ExperimentalOptimizationofAnnularPolishing ...downloads.hindawi.com/journals/amse/2018/9019848.pdfIk...

Research ArticleExperimental Optimization of Annular PolishingParameters for Silicon Carbide

Yuan Liu1 La Han2 Haiying Liu3 Yikai Shi4 and Junjie Zhang 2

1School of Astronautics Harbin Institute of Technology Harbin 150001 China2Center for Precision Engineering Harbin Institute of Technology Harbin 150001 China3Xiaguang Optical Electron Co Ltd Yangzhou 225127 China4Science and Technology on Integrated Logistics Support Laboratory National University of Defense TechnologyChangsha 410073 China

Correspondence should be addressed to Junjie Zhang zhjj505gmailcom

Received 22 June 2018 Revised 3 August 2018 Accepted 27 August 2018 Published 25 September 2018

Academic Editor Fernando Lusquintildeos

Copyright copy 2018 Yuan Liu et al -is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Machined surface quality has a strong impact on the functionality of silicon carbide-based components and devices In the presentwork we first analytically investigate the complex coupling of motions in annular polishing based on the Preston equation whichderives the influential parameters for material removal Subsequently we conduct systematic annular polishing experiments ofreaction-bonded silicon carbide to investigate the influence of derived parameters on polished surface quality which yieldoptimized polishing parameters for achieving ultralow surface roughness of reaction-bonded silicon carbide

1 Introduction

Reaction-bonded (RB) silicon carbide (SiC) is one of thepreferred materials for manufacturing optical mirrors due toits unique characteristics of low density high strength lowthermal expansion high thermal conductivity and highchemical inertness [1] Machined surface quality plays animportant role in determining the functionality of SiC-basedcomponents and devices For instance according to thetheory of total integral scattering (TIS) the surface scatteringcapability of optical mirror is closely related to its surfaceroughness as the TIS increases sharply with the increase ofsurface roughness -e high surface scattering coefficientwill cause the system to produce stray light which decreasesthe reflectivity of SiCmirrors and consequently results in thedegradation of imaging quality of optical system [2] -usimproving machined surface quality of SiC is critical forfacilitating the performance of SiC mirrors

At present annular polishing technology is an efficientmethod to obtain SiC mirrors with high surface quality[3ndash6] Some typical work are as follows Rupp et al studiedthe grinding and polishing of conventional optics and found

that the contact pressure between the specimen and thepolishing pad changes dynamically and is a function of timeand location of points on the specimen [2] Aspden et aldeveloped a CNC surface polisher that uses a small tool toachieve the desired profile by convolution to calculate thedwell time of the widget In their topics there is no singlemathematical model that completely correlates the me-chanical motion of optical surfaces with the amount ofmaterial removed during grinding or polishing process [7]Wagner and Shannon established a model to describe therelationship between the mechanical motion and the changein surface area and to calculate the material removal of thespecimen surface through the mathematical method andoptical kinematics principle [8] Gao and Cao studied therelationship between motion parameters grinding mecha-nism and the trajectory of the specimen [9] Shen and Yuanstudied the influence of applied load on pressure profile inthe polishing process [10] Liu et al introduced the use ofannular polishing technology for the manufacturing oflarge-diameter square optical components [11] On the otherside the annular polishing is strongly dependent on pol-ishing conditions Wang et al found that as the pressure

HindawiAdvances in Materials Science and EngineeringVolume 2018 Article ID 9019848 6 pageshttpsdoiorg10115520189019848

increases the contact area between the polishing pad and theworkpiece increases while the mechanical friction is en-hanced and the material removal rate is high As the rotationspeed increases the thickness of the polishing liquid filmbetween the polishing pad and the workpiece graduallyincreases the flow rate of the polishing liquid increasesleading to increased materials taken away from the pro-cessed surface under an increased material removal rate [12]Sun et al found that the oxidant the complex agent contentand the polishing solution PH value in the polishing solutionhave a great influence on the material removal rate [13] Huet al studied the effects of abrasive types such as SiO2 Al2O3and CeO the concentration of abrasives and the size ofabrasive grains on the polishing effect [14] More recentlyZhang et al performed finite element simulations and ex-periments of annular polishing of SiC and found that thedistribution of contact pressure on the SiC specimen issignificantly affected by the polishing speed Poissonrsquos ratioand the elastic modulus of polishing pad [15]

