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Wear 266 (2009) 10911097Contents lists available at ScienceDirectWearjournal homepage: /locate/wearAn erosion-based model for abrasive waterjet turning of ductile materialsR. Manua, N. Ramesh BabubaDepartment of Mechanical Engineering, National Institute of Technology Calicut, NIT Campus PO, Calicut, 673 601, Kerala, IndiabDepartment of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, 600 036, Indiaa r t i c l ei n f oArticle history:Received 28 December 2007Received in revised form 24 June 2008Accepted 10 February 2009Available online 26 February 2009Keywords:Abrasive waterjetsTurningModellingErosionFlow stress determinationa b s t r a c tThis paper presents an attempt to model the abrasive waterjet (AWJ) turning process considering mate-rial removal from the circumference of a rotating cylindrical specimen. The methodology involves theuse of Finnies theory of erosion to estimate the volume of material removed by the impacting abrasiveparticles. The proposed model considers the impact of jet at an angle to the workpiece surface to accountfor the curvature of the workpiece. Unlike earlier works, this model considers the continuous change inlocal impact angle caused by the change in workpiece diameter. The flow stress of the workpiece materialis determined using a novel experiment involving the same abrasive and workpiece materials. The ade-quacy of the proposed model is examined through AWJ turning tests under various process parametercombinations. The final diameters predicted by the model are found to be in good agreement with theexperimental results. 2009 Elsevier B.V. All rights reserved.1. IntroductionAbrasive waterjet (AWJ) machining is a versatile process capa-ble of machining almost any material with reasonable finish onthe machined surface. Extremely low cutting forces and negligi-ble thermal effects are the characteristic features of this process1. Recent efforts include the application of abrasive waterjets forturning of cylindrical parts by traversing the jet along the radialand axial directions of rotating workpiece. Attempts made on AWJturning include the turning of long and small diameter parts andthe production of threads on difficult-to-machine materials likeceramics, composites, glass, etc. 2. The efforts made by Hashishandco-workers37inemployinghighvelocityabrasivewaterjetsfor turning a variety of materials are noteworthy. From a visualisa-tionstudy4conductedtounderstandthemacromechanicsofAWJturning process, it was reported that the material removal takesplace on the face of the workpiece rather than on the circumfer-enceoftheworkpiece.AnsariandHashishconductedexperimentalinvestigations to study the influence of various AWJ parameters onvolume removal trends in AWJ turning 5. The results showed thatthe volume of material removed in AWJ turning is similar to thatachieved in AWJ cutting. Studies on precision turning with AWJsshowed that the accuracy of turned parts is affected by the jet trailbackanddeflection6,7.Jetinstabilityathightraverseratescausesrougher surfaces, striation marks, poor roundness and inconsis-tency in achieved diameter. Recently, Zhong and Han 8 studiedCorresponding author. Tel.: +91 495 2286444; fax: +91 495 2287250.E-mail address: manunitc.ac.in (R. Manu).the influence of process parameters on the quality of glass partturned with abrasive waterjets. This study indicated that low tra-verse rate of jet and high rotational speed of workpiece resulted inlower values of roughness and waviness on the surface of turnedpart.Numerous attempts to model AWJ cutting of ductile metallicmaterials913andbrittleceramicmaterials1417canbefoundin the literature. Recently, simulation of AWJ cutting using uniteventapproach18,19andfiniteelementtechnique20havebeencarried out. However, efforts on modelling of AWJ turning pro-cess are very much limited. A semi-empirical approach to predictdepth of cut in turning utilising a regression model was developedby Zeng et al. 21. Based on the functional relationship obtainedfrom an analytical model, a parameter prediction regression modelwas developed. The exponents were obtained by regression anal-ysis of the data obtained from turning tests. The model uses amachinability number for AWJ turning to account for the materialserosion resistance. A term called overlapping index was introducedto represent the relation between workpiece rotational