資源目錄里展示的全都有，所見即所得。下載后全都有,請放心下載。原稿可自行編輯修改=【QQ：401339828 或11970985 有疑問可加】 International Journal of Machine Tools & Manufacture 42 (2002) 505520Five-axis milling machine tool kinematic chain design and analysisE.L.J. Bohez*Department of Design and Manufacturing Engineering, Asian Institute of Technology, P.O. Box 4, Klong Luang, 12120 Pathumthani, ThailandReceived 23 May 2000; received in revised form 12 September 2001; accepted 13 September 2001AbstractFive-axis CNC machining centers have become quite common today. The kinematics of most of the machines are based on arectangular Cartesian coordinate system. This paper classifies the possible conceptual designs and actual existing implementationsbased on the theoretically possible combinations of the degrees of freedom. Some useful quantitative parameters, such as theworkspace utilization factor, machine tool space efficiency, orientation space index and orientation angle index are defined. Theadvantages and disadvantages of each concept are analyzed. Criteria for selection and design of a machine configuration are given.New concepts based on the Stewart platform have been introduced recently in industry and are also briefly discussed. 2002Elsevier Science Ltd. All rights reserved.Keywords: Five-axis; Machine tool; Kinematic chain; Workspace; CNC; Rotary axis1. IntroductionThe main design specifications of a machine tool canbe deduced from the following principles:? The kinematics should provide sufficient flexibility inorientation and position of tool and part.? Orientation and positioning with the highest poss-ible speed.? Orientation and positioning with the highest poss-ible accuracy.? Fast change of tool and workpiece.? Save for the environment.? Highest possible material removal rate.The number of axes of a machine tool normally refersto the number of degrees of freedom or the number ofindependent controllable motions on the machine slides.The ISO axes nomenclature recommends the use of aright-handed coordinate system, with the tool axis corre-sponding to the Z-axis. A three-axis milling machine hasthree linear slides X, Y and Z which can be positionedeverywhere within the travel limit of each slide. The toolaxis direction stays fixed during machining. This limits* Tel.: +66-2-524-5687; fax: +66-2-524-5697.E-mail address: bohezait.ac.th (E.L.J. Bohez).0890-6955/02/$ - see front matter 2002 Elsevier Science Ltd. All rights reserved.PII: S0890-6955(01)00134-1the flexibility of the tool orientation relative to the work-piece and results in a number of different set ups. Toincrease the flexibility in possible tool workpiece orien-tations, without need of re-setup, more degrees of free-dom must be added. For a conventional three linear axesmachine this can be achieved by providing rotationalslides. Fig. 1 gives an example of a five-axis millingmachine.Fig. 1.Five-axis machine tool.506E.L.J. Bohez / International Journal of Machine Tools & Manufacture 42 (2002) 5055202. Kinematic chain diagramTo analyze the machine it is very useful to make akinematic diagram of the machine. From this kinematic(chain) diagram two groups of axes can immediately bedistinguished: the workpiece carrying axes and the toolcarrying axes. Fig. 2 gives the kinematic diagram of thefive-axis machine in Fig. 1. As can be seen the work-piece is carried by four axes and the tool only by oneaxis.The five-axis machine is similar to two cooperatingrobots, one robot carrying the workpiece and one robotcarrying the tool.Five degrees of freedom are the minimum required toobtain maximum flexibility in tool workpiece orien-tation, this means that the tool and workpiece can beoriented relative to each other under any angle. Theminimum required number of axes can also be under-stood from a rigid body kinematics point of view. Toorient two rigid bodies in space relative to each other 6degrees of freedom are needed for each body (tool andworkpiece) or 12 degrees. However any common trans-lation and rotation which does not change the relativeorientation is permitted reducing the number of degreesby 6. The distance between the bodies is prescribed bythe toolpath and allows elimination of an additionaldegree of freedom, resulting in a minimum requirementof 5 degrees.3. Literature reviewOne of the earliest (1970) and still very useful intro-ductions to five-axis milling was given by Baughman 1clearly stating the applications. The APT language wasthen the only tool to program five-axis contouring appli-cations. The problems in postprocessing were alsoFig. 