基于UG的三軸銑床運(yùn)動(dòng)仿真設(shè)計(jì)【說明書+CAD+仿真】

基于UG的三軸銑床運(yùn)動(dòng)仿真設(shè)計(jì)【說明書+CAD+仿真】,說明書+CAD+仿真,基于UG的三軸銑床運(yùn)動(dòng)仿真設(shè)計(jì)【說明書+CAD+仿真】,基于,ug,銑床,運(yùn)動(dòng),仿真,設(shè)計(jì),說明書,仿單,cad calculations in 3-axis milling which can be extended to 5-axis milling. However, all process models require toolpart engage- mentboundarieswhicharemorecomplicatedin5-axismillingdue to 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 ACIS 3 solid modeling environment to determine the engagement region for force simulations of flank milling. Kim et al. 4 determined the engagement region using Z-mapping. Ozturk and Budak 5, on the other hand, determined the engagement regions analytically, and modeled the cutting forces and tool deflections. Chatter is one of the main limitations in 5-axis milling. 2. Process geometry and force model Compared with conventional milling operations, 5-axis milling geometry is more complicated due to the additional degrees of freedom.Inthissection,5-axismillinggeometryispresentedbriefly. A more detailed analysis can be found in 5. Three coordinate systems are used in modeling of 5-axis milling processes. MCS is a fixedcoordinatesystemonthemachinetool.TCSconsistsofthetool axisandtwoperpendiculartransversalaxes(x)and(y).FCNconsists ofthe 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 axis CIRP Annals - Manufacturing Technology 58 (2009) 347350 th process very force ted. Contents lists available at ScienceDirect CIRP Annals - Manufacturing elsevier.co Forceand thestability modelscan be used bothin planningand analysis. In planning phase, better process parameters can be selected through simulations. In 5-axis milling, however, process parameters may continuously vary along the tool path. In this study, these parameters are obtained using a procedure 13 determine the varying engagement boundaries (Fig. 1). The engagement model 5 is used to determine the elements that are in cut. Differential cutting forces in radial, tangential and axial directions shown in Fig. 2 are calculated in terms of the local chip thickness and width, and the local cutting force coefficients. Local chip thickness and cutting force coefficients are variable along the cutting flute depending on the immersion angle w and z coordinate as presented in Fig. 3.* Corresponding author. 0007-8506/$ see front matter C223 2009 CIRP. doi:10.1016/j.cirp.2009.03.044 Although chatter stability in milling has been extensively studied analytically68andbysimulations9,thishasbeenverylimited forball-endmillingand5-axismillingprocesses.Altintasetal.10 extended the analytical milling stability model to the ball-end milling whereas Ozturk and Budak 11,12 included the effect of lead and tilt angles using single- and multi-frequency methods. withrespecttothesurfacenormal.Leadandtiltanglestogetherwith ball-end mill geometry, cutting depth and step over determine the engagement region between the cutting tool and workpiece. In Fig.1,engagementregion,variationofstart(w st )andexitangles(w ex ) along the tool axis are demonstrated for a representative case. The cutting tool is divided into differential cutting elements to Modeling and simulation of 5-axis milling E. Budak (2)*, E. Ozturk, L.T. Tunc Faculty of Engineering and Natural Sciences, Sabanci University, Istanbul, Turkey 1. Introduction 5-axis milling has become a widely used process due to its ability to machine complex surfaces. In most of these applications high productivity is required due to the cost of machine tools and parts. Productivity and quality in 5-axis milling can be increased using process models. However, unlike other processes, modeling of 5-axis milling has been very limited. The objective of this paper is to demonstrate selection of process parameters in 5-axis milling for increased productivity using process models and simulations. Altintas and Engin 1 modeled the cutting edge for generalized milling cutters, and used it in cutting force and stability ARTICLE INFO Keywords: Milling Force Stability ABSTRACT 5-axis milling is widely used extremelyimportantdueto for the selection of proper milling process modeling, process geometry, cutting parametersisalsodemonstra used in simulation of a compl journal homepage: http:/ees. processes developed for extraction of milling conditions from cutter location (CL) data. As all CAD/CAM software provides CL files, this approach presents a practical method for integration of the models with the CAD/CAM systems. In the next section, the geometry of 5-axis milling is briefly introduced together with the force model. The application of the model in lead and tilt angle selection is also demonstrated. For chatter stability analysis of 5-axis milling, single- and multi- frequency solutions are summarized, and used for generation of stability diagrams. The last section of the paper presents simulation of 5-axis milling cycles with example cases. in machining of complex surfaces. Part quality and productivity