speed, jetdiameter and traverse rate. A smaller value of overlapping indexmeanslargeroverlappinganditwasobservedthatthevalueshouldbe less than or equal to 0.5 to avoid threading. In an empiricalapproach to model AWJ turning presented by Henning 22, thematerialremovalinAWJturningprocessisassumedtobethecumu-lative effect of volume removed by individual particle impacts onthe circumference of the workpiece. Relations were developed todetermine the kerf area, kerfing performance, ablation rate andvolume of material removed. Empirical approaches 21,22 usemathematical relations that correlate the relevant process vari-ables to the process results. Empirical models do not provide any0043-1648/$ see front matter 2009 Elsevier B.V. All rights reserved.doi:10.1016/j.wear.2009.02.0081092R. Manu, N.R. Babu / Wear 266 (2009) 10911097insight into the mechanics of the process. Also they depend upona large number of parameters or exponents that are determined byregression analysis.An attempt was made by Ansari and Hashish 23 to suggestan analytical model that related the volume sweep rate to mate-rial removal rate. The model could predict the final diameter ofpart when turned with a given set of AWJ process parameters. Thismodel is essentially an adaptation of Hashishs model for linearAWJ cutting 9. It considers material removal from the face of therotating workpiece and is based on the assumption that the totaldepth of cut consists of two parts, viz. cutting-wear depth in turn-inganddeformation-weardepthinturning.ThemodelusesFinniestheory of erosion 24 to estimate cutting wear depth for shallowangle impact zone and Bitters theory of erosion 25,26 to calcu-late deformation wear depth for regions where abrasive particlesimpact normally. The total depth of cut thus computed is used topredict the final turned radius.This model assumed the impact angle in the cutting wear zone(shallow angle impact zone) to be constant and equal to the impactangle at the top edge of the workpiece. This contradicts the gradualdecreaseinimpactangletozero,whichistheveryreasonforassum-ing step formation similar to that in AWJ cutting. In other words,the existing analytical model of AWJ does not consider the contin-uous change in impact angle, which is the result of the reductionin diameter of the workpiece. In the deformation wear zone (highangle impact zone), the jet is assumed to impact normally on thestep formed by cutting wear mechanism. It is unlikely that two dis-tinct zones exist, which are characterised by two discrete impactangle values. Moreover, the visualization study on AWJ turning 4could not provide conclusive evidence on the steps formed at theend of shallow angle impact erosion. This model based on the con-cept of material removal from the face of the workpiece could notexplain the case of slotting in lathe. A different approach consid-ering the varying local impact angle was used to predict the finaldiameter in the case of lathe slotting 27. There were no system-atic attempts by earlier researchers to experimentally validate thepredicted results. Moreover, existing theories fail to explain cer-tainobservationslikeincreasingnegativediametererror6,7whileattempting large reduction in diameters using AWJs.Hence the objective of the present work is to develop and exper-imentallyvalidateacomprehensiveprocessmodelforAWJturning.2. MethodologyIn AWJ turning, the jet with a velocity of V is assumed tostrike the periphery of the workpiece having an initial diameterof D, rotating at a speed of N revolutions per minute. The dis-tance between the workpiece centerline and point of impact of jetis termed as the radial position of jet, x. As shown in Fig. 1, at theFig. 1. Schematic diagram of AWJ turning showing impact of jet on a rotating cylin-drical specimen.pointofimpact,thejetmakesanangleofwiththetangenttothesurface 22,23,27. The local impact angle of the jet with respect tothe workpiece surface can be computed as = cos1?2xD?