2.Kinematic chain diagram.clearly stated by Sim 2 in those earlier days of numeri-cal control and most issues are still valid. Boyd in Ref.3 was also one of the early introductions. Beziers book4 is also still a very useful introduction. Held 5 givesa very brief but enlightening definition of multi-axismachining in his book on pocket milling. A recent paperapplicable to the problem of five-axis machine work-space computation is the multiple sweeping using theDenawit-Hartenberg representation method developedby Abdel-Malek and Othman 6.Many types and design concepts of machine toolswhich can be applied to five-axis machines are discussedin Ref. 7 but not specifically for the five-axis machine.The number of setups and the optimal orientation ofthe part on the machine table is discussed in Ref. 8. Areview about the state of the art and new requirementsfor tool path generation is given by B.K. Choi et al. 9.Graphic simulation of the interaction of the tool andworkpiece is also a very active area of research and agood introduction can be found in Ref. 10.4. Classification of five-axis machines kinematicstructureStarting from Rotary (R) and Translatory (T) axes fourmain groups can be distinguished: (i) three T axes andtwo R axes; (ii) two T axes and three R axes; (iii) oneT axis and four R axes and (iv) five R axes. Nearly allexisting five-axis machine tools are in group (i). Also anumber of welding robots, filament winding machinesand laser machining centers fall in this group. Only lim-ited instances of five-axis machine tools in group (ii)exist for the machining of ship propellers. Groups (iii)and (iv) are used in the design of robots usually withmore degrees of freedom added.The five axes can be distributed between the work-piece or tool in several combinations. A first classi-fication can be made based on the number of workpieceand tool carrying axes and the sequence of each axis inthe kinematic chain. Another classification can be basedon where the rotary axes are located, on the workpieceside or tool side. The five degrees of freedom in a Car-tesian coordinates based machine are: three translatorymovements X,Y,Z (in general represented as TTT) andtwo rotational movements AB, AC or BC (in general rep-resented as RR).Combinations of three rotary axes (RRR)and two linear axes (TT) are rare. If an axis is bearingthe workpiece it is the habit of noting it with anadditional accent. The five-axis machine in Fig. 1 canbe characterized by X?Y?A?B?Z. The XYAB axes carry theworkpiece and the Z-axis carries the tool. Fig. 3 showsa machine of the type XYZA?B?, the three linear axescarry the tool and the two rotary axes carry the work-piece.507E.L.J. Bohez / International Journal of Machine Tools & Manufacture 42 (2002) 505520Fig. 3.XYZA?B? machinery.4.1. Classification based on the sequence of workpieceand tool carrying axesTheoretically the number of possible configurations isquite large if the order of the axes in the two kinematicchains of the tool and workpiece carrying axes is countedas a different configuration. Also the combinations withonly two linear axes and three rotary axes are included.One tool carrying axis and four workpiece carryingaxes can be combined in a five-axis machine as follows:for each possible tool carrying axis X,Y,Z,A,B,C the otherfour workpiece carrying axes can be selected from thefive remaining axes. So the number of combinations offour axes out of five with considering different permu-tation as another configuration is 54!=120 for eachpossible tool axis selection (1 out of 6 or 6 possibilities).So theoretically there are 6120=720 possible five-axismachines with one tool carrying axis. The same analysiscan be done for all other combinations. With t the num-ber of tool carrying axes and w the number of workpiececarrying axes (w+t=5) the total number of combinationsis as follows.Ncomb=?6t?t!?6tw?w! t?3, t+w=5(1)Ncomb=?6w?w!?6wt?t! t?3, t+w=5(2)The value of this equation is always equal to 6! or720 when w+t=5. Some of these 720 combinations willbe containing only two linear axis. If only five-axismachines with three linear axes are considered, only35!=360 combinations are still possible.The set Gt of combinations is characterized by a fixedvalue of t. This set is identical to the set G?w charac-terized by a fixed value of w, w=5?t. Using above defi-nitions following subgroups of five-axis machines exist:(i) Group G0/G?5; (ii) Group G1/G?4; (iii) GroupG2/G?3; (iv) Group G3/G?2; (v) Group G4/G?1; (vi)Group G5/G?0.4.1.1. G5/G0? machineAll axes carry the tool and the workpiece is fixed ona fixed table. Fig. 4 shows a machine with all the fiveaxes carrying the tool. The kinematic chain is XBYAZ(TRTRT). This machine was one of the earliest modelsof five-axis machines to handle very heavy workpieces.As there are many links in the tool carrying kinematicchain, there can be a considerable error due to elasticdeformations and backlash in the slides.4.1.2. G0/G5? machineAll axes carry the workpiece and the tool is fixed inspace. This construction is best used for very smallworkpieces (see Section 6.3).Fig. 4.XBYAZ machine.508E.L.J. Bohez / International Journal of Machine Tools & Manufacture 42 (2002) 5055204.1.3. G4/G1? machineFour axes carry the tool and one axis carries the work-piece. There are basically two possibilities, the work-piece carrying axis can be R? or T?.4.1.4. G1/G4? machineOne axis carries the tool and the other four axes carrythe workpiece. There are basically two