are ehighcostofmachinetoolsandpartsinvolved.Processmodelscanbeused parameters. Although extensive research has been conducted on few are on 5-axis milling. This paper presents models for 5-axis milling and stability. The application of the models in selection of important Apracticalmethod,developedfortheextractionofcuttinggeometry,is ete 5-axis cycle. C223 2009 CIRP. Technology m/cirp/default.asp Fig. 1. Engagement region, start and exit angles. E. Budak et al./CIRP Annals - Manufacturing Technology 58 (2009) 347350348 Cutting forces, torque and power are calculated by integrating the differential forces within the engagement region. Tool deflections are calculated using the structural properties of the cutting tool and forces at surface generation points 5. 2.1. Force model results Theforcemodelwasverifiedwithmorethan70cuttingtests5. Fig. 3. Chip thickness and force coefficient variation. Fig. 2. Tool geometry and differential cutting forces. The force model can be used in the selection of lead and tilt angles. Theeffectofleadandtiltanglesonthemaximumtransversalcutting force, F max xy , is simulated for a representative following-cut case in Fig.4.Thecuttingdepthandthestepoverare5 mm, thefeed rateis 0.05 mm/tooth, the spindle speed is 1000 rpm and cross-feed direction 5 is negative. A 12 mm-diameter, two-fluted ball-end millwith308helixand88rakeangleisused.Theworkpiecematerial is Ti6Al4V which is commonly used in aerospace industry. Three different lead and tilt combinations are selected in Fig. 4, and the simulations are verified by cutting tests. Comparison of measured and simulated F max xy is given in Fig. 4. The variation of measured and simulatedcuttingforcesinx,yandzdirectionsforonerevolutionof Fig. 4. Simulated and measured cutting forces. Fig. 5. Predicted forces and error distribution. thetoolisgiveninFig.5forthedatapoint2.Thefullcurvesrepresent simulation results whereas curves with markers are experimental measurements. It is seen that the model predictions are in good agreement with the measurements. Distribution of the prediction error for all tests is demonstrated in Fig. 5. 3. Stability model Inthestabilitymodel,thevariations ofengagementand cutting conditions are taken into account by dividing the tool into disc elements with thickness of Dz (Fig. 6). The dynamic cutting forces in x, y and z directions for reference immersion angle w on a disc element l is calculated as follows: F l x F l y F l z C138 T DaB l d (1) where Da is the height of the disc elements in surface normal direction, B l (w) is the lth discs directional coefficient matrix 8 at the reference immersion angle w. d is the dynamic displacement vector which can be expressed as the difference between the displacements at current time and one tooth period before (Fig. 7): d xtC0 xt C0t ytC0yt C0t ztC0zt C0tC138 T (2) where t is the tooth period. As the reference immersion angle is dependent on time, B l (w) is a time dependent periodic directional coefficient matrix. It can be represented by Fourier series expansion as follows 8: B l X r1 rC01 B l r e irn ;B l r 1 p Z p 0 B l e C0irn d (3) Depending on the Fourier series expansion of the directional coefficients, there are two different stability formulation methods 8. In the single-frequency solution, only the average of the direc- tionalcoefficientmatrixisusedwhereasinmulti-frequencysolution directionalcoefficientmatrixis represented by morethanoneterm. 3.1. Single-frequency solution In single-frequency solution, the dynamic displacement vector is assumed to be composed of only chatter frequency v c . Then, it canbedefinedintermsofthetransferfunctionofthestructureand cutting forces 11: d 1 C0 e C0ivct Giv c F x t F y t F z tC138 T (4) where F x (t), F y (t), F z (t) are total dynamic cutting forces and G is the transferfunctioninTCS.IfEq.(1)iswrittenformdiscelementsand summedwhereEq.(4)issubstitutedforthedynamicdisplacement vector, the following eigenvalue problem is obtained: Fig. 6. Dynamic forces on the disc element l. FC138e ivct Da1C0 e C0ivct X m l1 B l o ! Giv c C138FC138e ivct (5) Sincethenumberofdiscelementstobeincludedintheanalysis is not known, stability diagrams are obtained using an iterative procedure 12. In3-axisflatendmilling,itwasshownthatthesingle-frequency solutiongivesgoodresultsexceptlowradialimmersionwithrespect to the tool diameter. However, for low radial immersion, stability diagramswereshowntobeaffectedbymulti-frequencyeffects14. In this approach, tool orientation and position are directly obtained from the cutter location (CL) file whereas geometrical parameters, i.e. cutting depth, step over, lead and tilt angles are Fig. 8. Effect of lead, tilt angles on feed direction and stability. Table 1 Modal data for the example case. Direction f n (Hz) z (%) k (N/mm) E. Budak et al./CIRP Annals - Manufacturing Technology 58 (2009) 347350 349 3.2. Multi-frequency solution In multi-frequency solution, higher order terms are included in the representation of directional coefficients. Multiple frequencies are addition and subtraction of the chatter frequency and harmonics of the tooth passing frequency. In this case, the dynamic displacement vector in TCS can be written in terms of the transfer function G and total dynamic cutting forces 15: d 1 C0 e C0ivct X k1 kC01 Giv c ikv t FC138 k e ivckvtt (6) As performed in the single-frequency solution, Eq. (1) is summed side by side for all disc elements and Eq. (6) is substituted for the dynamic displacement vector. The resulting eigenvalue problem depends on both chatter and tooth passing frequencies unlike the single-frequencysolution.Thenumericalmulti-frequencysolution to obtain stability diagrams is presented in 12. 