Edge effect in fluid jet polishing

Edge effect influid jet polishingPeiji Guo,Hui Fang,and Jingchi YuThe edge effect is one of the most important subjects in optical manufacturing.The removal function atdifferent positions of the sample in the process offluid jet polishing(FJP)is investigated in the exper-iments.Furthermore,by usingfinite-element analysis(FEA),the distributions for velocity and pressureof slurry jets are simulated.Experimental results demonstrate that the removal function has a ring-shaped profile,except for a little change in the size at the operated area even if the nozzle extends beyondthe edge of the sample.FEA simulations reveal a similar distribution of velocity with a cavity resultingin the ring-shaped profile of material removal at different impact positions.To a certain extent,therefore,the removal function at the edge of the surface of the sample appears similar to that inside of it,so thatthe classical edge effect can be neglected in FJP.©2006Optical Society of AmericaOCIS codes:220.0220,220.4610,220.5450.1.IntroductionIn the classical polishing method,the amount of re-moved material is affected when the polishing tool extends beyond the edge of the workpiece and the wear is greater at the edge than at the inner section of the workpiece.This phenomenon is called the edge effect.The edge effect is explained as the result of excessive pressure applied by the tool when it is at maximum stroke,since the contact area between the tool and the workpiece is reduced,and therefore the wear is increased.1To obtain a proper profile at the edge of the work-piece while it is being polished,much research was carried out and several methods have also been de-veloped.1In classical polishing methods,the utiliza-tion of a small-size tool,which minimizes the variable contact area problem and the utilization of an adjust-able aluminum collar around the workpiece were brought forward.One of the most common ways is to embed the workpiece in a large domain and then discard that portion at which the edge effect occurs, while a stressed lap that changes its shape actively as needed was used in stressed lap polishing.In the chemical mechanical polishing(CMP)process,one method called the airfloat carrier2was developed to achieve uniform polishing with a continuous air sup-ply during the polishing of the sample.Retainer pres-sure enables the supportfilm to push the wafer edge down to the pad locally to control the edge-polishing profile.In the magnetorheologicalfinishing(MRF) process,3several approaches such as edge extension, variable plunge depth,model spot changes near edges,and adjusted dwell schedule have been iden-tified to minimize the edge effect.However,all the methods cannot conquer the edge effect completely, and the edge effect has become one of the most im-portant problems in various polishing methods.As forfluid jet polishing4(FJP),a newly developed technology in optical fabrication,the problem of how to understand the edge effect and solve it has not been referred to in previous studies.Therefore the primary goal of this paper is to understand the processing dif-ferences at the edge and develop an approach to deal with them,which is crucial in successfully applying FJP to modern optical manufacturing.In this paper,experiments were carried out to un-derstand the removal function when the polishing tool extends beyond the edge of the sample,and then thefinite-element analysis(FEA)method was intro-duced to establish the hydrodynamicfluid pressure andfluid velocity when the slurry jet impacts on the surface of the sample.Experimental and simulation results imply that the edge effect was nearly not pro-duced.Therefore to a certain extent it can be ignored in the practical application of FJP.2.Removal FunctionIn polishing methods,the amount of removed mate-rial can be described by a2D convolution:The authors are with the Province Key Laboratory of ModernOptical Technology of Jiangsu,Soochow University,Suzhou,215006,China.P.Guo’s e-mail address is gpj@.Received20March2006;revised22April2006;accepted24April2006;posted28April2006(Doc.ID69163).0003-6935/06/266729-07$15.00/0©2006Optical Society of America10September2006͞Vol.45,No.26͞APPLIED OPTICS6729⌬z͑x,y͒ϭR͑x,y͒ءءD͑x,y͒.(1) Here R͑x,y͒denotes the removal function;D͑x,y͒is the dwell time at point͑x,y͒.Equation(1)implies that material removal is de-termined by the removal function and dwell time. Generally,the dwell time can easily be controlled in the polishing process,but the removal function can-not,especially at the edge of the workpiece.It is the change of the removal function that leads to the variety or nonuniformity of the material removal at the edge and then causes edge effect.Similarly to FJP,the proper dwell time can easily be realized by using a computer that controls the movement of the nozzle.The distribution of the removal function, which is affected by working pressure and the char-acteristics of the nozzle,is constant inside the work-piece.However,it may be influenced by the edge of the sample and cannot easily