possibilities, thesingle axis kinematic chain can be R or T. Fig. 1 is anexample of such a machine, with the single tool carryingaxis T.4.1.5. G3/G2? machineThree axes carry the tool and two axes carry the work-piece. There are basically three possibilities, the work-piece carrying axes can be both linear (T?T?) bothrotational (R?R?) or mixed (T?R?). Fig. 5 gives anexample of a machine with the tool carried by two rotaryaxes and one linear axis. This machine allows processingof large workpieces but the construction of the toolsideis complicated. The most common configuration is theworkpiece carried by the two rotary axes such as the onegiven in Figs. 3, 6 and 8.4.1.6. G2/G3? machineTwo axes carry the tool and three axes carry the work-piece. There are basically three possibilities, the tool car-rying axis can be both linear (TT) both rotational (RR)or mixed (TR). Fig. 7 shows the mixed construction. Fig.8 shows two linear axes carrying the tool.4.2. Classification based on the location of rotaryaxesThe machines can be classified depending on the placewhere the rotation axes are implemented.Fig. 5.X?Z?CAY machine.Fig. 6.B?C?ZYX machine.Fig. 7.Z?X?C?BY machine.509E.L.J. Bohez / International Journal of Machine Tools & Manufacture 42 (2002) 505520Fig. 8.Z?A?B?YX machine.Only machines with two rotary axes and three linearaxes will be considered further. The possible configur-ations are:(a) rotation axes are implemented on tool spindle;(b) rotation axes are implemented on machine table;(c) combination of both.The sequence of the axes in the tool or workpiececarrying kinematic chain is not important if the axes areof the same type R or T. In general, if there are N?Ttrans-latory axes and N?Rrotary axes in the workpiece carryingkinematic chain and NTtranslatory axes and NRrotaryaxes in the tool kinematic chain, then the numbers ofcombinations is 11:Ncomb?(N?T?N?R)!N?T!N?R!(NT?NR)!NT!NR(3)with N?T?NT?3, N?R?NR?2The number of combinations of each group will be givenbelow case by case. The total number of combinationsover all groups is 60. From the design point of view thisis a more tractable number of alternatives to be con-sidered.4.2.1. R?R? machineThe two rotary axes carry the workpiece. The tool axiscan be fixed or carried by one (T), two (TT) or three(TTT) linear axes.The number of possible designs is the sum of the fol-lowing combinations:(i) For the group G0/G5? the tool is fixed in space allthe five axes will carry the workpiece. The numberof different designs is 10 (NT?=3 and NR? =2), (Figs.15 and 16).(ii) For the group G1/G4?, NT+NR=1, so NT=1 and NR=0,is the only possible choice for the tool kinematicchain. Equation (3) gives NCOMB=6. The combi-nationsare:R?R?T?T?T;T?T?R?R?T;R?T?R?T?T;T?R?T?R?T; R?T?T?R?T; T?R?R?T?T. Fig. 9 showsthese six designs.(iii)For the group G2/G3? the tool axes are TT so NT?=1,NR?=2, NT=2, NR=0 and Equation (2) gives NCOMB=3.The three design combinationsare: R?R?T?TT;R?T?R?TT and T?R?R?TT. The group G2/G3? containsthree instances of the R?R? machine. These instancesare represented in Fig. 10.(vi) If the tool axes are TTT the workpiece carrying axescan only be R?R?. So only one design combinationis possible.From the above-mentioned findings it can also be con-cluded that the total number of R?R? five-axis machineconfigurations is 20.Machines with two axes on the clamping table can beseen in Figs. 1, 3, 6 and 8. The advantages are:Fig. 9.Members of group G1/G4?.510E.L.J. Bohez / International Journal of Machine Tools & Manufacture 42 (2002) 505520Fig. 10.R?R? machines in group G2/G3?.? In case the spindle is horizontal, optimal chip removalis obtained through the gravitational effect of thechips just dropping.? The tool axis during machining is always parallel tothe Z axis of the machine. So the drilling cycles canbe executed along the Z-axis of the machine. Circlesunder a certain orientation of the workpiece arealways executed in the XY plane of the machine. Theabove-mentioned functions can be executed in thesimple three-axis numerical control mode.? The compensation of the tool length happens all thetime in the NC control of the machine, as with three-axis machines.Disadvantages:? Machines with a rotating table are only for work-pieces with limited dimensions.? The useful workspace is usually much smaller thanthe product of the travel in X,Y and Z axis.? The transformation of the Cartesian CAD/CAM coor-dinate (XYZIJK) of the tool position to the machineaxes positions (XYZAB or C) is dependent on the pos-ition of the workpiece on the machine table. Thismeans that in case the position of the workpiece onthe table is changed this cannot be modified by atranslation of the axes system in the NC program.They must be recalculated. In case the control of theNC machine cannot transform Cartesian coordinatesto machine coordinates, then a new CNC programmust be generated with the postprocessor of theCAD/CAM system every time the position of theworkpiece changes.Important applications for this type:? Five-sided