mms 5mms 10mms and15mms respectively and the corresponding loads reach00481mN 00472mN 00475mN and 00474mN respec-tively At the same time the normal force in simulation
0 2 4 6 8 10 12 14 16004
0042
0044
0046
0048
005
Velocity (mms)
Load
(mN
)
Figure 17 Load change based on the velocity
achieves 00466 120583N 00474120583N 00483 120583N and 00491 120583Nas shown in Figure 13 The data shown in the experimentand simulation vividly mean that triangular pyramid headload hardly goes with the change of velocity Above all goodagreement is shown between the experimental results and thesimulation results by Abaqus
5 Conclusions
Based on the simulation of SiC microgrinding process pre-sented in the paper the following conclusions can be drawn
(1) The depth of microgrinding plays a great role inthe machining process The process owns a 40 nmmicrogrinding depth having both small fluctuationand superior efficiency
(2) For negative rake angle a small one is a benefit toobtain the surface of SiC optical component
(3) The clearance angle has barely an influence on themanufacturing of SiC surface in microgrinding pro-cess
(4) To obtain a high accuracy of machining process theabrasive nose radium of cutting edge needs to becompressed
Journal of Nanomaterials 9
(5) Velocity of about 1ms is a proper choice in simula-tion of microgrinding process
(6) Simulations of finite element in microgrinding pro-cess could provide a reference for the load in thecoarse and fine grinding process of SiC mirror
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by the National Key Basic Researchand Development Program (973 Program) of China (Grantno 2011CB706702) Natural Science Foundation of China(Grant nos 51305161 and 51135006) and Jilin Province Sci-ence and Technology Development Plan Item (Grant no20130101042JC)
References
[1] R Naslain ldquoDesign preparation and properties of non-oxideCMCs for application in engines and nuclear reactors anoverviewrdquo Composites Science and Technology vol 64 no 2 pp155ndash170 2004
[2] W Krenkel and F Berndt ldquoCC-SiC composites for spaceapplications and advanced friction systemsrdquo Materials Scienceand Engineering A vol 412 no 1-2 pp 177ndash181 2005
[3] Y Julong Ultraprecision Machining of Functional CeramicsHarbin Institute of Technology Press Harbin China 2000
[4] P-H Lee H Chung and S W Lee ldquoOptimization of micro-grinding process with compressed air using response surfacemethodologyrdquo Proceedings of the Institution of MechanicalEngineers Part B Journal of Engineering Manufacture vol 225no 11 pp 2040ndash2050 2011
[5] F J Chen S H Yin H Huang et al ldquoProfile error compen-sation in ultra-precision grinding of aspheric surfaces with on-machine measurementrdquo International Journal of Machine Toolsand Manufacture vol 50 no 5 pp 480ndash486 2010
[6] J Feng B S Kim A Shih and J Ni ldquoTool wear monitoring formicro-end grinding of ceramic materialsrdquo Journal of MaterialsProcessing Technology vol 209 no 11 pp 5110ndash5116 2009
[7] J Feng P Chen and J Ni ldquoPrediction of surface generation inmicrogrinding of ceramic materials by coupled trajectory andfinite element analysisrdquo Finite Elements in Analysis and Designvol 57 pp 67ndash80 2012
[8] Z Yuan K-I Nomura and A Nakano ldquoA coreshell mecha-nism for stacking-fault generation in GaAs nanowiresrdquo AppliedPhysics Letters vol 100 no 16 Article ID 163103 2012
[9] B K Tanner M C Fossati J Garagorri et al ldquoPrediction ofthe propagation probability of individual cracks in brittle singlecrystal materialsrdquo Applied Physics Letters vol 101 no 4 ArticleID 041903 2012
[10] S Goel X Luo P Comley R L Reuben and A Cox ldquoBrittle-ductile transition during diamond turning of single crystalsilicon carbiderdquo International Journal of Machine Tools andManufacture vol 65 pp 15ndash21 2013
[11] D A Doman Rubbing and Plowing Phases in Single GrainGrinding Dalhousie University Halifax Canada 2006
[12] M Barge J Rech H Hamdi and J-M Bergheau ldquoExperimen-tal study of abrasive processrdquo Wear vol 264 no 5-6 pp 382ndash388 2008
[13] W Qiuning Experimental study on single diamond graingrinding of silicon wafers [MS thesis] Dalian University ofTechnology Dalian China 2006
[14] J Wang R Ye and Y Tang ldquo3D dynamic finite elementsimulation analysis of single abrasive grain during surfacegrindingrdquo Diamond amp Abrasive Engineering vol 173 no 5 pp41ndash45 2009
[15] P J Arrazola and T Ozel ldquoNumerical modelling of 3D hardturning using arbitrary Lagrangian Eulerian finite elementmethodrdquo International Journal of Machining and Machinabilityof Materials vol 4 no 1 pp 14ndash25 2008
[16] M Gunay I Korkut E Aslan and U Seker ldquoExperimentalinvestigation of the effect of cutting tool rake angle on maincutting forcerdquo Journal of Materials Processing Technology vol166 no 1 pp 44ndash49 2005
[17] Y-C Yen A Jain and T Altan ldquoA finite element analysis oforthogonal machining using different tool edge geometriesrdquoJournal of Materials Processing Technology vol 146 no 1 pp72ndash81 2004
[18] H Saglam F Unsacar and S Yaldiz ldquoInvestigation of the effectof rake angle and approaching angle on main cutting force andtool tip temperaturerdquo International Journal ofMachine Tools andManufacture vol 46 no 2 pp 132ndash141 2006
[19] J A Badger and A A Torrance ldquoComparison of two modelsto predict grinding forces from wheel surface topographyrdquoInternational Journal ofMachine Tools andManufacture vol 40no 8 pp 1099ndash1120 2000
[20] ABAQUS Userrsquos Manual Version 66 Hibbitt Karlsson andSorensen Inc Proxidence RI USA 2006
[21] J S Johnson K D Grobsky and D Bray ldquoRapid fabricationof lightweight silicon-carbide mirrorsrdquo in Proceedings of theInternational Symposium on Optical Science and Technology pp243ndash253 International Society for Optics and Photonics 2002
[22] B Li and B Zhao Modern Grinding Technology CMP BeijingChina 2003
[23] E H Lee and B W Shaffer ldquoThe theory of plasticity applied toa problem of machiningrdquo Journal of Applied Mechanics vol 18pp 405ndash413 1951
+24800e + 00+22733e + 00+20667e + 00+18600e + 00+16533e + 00+14467e + 00+12400e + 00+10333e + 00+82667e minus 01+62000e minus 01+41333e minus 01+20667e minus 01+00000e + 00
(a) Microgrinding depth 20 nm
+27300e + 00+25025e + 00+22750e + 00+20475e + 00+18200e + 00+15925e + 00+13650e + 00+11375e + 00+91000e minus 01+68250e minus 01+45500e minus 01+22750e minus 01+00000e + 00
PEEQ(avg 75)
(b) Microgrinding depth 30 nm
+27300e + 00+25025e + 00+22750e + 00+20475e + 00+18200e + 00+15925e + 00+13650e + 00+11375e + 00+91000e minus 01+68250e minus 01+45500e minus 01+22750e minus 01+00000e + 00
PEEQ(avg 75)
(c) Microgrinding depth 40 nm
+29200e + 00+26767e + 00+24333e + 00+21900e + 00+19467e + 00+17033e + 00+14600e + 00+12167e + 00+97333e minus 01+73000e minus 01+48667e minus 01+24333e minus 01+00000e + 00
PEEQ(avg 75)
(d) Microgrinding depth 50 nm
Figure 8 Comparison of the maximum equivalent plastic strain
The third generation of mirror is made from SiC andcarbon fiber reinforced SiC composites SiC mirror hasadvantage in lightweight whose radius-thickness ratio couldreach 20 1 easily The optical properties of SiC can be on apar with optical glass so that high polishing accuracy couldbe achieved [21] As rough SiC surface would be achieved inthe brittle machining process the plastic processing is mainlystudied in order to achieve higher precision SiC mirror Thecritical microgrinding depth of SiC material is 65 nm thusseveral microgrinding depths of models in simulation are20 nm 30 nm 40 nm and 50 nm As shown in Figure 4 thecorresponding tangential forces are 004428120583N 007368120583N009302120583N and 01109 120583N respectively and the homolo-gous normal forces are 002376 120583N 003765 120583N 004647 120583Nand 005758120583N respectively With the steady increase ofmicrogrinding depth the tangential force and the normalforce rise stably Due to the increase of microgrinding depthundeformed chip thickens and abrasive cutting area involvedbecomes bigger Thus the plastic deformation energy theabrasive needed to overcome and the grinding force growbigger Comparing the curve shape in Figure 4 with thosein Figure 5 the tangential force is larger than the normalforce inmicrogrinding process of identical depth At the sametime the fluctuation of grinding force of group 1-model 4whosemicrogrinding depth is 50 nmbecomes bigger than theother models in group 1 resulting from the microgrinding
depth close to critical depth The maximum equivalentstresses of group 1 are 13838MPa 13792MPa 13691MPa and13552MPa respectively and themaximum equivalent plasticstrains are 248 273 285 and 292 respectively As shownin Figure 6 with the increment of microgrinding depththe maximum equivalent stress decreases successively whilethe maximum equivalent plastic strain increases graduallyFigures 7 and 8 show that the maximum equivalent stressmainly emerges in the primary deformation zone and thesecond deformation zone while the maximum equivalentplastic strain appears in the second deformation zone