(1)This is equivalent to the impact of a jet which is inclined at thecorresponding local impact angle to a flat surface and moving witha relative velocity equal to the tangential surface speed of the rotat-ing workpiece 28. Further, the jet moves along the axial directionof the rotating part so as to extend the cutting action along thelength of the part. For acceptable turning results, the axial distancemoved by the jet during one revolution of the workpiece should bea fraction of the jet diameter 21. This results in the workpiece sur-face being subjected to a definite number of cutting passes duringthe time the jet moves unit axial distance 29. The objective of theproposed process model is to predict the final diameter achieved inAWJ turning under a given set of process parameters. The method-ology involves estimating the volume of material removed by theimpactingabrasiveparticlesbyemployingasuitableerosionmodel.The scope of the present work is limited to AWJ turning of ductilematerials at low impact angles. The workpiece material consideredis aluminium 6063-T6. The effectiveness of the proposed model isvalidated through a set of AWJ turning experiments.3. Proposed model of AWJ turning3.1. Estimation of velocity of abrasive particle3.1.1. Velocity of high-speed waterjetsHigh-velocitywaterjetisformedwhenacertainvolumeofpres-surised water exits through an orifice. Application of Bernoullisprinciple gives the theoretical velocity of waterjet asVw(th)=?2P?0.5(2)where P is the water pressure. The density of water ? is takenas 1000kg/m3. In practice, an efficiency coefficient (velocity coef-ficient of orifice) Cv is introduced to account for the momentumlosses due to wall friction, fluid flow disturbances and compress-ibility of water. Thus, the exit velocity of waterjet becomesVw= Cv?2P?0.5(3)3.1.2. Velocity of abrasive waterjetsAbrasive waterjet is formed as a result of momentum transferbetweenthehighvelocitywaterjetandtheabrasiveparticles,whichare entrained in to the waterjet. Considering the momentum bal-ance between abrasive and the waterjet at the entry of focussingnozzle, the velocity of abrasive waterjet is given byVa= ?Vw1 + (.mp/.mw)(4)where .mp and .mw are mass flow rates of abrasive and water,respectivelyand?isthemomentumtransfercoefficientthatchar-acterises the losses during mixing and acceleration processes. Themass flow rate of water .mw is estimated using the expressionrelating the diameter of waterjet orifice do, waterjet velocity Vw,density of water ? and velocity coefficient of orifice Cd as.mw= Cd?4d2oVw?(5)ThetypicalvaluesofCv,Cdand?arefoundtobe0.98,0.70and0.80, respectively from experimental studies reported in literature30,31.R. Manu, N.R. Babu / Wear 266 (2009) 1091109710933.2. Prediction of workpiece diameter after each revolutionThe local impact angle of jet on the work for kth revolution isgiven byk= cos1?2xDk?(6)If the jet is considered to be stationary at any radial location,the volume of material removed during each revolution can beestimated from the rectangular strip of length equal to the circum-ference of the workpiece, width equal to the jet diameter and thedepth equal to the radial depth of penetration during that partic-ular revolution. Thus the radial depth of penetration of jet for thekth revolution is given bydrk=Qk?Dkdj(7)where Qk is the volume of material removed during the kth rev-olution, Dk is the workpiece diameter at the beginning of the kthrevolution and dj is the jet diameter. The workpiece diameter forthe (k+1)th revolution can be obtained asDk+1= Dk 2drk(8)3.3. Estimation of volume of material removedThemechanismofmaterialremovalinAWJmachiningprocessesis well accepted as erosion caused by free moving abrasive parti-cles 1,2. Various theories of erosion have been proposed duringthe past few decades 2426,3235. Finnies theory of erosion 24is one of the pioneering works in this area and has formed the basisof many research works later. The present work employs Finniestheory of erosion to estimate the volume of material removed bythe impacting particles. The major limitation of the theory is itsinabilitytoaccountfortheerosionbehaviouratlargeimpactangles.However, AWJ turning mostly employs low initial impact angleswhich gradually reduce to zero as the desired final diameter isachieved.Moreover,controllingthedepthofpenetrationandhencethe final diameter achieved is difficult, while employing a normalimpact angle turning approach. A recent experimental study 36comparing the low and normal impact angle turning approacheshighlighted the poor surface finish achieved on the parts turnedwith normal impact angles. The rough surface obtained in AWJturning of aluminium alloy specimens at normal impact angles isprobablybecauseductilematerialstendtoflow(deformationwear)compared to material removal by micro-cutting, which is predomi-nantatlowimpactangles.Hencethescopeofthepresentmodellingattempt