cutting of electrodes for EDM and otherworkpiece.? Machining of precision workpieces.? Turbines and tire profiles with a certain workpiecegeometry rotated over a certain angle. The same NCprogram can be repeated after the zero of the rotationaxis has been inclined over a certain angle.4.2.2. RR-machineThenumberofpossibledesigncombinations(NCOMP=20) is the same as in the case of the R?R?machine because of the symmetry. Five-axis machineswith the rotation axes implemented on the tool axisspindle can be seen in Figs. 4 and 5.Advantages:? These machines can machine very large workpieces.? The machine axis values of the NC program XYZ,depend on the tool length only. A new clamping pos-ition of the workpiece is corrected with a simpletranslation. This happens with a zero translation in theCNC control of the machine.Disadvantages:? The drive of the main spindle is very complex. Simpledesign and construction is only obtained when thewhole spindle with the motor itself is rotating.? There is a lower stiffness because the rotation axis ofthe spindle is limiting the force transmission. At highrevolutions per minute (higher than 5000 rpm) thereis also a counter acting moment because of the gyro-scopic effect which could be a disadvantage in casethe tool spindle is turning very fast.? Circular interpolation in a random plane and drillingcyclesunderrandomorientationareoftennotimplemented.? A change in the tool length cannot be adjusted by azero translation in the control unit, often a completerecalculation of the program (or postprocessing) isrequired.Important applications of this type of machine tool are:? All types of very large workpieces such as air planewings.4.2.3. R?R machineOne rotary axis is implemented in the workpiece kine-matic chain and the other rotary axes in the tool kinem-atic chain (e.g. Fig. 7).The groups G4/G1?, G4?/G1, G3?/G2, G3/G2? coverthis design. Nowadays there are many machines on themarket with one rotation axis on the tool spindle and511E.L.J. Bohez / International Journal of Machine Tools & Manufacture 42 (2002) 505520one rotation axis on the table. They are, however, com-bining most of the disadvantages of both previous typesof machines and are often used for the production ofsmaller workpieces. The application range of thismachine is about the same as with machines with tworotation axes implemented on the table.In all possible designs of this machine the NR?=NR=1and NT?+NT=3. The total number of possible designs is:NCOMBNT?0,N?T?3?NCOMBNT?1,N?T?2?NCOMBNT?2,N?T?1?NCOMBNT?3, NT?0or 4+6+6+4=20 possible designs.(i) ForNT?=0andNT=3thefourcombinationsare:R?RTTT; R?TRTT; R?TTRT; R?TTTR.(ii) ForNT?=1andNT=2thesixcombinationsare:T?R?RTT;T?R?TRT;T?R?TTR;R?T?RTT;R?T?TRT; R?T?TTR.(iii)For NT?=2 and NT=1 the six combinations are (seeFig.11):R?T?T?TR;T?R?T?TR;T?T?R?TR;R?T?T?RT; T?R?T?RT; T?T?R?RT.(iv)ForNT?=3andNT=0thefourcombinationsare:R?T?T?T?R; T?R?T?T?R; T?T?R?T?R; T?T?T?R?R.5. Workspace of a five-axis machineBeforedefiningtheworkspaceofthefive-axismachine tool, it is appropriate to define the workspaceof the tool and the workspace of the workpiece. TheFig. 11.R?R machines in the group G2/G3?.workspace of the tool is the space obtained by sweepingthe tool reference point (e.g. tool tip) along the path ofthe tool carrying axes. The workspace of the workpiececarrying axes is defined in the same way (the center ofthe machine table can be chosen as reference point).These workspaces can be determined by computing theswept volume 6.Based on the above-definitions some quantitativeparameters can be defined which are useful for compari-son, selection and design of different types of machines.5.1. Workspace utilization factor WRA possible definition for this is the ratio of theBoolean intersection of the workpiece workspace andtool workspace and the union of the tool workspace andworkpiece workspace.WR?WSTOOL?WSWORKPIECEWSTOOL?WSWORKPIECE(4)A large value for WRmeans that the workspace of thetool and the workspace of the workpiece are about equalin size and overlap almost completely. A small value ofWRmeans that the overlap of tool workspace and work-piece workspace is small and that a large part of theworkpiece workspace cannot be reached by the tool. Theanalogy with two cooperating robots can be clearly seen.It is only in the intersection of the two workspaces ofeach robot that they can shake hands. For the five-axismachine tool this corresponds to the volume in whichthe tool and workpiece reference point can meet.However, in the case where all the five axes carry theworkpiece and the tool is fixed in space the above defi-nition would give a zero value for the workspace utiliz-ation. In the case of cooperating robots it would meanthat there is only one point were they can shake hands.In the case of a five-axis machine, the workpiece canstill be moved in front of the tool and remove metal.The reason is that many points from the workpiece canserve as reference point on the workpiece. All pointswhich can cut on the toolsurface c