Previous studies have obtained many valuable insightsHowever most of previous work is mainly utilizing a solemethod either experiment or simulation In particular thelack of systematic experimental demonstration of theoreticalanalysis greatly restricts the deep understanding of the an-nular polishing mechanism of SiC -erefore based on thePreston equation and motion simulation this paper analyzesthe law of motion coupling in annular polishing and sum-marizes the polishing parameters that affect the annularpolishing Based on the analytical theoretical investigationsannular polishing experiments are carried out to further studythe influence of different polishing parameters and ultimatelyobtain the optimized polishing parameters -is research hasimportant theoretical significance and practical value to guidethe annular polishing processing of SiC

2 Analytical Investigation of Annular Polishing

21 Kinematic Coupling of Motions Figure 1(a) illustratesa typical annular polisher which mainly consists of a pol-ishing disc a carrier disc and a swinging bracket re-spectively -e specimen is pasted on the carrier disc withparaffin which means that the specimen has a synchronousspeed with the carrier disc -e applied pressure is providedby the weight of carrier disc Accordingly Figure 1(b) il-lustrates the simplified motion diagram in the annularpolishing which indicates that the kinematic coupling ofrelative motions mainly includes the rotation of polishingdisc and the rotation of carrier disc As indicated inFigure 1(b) the speed of carrier disc is ω and the speed ofpolishing disc is δ -e distance from the center of specimenO2 to a point A on the carrier disc is r and the distance fromthe center of polishing disc O1 to the center of the carrier discO2 is R -e angle between the line segments AO2 and O1O2is θ -e speed at the point A on the polishing disc relative toO1 is V1 and the speed at the point A on the specimenrelative to O2 is V2 so the relative speed of the specimen andthe polishing disc at point A is V which can be derived fromthe following equation [16]

V(r θ) R2δ2 + r

2(δ minusω)

2+ 2rRδ(δ minusω)cos θ1113960 1113961

12 (1)

22 Preston Equation Both material removal rate andsurface quality of specimen in the annular polishing processare strongly affected by processing polishing parameterswhich have complex interactions Preston et al simplifiedthe Preston equation [17] to characterize the relationshipbetween material removal and polishing speed V appliedpressure P and other external factors as shown in thefollowing equation [17]

dh

dt kPV kP

ds

dt (2)

where h is the amount of material removal and k is a pro-portional constant that is related to various environmentalfactors -erefore the amount of material removal at onespecific point can be derived according to Equation (2)However the contact between specimen and polishing discchanges dynamically with polishing time which inducesuncertainties in the analytical investigation of annularpolishing process -erefore three main assumptions aremade to simplify the operation (1) specimen and polishingdisc are fully contacted without separation (2) the appliedpressure does not change with polishing time and (3) theproportional constant k does not change with polishingtime According to the Preston equation the amount ofmaterial removal within a specific polishing time can bederived by integrating over time t as shown in the followingequation

h(r) k 1113946T

0P(r t) middot V(r t) dt (3)

It can be seen from Equation (3) that the material re-moval is only dependent on the resultant speedV given the kand the P are constant values By substituting the relativevelocity derived from Equation (1) into Equation (3) thematerial removal at point A can be derived as shown in thefollowing equation [15]

h(r) k 1113946T

0P(r t)

middot R2δ2 + r

2(δ minusω)

2+ 2rRδ(δ minusω)cos θ1113960 1113961

12dt

(4)

-e amount of material removal at any point on thespecimen can be calculated from Equation (4) -e pressureP is affected by the type of polishing pad and polishingsolution Based on the annular polishing motion simulationand the Preston equation four influential parameters can bedetermined as polishing solution polishing pad polishingtime and rotation speed of polishing disc respectively

3 Annular Polishing Experiment of RB-SiC

31 Effect of Polishing Solution Material It has been dem-onstrated that polishing solutionrsquos particle size particlehardness and concentration have a strong impact on the