The theoretical formula of single abrasive grinding force[22]
119865119905119892=120587
41198651198751198862119892sin 120579
119865119899119892= 1198651198751198862119892sin 120579 tan 120579
(6)
where 120579 is semitip angle 80∘ le 2120579 le 140∘ 119886119892is undeformed
microgrinding depth 119865119901is unit microgrinding force
1198651199011 =
4119865119905119892
1205871198862119892sin 120579
1198651199012 =
119865119899119892
1198862119892sin 120579 tan 120579
(7)
6 Journal of Nanomaterials
0
002
004
006
008
01
012
1
2
3
4
5
6
7
FtFn
Forc
e(120583
N)
Rake angle (∘)minus30 minus20 minus10 0
Tangential forceNormal forceFtFn
Figure 9 Changes of grinding force based on rake angle
Figure 10 Changes of the strain based on rake angle
The average of 1198651199011 and 1198651199012 is adopted as 119865
119901
119865119901=1198651199011 + 1198651199012
2 (8)
Taking the efficiency and accuracy of microgrinding intoaccount 119886
119892is used as 40 nm The unit microgrinding force
can be calculated as approximate 844 times 107N according tothe simulation by Abaqus The macroscopic force could befigured out simply after that
Comparing the models in group 2 the result is shownin Figure 9 With the negative rake angle increasing steadilythe microgrinding force grows stably while the ratio of thetangential force and the normal force of microgrinding 119865
119905119865119899
monotonically decreasesThis is because the increment of thenegative rake angle makes the contact area of abrasive andworkpiece bigger so does the load of abrasive cutting edgeThe shear angles of the corresponding models are shown tobe 3289∘ 2750∘ 2337∘ and 2122∘ respectivelyThe balancedaugmenter of the negative rake angle gets the shear angledown However the cutting deformation changes converselyThus the relation between the negative rake angle and theshear angle is consistent with Lee and Shaffer shear angle
12 16 20 240
005
01
17
19
21
FtFn
Forc
e(120583
N)
Tangential forceNormal forceFtFn
Clearance angle (∘)
Figure 11 Changes based on the clearance angle
01 02 03 04 050
005
01
1
15
2
FtFn
Forc
e(120583
N)
Tangential forceNormal forceFtFn
r040
Figure 12 Changes based on the nose radium of the cutting edge
theory [23] Knowing the rake angle and the shear angle theshear strain 120574
0can be further computed as follows
1205740 =cos 120574
sin120601 cos (120601 minus 120574) (9)
where 120574 is the rake angle of abrasive andB is the shear angleAs shown in Figure 10 there is a rise of the maximum
equivalent plastic strain and the shear strain along with thenegative rake angle being larger Furthermore both alphabetsof lines have the same trends
With the clearance angle increasing gradually the chang-ing trends of the tangential force and the normal force areshown in Figure 11 The slight increase of the tangential forceand the normal force can be negligible What is more theratio of the tangential force and the normal force119865
119905119865119899almost
has no change In other words the changes of clearance angledo not affect the stability of the machining process of SiC
As shown in Figure 12 the elevation of the abrasivenose radium of cutting edge makes the microgrinding forcebecome larger Nevertheless the tangential force has a smallamplification and the normal force has a big one Whenthe abrasive nose radium of cutting edge is far less than themicrogrinding depth the ratio of the abrasive nose radium
Journal of Nanomaterials 7
1 5 10004
005
006
007
008
009
01
Microgrinding velocity (ms)15
136
137
138
139
14
141
142
Equi
vale
nt st
ress
(MPa
)
Tangential forceNormal forceThe maximum equivalent stress
of cutting edge and the microgrinding depth is nearly 0Certainly the changes of the abrasive nose radium of cuttingedge do not affect the machining process of SiC In otherwords once the abrasive nose radium of cutting edge is atthe same order of magnitude with the microgrinding depththe nose radium of cutting edge can be ignored In factthe ratio of the tangential force and the normal force 119865
119905119865119899
is almost determined by the geometrical parameters of theabrasive barely influenced by the microgrinding depth Dueto the rise of the nose radium of cutting edge the ratio of thenose radium of cutting edge and the reference microgrindingdepth 119903
040 ascends whereas 119865
119905119865119899comes down gradually
As shown in Figure 13 with the velocity of microgrindingprocess increasing progressively the tangential force andthe normal force improve slightly and both have weakincreasing trends The maximum equivalent stresses become13699MPa 13967MPa 14074MPa and 14117MPa respec-tively Considering the reduction of loss of machine tool andthe perspective of energy conservation 1ms is regarded as agood choice
4 Experiments
According to the present limited research condition to verifythe validity of the above theoretical simulation model for theSiC microgrinding process a series of scratch experimentshave been conducted on the nanoindentation apparatusAgilent Nano Indenter G200 shown in Figure 14 And thescratch picture is given in Figure 15
Figure 14 Agilent Nano Indenter G200
In the experiments simple variable method was adoptedto observe the variation caused by microgrinding depth andthe velocity As to every depth and velocity data of groups areobtained by the scratch experiments Thus the average loadcalculated in Table 3 could definitely give expression to therelationship between load and microgrinding depth
After SiC workpiece polished finely triangular pyramidhead loading 1mN scratched the SiC workpiece for 2mmdisplacement whose velocity is 1mms As the scratchimproves from 20 nm to 30 nm to 40 nm to 50 nm the loadof triangular pyramid head reaches 00455mN 00463mN00481mN and 00492mN as illustrated in Figure 16 Thenormal force given in Figure 5 changes from 00238 120583N to00387 120583N to 00471 120583N to 00570 120583N in simulation Althoughthe specific data is not in full consistency due to the situation
8 Journal of Nanomaterials
Table 3 Changes of load due to the depth and velocity
Simple variablemethod depth (nm) Load (mN) Average load (mN)
Simple variablemethod velocity
(mms)Load (mN) Average load (mN)
20004570045000458
00455 1004800048600476
00481
30004650046200462
00463 5004770047300466
00472
40004690049100483
00481 10004770047600472
00475
50004920049500489
00492 15004680047600478
00474
Figure 15 Scratched SiC workpiece
15 20 25 30 35 40 45 50 55004
0042
0044
0046
0048
005
Depth (nm)
Load
(mN
)
Figure 16 Load change based on the depth
difference between the scratch and the grinding both theexperiment data and the simulation data show an obviousrising trend accompanied by the increase of scratch depthIn addition a group of experiments with same triangularpyramid parameters and 40 nm microgrinding depth wereimplemented to indicate the effect of velocity the nodesvelocities in Figure 17 are 1mms 5mms 10mms and15mms respectively and the corresponding loads reach00481mN 00472mN 00475mN and 00474mN respec-tively At the same time the normal force in simulation
0 2 4 6 8 10 12 14 16004
0042
0044
0046
0048
005
Velocity (mms)
Load
(mN
)
Figure 17 Load change based on the velocity
achieves 00466 120583N 00474120583N 00483 120583N and 00491 120583Nas shown in Figure 13 The data shown in the experimentand simulation vividly mean that triangular pyramid headload hardly goes with the change of velocity Above all goodagreement is shown between the experimental results and thesimulation results by Abaqus
5 Conclusions
Based on the simulation of SiC microgrinding process pre-sented in the paper the following conclusions can be drawn
(1) The depth of microgrinding plays a great role inthe machining process The process owns a 40 nmmicrogrinding depth having both small fluctuationand superior efficiency
(2) For negative rake angle a small one is a benefit toobtain the surface of SiC optical component
(3) The clearance angle has barely an influence on themanufacturing of SiC surface in microgrinding pro-cess
(4) To obtain a high accuracy of machining process theabrasive nose radium of cutting edge needs to becompressed
Journal of Nanomaterials 9
(5) Velocity of about 1ms is a proper choice in simula-tion of microgrinding process
(6) Simulations of finite element in microgrinding pro-cess could provide a reference for the load in thecoarse and fine grinding process of SiC mirror
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by the National Key Basic Researchand Development Program (973 Program) of China (Grantno 2011CB706702) Natural Science Foundation of China(Grant nos 51305161 and 51135006) and Jilin Province Sci-ence and Technology Development Plan Item (Grant no20130101042JC)
References