be controlled when thenozzle moves near the edge.Therefore study of the removal function,especially at the edge,is the main subject in understanding the edge effect.3.Experiments and SimulationsThe purpose of the present work is to investigate the distribution of material removal in the sample-jet contact area.In this section,the characteristics of material removal and the impacting slurry jet will be captured by experimental observations and FEA models,respectively.A.Polishing Away from the EdgeExperiments have been constructed to validate the removal function by operating the sample at different positions,including the periphery area.In experi-ments,premixed slurry(water containing5%Cerox 1650grinding compound)and a cylindrical nozzle with a length of lϭ20mm and a diameter of␸ϭ1.2mm are chosen.The workpiece(flat K9sample)isfixed, and the relative position of the workpiece and slurry jet is realized by moving the nozzle,which is posi-tioned above the workpiece with a standoff distance of dϭ7mm.1.Experiments and SimulationsDistribution of material removal will be obtained at different positions of the sample with some parame-ters being kept constant(working pressure pϭ6 bars,1barϭ100kPa,standoff distance dϭ7mm, processing time tϭ5min).A picture depicting the process of an impact of the slurry jet on the sample with a normal incidence angle is shown in Fig.1,and a stationary footprint describing the distribution of the removal function is observed by using a ZYGO Mark IV interferometer when the nozzle isfixed far away from the edge of the sample.The stationary footprint is shown in Fig.2.It is a circular ring with a maximum amount of removal in the periphery and a minimum at the center of the operated area on the surface of the sample.By using FEA,5the characteristic of the slurry jet is simulated when it impacts the sample vertically.Figure3(a)describes the characteristics of the slurry jet when it runs out from the nozzle and impacts the sample with a normal incidence angle.From thisfig-ure,we canfind a velocity cavity appearing in the center of the impacted area where nearly no slurry can arrive.This cavity is caused by circumfluence of the slurry jet after impact.The distributions of pres-sure and the velocityfield are shown in Fig.3(b). They possess the maximum value of pressure and the minimum value of velocity in the center of the im-pacted area.Then,the pressure will decrease quickly close to zero while the velocity increases gradually with the slurry jetflowing outside and arrives at the maximum at the boundary of the impacted area. 2.DiscussionsFrom the experimental(Fig.2)and simulation re-sults(Fig.3),we can get a conclusion,5which is as follows.The slurry runs out from the nozzle and im-pacts the workpiece at a high speed,while the slurry in the center of the streamline streams outside radi-ally under high pressure and a pressure gradient without directly contacting the surface,which causes one cavity of velocity and leads to hardly any material removal.Otherwise,whenflowing outside,the slurry has a maximum relative speed to the workpiece, which results in the maximum materialremoval. Fig.1.(Color online)Drawing of the impact of the slurry jet and thesample.Fig.2.(Color online)Distribution of material removal with a normal incident angle.6730APPLIED OPTICS͞Vol.45,No.26͞10September2006Further,the distribution of removed material is sim-ilar to that of the fluid velocity field.The maximum amount of removed material appears on the area where the fluid velocity reaches the maximum value and the minimum velocity in the center leads to hardly any removal.Therefore we can conclude that the removal is controlled by the relative velocity between the slurry jet and the sample in FJP,and the collision and shearing actions between abrasive par-ticles in the slurry and sample play a dominant role in material removal.Then,we will only investigate the velocity field of the slurry jet to understand the removal function in a later work.B.Polishing at the Edge1.Experiments and SimulationsThe other experiments were also carried out to vali-date the change of the removal function at the edge of the sample,which is responsible for the nonuniform removal of the surface.In operation,the process pa-rameters are kept constant as referred to in Subsec-tion 3.A,while the nozzle is fixed vertically to the surface with different relative positions to the edge of the sample.Figure 4shows the stationary footprint of the re-moved material when the nozzle was fixed with a distance of approximately s ϭ3mm between the center of the nozzle and the edge of the sample.It is also a circular ring with minimum removal in the center,and the removal function is almost the same as that inside the sample.Then,using the FEA method,we investigated the velocity field of the slurry jet,as shown in Fig.5.From this figure,wecanFig.3.(Color online)Characteristics of the fluid field after impact:(a)distribution of the fluid field,(b)pressure and velocity field on thesurface.Fig.4.