【机械类毕业论文中英文对照文献翻译】五轴铣削加工的建模和仿真
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机械类毕业论文中英文对照文献翻译
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【机械类毕业论文中英文对照文献翻译】五轴铣削加工的建模和仿真,机械类毕业论文中英文对照文献翻译,机械类,毕业论文,中英文,对照,文献,翻译,铣削,加工,建模,仿真
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Modeling and simulation of 5-axis milling processesE. Budak (2)*, E. Ozturk, L.T. TuncFaculty of Engineering and Natural Sciences, Sabanci University, Istanbul, Turkey1. Introduction5-axis milling has become a widely used process due to itsability to machine complex surfaces. In most of these applicationshigh productivity is required due to the cost of machine tools andparts. Productivity and quality in 5-axis milling can be increasedusing process models. However, unlike other processes, modelingof 5-axis milling has been very limited. The objective of this paperis to demonstrate selection of process parameters in 5-axis millingfor increased productivity using process models and simulations.Altintas and Engin 1 modeled the cutting edge for generalizedmilling cutters,and usedit incutting forceandstabilitycalculations in 3-axis milling which can be extended to 5-axismilling. However, all process models require toolpart engage-mentboundarieswhicharemorecomplicatedin5-axismillingdueto the additional degrees of freedom. The calculation of engage-ment limits in 5-axis milling has been mainly done using non-analytical methods. For example, Larue and Altintas 2 used ACIS3 solid modeling environment to determine the engagementregion for force simulations of flank milling. Kim et al. 4determined the engagement region using Z-mapping. Ozturk andBudak 5, on the other hand, determined the engagement regionsanalytically, and modeled the cutting forces and tool deflections.Chatter is one of the main limitations in 5-axis milling.Although chatter stability in milling has been extensively studiedanalytically68andbysimulations9,thishasbeenverylimitedfor ball-end milling and 5-axis millingprocesses. Altintas et al. 10extended the analytical milling stability model to the ball-endmilling whereas Ozturk and Budak 11,12 included the effect oflead and tilt angles using single- and multi-frequency methods.Force and the stability models can be used both in planning andanalysis. In planning phase, better process parameters can beselected through simulations. In 5-axis milling, however, processparameters may continuously vary along the tool path. In thisstudy, these parameters are obtained using a procedure 13developed for extraction of milling conditions from cutter location(CL) data. As all CAD/CAM software provides CL files, this approachpresents a practical method for integration of the models with theCAD/CAM systems.In the next section, the geometry of 5-axis milling is brieflyintroduced together with the force model. The application of themodel in lead and tilt angle selection is also demonstrated. Forchatter stability analysis of 5-axis milling, single- and multi-frequency solutions are summarized, and used for generation ofstabilitydiagrams.Thelastsectionofthepaperpresentssimulation of 5-axis milling cycles with example cases.2. Process geometry and force modelCompared with conventional milling operations, 5-axis millinggeometry is more complicated due to the additional degrees offreedom.Inthissection,5-axismillinggeometryispresentedbriefly.A more detailed analysis can be found in 5. Three coordinatesystems are used in modeling of 5-axis milling processes. MCS is afixedcoordinatesystemonthemachinetool.TCSconsistsofthetoolaxisandtwoperpendiculartransversalaxes(x)and(y).FCNconsistsof the feed, F, the surface normal, N and the cross-feed, C, directions(Fig.1).Theleadangleistherotationofthetoolaxisaboutthecross-feed axis, whereas the tilt angle is the rotation about the feed axiswithrespecttothesurfacenormal.Leadandtiltanglestogetherwithball-end mill geometry, cutting depth and step over determine theengagement region between the cutting tool and workpiece. InFig.1,engagementregion,variationofstart(wst)andexitangles(wex)along the tool axis are demonstrated for a representative case.The cutting tool is divided into differential cutting elements todetermine the varying engagement boundaries (Fig. 1). Theengagement model 5 is used to determine the elements that arein cut. Differential cutting forces in radial, tangential and axialdirections shown in Fig. 2 are calculated in terms of the local chipthickness and width, and the local cutting force coefficients. Localchip thickness and cutting force