[1] R Naslain ldquoDesign preparation and properties of non-oxideCMCs for application in engines and nuclear reactors anoverviewrdquo Composites Science and Technology vol 64 no 2 pp155ndash170 2004
[2] W Krenkel and F Berndt ldquoCC-SiC composites for spaceapplications and advanced friction systemsrdquo Materials Scienceand Engineering A vol 412 no 1-2 pp 177ndash181 2005
[3] Y Julong Ultraprecision Machining of Functional CeramicsHarbin Institute of Technology Press Harbin China 2000
[4] P-H Lee H Chung and S W Lee ldquoOptimization of micro-grinding process with compressed air using response surfacemethodologyrdquo Proceedings of the Institution of MechanicalEngineers Part B Journal of Engineering Manufacture vol 225no 11 pp 2040ndash2050 2011
[5] F J Chen S H Yin H Huang et al ldquoProfile error compen-sation in ultra-precision grinding of aspheric surfaces with on-machine measurementrdquo International Journal of Machine Toolsand Manufacture vol 50 no 5 pp 480ndash486 2010
[6] J Feng B S Kim A Shih and J Ni ldquoTool wear monitoring formicro-end grinding of ceramic materialsrdquo Journal of MaterialsProcessing Technology vol 209 no 11 pp 5110ndash5116 2009
[7] J Feng P Chen and J Ni ldquoPrediction of surface generation inmicrogrinding of ceramic materials by coupled trajectory andfinite element analysisrdquo Finite Elements in Analysis and Designvol 57 pp 67ndash80 2012
[8] Z Yuan K-I Nomura and A Nakano ldquoA coreshell mecha-nism for stacking-fault generation in GaAs nanowiresrdquo AppliedPhysics Letters vol 100 no 16 Article ID 163103 2012
[9] B K Tanner M C Fossati J Garagorri et al ldquoPrediction ofthe propagation probability of individual cracks in brittle singlecrystal materialsrdquo Applied Physics Letters vol 101 no 4 ArticleID 041903 2012
[10] S Goel X Luo P Comley R L Reuben and A Cox ldquoBrittle-ductile transition during diamond turning of single crystalsilicon carbiderdquo International Journal of Machine Tools andManufacture vol 65 pp 15ndash21 2013
[11] D A Doman Rubbing and Plowing Phases in Single GrainGrinding Dalhousie University Halifax Canada 2006
[12] M Barge J Rech H Hamdi and J-M Bergheau ldquoExperimen-tal study of abrasive processrdquo Wear vol 264 no 5-6 pp 382ndash388 2008
[13] W Qiuning Experimental study on single diamond graingrinding of silicon wafers [MS thesis] Dalian University ofTechnology Dalian China 2006
[14] J Wang R Ye and Y Tang ldquo3D dynamic finite elementsimulation analysis of single abrasive grain during surfacegrindingrdquo Diamond amp Abrasive Engineering vol 173 no 5 pp41ndash45 2009
[15] P J Arrazola and T Ozel ldquoNumerical modelling of 3D hardturning using arbitrary Lagrangian Eulerian finite elementmethodrdquo International Journal of Machining and Machinabilityof Materials vol 4 no 1 pp 14ndash25 2008
[16] M Gunay I Korkut E Aslan and U Seker ldquoExperimentalinvestigation of the effect of cutting tool rake angle on maincutting forcerdquo Journal of Materials Processing Technology vol166 no 1 pp 44ndash49 2005
[17] Y-C Yen A Jain and T Altan ldquoA finite element analysis oforthogonal machining using different tool edge geometriesrdquoJournal of Materials Processing Technology vol 146 no 1 pp72ndash81 2004
[18] H Saglam F Unsacar and S Yaldiz ldquoInvestigation of the effectof rake angle and approaching angle on main cutting force andtool tip temperaturerdquo International Journal ofMachine Tools andManufacture vol 46 no 2 pp 132ndash141 2006
[19] J A Badger and A A Torrance ldquoComparison of two modelsto predict grinding forces from wheel surface topographyrdquoInternational Journal ofMachine Tools andManufacture vol 40no 8 pp 1099ndash1120 2000
[20] ABAQUS Userrsquos Manual Version 66 Hibbitt Karlsson andSorensen Inc Proxidence RI USA 2006
[21] J S Johnson K D Grobsky and D Bray ldquoRapid fabricationof lightweight silicon-carbide mirrorsrdquo in Proceedings of theInternational Symposium on Optical Science and Technology pp243ndash253 International Society for Optics and Photonics 2002
[22] B Li and B Zhao Modern Grinding Technology CMP BeijingChina 2003
[23] E H Lee and B W Shaffer ldquoThe theory of plasticity applied toa problem of machiningrdquo Journal of Applied Mechanics vol 18pp 405ndash413 1951
+24800e + 00+22733e + 00+20667e + 00+18600e + 00+16533e + 00+14467e + 00+12400e + 00+10333e + 00+82667e minus 01+62000e minus 01+41333e minus 01+20667e minus 01+00000e + 00
(a) Microgrinding depth 20 nm
+27300e + 00+25025e + 00+22750e + 00+20475e + 00+18200e + 00+15925e + 00+13650e + 00+11375e + 00+91000e minus 01+68250e minus 01+45500e minus 01+22750e minus 01+00000e + 00
PEEQ(avg 75)
(b) Microgrinding depth 30 nm
+27300e + 00+25025e + 00+22750e + 00+20475e + 00+18200e + 00+15925e + 00+13650e + 00+11375e + 00+91000e minus 01+68250e minus 01+45500e minus 01+22750e minus 01+00000e + 00
PEEQ(avg 75)
(c) Microgrinding depth 40 nm
+29200e + 00+26767e + 00+24333e + 00+21900e + 00+19467e + 00+17033e + 00+14600e + 00+12167e + 00+97333e minus 01+73000e minus 01+48667e minus 01+24333e minus 01+00000e + 00
PEEQ(avg 75)
(d) Microgrinding depth 50 nm
Figure 8 Comparison of the maximum equivalent plastic strain
The third generation of mirror is made from SiC andcarbon fiber reinforced SiC composites SiC mirror hasadvantage in lightweight whose radius-thickness ratio couldreach 20 1 easily The optical properties of SiC can be on apar with optical glass so that high polishing accuracy couldbe achieved [21] As rough SiC surface would be achieved inthe brittle machining process the plastic processing is mainlystudied in order to achieve higher precision SiC mirror Thecritical microgrinding depth of SiC material is 65 nm thusseveral microgrinding depths of models in simulation are20 nm 30 nm 40 nm and 50 nm As shown in Figure 4 thecorresponding tangential forces are 004428120583N 007368120583N009302120583N and 01109 120583N respectively and the homolo-gous normal forces are 002376 120583N 003765 120583N 004647 120583Nand 005758120583N respectively With the steady increase ofmicrogrinding depth the tangential force and the normalforce rise stably Due to the increase of microgrinding depthundeformed chip thickens and abrasive cutting area involvedbecomes bigger Thus the plastic deformation energy theabrasive needed to overcome and the grinding force growbigger Comparing the curve shape in Figure 4 with thosein Figure 5 the tangential force is larger than the normalforce inmicrogrinding process of identical depth At the sametime the fluctuation of grinding force of group 1-model 4whosemicrogrinding depth is 50 nmbecomes bigger than theother models in group 1 resulting from the microgrinding
depth close to critical depth The maximum equivalentstresses of group 1 are 13838MPa 13792MPa 13691MPa and13552MPa respectively and themaximum equivalent plasticstrains are 248 273 285 and 292 respectively As shownin Figure 6 with the increment of microgrinding depththe maximum equivalent stress decreases successively whilethe maximum equivalent plastic strain increases graduallyFigures 7 and 8 show that the maximum equivalent stressmainly emerges in the primary deformation zone and thesecond deformation zone while the maximum equivalentplastic strain appears in the second deformation zone
The theoretical formula of single abrasive grinding force[22]
119865119905119892=120587
41198651198751198862119892sin 120579
119865119899119892= 1198651198751198862119892sin 120579 tan 120579
(6)
where 120579 is semitip angle 80∘ le 2120579 le 140∘ 119886119892is undeformed
microgrinding depth 119865119901is unit microgrinding force
1198651199011 =
4119865119905119892
1205871198862119892sin 120579
1198651199012 =
119865119899119892
1198862119892sin 120579 tan 120579
(7)
6 Journal of Nanomaterials
0
002
004
006
008
01
012
1
2
3
4
5
6
7
FtFn
Forc
e(120583
N)
Rake angle (∘)minus30 minus20 minus10 0
Tangential forceNormal forceFtFn
Figure 9 Changes of grinding force based on rake angle
Figure 10 Changes of the strain based on rake angle
The average of 1198651199011 and 1198651199012 is adopted as 119865
119901
119865119901=1198651199011 + 1198651199012
2 (8)
Taking the efficiency and accuracy of microgrinding intoaccount 119886
119892is used as 40 nm The unit microgrinding force
can be calculated as approximate 844 times 107N according tothe simulation by Abaqus The macroscopic force could befigured out simply after that
Comparing the models in group 2 the result is shownin Figure 9 With the negative rake angle increasing steadilythe microgrinding force grows stably while the ratio of thetangential force and the normal force of microgrinding 119865
119905119865119899
monotonically decreasesThis is because the increment of thenegative rake angle makes the contact area of abrasive andworkpiece bigger so does the load of abrasive cutting edgeThe shear angles of the corresponding models are shown tobe 3289∘ 2750∘ 2337∘ and 2122∘ respectivelyThe balancedaugmenter of the negative rake angle gets the shear angledown However the cutting deformation changes converselyThus the relation between the negative rake angle and theshear angle is consistent with Lee and Shaffer shear angle