2 Advances in Materials Science and Engineering

polishing process [18] We first investigate the influence ofpolishing solution material on the polishing results -reekinds of polishing solution materials such as alumina silicaand diamond are considered For each polishing solutionmaterial the average particle size is the same as 250 nm Inthe polishing experiments the polyurethane polishing pad isused with a rotation speed of 120 rmin -e polishing timeis 60min After polishing the surface roughness of thespecimen is measured by a Taylor Hobson surface profiler

Figure 2 presents the value of surface roughness for eachpolishing solution material -e surface roughness is themaximum of 73 nm for the alumina followed by 61 nm forthe silica and the minimum of 32 nm for the diamond Itcan be seen from Figure 2 that with the increase of abrasivehardness of the polishing solution the surface roughness ofthe specimen decreases gradually as the increase of abrasivehardness results in an improvement not only in the me-chanical force between the specimen and abrasive but also inthe quality of the specimen surface

32 Effect of Polishing Pad Material -e polishing padshould has the following conditions appropriate rigidity andhardness a certain elasticity good retention of the polishingsolution excluding the by-product of polishing process andlow impurities of the polishing pad [19] In this paper we usefour kinds of polishing pad materials the cot polishing padthe matte leather polishing pad the synthetic leather pol-ishing pad and the polyurethane polishing pad

In different polishing experiments with different pol-ishing pad materials all the polishing parameters are keptconstant And the diamond suspension solution is used asthe polishing solution for each experiment -e speed ofpolishing plate is 120 rmin and the polishing time is 60minAfter the polishing experiment the measured surfaceroughness of SiC is 76 nm 69 nm 81 nm and 28 nm forthe cot polishing pad the matte leather polishing pad thesynthetic leather polishing pad and the polyurethane pol-ishing pad respectively as shown in Figure 3

It can be seen from Figure 3 that surface roughness dropsto the smallest value when using the polyurethane polishingpad It can be concluded that due to the higher hardness ofSiC specimen than the cot polishing pad abrasive particlesare pressed into the polishing pad and thus are unable toproduce effective force on the SiC surface resulting in lowprocessing precision and high surface roughness -ehardness of matte leather and synthetic leather polishing padis higher but the surface is easier to be scratched as a resultof the higher interaction force which results in highersurface roughness -e hardness of polyurethane polishingpad is moderate which can obtain the best polishing effectwith the lowest surface roughness of 28 nm

33 Effect of Polishing Time We further investigate the in-fluence of polishing time on the machined surface quality ofSiC While maintaining the other polishing parameters

2

3

4

5

6

7

8V

alue

of s

urfa

ce ro

ughn

ess (

nm)

Alumina Silica Diamond

Figure 2 -e relationship between the surface roughness and thetype of polishing solution

Swing bracket

Carrier discPolishing disc

(a)

δ

θ

ω

A

RO2

O1

r

V V1

V2

Carrier disc

Polishing disc

(b)

Figure 1 Illustration of annular polishing (a) Model of annular polisher (b) motion analysis of annular polishing Reproduced from Zhanget al [15] (under the Creative Commons Attribution Licensepublic domain)

Advances in Materials Science and Engineering 3

unchanged only the polishing time is changed -e pol-ishing time is divided into six groups 30min 60min90min 120min 150min and 180min respectively In eachexperiment the diamond suspension is used as the polishingsolution and the polyurethane polishing pad is utilized -epolishing pad speed is 120 rmin After the polishing themeasured surface roughness is 32 nm 25 nm 21 nm16 nm 08 nm and 12 nm for the polishing time of 30min60min 90min 120min 150min and 180min respectivelyas shown in Figure 4

It can be seen from Figure 4 that the surface roughnesschanges with the polishing time it first decreases steadilyand then starts to increase from the polishing time of150min indicating a critical polishing time of 150min Inthe initial stage of the polishing experiment large abrasiveparticles are embedded into the surface to accommodatelarge pressure which leads to generation of surfacescratches thus affecting the surface quality With the in-crease of polishing time abrasive particles break up to smallparticles with sharp edges that have good cutting perfor-mance which facilitates the formation of smooth surface ofthe specimen -e surface roughness reaches the lowestvalue of 08 nm at the polishing time of 150 minutesHowever with the further increase of polishing time theincrease of surface temperature produces thermal stresswhich affects the machining accuracy and lowers the surfaceroughness