5-axis milling is used especially in finishing operations where radial depth, i.e. step over, is low. Hence, one would expect to see significant multi-frequency effects on the stability diagrams based ontheobservationsfromflat-endmilling14.However,duetothe effect of lead and tilt angles and ball-end mill geometry, these affects are suppressed in 5-axis milling. This is due to the fact that the ratio of time spent in cutting to non-cutting in 5-axis milling is higherwithrespecttoflat-endmilling.Thisisdemonstratedin12 by comparing the directional coefficients for flat-end milling and for ball-end milling. 3.3. Effect of machine tool kinematics configuration The feed direction may have effect on the chatter stability if the transfer functions in two orthogonal directions are not equal. For machine tool configurations, where the rotary motions are on the tool side, lead and tilt angles do not affect the feed direction. However, if the rotary axes are on the table side, the feed vector with respect to an inertial reference frame (i.e. MCS) may become dependent on lead and tilt angles (Fig. 8a). For these cases, the measuredtransferfunctionsmustbeorientedconsideringthefeed direction. The orientation of a measured transfer functionH(iv c )is performed using T G matrix which depends on the lead and tilt angles, and orientation of FCN with respect to MCS 12: G T T G HT G (7) 3.4. Stability model results Fig. 7. The dynamic chip thickness. The results of the stability model are presented for a case where the workpiece material AISI 1050 steel is slotted using a 20 mm diameter ball-end mill. The modal data measured at the tool tip is given in Table 1. Firstly, the effects of lead and tilt angles on the absolute stability limit using the single-frequency method are demonstrated in Fig. 8b. For 3 lead and tilt angle combinations experimentally determined absolute stability limits are also shown. Fortheleadandtiltcombinationof(158,C0158),thestabilitydiagrams using single-frequency and multi-frequency methods were gener- ated. It was observed that the measured chatter frequencies were lower than the predicted ones. This can be due to the fact that the most flexible mode presented in Table 1 is the spindle mode which was measured in idle condition, but the modal frequencies of the spindle may shift during cutting. Based on this observation, the measured frequencies under static conditions were modified in the simulations in order to match the measured chatter frequencies with the predicted ones. The simulation results using unmodified modal data with single-frequency method (hk0), modified modal data with single-frequency method (hk0_mod) and with multi- frequency method with one harmonics (hk1_mod) are presented in Fig.9.Itisseenthatthesimulatedstabilitydiagramsagreebetterwith the experimental results after modified modal data is used. Furthermore, it was observed that using higher harmonics did not change the simulated stability diagrams. For the modified modal data,atime-domainmodel12wasrunatseveralspindlespeedsand corresponding stability limits are presented in Fig. 9. The power spectrumofthesimulateddisplacementsisusedtojudgethestability ofthesystem.Thereissomediscrepancybetweenfrequency-domain andtime-domainresultswhichcanbeattributedtothediscretization procedureemployed.Atastablepoint(A)andatanunstablepoint(B), power spectrums of cutting tool displacements predicted by the time-domain model are presented in Fig. 9 to be representative. 4. Process simulation Forsimulations,cuttinggeometryandconditionsmustbeknown whereas they,ingeneral,varycontinuously in5-axis millingcycles. A practical method has been developed 13, and it is briefly described here, for identification of these parameters to simulate a full cycle. 