coefficients are variable along thecutting flute depending on the immersion anglewand z coordinateas presented in Fig. 3.CIRP Annals - Manufacturing Technology 58 (2009) 347350A R T I C L EI N F OKeywords:MillingForceStabilityA B S T R A C T5-axis milling is widely used in machining of complex surfaces. Part quality and productivity areextremelyimportantduetothehighcostofmachinetools andpartsinvolved.Processmodelscanbeusedfor the selection of proper process parameters. Although extensive research has been conducted onmilling process modeling, very few are on 5-axis milling. This paper presents models for 5-axis millingprocess geometry, cutting force and stability. The application of the models in selection of importantparameters is also demonstrated. A practical method, developed for the extraction of cutting geometry, isused in simulation of a complete 5-axis cycle.? 2009 CIRP.* Corresponding author.Contents lists available at ScienceDirectCIRP Annals - Manufacturing Technologyjournal homepage: /cirp/default.asp0007-8506/$ see front matter ? 2009 CIRP.doi:10.1016/j.cirp.2009.03.044Cutting forces, torque and power are calculated by integratingthedifferentialforceswithintheengagementregion.Tooldeflections are calculated using the structural properties of thecutting tool and forces at surface generation points 5.2.1. Force model resultsTheforcemodelwasverifiedwithmorethan70cutting tests5.The force model can be used in the selection of lead and tilt angles.Theeffectofleadandtiltanglesonthemaximumtransversalcuttingforce, Fmaxxy, is simulated for a representative following-cut case inFig. 4. The cutting depth and the step over are 5 mm, the feed rate is0.05 mm/tooth, the spindle speed is 1000 rpm and cross-feeddirection 5 is negative. A 12 mm-diameter, two-fluted ball-endmillwith308helixand88rakeangleisused.Theworkpiecematerialis Ti6Al4V which is commonly used in aerospace industry. Threedifferent lead and tilt combinations are selected in Fig. 4, and thesimulations are verified by cutting tests. Comparison of measuredand simulated Fmaxxyis given in Fig. 4. The variation of measured andsimulated cutting forces inx, y and z directionsforonerevolution ofthetoolisgiveninFig.5forthedatapoint2.Thefullcurvesrepresentsimulation results whereas curves with markers are experimentalmeasurements. It is seen that the model predictions are in goodagreement with the measurements. Distribution of the predictionerror for all tests is demonstrated in Fig. 5.3. Stability modelIn the stability model, the variations of engagement and cuttingconditions are taken into account by dividing the tool into discelements with thickness ofDz (Fig. 6). The dynamic cutting forcesin x, y and z directions for reference immersion anglewon a discelement l is calculated as follows:FlxFlyFlz?TDaBld(1)whereDa is the height of the disc elements in surface normaldirection, Bl(w) is the lth discs directional coefficient matrix 8 atthe reference immersion anglew. d is the dynamic displacementvector which can be expressed as the difference between thedisplacements at current time and one tooth period before (Fig. 7):d xt ? xt ?tyt ? yt ?tzt ? zt ?t?T(2)wheretis the tooth period. As the reference immersion angle isdependent on time, Bl(w) is a time dependent periodic directionalcoefficient matrix. It can be represented by Fourier seriesexpansion as follows 8:Bl Xr1r?1Blreirn;Blr1pZp0Ble?irnd(3)Depending on the Fourier series expansion of the directionalcoefficients, there are two different stability formulation methods8. In the single-frequency solution, only the average of the direc-tionalcoefficientmatrixisusedwhereasinmulti-frequencysolutiondirectional coefficient matrix is represented by more than one term.3.1. Single-frequency solutionIn single-frequency solution, the dynamic displacement vectoris assumed to be composed of only chatter frequencyvc. Then, itcanbe defined interms of the transferfunctionof the structureandcutting forces 11:d 1 ? e?ivctGivcFxtFytFzt?T(4)where Fx(t), Fy(t), Fz(t) are total dynamic cutting forces and G is thetransfer functioninTCS.If Eq. (1) iswrittenform disc elements andsummedwhereEq. (4)issubstitutedfor thedynamicdisplacementvector, the following eigenvalue problem is obtained:F?eivctDa1 ? e?ivctXml1Blo !Givc?F?eivct(5)Since the number of disc elements to be includedin the analysisis not known, stability diagrams are obtained using an iterativeprocedure 12.In 3-axis flat end milling, it was shown that the single-frequencysolutiongivesgoodresultsexceptlowradialimmersionwithrespectto