12 16 20 240
005
01
17
19
21
FtFn
Forc
e(120583
N)
Tangential forceNormal forceFtFn
Clearance angle (∘)
Figure 11 Changes based on the clearance angle
01 02 03 04 050
005
01
1
15
2
FtFn
Forc
e(120583
N)
Tangential forceNormal forceFtFn
r040
Figure 12 Changes based on the nose radium of the cutting edge
theory [23] Knowing the rake angle and the shear angle theshear strain 120574
0can be further computed as follows
1205740 =cos 120574
sin120601 cos (120601 minus 120574) (9)
where 120574 is the rake angle of abrasive andB is the shear angleAs shown in Figure 10 there is a rise of the maximum
equivalent plastic strain and the shear strain along with thenegative rake angle being larger Furthermore both alphabetsof lines have the same trends
With the clearance angle increasing gradually the chang-ing trends of the tangential force and the normal force areshown in Figure 11 The slight increase of the tangential forceand the normal force can be negligible What is more theratio of the tangential force and the normal force119865
119905119865119899almost
has no change In other words the changes of clearance angledo not affect the stability of the machining process of SiC
As shown in Figure 12 the elevation of the abrasivenose radium of cutting edge makes the microgrinding forcebecome larger Nevertheless the tangential force has a smallamplification and the normal force has a big one Whenthe abrasive nose radium of cutting edge is far less than themicrogrinding depth the ratio of the abrasive nose radium
Journal of Nanomaterials 7
1 5 10004
005
006
007
008
009
01
Microgrinding velocity (ms)15
136
137
138
139
14
141
142
Equi
vale
nt st
ress
(MPa
)
Tangential forceNormal forceThe maximum equivalent stress
of cutting edge and the microgrinding depth is nearly 0Certainly the changes of the abrasive nose radium of cuttingedge do not affect the machining process of SiC In otherwords once the abrasive nose radium of cutting edge is atthe same order of magnitude with the microgrinding depththe nose radium of cutting edge can be ignored In factthe ratio of the tangential force and the normal force 119865
119905119865119899
is almost determined by the geometrical parameters of theabrasive barely influenced by the microgrinding depth Dueto the rise of the nose radium of cutting edge the ratio of thenose radium of cutting edge and the reference microgrindingdepth 119903
040 ascends whereas 119865
119905119865119899comes down gradually
As shown in Figure 13 with the velocity of microgrindingprocess increasing progressively the tangential force andthe normal force improve slightly and both have weakincreasing trends The maximum equivalent stresses become13699MPa 13967MPa 14074MPa and 14117MPa respec-tively Considering the reduction of loss of machine tool andthe perspective of energy conservation 1ms is regarded as agood choice
4 Experiments
According to the present limited research condition to verifythe validity of the above theoretical simulation model for theSiC microgrinding process a series of scratch experimentshave been conducted on the nanoindentation apparatusAgilent Nano Indenter G200 shown in Figure 14 And thescratch picture is given in Figure 15
Figure 14 Agilent Nano Indenter G200
In the experiments simple variable method was adoptedto observe the variation caused by microgrinding depth andthe velocity As to every depth and velocity data of groups areobtained by the scratch experiments Thus the average loadcalculated in Table 3 could definitely give expression to therelationship between load and microgrinding depth
After SiC workpiece polished finely triangular pyramidhead loading 1mN scratched the SiC workpiece for 2mmdisplacement whose velocity is 1mms As the scratchimproves from 20 nm to 30 nm to 40 nm to 50 nm the loadof triangular pyramid head reaches 00455mN 00463mN00481mN and 00492mN as illustrated in Figure 16 Thenormal force given in Figure 5 changes from 00238 120583N to00387 120583N to 00471 120583N to 00570 120583N in simulation Althoughthe specific data is not in full consistency due to the situation
8 Journal of Nanomaterials
Table 3 Changes of load due to the depth and velocity
Simple variablemethod depth (nm) Load (mN) Average load (mN)
Simple variablemethod velocity
(mms)Load (mN) Average load (mN)
20004570045000458
00455 1004800048600476
00481
30004650046200462
00463 5004770047300466
00472
40004690049100483
00481 10004770047600472
00475
50004920049500489
00492 15004680047600478
00474
Figure 15 Scratched SiC workpiece
15 20 25 30 35 40 45 50 55004
0042
0044
0046
0048
005
Depth (nm)
Load
(mN
)
Figure 16 Load change based on the depth
difference between the scratch and the grinding both theexperiment data and the simulation data show an obviousrising trend accompanied by the increase of scratch depthIn addition a group of experiments with same triangularpyramid parameters and 40 nm microgrinding depth wereimplemented to indicate the effect of velocity the nodesvelocities in Figure 17 are 1mms 5mms 10mms and15mms respectively and the corresponding loads reach00481mN 00472mN 00475mN and 00474mN respec-tively At the same time the normal force in simulation
0 2 4 6 8 10 12 14 16004
0042
0044
0046
0048
005
Velocity (mms)
Load
(mN
)
Figure 17 Load change based on the velocity
achieves 00466 120583N 00474120583N 00483 120583N and 00491 120583Nas shown in Figure 13 The data shown in the experimentand simulation vividly mean that triangular pyramid headload hardly goes with the change of velocity Above all goodagreement is shown between the experimental results and thesimulation results by Abaqus
5 Conclusions
Based on the simulation of SiC microgrinding process pre-sented in the paper the following conclusions can be drawn
(1) The depth of microgrinding plays a great role inthe machining process The process owns a 40 nmmicrogrinding depth having both small fluctuationand superior efficiency
(2) For negative rake angle a small one is a benefit toobtain the surface of SiC optical component
(3) The clearance angle has barely an influence on themanufacturing of SiC surface in microgrinding pro-cess
(4) To obtain a high accuracy of machining process theabrasive nose radium of cutting edge needs to becompressed
Journal of Nanomaterials 9
(5) Velocity of about 1ms is a proper choice in simula-tion of microgrinding process
(6) Simulations of finite element in microgrinding pro-cess could provide a reference for the load in thecoarse and fine grinding process of SiC mirror
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by the National Key Basic Researchand Development Program (973 Program) of China (Grantno 2011CB706702) Natural Science Foundation of China(Grant nos 51305161 and 51135006) and Jilin Province Sci-ence and Technology Development Plan Item (Grant no20130101042JC)
References
[1] R Naslain ldquoDesign preparation and properties of non-oxideCMCs for application in engines and nuclear reactors anoverviewrdquo Composites Science and Technology vol 64 no 2 pp155ndash170 2004
[2] W Krenkel and F Berndt ldquoCC-SiC composites for spaceapplications and advanced friction systemsrdquo Materials Scienceand Engineering A vol 412 no 1-2 pp 177ndash181 2005
[3] Y Julong Ultraprecision Machining of Functional CeramicsHarbin Institute of Technology Press Harbin China 2000
[4] P-H Lee H Chung and S W Lee ldquoOptimization of micro-grinding process with compressed air using response surfacemethodologyrdquo Proceedings of the Institution of MechanicalEngineers Part B Journal of Engineering Manufacture vol 225no 11 pp 2040ndash2050 2011
[5] F J Chen S H Yin H Huang et al ldquoProfile error compen-sation in ultra-precision grinding of aspheric surfaces with on-machine measurementrdquo International Journal of Machine Toolsand Manufacture vol 50 no 5 pp 480ndash486 2010
[6] J Feng B S Kim A Shih and J Ni ldquoTool wear monitoring formicro-end grinding of ceramic materialsrdquo Journal of MaterialsProcessing Technology vol 209 no 11 pp 5110ndash5116 2009
[7] J Feng P Chen and J Ni ldquoPrediction of surface generation inmicrogrinding of ceramic materials by coupled trajectory andfinite element analysisrdquo Finite Elements in Analysis and Designvol 57 pp 67ndash80 2012
[8] Z Yuan K-I Nomura and A Nakano ldquoA coreshell mecha-nism for stacking-fault generation in GaAs nanowiresrdquo AppliedPhysics Letters vol 100 no 16 Article ID 163103 2012
[9] B K Tanner M C Fossati J Garagorri et al ldquoPrediction ofthe propagation probability of individual cracks in brittle singlecrystal materialsrdquo Applied Physics Letters vol 101 no 4 ArticleID 041903 2012
[10] S Goel X Luo P Comley R L Reuben and A Cox ldquoBrittle-ductile transition during diamond turning of single crystalsilicon carbiderdquo International Journal of Machine Tools andManufacture vol 65 pp 15ndash21 2013