4.1. Identification of cutting conditions X 747.3 3.89 26,300 Y 766 3.98 36,000 Fig. 9. Stability diagram for (158, C0158) combination. E. Budak et al./CIRP Annals - Manufacturing Technology 58 (2009) 347350350 calculated analytically 13. Finally, the process model is used for simulations at certain CL points along the tool path. The cutting Fig. 10. Extraction of cutting depth. Fig. 11. Tool path pattern and workpiece geometry. Fig. 12. Calculated cutting depth and step over. depths at each tool location in a cutting pass are determined from therelevantpointsonthesuccessivetoolpathsasshowninFig.10. A reference CL file is generated to obtain the finished surface information, by applying 08 lead and tilt angles on the tool path. Thedesignsurfaceinformationisusedincalculationofleadandtilt angles in semi-finish and finish passes, as well. In order to apply theproposedapproach13tonon-prismaticgeometries(Fig.10b), the rough workpiece information is obtained in STL format from the CAD software. In Fig. 10, points P 1 ,P 2 and P 3 representthe correspondingfacet of the rough surface at the given CL point. Cutting depth, a, is the distance between the points P 4 and P 5 . Point P 5 is the intersection of the stock surface and the line passing through P 4 and coincident with stock surface normal (n). By analytically calculating the geometrical parameters from the CL file the process model can be used in simulation of a 5-axis cycle. 4.2. Machining of a compressor disk AcompressorblademillingprocessshowninFig.11isanalyzed using the developed method 13. The process parameters are identified from CL files and used in force simulations, and feed scheduling. The workpiece material is Ti6Al4V. In roughing and semi-finishing cycles 20 and 16 mm diameter ball-end mills are used with feed rates of 0.16 and 0.12 mm/tooth, respectively. The lead and tilt angles are 108 and C0108. The variation of the cutting depth and the step over for the roughing pass along each side of a bladearegiveninFig.12.Theanalyticalcalculationsareverifiedby the data from the CAD software at 5 points. For the semi-finishing pass, F max xy , is simulated for every 5 CL points where there are nearly 200 points per cutting step. Calculation of the geometrical parameters for the complete blade takes 140 s whereas the force simulations for one cutting step along the blade takes 160 s on a 2.2 GHz Dual Core PC. In addition, the feed is adjusted to keep F max xy almost constant where the step over is 2 mm. The simulated (sim.) and measured (exp.) F max xy for both scheduled (sch.) and constant (cons.) feed cases are shown in Fig. 13. Approximately 25% of time saving is achieved by applying feed scheduling. 5. Conclusion The productivity and quality in 5-axis milling operations can be improved by using process models. In this paper, cutting force and chatter stability models developed for 5-axis milling are briefly introduced, and their use in selection of process parameters is demonstrated through examples. It is shown that the CL files can be used to extract parameters required for simulation of a 5-axis cycle. Using this approach, the milling forces in a cycle can be simulated, and the feed rate can be scheduled to shorten the cycle time which is demonstrated on a blade-machiningexample.Themethodspresentedherecaneasily be integrated with CAD/CAM software for simulation of 5-axis milling operations. References 1 AltintasY,EnginS(2001)GeneralizedModelingofMechanicsandDynamicsof Milling Cutters. Annals of the CIRP 50(1):2530. 2 Larue A, Altintas Y (2005) Simulation of Flank Milling Processes. International Journal of Machine Tools and Manufacture 45:549559. 3 http:/ 4 Kim GM, Kim BH, Chu CN (2003) Estimation of Cutter Deflection and Form Error in Ball-end Milling Processes. International Journal of Machine Tools and Manufacture 43:917924. 5 Ozturk E, Budak E (2007) Modeling of 5-axis Milling Processes. Machining Science and Technology 11(3):287311. 6 Tlusty J, Polacek M (1963) The Stability of Machine Tools against Self-excited Fig. 13. Variations of F max xy and scheduled feed rate. Vibrations in Machining. ASME International Research in Production Engineering 465474. 7 Minis I, Yanushevsky T, Tembo R, Hocken R (1990) Analysis of Linear and Nonlinear Chatter in Milling. Annals of the CIRP 39:459462. 8 Altintas Y, Budak E (1995) Analytical Prediction of Stability Lobes in Milling. Annals of the CIRP 44(1):357362. 9 Smith S, Tlusty J (1993) Efficient Simulation Programs for Chatter in Milling. Annals of the CIRP 42(1):463466. 10 Altintas Y, Shamoto E, Lee P, Budak E (1999) Analytical Prediction of Stability Lobes in Ball-end Milling. Transactions of the ASME Journal of Manufacturing Science and Engineering 121(4):586592. 11 Ozturk E, Ozlu E, Budak E (2007) Modeling Dynamics and Stability of 5-axis Milling Processes. Proceedings of 10th CIRP Workshop on Modeling of Machining Operations, Calabria, Italy, 469476. 12 Ozturk E, Budak E (2008) Chatter Stability of 5-axis Milling Using Multi- frequency Solution. Proceedings of 3rd CIRP International Conference High Performance Cutting, vol. 1, Dublin, Ireland, 429444. 13 Tunc LT, Budak E (2008) Extraction of Milling Conditions from CAM Data for Process Simulation. International Journal of Advanced Machining Technology . 10.1007/s00170-008-1735-7. 14 Davies MA, Pratt JR, Dutterer BS, Burns TJ (2000) The Stability of Low Radial Immersion Milling. Annals of the CIRP 49(1):