34 Effect of Rotation Speed of Polishing Disc We also in-vestigate the influence of rotation speed of polishing disc Sixrotation speeds of polishing disc are considered 50 rmin70 rmin 90 rmin 120 rmin 140 rmin and 160 rminrespectively For each rotation speed all the other polish-ing parameters are the same -e diamond suspension isused as the polishing solution and the polyurethane pol-ishing pad is utilized -e polishing time is 60min After thepolishing experiment the measured surface roughness is

33 nm 27 nm 25 nm 16 nm 12 nm and 26 nm for therotation speed of 50 rmin 70 rmin 90 rmin 120 rmin140 rmin and 160 rmin respectively as shown in Figure 5

It can be seen from Figure 5 that with increasing rotationspeed the surface roughness first decreases and reaches thelowest value of 12 nm at the rotation speed of 140 rmin andthen increases with a further increase of rotation speed It isknown that a high rotation speed of the polishing disk canincrease the efficiency of the polishing process However thehigher the rotation speed of polishing disc the lower theprocessing stability which result in the lower surface for-mation accuracy

Based on the above analysis the optimized parameters ofannular polishing of SiC are summarized as follows a ro-tating speed of polishing disc is 140 rmin a polishing time is150min using the polyurethane polishing pad and the di-amond suspension solution Under the optimized polishingconditions a high-quality SiC specimen with a surfaceroughness of 131 nm is obtained Figure 6 shows thecharacterized SiC specimen before and after polishing in-dicating polished SiC with good surface quality can beobtained by using the optimized annular polishingparameters

4 Summary

In this work we experimentally investigate the optimizationof annular polishing parameters of RB-SiC by first analyticalinvestigation of influential parameters based on the Prestonequation and the coupling of polishing motions and thensystematic polishing experiments and characterization It isfound that the annular polishing process can be greatlyinfluenced by the polishing solution the polishing padmaterial the polishing time and the rotation speed ofpolishing disc -e optimized annular polishing parametersare a rotating speed of polishing disc of 140 rmin a pol-ishing time of 150min using polyurethane polishing pad

30 60 90 120 150 18005

10

15

20

25

30

35

Val

ue o

f sur

face

roug

hnes

s (nm

)

Polishing time (min)

Figure 4 -e relationship between the surface roughness and thepolishing time

2

3

4

5

6

7

8

9

Val

ue o

f sur

face

roug

hnes

s (nm

)

Cot Matte leather Syntheticleather

Polyurethane

Figure 3 -e relationship between the surface roughness and thetype of polishing pad


(a) (b)

(c) (d)

ndash01nm

106nm

10μm

10μm

10μm 8 6 4 2

10

8

6

4

2

8

6

4

2

(e)

07nm

312nm

10μm

10μm

10μm 8 6 4 2

10

8

6

4

2

8

6

4

2

(f )

Figure 6 Morphology andmicrostructure of polished SiC (a) Before polishing (b) after polishing (c) surfacemorphology before polishing(d) surface morphology after polishing (e) surface microstructure before polishing and (f) surface microstructure after polishing

40 50 60 70 80 90 100 110 120 130 140 150 160 17010

12

14

16

18

20

22

24

26

28

30

32

34

Val

ue o

f sur

face

roug

hnes

s (nm

)

Rotation speed (rmin)

Figure 5 -e relationship between the surface roughness and the rotation speed


and diamond suspension solution which lead to a surfaceroughness of 131 nm of RB-SiC by annular polishing

Data Availability

-e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Authorsrsquo Contributions

Y L H L and J Z conceived and designed the experi-ments L H and Y S performed the analytical investigationand experiments Y L and J Z analyzed the data and wrotethe paper

Acknowledgments

-e authors acknowledge financial support from the Na-tional Natural Science Foundation of China (NSFC)(51875119 and 61473096) the Fundamental Research Fundsfor the Central Universities the German Research Foun-dation (DFG) International Joint Research Program(51761135106) and the National Key RampD Program ofChina (2016YFB0501203)