(Color online)Distribution of material removal when the nozzle was fixed with a distance of approximately 3mm.10September 2006͞Vol.45,No.26͞APPLIED OPTICS6731see that the distribution of the velocity field is almost the same as that impacted far away from the edge,except an infinitesimal deviation that appears out-side of the sample [Fig.5(b)].This phenomenon can be attributed to the fact that the characteristics of the slurry jet are not nearly influenced by the edge of the sample,which is far away from the boundary of the impacted area by approximately s ϭ1.8mm.How-ever,this change fails to cause a difference in the removal function,for it is minimal and only appears outside the operated area.Therefore it can be con-cluded that the removal function is constant at this position and is not influenced by the edge of the sam-ple.When the nozzle moves near the edge with a dis-tance of approximately s ϭ0.5mm,the simulation of the slurry jet (see Fig.6)implies that the character-istic of the velocity field after impact is different from that inside the sample.This distribution has deviated from the symmetry with a larger value of velocity appearing outside of the sample and a smaller one inside the sample.However,a velocity cavity also appears on the impacted area,except for a deviation from the center of the slurry jet to the inner portionof the impacted area.Obviously,this cavity cannot cause material removal at this point and the material removal will also be a ring-shaped profile.Figure 7shows the velocity field when the nozzle lies just above the edge.Similar to Fig.6,more slurry jet streams out of the sample and only a smaller part impacts the sample (shown in the left part of Fig.7).Furthermore,the velocity at the ragged edge of the sample is no longer zero for the deviation of the ve-locity cavity,which results in material removal.An experimental result also shows that some material is removed at this ragged edge,while the profile of the removed material is also ring shaped,as shown in Fig.8.Similarly,when the nozzle center extends the edge of the sample at approximately s ϭ0.8mm,the sim-ulation shows that the velocity cavity also appears on the impacted area [see Fig.9(a)],and the distribution of removal [see Fig.9(b)]also appears as a ring-shaped profile with more material removal at the ragged area,which is coincident with the simulation result.2.DiscussionsFrom the experimental results [Figs.8and 9(b)],we can easily find that,when the nozzle moves to the edge gradually,the distribution of the removalfunc-Fig.5.(Color online)Characteristics of the fluid field after im-pact:(a)distribution of the fluid field without showing the work-piece that lays on the bottom of the left side,(b)description of the velocityfield.Fig.6.(Color online)Characteristics of the fluid field after im-pacting when the nozzle was fixed with a distance of approximately 0.5mm.6732APPLIED OPTICS ͞Vol.45,No.26͞10September 2006tion is also ring shaped with hardly any removal in the center that is related to the velocity cavity.While material is also removed at the ragged edge of the sample,the depth of removal is larger than that appearing on the ring-shaped area.Furthermore,from the cross section of material removal (see Fig.10),we can calculate the removal area at the ragged edge with a width of approximately 0.2mm.Further experiments show that the width is influenced by the operated area,and a smaller impacted area leads to a larger width and a deeper removal.This phenom-enon can be contributed to the deviation of the veloc-ity cavity from the center of the slurry jet.Furthermore,the velocity cavity appears on theimpacted area,instead of on the center of the slurry jet,leading to the nonzero velocity at the ragged edge.Furthermore,the slurry jet is not blocked when it runs out of sample,so the direction of the slurry jet outside is not parallel to the surface but streams out directly with the vertical portion.The characteristics of the velocity cause the abrasive particles in the slurry to impact the ragged edge with an almost ver-tical velocity,whereas they impact the inner surface with a horizontal one.Therefore it is the abrasive particles with an almost vertical velocity that stream out of the surface directly causing more removal at the ragged edge.C.Influence of DistanceThe material removal rate on the surface is computed as a function of the position of the nozzle.When the nozzle is fixed far away from the edge,results show that the removal is not affected by the position,and it can be comprehended easily,for it is consistent with the classical polishing methods.However,the distri-bution and removal will be influenced and presents a little change near the edge.Table 1shows the amount of removed material as a function of distance.Here,the position of the nozzle refers to the distance of the nozzle axis to the edge of the sample,and theminusFig.7.(Color online)Description of the fluid field when the nozzle was fixed with a distance of approximately 0mm.Fig.8.(Color online)Distribution of material removal when the nozzle was fixed with a distance of approximately 0mm.Fig.9.