[11] D A Doman Rubbing and Plowing Phases in Single GrainGrinding Dalhousie University Halifax Canada 2006
[12] M Barge J Rech H Hamdi and J-M Bergheau ldquoExperimen-tal study of abrasive processrdquo Wear vol 264 no 5-6 pp 382ndash388 2008
[13] W Qiuning Experimental study on single diamond graingrinding of silicon wafers [MS thesis] Dalian University ofTechnology Dalian China 2006
[14] J Wang R Ye and Y Tang ldquo3D dynamic finite elementsimulation analysis of single abrasive grain during surfacegrindingrdquo Diamond amp Abrasive Engineering vol 173 no 5 pp41ndash45 2009
[15] P J Arrazola and T Ozel ldquoNumerical modelling of 3D hardturning using arbitrary Lagrangian Eulerian finite elementmethodrdquo International Journal of Machining and Machinabilityof Materials vol 4 no 1 pp 14ndash25 2008
[16] M Gunay I Korkut E Aslan and U Seker ldquoExperimentalinvestigation of the effect of cutting tool rake angle on maincutting forcerdquo Journal of Materials Processing Technology vol166 no 1 pp 44ndash49 2005
[17] Y-C Yen A Jain and T Altan ldquoA finite element analysis oforthogonal machining using different tool edge geometriesrdquoJournal of Materials Processing Technology vol 146 no 1 pp72ndash81 2004
[18] H Saglam F Unsacar and S Yaldiz ldquoInvestigation of the effectof rake angle and approaching angle on main cutting force andtool tip temperaturerdquo International Journal ofMachine Tools andManufacture vol 46 no 2 pp 132ndash141 2006
[19] J A Badger and A A Torrance ldquoComparison of two modelsto predict grinding forces from wheel surface topographyrdquoInternational Journal ofMachine Tools andManufacture vol 40no 8 pp 1099ndash1120 2000
[20] ABAQUS Userrsquos Manual Version 66 Hibbitt Karlsson andSorensen Inc Proxidence RI USA 2006
[21] J S Johnson K D Grobsky and D Bray ldquoRapid fabricationof lightweight silicon-carbide mirrorsrdquo in Proceedings of theInternational Symposium on Optical Science and Technology pp243ndash253 International Society for Optics and Photonics 2002
[22] B Li and B Zhao Modern Grinding Technology CMP BeijingChina 2003
[23] E H Lee and B W Shaffer ldquoThe theory of plasticity applied toa problem of machiningrdquo Journal of Applied Mechanics vol 18pp 405ndash413 1951
Figure 10 Changes of the strain based on rake angle
The average of 1198651199011 and 1198651199012 is adopted as 119865
119901
119865119901=1198651199011 + 1198651199012
2 (8)
Taking the efficiency and accuracy of microgrinding intoaccount 119886
119892is used as 40 nm The unit microgrinding force
can be calculated as approximate 844 times 107N according tothe simulation by Abaqus The macroscopic force could befigured out simply after that
Comparing the models in group 2 the result is shownin Figure 9 With the negative rake angle increasing steadilythe microgrinding force grows stably while the ratio of thetangential force and the normal force of microgrinding 119865
119905119865119899
monotonically decreasesThis is because the increment of thenegative rake angle makes the contact area of abrasive andworkpiece bigger so does the load of abrasive cutting edgeThe shear angles of the corresponding models are shown tobe 3289∘ 2750∘ 2337∘ and 2122∘ respectivelyThe balancedaugmenter of the negative rake angle gets the shear angledown However the cutting deformation changes converselyThus the relation between the negative rake angle and theshear angle is consistent with Lee and Shaffer shear angle
12 16 20 240
005
01
17
19
21
FtFn
Forc
e(120583
N)
Tangential forceNormal forceFtFn
Clearance angle (∘)
Figure 11 Changes based on the clearance angle
01 02 03 04 050
005
01
1
15
2
FtFn
Forc
e(120583
N)
Tangential forceNormal forceFtFn
r040
Figure 12 Changes based on the nose radium of the cutting edge
theory [23] Knowing the rake angle and the shear angle theshear strain 120574
0can be further computed as follows
1205740 =cos 120574
sin120601 cos (120601 minus 120574) (9)
where 120574 is the rake angle of abrasive andB is the shear angleAs shown in Figure 10 there is a rise of the maximum
equivalent plastic strain and the shear strain along with thenegative rake angle being larger Furthermore both alphabetsof lines have the same trends
With the clearance angle increasing gradually the chang-ing trends of the tangential force and the normal force areshown in Figure 11 The slight increase of the tangential forceand the normal force can be negligible What is more theratio of the tangential force and the normal force119865
119905119865119899almost
has no change In other words the changes of clearance angledo not affect the stability of the machining process of SiC
As shown in Figure 12 the elevation of the abrasivenose radium of cutting edge makes the microgrinding forcebecome larger Nevertheless the tangential force has a smallamplification and the normal force has a big one Whenthe abrasive nose radium of cutting edge is far less than themicrogrinding depth the ratio of the abrasive nose radium
Journal of Nanomaterials 7
1 5 10004
005
006
007
008
009
01
Microgrinding velocity (ms)15
136
137
138
139
14
141
142
Equi
vale
nt st
ress
(MPa
)
Tangential forceNormal forceThe maximum equivalent stress
of cutting edge and the microgrinding depth is nearly 0Certainly the changes of the abrasive nose radium of cuttingedge do not affect the machining process of SiC In otherwords once the abrasive nose radium of cutting edge is atthe same order of magnitude with the microgrinding depththe nose radium of cutting edge can be ignored In factthe ratio of the tangential force and the normal force 119865
119905119865119899
is almost determined by the geometrical parameters of theabrasive barely influenced by the microgrinding depth Dueto the rise of the nose radium of cutting edge the ratio of thenose radium of cutting edge and the reference microgrindingdepth 119903
040 ascends whereas 119865
119905119865119899comes down gradually
As shown in Figure 13 with the velocity of microgrindingprocess increasing progressively the tangential force andthe normal force improve slightly and both have weakincreasing trends The maximum equivalent stresses become13699MPa 13967MPa 14074MPa and 14117MPa respec-tively Considering the reduction of loss of machine tool andthe perspective of energy conservation 1ms is regarded as agood choice
4 Experiments
According to the present limited research condition to verifythe validity of the above theoretical simulation model for theSiC microgrinding process a series of scratch experimentshave been conducted on the nanoindentation apparatusAgilent Nano Indenter G200 shown in Figure 14 And thescratch picture is given in Figure 15
Figure 14 Agilent Nano Indenter G200
In the experiments simple variable method was adoptedto observe the variation caused by microgrinding depth andthe velocity As to every depth and velocity data of groups areobtained by the scratch experiments Thus the average loadcalculated in Table 3 could definitely give expression to therelationship between load and microgrinding depth
After SiC workpiece polished finely triangular pyramidhead loading 1mN scratched the SiC workpiece for 2mmdisplacement whose velocity is 1mms As the scratchimproves from 20 nm to 30 nm to 40 nm to 50 nm the loadof triangular pyramid head reaches 00455mN 00463mN00481mN and 00492mN as illustrated in Figure 16 Thenormal force given in Figure 5 changes from 00238 120583N to00387 120583N to 00471 120583N to 00570 120583N in simulation Althoughthe specific data is not in full consistency due to the situation
8 Journal of Nanomaterials
Table 3 Changes of load due to the depth and velocity
Simple variablemethod depth (nm) Load (mN) Average load (mN)
Simple variablemethod velocity
(mms)Load (mN) Average load (mN)
20004570045000458
00455 1004800048600476
00481
30004650046200462
00463 5004770047300466
00472
40004690049100483
00481 10004770047600472
00475
50004920049500489
00492 15004680047600478
00474
Figure 15 Scratched SiC workpiece
15 20 25 30 35 40 45 50 55004
0042
0044
0046
0048
005
Depth (nm)
Load
(mN
)
Figure 16 Load change based on the depth
difference between the scratch and the grinding both theexperiment data and the simulation data show an obviousrising trend accompanied by the increase of scratch depthIn addition a group of experiments with same triangularpyramid parameters and 40 nm microgrinding depth wereimplemented to indicate the effect of velocity the nodesvelocities in Figure 17 are 1mms 5mms 10mms and15mms respectively and the corresponding loads reach00481mN 00472mN 00475mN and 00474mN respec-tively At the same time the normal force in simulation
0 2 4 6 8 10 12 14 16004
0042
0044
0046
0048
005
Velocity (mms)
Load
(mN
)
Figure 17 Load change based on the velocity