References

[1] R Joseph S Jay and L David ldquoRecent advances in reactionbonded silicon carbide optics and optical systemsrdquo Proceedingof SPIE vol 5868 article 586802 2005

[2] V Rupp ldquo-e development of optical surfaces during thegrinding processrdquo Applied Optics vol 4 no 6 pp 743ndash7481965

[3] F Gritti and G Guiochon ldquoGradient chromatography underconstant frictional heat Realization and applicationrdquo Journalof Chromatography A vol 1289 pp 1ndash12 2013

[4] X C Wang C C Wang X T Shen and F H Sun ldquoPotentialmaterial for fabricating optical mirrors polished diamondcoated silicon carbiderdquo Applied Optics vol 56 no 14pp 4113ndash4122 2017

[5] Q T Fan J Q Zhu and B A Zhang ldquoEffect of the geometryof workpiece on polishing velocity in free annular polishingrdquoChinese Optics Letters vol 5 pp 298ndash300 2007

[6] Y Hashimoto S Oshika N Suzuki and E Shamoto ldquoA newcontact model of pad surface asperities utilizing measuredgeometrical featuresrdquo in Proceedings of the InternationalConference on PlanarizationCMP Technology pp 1ndash4Chandler AZ USA SeptemberndashOctober 2015

[7] R Aspden R Mcdonough and F R Nitchie ldquoComputerassisted optical surfacingrdquo Applied Optics vol 11 no 12pp 2739ndash2747 1972

[8] R E Wagner and R R Shannon ldquoFabrication of asphericsusing a mathematical model for material removalrdquo AppliedOptics vol 13 no 7 pp 1683ndash1689 1974

[9] H G Gao and J L Cao ldquoSimulation of stock removal uni-formity during eccentric plane polishing by a tin laprdquo ChineseJournal of Scientific Instrument vol 21 pp 83ndash85 2000

[10] Z W Shen and J L Yuan ldquoUltra-precision planarization forcrystalsrdquo Journal of Zhejiang University-Technology vol 29pp 20ndash25 2001

[11] M C Liu X Y Hu and Z S Li ldquoResearch of fabricating largequadrate high-precision plane optical elmentsrdquo Optics Tech-nology vol 27 pp 518-519 2004

[12] B L Wang H Gao X J Teng and R K Kang ldquoEffect ofpolishing parameter on material removal and surface qualityof KDP crystalrdquo Journal of Synthetic Crystals vol 39pp 29ndash33 2010

[13] J Z Sun G S Pan Y H Zhu Y J Dai J B Luo andW M Li ldquoInfluence of slurry ingredients as particle on harddisk substrate polishingrdquo in Advanced Tribology J LuoY Meng T Shao and Q Zhao Eds pp 993-994 SpringerBerlin Heidelberg 2007

[14] W Hu X Wei X Z Xie and B P Xiang ldquoStudy on theperformance of polishing slurry in chemical mechanicalpolishingrdquo Diamond and Abrasives Engineering vol 156pp 78ndash80 2006

[15] J J Zhang L Han H Y Liu Y K Shi Y D Yan and T Sunldquo-eoretical and experimental studies of over-polishing ofsilicon carbide in annular polishingrdquo Machines vol 6 no 2p 15 2018

[16] R L Goedecke and R M Jackson ldquoA fractal expansion ofa three dimensional elastic-plastic multi-scale rough surfacecontact modelrdquo Tribology International vol 59 pp 230ndash2392013

[17] F Preston ldquo-e theory and design of plate glass polishingmachinesrdquo Journal of the Society of Glass Technology vol 11pp 214ndash256 1927

[18] Y D Filatov A G Vetrov and V I Sidorko ldquoPolishing ofoptoelectronic components made of monocrystalline siliconcarbiderdquo Journal of Superhard Materials vol 37 no 1pp 48ndash56 2015

[19] D Liu G Chen and Q Hu ldquoMaterial removal model ofchemical mechanical polishing for fused silica using softnanoparticlesrdquo International Journal of AdvancedManufacturing Technology vol 88 no 9-12 pp 3215ndash35252016