the tool diameter. However, for low radial immersion, stabilitydiagramswereshowntobeaffectedbymulti-frequencyeffects14.Fig. 1. Engagement region, start and exit angles.Fig. 3. Chip thickness and force coefficient variation.Fig. 4. Simulated and measured cutting forces.Fig. 5. Predicted forces and error distribution.Fig. 6. Dynamic forces on the disc element l.Fig. 2. Tool geometry and differential cutting forces.E. Budak et al./CIRP Annals - Manufacturing Technology 58 (2009) 3473503483.2. Multi-frequency solutionIn multi-frequency solution, higher order terms are included inthe representation of directional coefficients. Multiple frequenciesare addition and subtraction of the chatter frequency andharmonics of the tooth passing frequency. In this case, thedynamic displacement vector in TCS can be written in terms of thetransfer function G and total dynamic cutting forces 15:d 1 ? e?ivctXk1k?1Givc ikvtF?keivckvtt(6)As performed in the single-frequency solution, Eq. (1) is summedside by side for all disc elements and Eq. (6) is substituted for thedynamic displacement vector. The resulting eigenvalue problemdepends on both chatter and tooth passing frequencies unlike thesingle-frequencysolution.Thenumericalmulti-frequencysolutionto obtain stability diagrams is presented in 12.5-axis milling is used especially in finishing operations whereradial depth, i.e. step over, is low. Hence, one would expect to seesignificant multi-frequency effects on the stability diagrams basedonthe observationsfromflat-end milling14. However,due totheeffect of lead and tilt angles and ball-end mill geometry, theseaffects are suppressed in 5-axis milling. This is due to the fact thatthe ratio of time spent in cutting to non-cutting in 5-axis milling ishigherwithrespecttoflat-endmilling.Thisisdemonstratedin12by comparing the directional coefficients for flat-end milling andfor ball-end milling.3.3. Effect of machine tool kinematics configurationThe feed direction may have effect on the chatter stability if thetransfer functions in two orthogonal directions are not equal. Formachine tool configurations, where the rotary motions are on thetool side, lead and tilt angles do not affect the feed direction.However, if the rotary axes are on the table side, the feed vectorwith respect to an inertial reference frame (i.e. MCS) may becomedependent on lead and tilt angles (Fig. 8a). For these cases, themeasured transfer functions must be oriented considering the feeddirection. The orientation of a measured transfer function H(ivc) isperformed using TGmatrix which depends on the lead and tiltangles, and orientation of FCN with respect to MCS 12:G TTGHTG(7)3.4. Stability model resultsThe results of the stability model are presented for a case wherethe workpiece material AISI 1050 steel is slotted using a 20 mmdiameter ball-end mill. The modal data measured at the tool tip isgiven in Table 1. Firstly, the effects of lead and tilt angles on theabsolute stability limit using the single-frequency method aredemonstrated in Fig. 8b. For 3 lead and tilt angle combinationsexperimentally determined absolute stability limits are also shown.Fortheleadandtiltcombinationof(158,?158),thestabilitydiagramsusing single-frequency and multi-frequency methods were gener-ated. It was observed that the measured chatter frequencies werelower than the predicted ones. This can be due to the fact that themost flexible mode presented in Table 1 is the spindle mode whichwas measured in idle condition, but the modal frequencies of thespindle may shift during cutting. Based on this observation, themeasured frequencies under static conditions were modified inthe simulations in order to match the measured chatter frequencieswith the predicted ones. The simulation results using unmodifiedmodal data with single-frequency method (hk0), modified modaldata with single-frequency method (hk0_mod) and with multi-frequency method with one harmonics (hk1_mod) are presented inFig.9.Itisseenthatthesimulatedstabilitydiagramsagreebetterwiththe experimental results after modified modal data is used.Furthermore, it was observed that using higher harmonics did notchange the simulated stability diagrams. For the modified modaldata,atime-domainmodel12wasrunatseveralspindlespeedsandcorresponding stability limits are presented in Fig. 9. The powerspectrumofthesimulateddisplacementsisusedtojudgethestabilityofthesystem.Thereissomediscrepancybetweenfrequency-domainandtime-domainresultswhichcanbeattributedtothediscretizationprocedureemployed.Atastablepoint(A)andatanunstablepoint(B),power spectrums of cutting tool displacements predicted by thetime-domain model are presented in Fig. 9 to be representative.4. Process simulationForsimulations,cuttinggeometryandconditionsmustbeknownwhereas they, in general, vary continuously in 5-axis milling cycles.A practical method has been developed 13, and it is brieflydescribed here, for identification of these parameters to simulate afull cycle.4.1. Identification of cutting conditionsIn this approach, tool orientation and position are directlyobtained from the cutter location (CL) file whereas geometricalparameters, i.e. cutting depth, step over, lead and tilt angles areFig. 