is limited to low impact angle turning of ductile materials,which justifies the choice of Finnies theory as the erosion model.3.3.1. Volume of material removed with abrasive water jetFinnie 24 proposed a model for estimating the materialremoval due to impact of particles at different angles of impact.It is based on the equations of motion of a single rigid abrasiveparticle moving with a velocity Va and striking the surface at anangle . It is assumed that the particle is angular with the frontface being flat with uniform width. In this, the elastic deforma-tion of the target material is neglected and the abrasive particle isassumed to remove material in a ductile manner by plastic flowalone. The resulting expression for the volume of material removedQby a single abrasive particle of mass mand velocity Vais givenby 24:Q =mV2apK ?sin2 6Ksin2?if tan K6(9)Q =mV2apK ?K cos26?iftan K6(10)where p is the flow stress of material, K is the ratio of verticalto horizontal force components, and is the ratio of the depth ofcontact lto the depth of the cut yt. From practical considerations,thevaluesforKand weretakentobe224.Whenmultiplepar-ticle impact is considered, interaction among the particles causesdeviation in the predicted volume of material removed from theideal case. To account for this, a factor c was introduced, whosevalue was taken arbitrarily equal to 0.5 by Finnie. For the total massofimpactingabrasiveparticlesequaltoM,theequationforvolumeof material removed by erosion can be rewritten asQ =cMV2a4p(sin2 3sin2)for 18.5(11)Q =cMV2a12pcos2for 18.5(12)3.3.2. Determination of flow stressTheonlyunknowninEqs.(11)and(12)istheflowstress,pofthematerial. Hashish 10 found good correlation between predictedand experimental depth of penetration values when the flow stressvalue was assumed to be E/14, where E is the Youngs modulus inGPa. Since erosion involves very high strain rates and large totalstrains, the flow stress values obtained from conventional tensionor compression tests may not be applicable to a case of erosion.Finnie 24 suggested that the flow stress may be determined froman erosion experiment involving the same abrasive and workpiecematerials.In the present work, an AWJ turning experiment was conductedin order to determine the flow stress value that may be used inthe proposed process model. The objective of the experiment is todetermine the volume of material removed under a known set ofimpact angle, abrasive velocity and total mass of abrasive particles.From the measured value of volume of material removed, the flowstress can be calculated using Eq. (11) or (12) depending on thevalue of impact angle.3.4. Estimation of number of revolutions required to achievedesired diameterDuetotheinteractionbetweenthehighvelocityabrasivewater-jet and the rotating workpiece, material removal takes place on thesurface of the part, resulting in the formation of a shallow groove,the depth of which is determined by the combination of processparameters employed. Further, the jet is moved along the axialdirection of the part so as to extend the cutting action along thelength of the part. For acceptable turning results, the axial distancemoved by the jet during one revolution of the workpiece shouldbe a fraction of the jet diameter. This results in the workpiece sur-face being subjected to a definite number of cutting passes duringthe time the jet moves unit axial distance. In other words, the timeduration for which any point on the workpiece surface is exposedto the jet is determined by the feed per revolution.3.4.1. Number of passes (np)Considerajetofdiameterdjpassingoverastripofinfinitesimalwidth dx as shown in Fig. 2. The workpiece makes N revolu-tions per minute and the jet moves along the workpiece axis witha velocity of u mm/min (traverse rate). The jet has to travel anaxial distance of dx+dj to completely cover the strip of width dx.Hence, the time taken td to cover the distance dj+dx is givenby (dj+dx)/u. The number of revolutions made by the workpiece1094R. Manu, N.R. Babu / Wear 266 (2009) 10911097Fig. 2. Isometric view of AWJ turning process showing jet axial movement over arotating cylindrical specimen.during this time is given bynp= N?dj+ dxu?