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increases the contact area between the polishing pad and theworkpiece increases while the mechanical friction is en-hanced and the material removal rate is high As the rotationspeed increases the thickness of the polishing liquid filmbetween the polishing pad and the workpiece graduallyincreases the flow rate of the polishing liquid increasesleading to increased materials taken away from the pro-cessed surface under an increased material removal rate [12]Sun et al found that the oxidant the complex agent contentand the polishing solution PH value in the polishing solutionhave a great influence on the material removal rate [13] Huet al studied the effects of abrasive types such as SiO2 Al2O3and CeO the concentration of abrasives and the size ofabrasive grains on the polishing effect [14] More recentlyZhang et al performed finite element simulations and ex-periments of annular polishing of SiC and found that thedistribution of contact pressure on the SiC specimen issignificantly affected by the polishing speed Poissonrsquos ratioand the elastic modulus of polishing pad [15]

Previous studies have obtained many valuable insightsHowever most of previous work is mainly utilizing a solemethod either experiment or simulation In particular thelack of systematic experimental demonstration of theoreticalanalysis greatly restricts the deep understanding of the an-nular polishing mechanism of SiC -erefore based on thePreston equation and motion simulation this paper analyzesthe law of motion coupling in annular polishing and sum-marizes the polishing parameters that affect the annularpolishing Based on the analytical theoretical investigationsannular polishing experiments are carried out to further studythe influence of different polishing parameters and ultimatelyobtain the optimized polishing parameters -is research hasimportant theoretical significance and practical value to guidethe annular polishing processing of SiC

2 Analytical Investigation of Annular Polishing

21 Kinematic Coupling of Motions Figure 1(a) illustratesa typical annular polisher which mainly consists of a pol-ishing disc a carrier disc and a swinging bracket re-spectively -e specimen is pasted on the carrier disc withparaffin which means that the specimen has a synchronousspeed with the carrier disc -e applied pressure is providedby the weight of carrier disc Accordingly Figure 1(b) il-lustrates the simplified motion diagram in the annularpolishing which indicates that the kinematic coupling ofrelative motions mainly includes the rotation of polishingdisc and the rotation of carrier disc As indicated inFigure 1(b) the speed of carrier disc is ω and the speed ofpolishing disc is δ -e distance from the center of specimenO2 to a point A on the carrier disc is r and the distance fromthe center of polishing disc O1 to the center of the carrier discO2 is R -e angle between the line segments AO2 and O1O2is θ -e speed at the point A on the polishing disc relative toO1 is V1 and the speed at the point A on the specimenrelative to O2 is V2 so the relative speed of the specimen andthe polishing disc at point A is V which can be derived fromthe following equation [16]

V(r θ) R2δ2 + r

2(δ minusω)

2+ 2rRδ(δ minusω)cos θ1113960 1113961

12 (1)

22 Preston Equation Both material removal rate andsurface quality of specimen in the annular polishing processare strongly affected by processing polishing parameterswhich have complex interactions Preston et al simplifiedthe Preston equation [17] to characterize the relationshipbetween material removal and polishing speed V appliedpressure P and other external factors as shown in thefollowing equation [17]

dh

dt kPV kP

ds

dt (2)

where h is the amount of material removal and k is a pro-portional constant that is related to various environmentalfactors -erefore the amount of material removal at onespecific point can be derived according to Equation (2)However the contact between specimen and polishing discchanges dynamically with polishing time which inducesuncertainties in the analytical investigation of annularpolishing process -erefore three main assumptions aremade to simplify the operation (1) specimen and polishingdisc are fully contacted without separation (2) the appliedpressure does not change with polishing time and (3) theproportional constant k does not change with polishingtime According to the Preston equation the amount ofmaterial removal within a specific polishing time can bederived by integrating over time t as shown in the followingequation

h(r) k 1113946T

0P(r t) middot V(r t) dt (3)

It can be seen from Equation (3) that the material re-moval is only dependent on the resultant speedV given the kand the P are constant values By substituting the relativevelocity derived from Equation (1) into Equation (3) thematerial removal at point A can be derived as shown in thefollowing equation [15]

h(r) k 1113946T

0P(r t)

middot R2δ2 + r

2(δ minusω)