achieves 00466 120583N 00474120583N 00483 120583N and 00491 120583Nas shown in Figure 13 The data shown in the experimentand simulation vividly mean that triangular pyramid headload hardly goes with the change of velocity Above all goodagreement is shown between the experimental results and thesimulation results by Abaqus
5 Conclusions
Based on the simulation of SiC microgrinding process pre-sented in the paper the following conclusions can be drawn
(1) The depth of microgrinding plays a great role inthe machining process The process owns a 40 nmmicrogrinding depth having both small fluctuationand superior efficiency
(2) For negative rake angle a small one is a benefit toobtain the surface of SiC optical component
(3) The clearance angle has barely an influence on themanufacturing of SiC surface in microgrinding pro-cess
(4) To obtain a high accuracy of machining process theabrasive nose radium of cutting edge needs to becompressed
Journal of Nanomaterials 9
(5) Velocity of about 1ms is a proper choice in simula-tion of microgrinding process
(6) Simulations of finite element in microgrinding pro-cess could provide a reference for the load in thecoarse and fine grinding process of SiC mirror
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by the National Key Basic Researchand Development Program (973 Program) of China (Grantno 2011CB706702) Natural Science Foundation of China(Grant nos 51305161 and 51135006) and Jilin Province Sci-ence and Technology Development Plan Item (Grant no20130101042JC)
References
[1] R Naslain ldquoDesign preparation and properties of non-oxideCMCs for application in engines and nuclear reactors anoverviewrdquo Composites Science and Technology vol 64 no 2 pp155ndash170 2004
[2] W Krenkel and F Berndt ldquoCC-SiC composites for spaceapplications and advanced friction systemsrdquo Materials Scienceand Engineering A vol 412 no 1-2 pp 177ndash181 2005
[3] Y Julong Ultraprecision Machining of Functional CeramicsHarbin Institute of Technology Press Harbin China 2000
[4] P-H Lee H Chung and S W Lee ldquoOptimization of micro-grinding process with compressed air using response surfacemethodologyrdquo Proceedings of the Institution of MechanicalEngineers Part B Journal of Engineering Manufacture vol 225no 11 pp 2040ndash2050 2011
[5] F J Chen S H Yin H Huang et al ldquoProfile error compen-sation in ultra-precision grinding of aspheric surfaces with on-machine measurementrdquo International Journal of Machine Toolsand Manufacture vol 50 no 5 pp 480ndash486 2010
[6] J Feng B S Kim A Shih and J Ni ldquoTool wear monitoring formicro-end grinding of ceramic materialsrdquo Journal of MaterialsProcessing Technology vol 209 no 11 pp 5110ndash5116 2009
[7] J Feng P Chen and J Ni ldquoPrediction of surface generation inmicrogrinding of ceramic materials by coupled trajectory andfinite element analysisrdquo Finite Elements in Analysis and Designvol 57 pp 67ndash80 2012
[8] Z Yuan K-I Nomura and A Nakano ldquoA coreshell mecha-nism for stacking-fault generation in GaAs nanowiresrdquo AppliedPhysics Letters vol 100 no 16 Article ID 163103 2012
[9] B K Tanner M C Fossati J Garagorri et al ldquoPrediction ofthe propagation probability of individual cracks in brittle singlecrystal materialsrdquo Applied Physics Letters vol 101 no 4 ArticleID 041903 2012
[10] S Goel X Luo P Comley R L Reuben and A Cox ldquoBrittle-ductile transition during diamond turning of single crystalsilicon carbiderdquo International Journal of Machine Tools andManufacture vol 65 pp 15ndash21 2013
[11] D A Doman Rubbing and Plowing Phases in Single GrainGrinding Dalhousie University Halifax Canada 2006
[12] M Barge J Rech H Hamdi and J-M Bergheau ldquoExperimen-tal study of abrasive processrdquo Wear vol 264 no 5-6 pp 382ndash388 2008
[13] W Qiuning Experimental study on single diamond graingrinding of silicon wafers [MS thesis] Dalian University ofTechnology Dalian China 2006
[14] J Wang R Ye and Y Tang ldquo3D dynamic finite elementsimulation analysis of single abrasive grain during surfacegrindingrdquo Diamond amp Abrasive Engineering vol 173 no 5 pp41ndash45 2009
[15] P J Arrazola and T Ozel ldquoNumerical modelling of 3D hardturning using arbitrary Lagrangian Eulerian finite elementmethodrdquo International Journal of Machining and Machinabilityof Materials vol 4 no 1 pp 14ndash25 2008
[16] M Gunay I Korkut E Aslan and U Seker ldquoExperimentalinvestigation of the effect of cutting tool rake angle on maincutting forcerdquo Journal of Materials Processing Technology vol166 no 1 pp 44ndash49 2005
[17] Y-C Yen A Jain and T Altan ldquoA finite element analysis oforthogonal machining using different tool edge geometriesrdquoJournal of Materials Processing Technology vol 146 no 1 pp72ndash81 2004
[18] H Saglam F Unsacar and S Yaldiz ldquoInvestigation of the effectof rake angle and approaching angle on main cutting force andtool tip temperaturerdquo International Journal ofMachine Tools andManufacture vol 46 no 2 pp 132ndash141 2006
[19] J A Badger and A A Torrance ldquoComparison of two modelsto predict grinding forces from wheel surface topographyrdquoInternational Journal ofMachine Tools andManufacture vol 40no 8 pp 1099ndash1120 2000
[20] ABAQUS Userrsquos Manual Version 66 Hibbitt Karlsson andSorensen Inc Proxidence RI USA 2006
[21] J S Johnson K D Grobsky and D Bray ldquoRapid fabricationof lightweight silicon-carbide mirrorsrdquo in Proceedings of theInternational Symposium on Optical Science and Technology pp243ndash253 International Society for Optics and Photonics 2002
[22] B Li and B Zhao Modern Grinding Technology CMP BeijingChina 2003
[23] E H Lee and B W Shaffer ldquoThe theory of plasticity applied toa problem of machiningrdquo Journal of Applied Mechanics vol 18pp 405ndash413 1951
of cutting edge and the microgrinding depth is nearly 0Certainly the changes of the abrasive nose radium of cuttingedge do not affect the machining process of SiC In otherwords once the abrasive nose radium of cutting edge is atthe same order of magnitude with the microgrinding depththe nose radium of cutting edge can be ignored In factthe ratio of the tangential force and the normal force 119865
119905119865119899
is almost determined by the geometrical parameters of theabrasive barely influenced by the microgrinding depth Dueto the rise of the nose radium of cutting edge the ratio of thenose radium of cutting edge and the reference microgrindingdepth 119903
040 ascends whereas 119865
119905119865119899comes down gradually
As shown in Figure 13 with the velocity of microgrindingprocess increasing progressively the tangential force andthe normal force improve slightly and both have weakincreasing trends The maximum equivalent stresses become13699MPa 13967MPa 14074MPa and 14117MPa respec-tively Considering the reduction of loss of machine tool andthe perspective of energy conservation 1ms is regarded as agood choice
4 Experiments
According to the present limited research condition to verifythe validity of the above theoretical simulation model for theSiC microgrinding process a series of scratch experimentshave been conducted on the nanoindentation apparatusAgilent Nano Indenter G200 shown in Figure 14 And thescratch picture is given in Figure 15
Figure 14 Agilent Nano Indenter G200
In the experiments simple variable method was adoptedto observe the variation caused by microgrinding depth andthe velocity As to every depth and velocity data of groups areobtained by the scratch experiments Thus the average loadcalculated in Table 3 could definitely give expression to therelationship between load and microgrinding depth
After SiC workpiece polished finely triangular pyramidhead loading 1mN scratched the SiC workpiece for 2mmdisplacement whose velocity is 1mms As the scratchimproves from 20 nm to 30 nm to 40 nm to 50 nm the loadof triangular pyramid head reaches 00455mN 00463mN00481mN and 00492mN as illustrated in Figure 16 Thenormal force given in Figure 5 changes from 00238 120583N to00387 120583N to 00471 120583N to 00570 120583N in simulation Althoughthe specific data is not in full consistency due to the situation
8 Journal of Nanomaterials
Table 3 Changes of load due to the depth and velocity
Simple variablemethod depth (nm) Load (mN) Average load (mN)
Simple variablemethod velocity
(mms)Load (mN) Average load (mN)
20004570045000458
00455 1004800048600476
00481
30004650046200462
00463 5004770047300466
00472
40004690049100483
00481 10004770047600472
00475
50004920049500489
00492 15004680047600478
00474
Figure 15 Scratched SiC workpiece
15 20 25 30 35 40 45 50 55004
0042
0044
0046
0048
005
Depth (nm)
Load
(mN
)
Figure 16 Load change based on the depth
difference between the scratch and the grinding both theexperiment data and the simulation data show an obviousrising trend accompanied by the increase of scratch depthIn addition a group of experiments with same triangularpyramid parameters and 40 nm microgrinding depth wereimplemented to indicate the effect of velocity the nodesvelocities in Figure 17 are 1mms 5mms 10mms and15mms respectively and the corresponding loads reach00481mN 00472mN 00475mN and 00474mN respec-tively At the same time the normal force in simulation