(13)Sincethisdistancedxisverysmallcomparedtothejetdiameterdj, dx is neglected in Eq. (13). Thus the number of cutting passesmade by the jet over the strip of infinitesimal width becomesnp= Ndju(14)Hence it is assumed that the entire surface of the workpiece isexposed to the jet for nptimes.3.5. Prediction of final workpiece diameterDuring each revolution, the workpiece diameter changes andthis in turn changes the local impact angle. By applying Eqs.(2)(12), the volume of material removed, radial depth and thediameter of work after each revolution can be determined. Byrepeatingtheaboveprocedurefornptimes,asgivenbyEq.(14),thefinal workpiece diameter achieved under any given set of processparameters can be estimated.4. Experimental workTwodifferentsetsofexperimentswereconductedinthepresentwork. The first set of experiments was conducted in order to deter-mine the flow stress value of the workpiece material, which is tobe used in the proposed model for AWJ turning. The second setof experiments was basically turning tests intended to validatethe proposed model for AWJ turning. The experiments were con-ducted on 6063-T6 aluminium alloy specimens with an injectiontypeabrasivewaterjetcuttingmachinecapableofgeneratingwaterpressure in the range of 60360MPa with a rated discharge of 2.2lperminute.Waterjetorificeof0.25mmdiameterandfocusingnoz-zles of diameters 0.76mm, 1.2mm and 1.6mm were employed inthe cutting head. Garnet with a mesh size of 80 was used as theabrasive material. All the experiments were conducted at a waterpressure of 250MPa, abrasive mass flow rate of 5g/s and a stand offdistance of 2mm.Experiments were conducted on cylindrical specimens of25.4mm diameter using the specially designed AWJ turning setup.Fig. 3. Photograph of the setup used for AWJ turning of cylindrical parts.The setup consists of a four jaw chuck to hold the workpiece. Thechuck is attached to a shaft driven by a stepper motor. The driveshaft is supported on two ball bearings. The stepper motor andthe drive shaft assembly are mounted on a steel frame. The entireassembly is enclosed in a transparent casing for preventing theentryofwatersplashedduringtheexperimentation.Asuitablecon-troller was used to vary the speed of stepper motor between 8rpmand250rpm.InFig.3,thearrangementofthesetuponthemachinefor conducting turning experiments with AWJs is shown.Before conducting the experiments, the concentric rotation ofthe specimen with respect to the axis of rotation of stepper motorwas ensured by centering the specimen in the four jaw chuck withthe help of a dial gauge. Further, the parallelism between the axisof rotation of the specimen and the traverse direction of jet wasensured by touching the periphery of the rotating specimen withlowpressurewaterjetandthenmovingitalongtheaxialdirectionoftherotatingspecimen.Thisisdonetominimiseformerrorsthatcanarise due to misalignment between the jet and rotating workpiece.4.1. Determination of flow stressIn order to calculate the flow stress, the volume of materialremoved under a known set of impact angle, abrasive velocity andtotal mass of abrasive particles is to be determined. The impactangle is decided by the radial position of the jet with respectto the cylindrical part surface. For conducting the tests with lowangle impact of jet, the jet was positioned at a distance of 1.7mmfrom the periphery of the specimen. This particular position ofjet corresponds to 30impact angle for a part having an initialdiameter of 25.4mm. The abrasive velocity depends on the waterpressure employed and is estimated using Eq. (4). The total massof abrasive particles is the product of abrasive mass flow rateand exposure time. The exposure time is the time taken by thejet to cover the length of the specimen, which can be calculatedas the ratio of length of the specimen to the jet axial traverserate.Theexperimentswereconductedatworkpiecerotationalspeedsof 13rpm, 25rpm, 37rpm and 50rpm in order to achieve surfacespeeds of approximately 1000, 2000, 3000 and 4000, respectively.The experiments were repeated using three different focussingnozzle diameters viz., 0.76mm, 1.20mm and 1.60mm. The tra-verse rate of the jet along the axial direction of the specimen wasselected based on the workpiece rotational speed such that thejet moves a distance larger than the jet diameter during the timethe workpiece makes one revolution. This results in the forma-R. Manu, N.R. Babu / Wear 266 (2009) 109110971095Fig. 4. Stepped part geometry for validation tests.tion of a helical groove on the specimen surface. This is necessaryto maintain the impact angle constant by ensuring that the jetdoes not impact a