8. Effect of lead, tilt angles on feed direction and stability.Table 1Modal data for the example case.Directionfn(Hz)z(%)k (N/mm)X747.33.8926,300Y7663.9836,000Fig. 9. Stability diagram for (158, ?158) combination.Fig. 7. The dynamic chip thickness.E. Budak et al./CIRP Annals - Manufacturing Technology 58 (2009) 347350349calculated analytically 13. Finally, the process model is used forsimulations at certain CL points along the tool path. The cuttingdepths at each tool location in a cutting pass are determined fromthe relevant pointson the successive toolpaths as shown in Fig. 10.A reference CL file is generated to obtain the finished surfaceinformation, by applying 08 lead and tilt angles on the tool path.Thedesignsurfaceinformationisusedincalculationofleadandtiltangles in semi-finish and finish passes, as well. In order to applytheproposedapproach13tonon-prismaticgeometries(Fig.10b),the rough workpiece information is obtained in STL format fromthe CAD software.In Fig. 10, points P1, P2and P3represent the corresponding facetof the rough surface at the given CL point. Cutting depth, a, is thedistance between the points P4and P5. Point P5is the intersectionof the stock surface and the line passing through P4and coincidentwith stock surface normal (n). By analytically calculating thegeometrical parameters from the CL file the process model can beused in simulation of a 5-axis cycle.4.2. Machining of a compressor diskA compressor blade millingprocess shown inFig. 11is analyzedusing the developed method 13. The process parameters areidentified from CL files and used in force simulations, and feedscheduling. The workpiece material is Ti6Al4V. In roughing andsemi-finishing cycles 20 and 16 mm diameter ball-end mills areused with feed rates of 0.16 and 0.12 mm/tooth, respectively. Thelead and tilt angles are 108 and ?108. The variation of the cuttingdepth and the step over for the roughing pass along each side of ablade aregivenin Fig.12. Theanalyticalcalculationsare verifiedbythe data from the CAD software at 5 points.For the semi-finishing pass, Fmaxxy, is simulated for every 5 CLpoints where there are nearly 200 points per cutting step.Calculation of the geometrical parameters for the complete bladetakes 140 s whereas the force simulations for one cutting stepalong the blade takes 160 s on a 2.2 GHz Dual Core PC. In addition,the feed is adjusted to keep Fmaxxyalmost constant where the stepover is 2 mm. The simulated (sim.) and measured (exp.) Fmaxxyforboth scheduled (sch.) and constant (cons.) feed cases are shown inFig. 13. Approximately 25% of time saving is achieved by applyingfeed scheduling.5. ConclusionThe productivity and quality in 5-axis milling operations canbe improved by using process models. In this paper, cutting forceand chatter stability models developed for 5-axis milling arebrieflyintroduced,andtheiruseinselectionofprocessparameters is demonstrated through examples. It is shown thatthe CL files can be used to extract parameters required forsimulation of a 5-axis cycle. Using this approach, the millingforces in a cycle can be simulated, and the feed rate can bescheduled to shorten the cycle time which is demonstrated on ablade-machiningexample.Themethodspresentedherecaneasilybe integrated with CAD/CAM software for simulation of 5-axismilling operations.References1 AltintasY,Engin S(2001) GeneralizedModelingof Mechanicsand DynamicsofMilling Cutters. Annals of the CIRP 50(1):2530.2 Larue A, Altintas Y (2005) Simulation of Flank Milling Processes. InternationalJournal of Machine Tools and Manufacture 45:549559.3 /components/acis.4 Kim GM, Kim BH, Chu CN (2003) Estimation of Cutter Deflection and FormError in Ball-end Milling Processes. International Journal of Machine Tools andManufacture 43:917924.5 Ozturk E, Budak E (2007) Mode
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