0 2 4 6 8 10 12 14 16004
0042
0044
0046
0048
005
Velocity (mms)
Load
(mN
)
Figure 17 Load change based on the velocity
achieves 00466 120583N 00474120583N 00483 120583N and 00491 120583Nas shown in Figure 13 The data shown in the experimentand simulation vividly mean that triangular pyramid headload hardly goes with the change of velocity Above all goodagreement is shown between the experimental results and thesimulation results by Abaqus
5 Conclusions
Based on the simulation of SiC microgrinding process pre-sented in the paper the following conclusions can be drawn
(1) The depth of microgrinding plays a great role inthe machining process The process owns a 40 nmmicrogrinding depth having both small fluctuationand superior efficiency
(2) For negative rake angle a small one is a benefit toobtain the surface of SiC optical component
(3) The clearance angle has barely an influence on themanufacturing of SiC surface in microgrinding pro-cess
(4) To obtain a high accuracy of machining process theabrasive nose radium of cutting edge needs to becompressed
Journal of Nanomaterials 9
(5) Velocity of about 1ms is a proper choice in simula-tion of microgrinding process
(6) Simulations of finite element in microgrinding pro-cess could provide a reference for the load in thecoarse and fine grinding process of SiC mirror
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by the National Key Basic Researchand Development Program (973 Program) of China (Grantno 2011CB706702) Natural Science Foundation of China(Grant nos 51305161 and 51135006) and Jilin Province Sci-ence and Technology Development Plan Item (Grant no20130101042JC)
References
[1] R Naslain ldquoDesign preparation and properties of non-oxideCMCs for application in engines and nuclear reactors anoverviewrdquo Composites Science and Technology vol 64 no 2 pp155ndash170 2004
[2] W Krenkel and F Berndt ldquoCC-SiC composites for spaceapplications and advanced friction systemsrdquo Materials Scienceand Engineering A vol 412 no 1-2 pp 177ndash181 2005
[3] Y Julong Ultraprecision Machining of Functional CeramicsHarbin Institute of Technology Press Harbin China 2000
[4] P-H Lee H Chung and S W Lee ldquoOptimization of micro-grinding process with compressed air using response surfacemethodologyrdquo Proceedings of the Institution of MechanicalEngineers Part B Journal of Engineering Manufacture vol 225no 11 pp 2040ndash2050 2011
[5] F J Chen S H Yin H Huang et al ldquoProfile error compen-sation in ultra-precision grinding of aspheric surfaces with on-machine measurementrdquo International Journal of Machine Toolsand Manufacture vol 50 no 5 pp 480ndash486 2010
[6] J Feng B S Kim A Shih and J Ni ldquoTool wear monitoring formicro-end grinding of ceramic materialsrdquo Journal of MaterialsProcessing Technology vol 209 no 11 pp 5110ndash5116 2009
[7] J Feng P Chen and J Ni ldquoPrediction of surface generation inmicrogrinding of ceramic materials by coupled trajectory andfinite element analysisrdquo Finite Elements in Analysis and Designvol 57 pp 67ndash80 2012
[8] Z Yuan K-I Nomura and A Nakano ldquoA coreshell mecha-nism for stacking-fault generation in GaAs nanowiresrdquo AppliedPhysics Letters vol 100 no 16 Article ID 163103 2012
[9] B K Tanner M C Fossati J Garagorri et al ldquoPrediction ofthe propagation probability of individual cracks in brittle singlecrystal materialsrdquo Applied Physics Letters vol 101 no 4 ArticleID 041903 2012
[10] S Goel X Luo P Comley R L Reuben and A Cox ldquoBrittle-ductile transition during diamond turning of single crystalsilicon carbiderdquo International Journal of Machine Tools andManufacture vol 65 pp 15ndash21 2013
[11] D A Doman Rubbing and Plowing Phases in Single GrainGrinding Dalhousie University Halifax Canada 2006
[12] M Barge J Rech H Hamdi and J-M Bergheau ldquoExperimen-tal study of abrasive processrdquo Wear vol 264 no 5-6 pp 382ndash388 2008
[13] W Qiuning Experimental study on single diamond graingrinding of silicon wafers [MS thesis] Dalian University ofTechnology Dalian China 2006
[14] J Wang R Ye and Y Tang ldquo3D dynamic finite elementsimulation analysis of single abrasive grain during surfacegrindingrdquo Diamond amp Abrasive Engineering vol 173 no 5 pp41ndash45 2009
[15] P J Arrazola and T Ozel ldquoNumerical modelling of 3D hardturning using arbitrary Lagrangian Eulerian finite elementmethodrdquo International Journal of Machining and Machinabilityof Materials vol 4 no 1 pp 14ndash25 2008
[16] M Gunay I Korkut E Aslan and U Seker ldquoExperimentalinvestigation of the effect of cutting tool rake angle on maincutting forcerdquo Journal of Materials Processing Technology vol166 no 1 pp 44ndash49 2005
[17] Y-C Yen A Jain and T Altan ldquoA finite element analysis oforthogonal machining using different tool edge geometriesrdquoJournal of Materials Processing Technology vol 146 no 1 pp72ndash81 2004
[18] H Saglam F Unsacar and S Yaldiz ldquoInvestigation of the effectof rake angle and approaching angle on main cutting force andtool tip temperaturerdquo International Journal ofMachine Tools andManufacture vol 46 no 2 pp 132ndash141 2006
[19] J A Badger and A A Torrance ldquoComparison of two modelsto predict grinding forces from wheel surface topographyrdquoInternational Journal ofMachine Tools andManufacture vol 40no 8 pp 1099ndash1120 2000
[20] ABAQUS Userrsquos Manual Version 66 Hibbitt Karlsson andSorensen Inc Proxidence RI USA 2006
[21] J S Johnson K D Grobsky and D Bray ldquoRapid fabricationof lightweight silicon-carbide mirrorsrdquo in Proceedings of theInternational Symposium on Optical Science and Technology pp243ndash253 International Society for Optics and Photonics 2002
[22] B Li and B Zhao Modern Grinding Technology CMP BeijingChina 2003
[23] E H Lee and B W Shaffer ldquoThe theory of plasticity applied toa problem of machiningrdquo Journal of Applied Mechanics vol 18pp 405ndash413 1951
Table 3 Changes of load due to the depth and velocity
Simple variablemethod depth (nm) Load (mN) Average load (mN)
Simple variablemethod velocity
(mms)Load (mN) Average load (mN)
20004570045000458
00455 1004800048600476
00481
30004650046200462
00463 5004770047300466
00472
40004690049100483
00481 10004770047600472
00475
50004920049500489
00492 15004680047600478
00474
Figure 15 Scratched SiC workpiece
15 20 25 30 35 40 45 50 55004
0042
0044
0046
0048
005
Depth (nm)
Load
(mN
)
Figure 16 Load change based on the depth
difference between the scratch and the grinding both theexperiment data and the simulation data show an obviousrising trend accompanied by the increase of scratch depthIn addition a group of experiments with same triangularpyramid parameters and 40 nm microgrinding depth wereimplemented to indicate the effect of velocity the nodesvelocities in Figure 17 are 1mms 5mms 10mms and15mms respectively and the corresponding loads reach00481mN 00472mN 00475mN and 00474mN respec-tively At the same time the normal force in simulation
0 2 4 6 8 10 12 14 16004
0042
0044
0046
0048
005
Velocity (mms)
Load
(mN
)
Figure 17 Load change based on the velocity
achieves 00466 120583N 00474120583N 00483 120583N and 00491 120583Nas shown in Figure 13 The data shown in the experimentand simulation vividly mean that triangular pyramid headload hardly goes with the change of velocity Above all goodagreement is shown between the experimental results and thesimulation results by Abaqus
5 Conclusions
Based on the simulation of SiC microgrinding process pre-sented in the paper the following conclusions can be drawn
(1) The depth of microgrinding plays a great role inthe machining process The process owns a 40 nmmicrogrinding depth having both small fluctuationand superior efficiency
(2) For negative rake angle a small one is a benefit toobtain the surface of SiC optical component
(3) The clearance angle has barely an influence on themanufacturing of SiC surface in microgrinding pro-cess
(4) To obtain a high accuracy of machining process theabrasive nose radium of cutting edge needs to becompressed
Journal of Nanomaterials 9
(5) Velocity of about 1ms is a proper choice in simula-tion of microgrinding process
(6) Simulations of finite element in microgrinding pro-cess could provide a reference for the load in thecoarse and fine grinding process of SiC mirror
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by the National Key Basic Researchand Development Program (973 Program) of China (Grantno 2011CB706702) Natural Science Foundation of China(Grant nos 51305161 and 51135006) and Jilin Province Sci-ence and Technology Development Plan Item (Grant no20130101042JC)
References
[1] R Naslain ldquoDesign preparation and properties of non-oxideCMCs for application in engines and nuclear reactors anoverviewrdquo Composites Science and Technology vol 64 no 2 pp155ndash170 2004