2+ 2rRδ(δ minusω)cos θ1113960 1113961

12dt

(4)

-e amount of material removal at any point on thespecimen can be calculated from Equation (4) -e pressureP is affected by the type of polishing pad and polishingsolution Based on the annular polishing motion simulationand the Preston equation four influential parameters can bedetermined as polishing solution polishing pad polishingtime and rotation speed of polishing disc respectively

3 Annular Polishing Experiment of RB-SiC

31 Effect of Polishing Solution Material It has been dem-onstrated that polishing solutionrsquos particle size particlehardness and concentration have a strong impact on the








2

3

4

5

6

7

8V

alue

of s

urfa

ce ro

ughn

ess (

nm)



Swing bracket


(a)

δ

θ

ω

A

RO2

O1

r

V V1

V2

Carrier disc

Polishing disc

(b)









4 Summary


30 60 90 120 150 18005

10

15

20

25

30

35

Val

ue o

f sur

face

roug

hnes

s (nm

)



2

3

4

5

6

7

8

9

Val

ue o

f sur

face

roug

hnes

s (nm

)


Polyurethane



(a) (b)

(c) (d)

ndash01nm

106nm

10μm

10μm

10μm 8 6 4 2

10

8

6

4

2

8

6

4

2

(e)

07nm

312nm

10μm

10μm

10μm 8 6 4 2

10

8

6

4

2

8

6

4

2

(f )


40 50 60 70 80 90 100 110 120 130 140 150 160 17010

12

14

16

18

20

22

24

26

28

30

32

34

Val

ue o

f sur

face

roug

hnes

s (nm

)





Data Availability






Acknowledgments


References























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls










2

3

4

5

6

7

8V

alue

of s

urfa

ce ro

ughn

ess (

nm)



Swing bracket


(a)

δ

θ

ω

A

RO2

O1

r

V V1

V2

Carrier disc

Polishing disc

(b)









4 Summary


30 60 90 120 150 18005

10

15

20

25

30

35

Val

ue o

f sur

face

roug

hnes

s (nm

)



2

3

4

5

6

7

8

9

Val

ue o

f sur

face

roug

hnes

s (nm

)


Polyurethane



(a) (b)

(c) (d)

ndash01nm

106nm

10μm

10μm

10μm 8 6 4 2

10

8

6

4

2

8

6

4

2

(e)

07nm

312nm

10μm

10μm

10μm 8 6 4 2

10

8

6

4

2

8

6

4

2

(f )


40 50 60 70 80 90 100 110 120 130 140 150 160 17010

12

14

16

18

20

22

24

26

28

30

32

34

Val

ue o

f sur

face

roug

hnes

s (nm

)





Data Availability






Acknowledgments


References























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls










4 Summary


30 60 90 120 150 18005

10

15

20

25

30

35

Val

ue o

f sur

face

roug

hnes

s (nm

)



2

3

4

5

6

7

8

9

Val

ue o

f sur

face

roug

hnes

s (nm

)


Polyurethane



(a) (b)

(c) (d)

ndash01nm

106nm

10μm

10μm

10μm 8 6 4 2

10

8

6

4

2

8

6

4

2

(e)

07nm

312nm

10μm

10μm

10μm 8 6 4 2

10

8

6

4

2

8

6

4

2

(f )


40 50 60 70 80 90 100 110 120 130 140 150 160 17010

12

14

16

18

20

22

24

26

28

30

32

34

Val

ue o

f sur

face

roug

hnes

s (nm

)





Data Availability






Acknowledgments


References























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




(a) (b)

(c) (d)

ndash01nm

106nm

10μm

10μm

10μm 8 6 4 2

10

8

6

4

2

8

6

4

2

(e)

07nm

312nm

10μm

10μm

10μm 8 6 4 2

10

8

6

4

2

8

6

4

2

(f )


40 50 60 70 80 90 100 110 120 130 140 150 160 17010

12

14

16

18

20

22

24

26

28

30

32

34

Val

ue o

f sur

face

roug

hnes

s (nm

)





Data Availability






Acknowledgments


References























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls





Data Availability






Acknowledgments


References























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls






Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




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