previously machined surface. The axial traverserates employed were 39mm/min, 75mm/min, 111mm/min and150mm/min, respectively corresponding to the rotational speedsof 13rpm, 25rpm, 37rpm and 50rpm.After machining the helical groove, the specimen is cut torequired length. The original volume is calculated from the dimen-sionsofthemachinedspecimen.Thespecimenisthenweighedandthe final volume is determined using the relation among mass, vol-ume and density. The volume removed thus calculated is used toestimate the flow stress of the material using Eq. (12).4.2. Validation of the proposed modelIn order to validate the final diameter predicted using the pro-posed model, tests were conducted on cylindrical specimens of25.4mm diameter using the specially designed AWJ turning setup.A part having a stepped geometry as shown in Fig. 4 was turned forthe validation tests. The position of the jet with respect to the cen-trelineofthepartdeterminestheimpactangleandtheradialdepthof cut. In order to locate the jet at a particular radial position, thejet was first made to touch the periphery of the workpiece and thenmoved through the required distance towards the centreline of thepart. At first the jet is manually positioned at the maximum depthof cut position. In order to achieve the desired stepped geometry,the jet is moved along the required path by executing a CNC pro-gram. Each specimen was turned at one particular traverse rate andbecause of the stepped geometry, five different depths of cut val-uescouldbeobservedonasinglespecimen.Table1liststheprocessTable 1Process parameters employed for turning tests.ParameterValuePressure, MPa250Focussing nozzle diameter, mm0.76Abrasive mass flow rate, g/s5.0Rotational speed of workpiece, rpm200Radial position of jet (x), mm11.7, 10.7, 9.7, 8.7, 7.7Axial traverse rate, mm/min1, 1.5, 2, 2.5, 3, 4, 5, 10, 20, 30, 40, 50parameters, radial positions of jet and axial feed rates employed forthe step turning tests. After completing each experiment, the partwas removed from the setup and the diameter of each step on theturned part was measured using vernier callipers having a leastcount of 0.02mm.5. Results and discussionFig. 5 shows a specimen with helical groove machined on it,which was used for measuring the volume removed by the impact-ing abrasive particles. Table 2 presents the flow stress valuescalculated employing Eq. (12) assuming a multi-particle interac-tion factor c of 0.5. The flow stress values obtained from all theexperiments involving three different focussing nozzle diametersare found to have a mean of 874MPa and standard deviation of215MPa. However, since the turning tests used a focussing nozzlediameter of 0.76mm, the corresponding average flow stress valueof 1000MPa was selected for use in the prediction model. The dif-ference in the flow stress values estimated in the present workfrom the value reported earlier 10 may be due to the difference inerosion mechanisms/modes in cutting and turning. In AWJ cutting,after an initial cutting wear zone, material removal takes place bydeformationwearmode,whichisnotveryefficientinductilemate-rials. In AWJ turning at low impact angles, material removal takesplace exclusively by micro-cutting. Further, the estimated veloc-ity of abrasive particles may be different from the actual valuesand due to jet-spreading; the actual impact angles of the individualabrasive particles may be different from the geometrically definedlocal impact angle.Since the value of flow stress has been calculated in the presentwork from an experiment involving the same abrasive and work-piece materials and the experimental setup used for turning tests,this may even be considered as an empirical constant whichaccounts for the material property and all other effects which arenot accounted for in the analytical model.Theproposedmodelwasusedtopredictthefinalturneddiame-terachievedemployingtheprocessparameterslistedinTable1.Thejet divergence is neglected and hence a jet diameter compensationFig. 