(Color online)Distribution of material removal and fluid velocity when the polishing head extends the sample by approxi-mately s ϭ0.8mm:(a)fluid velocity,(b)material removal.10September 2006͞Vol.45,No.26͞APPLIED OPTICS6733sign denotes that the nozzle axis has been extended out of the sample.Material removal is the removal that appears on the ring-shaped part,while removal at the edge appears at the ragged edge of the sample.These experimental results imply that the character-istics of removal are really affected by the edge of the sample.However,in practice,considering the smaller area of this removal with a length of approximately 0.2mm and only appearing on the ragged edge of the sample,this minimum change in removal and distri-bution from the edge can be neglected.D.PracticeThe change of velocity distribution induces the dif-ference in the removal rate at the edge.However,considering the smaller polishing area with a diam-eter of approximately 2.4mm,the computational al-gorithm referred to in Ref.6can also be used to calculate the dwell time in the polishing process,and this concept has also been tested in the experiment.This experiment was developed on a prepolished flat sample with a diameter of 100mm [shown in Fig.11(a)].In operation,the sample rotates with a rotational speed of ␻ϭ108rpm and the nozzle crosses through the center of the sample.To obtain equal material removal,the nozzle should have dif-ferent velocities at different radii.The surface area of a ring with width d r at a distance r from the center of rotation equals 2r d r ;it increases linearly with the distance r .The removal at a point of the surface will be inversely proportional to the distance r .Therefore,the nozzle should scan over the surface with different velocities,which are proportional to the radius r at different radii.The operated area is a zone with a radius ofr ϭ28–50mm,and the final surface curve is shown in Fig.11(b).It implies that the operated surface has the uniform curve except for more removal at the ragged edge with a width of approximately 0.8mm.This value exceeds 0.2mm referred to in Subsection 3.C.Perhaps this difference can be attributed to the rotary error or radial pulsation of the rotation axisofFig.10.(Color online)Profile of removal at the ragged edge:(a)cross section of removal,(b)2D profile ofremoval.Fig.11.(Color online)Curve of surface:(a)original surface:(b)final surface after operation.Table 1.Removal Rate as a Function of the Distance of the NozzlePosition of Nozzle (mm)4210.50Ϫ0.5Ϫ0.8Ϫ1.0Material removal (wave)0.1180.1200.1210.1140.1020.0880.0750.068Removal at edge (wave)0.0500.1020.1390.1550.1710.1956734APPLIED OPTICS ͞Vol.45,No.26͞10September 2006the sample or the initial surface error,and the higher precision axis will minimize this ragged edge area.4.ConclusionsAs to the classical polishing method,the distribution of the contact pressure causes the change of the re-moval function and significantly affects the polishing results when the polishing head extends the surface of the sample and is usually followed by its deforma-tion.Different from classical polishing methods,FJP is a noncontact machining technique in which a high-energy slurry jet is directed toward a target to remove material in a predetermined and controlled fashion. The characteristics of the polishing head are deter-mined by the pump and nozzle,which are usually kept constant.Therefore the polishing head’s defor-mation does not occur and it is not nearly influenced by the polishing position even at the edge of the work-piece.Furthermore,considering the smaller size of the polishing head,the minimal change in removal and distribution can be ignored.Therefore the com-putational algorithm used to calculate the dwell time and material removal can be applied on all the sur-faces of the workpiece.Accordingly,considering thatthe edge effect only appears at the ragged edge and on a smaller area of the sample,this influence can be neglected in practical applications.This work was supported by the National Natural Science Foundation of China,60278011.References1.A.Cordero-Dávila,J.González-García,M.Pedrayes-López,L.A.Aguilar-Chiu,J.Cuautle-Cortés,and C.Robledo-Sánchez,“Edge effects with the Preston equation for a circular tool and workpiece,”Appl.Opt.43,1250–1254(2004).2.T.Fujita,M.Touzov,S.Michiya,and T.K.Doy,Control of EdgePolishing Profile with Air Float Carrier(IEEE,2001),pp.183–186.3.A.Shorey,A.Jones,P.Dumas,and M.Tricard,“Improvededge performance in magnetorheologicalfinishing(MRF),”(QED Technologies,Inc.),/tech_days/ tech_days_2004/docs/17%20Aug%202004/15%20QED%20 Edge%20Effects.pdf.4.O.W.Fähnle,H.van Brug,and H.J.Frankena,“Fluid jetpolishing of optical surfaces,”Appl.Opt.37,6671–6673(1998).5.H.Fang,P.Guo,and J.Yu,“Analysis of material removalmechanism influid jet polishing byfinite element method,”Opt.Prec.Eng.2,218–223(2006).6.H.Fang,P.Guo,and J.Yu,“Dwell function algorithm influidjet polishing,”Appl.Opt.45,4291–4296(2006).10September2006͞Vol.45,No.26͞APPLIED OPTICS6735。