[2] W Krenkel and F Berndt ldquoCC-SiC composites for spaceapplications and advanced friction systemsrdquo Materials Scienceand Engineering A vol 412 no 1-2 pp 177ndash181 2005
[3] Y Julong Ultraprecision Machining of Functional CeramicsHarbin Institute of Technology Press Harbin China 2000
[4] P-H Lee H Chung and S W Lee ldquoOptimization of micro-grinding process with compressed air using response surfacemethodologyrdquo Proceedings of the Institution of MechanicalEngineers Part B Journal of Engineering Manufacture vol 225no 11 pp 2040ndash2050 2011
[5] F J Chen S H Yin H Huang et al ldquoProfile error compen-sation in ultra-precision grinding of aspheric surfaces with on-machine measurementrdquo International Journal of Machine Toolsand Manufacture vol 50 no 5 pp 480ndash486 2010
[6] J Feng B S Kim A Shih and J Ni ldquoTool wear monitoring formicro-end grinding of ceramic materialsrdquo Journal of MaterialsProcessing Technology vol 209 no 11 pp 5110ndash5116 2009
[7] J Feng P Chen and J Ni ldquoPrediction of surface generation inmicrogrinding of ceramic materials by coupled trajectory andfinite element analysisrdquo Finite Elements in Analysis and Designvol 57 pp 67ndash80 2012
[8] Z Yuan K-I Nomura and A Nakano ldquoA coreshell mecha-nism for stacking-fault generation in GaAs nanowiresrdquo AppliedPhysics Letters vol 100 no 16 Article ID 163103 2012
[9] B K Tanner M C Fossati J Garagorri et al ldquoPrediction ofthe propagation probability of individual cracks in brittle singlecrystal materialsrdquo Applied Physics Letters vol 101 no 4 ArticleID 041903 2012
[10] S Goel X Luo P Comley R L Reuben and A Cox ldquoBrittle-ductile transition during diamond turning of single crystalsilicon carbiderdquo International Journal of Machine Tools andManufacture vol 65 pp 15ndash21 2013
[11] D A Doman Rubbing and Plowing Phases in Single GrainGrinding Dalhousie University Halifax Canada 2006
[12] M Barge J Rech H Hamdi and J-M Bergheau ldquoExperimen-tal study of abrasive processrdquo Wear vol 264 no 5-6 pp 382ndash388 2008
[13] W Qiuning Experimental study on single diamond graingrinding of silicon wafers [MS thesis] Dalian University ofTechnology Dalian China 2006
[14] J Wang R Ye and Y Tang ldquo3D dynamic finite elementsimulation analysis of single abrasive grain during surfacegrindingrdquo Diamond amp Abrasive Engineering vol 173 no 5 pp41ndash45 2009
[15] P J Arrazola and T Ozel ldquoNumerical modelling of 3D hardturning using arbitrary Lagrangian Eulerian finite elementmethodrdquo International Journal of Machining and Machinabilityof Materials vol 4 no 1 pp 14ndash25 2008
[16] M Gunay I Korkut E Aslan and U Seker ldquoExperimentalinvestigation of the effect of cutting tool rake angle on maincutting forcerdquo Journal of Materials Processing Technology vol166 no 1 pp 44ndash49 2005
[17] Y-C Yen A Jain and T Altan ldquoA finite element analysis oforthogonal machining using different tool edge geometriesrdquoJournal of Materials Processing Technology vol 146 no 1 pp72ndash81 2004
[18] H Saglam F Unsacar and S Yaldiz ldquoInvestigation of the effectof rake angle and approaching angle on main cutting force andtool tip temperaturerdquo International Journal ofMachine Tools andManufacture vol 46 no 2 pp 132ndash141 2006
[19] J A Badger and A A Torrance ldquoComparison of two modelsto predict grinding forces from wheel surface topographyrdquoInternational Journal ofMachine Tools andManufacture vol 40no 8 pp 1099ndash1120 2000
[20] ABAQUS Userrsquos Manual Version 66 Hibbitt Karlsson andSorensen Inc Proxidence RI USA 2006
[21] J S Johnson K D Grobsky and D Bray ldquoRapid fabricationof lightweight silicon-carbide mirrorsrdquo in Proceedings of theInternational Symposium on Optical Science and Technology pp243ndash253 International Society for Optics and Photonics 2002
[22] B Li and B Zhao Modern Grinding Technology CMP BeijingChina 2003
[23] E H Lee and B W Shaffer ldquoThe theory of plasticity applied toa problem of machiningrdquo Journal of Applied Mechanics vol 18pp 405ndash413 1951
(5) Velocity of about 1ms is a proper choice in simula-tion of microgrinding process
(6) Simulations of finite element in microgrinding pro-cess could provide a reference for the load in thecoarse and fine grinding process of SiC mirror
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by the National Key Basic Researchand Development Program (973 Program) of China (Grantno 2011CB706702) Natural Science Foundation of China(Grant nos 51305161 and 51135006) and Jilin Province Sci-ence and Technology Development Plan Item (Grant no20130101042JC)
References
[1] R Naslain ldquoDesign preparation and properties of non-oxideCMCs for application in engines and nuclear reactors anoverviewrdquo Composites Science and Technology vol 64 no 2 pp155ndash170 2004
[2] W Krenkel and F Berndt ldquoCC-SiC composites for spaceapplications and advanced friction systemsrdquo Materials Scienceand Engineering A vol 412 no 1-2 pp 177ndash181 2005
[3] Y Julong Ultraprecision Machining of Functional CeramicsHarbin Institute of Technology Press Harbin China 2000
[4] P-H Lee H Chung and S W Lee ldquoOptimization of micro-grinding process with compressed air using response surfacemethodologyrdquo Proceedings of the Institution of MechanicalEngineers Part B Journal of Engineering Manufacture vol 225no 11 pp 2040ndash2050 2011
[5] F J Chen S H Yin H Huang et al ldquoProfile error compen-sation in ultra-precision grinding of aspheric surfaces with on-machine measurementrdquo International Journal of Machine Toolsand Manufacture vol 50 no 5 pp 480ndash486 2010
[6] J Feng B S Kim A Shih and J Ni ldquoTool wear monitoring formicro-end grinding of ceramic materialsrdquo Journal of MaterialsProcessing Technology vol 209 no 11 pp 5110ndash5116 2009
[7] J Feng P Chen and J Ni ldquoPrediction of surface generation inmicrogrinding of ceramic materials by coupled trajectory andfinite element analysisrdquo Finite Elements in Analysis and Designvol 57 pp 67ndash80 2012
[8] Z Yuan K-I Nomura and A Nakano ldquoA coreshell mecha-nism for stacking-fault generation in GaAs nanowiresrdquo AppliedPhysics Letters vol 100 no 16 Article ID 163103 2012
[9] B K Tanner M C Fossati J Garagorri et al ldquoPrediction ofthe propagation probability of individual cracks in brittle singlecrystal materialsrdquo Applied Physics Letters vol 101 no 4 ArticleID 041903 2012
[10] S Goel X Luo P Comley R L Reuben and A Cox ldquoBrittle-ductile transition during diamond turning of single crystalsilicon carbiderdquo International Journal of Machine Tools andManufacture vol 65 pp 15ndash21 2013
[11] D A Doman Rubbing and Plowing Phases in Single GrainGrinding Dalhousie University Halifax Canada 2006
[12] M Barge J Rech H Hamdi and J-M Bergheau ldquoExperimen-tal study of abrasive processrdquo Wear vol 264 no 5-6 pp 382ndash388 2008
[13] W Qiuning Experimental study on single diamond graingrinding of silicon wafers [MS thesis] Dalian University ofTechnology Dalian China 2006
[14] J Wang R Ye and Y Tang ldquo3D dynamic finite elementsimulation analysis of single abrasive grain during surfacegrindingrdquo Diamond amp Abrasive Engineering vol 173 no 5 pp41ndash45 2009
[15] P J Arrazola and T Ozel ldquoNumerical modelling of 3D hardturning using arbitrary Lagrangian Eulerian finite elementmethodrdquo International Journal of Machining and Machinabilityof Materials vol 4 no 1 pp 14ndash25 2008
[16] M Gunay I Korkut E Aslan and U Seker ldquoExperimentalinvestigation of the effect of cutting tool rake angle on maincutting forcerdquo Journal of Materials Processing Technology vol166 no 1 pp 44ndash49 2005
[17] Y-C Yen A Jain and T Altan ldquoA finite element analysis oforthogonal machining using different tool edge geometriesrdquoJournal of Materials Processing Technology vol 146 no 1 pp72ndash81 2004
[18] H Saglam F Unsacar and S Yaldiz ldquoInvestigation of the effectof rake angle and approaching angle on main cutting force andtool tip temperaturerdquo International Journal ofMachine Tools andManufacture vol 46 no 2 pp 132ndash141 2006
[19] J A Badger and A A Torrance ldquoComparison of two modelsto predict grinding forces from wheel surface topographyrdquoInternational Journal ofMachine Tools andManufacture vol 40no 8 pp 1099ndash1120 2000
[20] ABAQUS Userrsquos Manual Version 66 Hibbitt Karlsson andSorensen Inc Proxidence RI USA 2006
[21] J S Johnson K D Grobsky and D Bray ldquoRapid fabricationof lightweight silicon-carbide mirrorsrdquo in Proceedings of theInternational Symposium on Optical Science and Technology pp243ndash253 International Society for Optics and Photonics 2002
[22] B Li and B Zhao Modern Grinding Technology CMP BeijingChina 2003
[23] E H Lee and B W Shaffer ldquoThe theory of plasticity applied toa problem of machiningrdquo Journal of Applied Mechanics vol 18pp 405ndash413 1951