5. Specimens from flow stress determination tests. Focussing nozzle diameter: 0.76mm. Surface speeds (mm/min): (a) 1000; (b) 2000; (c) 3000; (d) 4000.1096R. Manu, N.R. Babu / Wear 266 (2009) 10911097Table 2Experimentally determined flow stress values.Focussing nozzle diameter, mmSurface speed of workpiece, mm/minVolume removed, mm3Exposure time, sFlow stress, MPa1.601000587.9121.381136.682000474.0411.30744.673000340.767.02643.444000186.643.93657.701.201000661.4917.85843.092000385.399.39761.573000288.085.37582.85400095.673.281071.420.761000673.3627.691285.182000454.7912.40852.043000360.7211.54999.324000290.748.28889.98Fig. 6. Specimens from validation tests. Axial traverse rate (mm/min): (a) 2; (b) 2.5; (c) 10; (d) 20.Fig.7. Comparisonofpredictedandexperimentallyachievedfinalturneddiameters.of 0.76mm was applied. Photographs of selected specimens fromthe validation tests are shown in Fig. 6. The comparison of finaldiameters predicted by the proposed model and those achievedexperimentally is shown in Fig. 7. The predicted results correlatevery well with the experimental results as indicated by the corre-lation coefficient of 0.97. The error in prediction is found to varyin the range of 1.3mm to 1.7mm, with a mean of 0.2mm andstandard deviation of 0.62mm. However, in order to make accu-rate predictions of the final diameters that can be achieved, the jetdivergenceeffectistobeconsideredwhileapplyingthejetdiametercompensation.6. ConclusionsAn attempt was made in this paper to propose a new analyticalmodel for the AWJ turning process, considering material removalfrom the circumference of a rotating part. The mechanism of mate-rial removal is erosion, caused by abrasive particles entrained in ahighvelocitywaterjet.Thevolumeofmaterialremovedbytheabra-sive particles during each revolution was estimated using Finniestheory of erosion, which required knowledge of flow stress of theworkpiece material. The flow stress of the material determinedfrom standard tests is not suitable for situations involving ero-sion. Hence a novel experiment using the same AWJ turning setupinvolvingthesameabrasiveandworkpiecematerialswasdevisedtodetermine the flow stress of the workpiece material. The proposedmodel employing the experimentally determined flow stress valuecould successfully predict the final diameters achieved when alu-minium alloy specimens were turned with AWJs, under differentcombinations of process parameters.References1 A.M. Hoogstrate, C.A. van Luttervelt, Opportunities in abrasive water-jetmachining, Annals of the CIRP 46 (2) (1997) 697714.2 R.Kovacevic,M.Hashish,R.Mohan,M.Ramulu,T.J.Kim,E.S.Geskin,Stateoftheart of research and development in abrasive waterjet machining, ASME Journalof Manufacturing Science and Engineering 119 (1997) 776785.3 M.Hashish,Turningwithabrasivewaterjetsafirstinvestigation,ASMEJournalof Engineering for Industry 109 (4) (1987) 281290.4 A.I. Ansari, M. Hashish, M.M. Ohadi, Flow visualization study of the macrome-chanics of abrasive waterjet turning, Experimental Mechanics 32 (4) (1992)358364.5 A.I. Ansari, M. Hashish, Effect of abrasive waterjet parameters on volumeremoval trends in turning, ASME Journal of Engineering for Industry 117 (4)(1995) 475484.6 M. Hashish, J. Stewart, Observations on precision turning with AWJ, in: Pro-ceedings of 15th International Conference on Jet Cutting Technology, Ronneby,Sweden, September 68, 2000, pp. 367380.7 M. Hashish, Macro characteristics of AWJ turned surfaces, in: Proceedings of2001 WJTA American Waterjet Conference, Minneapolis, Minnesota, August1821, Paper no. 4, 2001, pp. 114.8 Z.W. Zhong, Z.Z. Han, Turning of glass with abrasive waterjet, Materials andManufacturing Processes 17 (3) (2002) 330349.9 M. Hashish, A modelling study of metal cutting with abrasive waterjets, ASMEJournal of Engineering Materials and Technology 106 (1) (1984) 88100.10 M.Hashish,AmodelforAWJmachining,ASMEJournalofEngineeringMaterialsand Technology 111 (2) (1989) 154162.11 S. Paul, A.M. Hoogstrate, C.A. van Luttervelt, H.J.J. Kals, Analytical and experi-mental modeling of abrasive water jet cutting of ductile materials, Journal ofMaterials Processing Technology 73 (1998) 189199.12 A.M. Hoogstrate, B. Karpuschewski, C.A. van Luttervelt, H.J.J. Kals, Modellingof high velocity loose abrasive machining processes, Annals of the CIRP 51 (1)(2002) 263266.13 M.ElTobgy,E.-G.Ng,M.A.Elbestawi,Modellingofabrasivewaterjetmachining:a new approach, Annals of the CIRP 54 (1) (2005) 285288.R. Manu, N.R. Babu / Wear 266 (2009) 10911097109714 J.Zeng,T.J.Kim,Anerosionmodelofpolycrystallineceramicsinabrasivewater-jet cutting, Wear 193 (1996) 207217.15 A. Abdel-Rahman, A.A. El-Domiaty, Fracture mechanics-based model of abra-sive waterjet cutting for brittle materials, International Journal of AdvancedManufacturi
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