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Development of multi-axis numericalcontrol program for millturn machineChen-Hua She1* and Chih-Wei Hung21Department of Mechanical and Computer Aided Engineering, National Formosa University, Yunlin,Taiwan, Republic of China2Department of Mechanical and Automation Engineering, Da-Yeh University, Chang-Hua, Taiwan, Republicof ChinaThe manuscript was received on 1 January 2008 and was accepted after revision for publication on 15 January 2008.DOI: 10.1243/09544054JEM1098SCAbstract:A millturn machine combining a lathe and machining centre can perform turningand milling operations on the same machine. It can machine a workpiece in one set-up andeliminate errors that can be produced by moving the workpiece between turning and millingmachines. Since the millturn machine has a complex configuration in which linear and rotarymovements are non-orthogonal, generating the part program manually is almost impossible.This work develops an interface called a postprocessor that converts cutter location data gener-ated by a general commercial computer-aided design (CAD)/computer-aided manufacturing(CAM) system into the numerical control (NC) data dedicated for the millturn machine. Theform-shaping function matrix of the millturn machine, which describes the motion trajectoryof tool points relative to the workpiece, is derived by the homogeneous coordinate transforma-tion matrix. The complete analytical equations for NC data are obtained through a form-shaping function matrix and inverse kinematics. A window-based postprocessor system writtenin Borland C Builder and OpenGL was developed according to the proposed algorithm. Solidcutting simulation software is utilized to verify the effectiveness of the proposed algorithm.Keywords:multi-axis, millturn, postprocessor, numerical control1INTRODUCTIONGlobal competition has forced the manufacturingcompanies to machine the workpieces in one set-up. Consequently, multi-axis machining technologyhas been extensively used in automotive, naval, andaeronautic industries. For workpieces with millingand turning features, a multi-tasking millturn ma-chine that combines the functionality of milling andturning machines can machine such workpieces effi-ciently with a single set-up, minimizing cycle timeand errors owing to reclamping operations.Millturn machines are mainly divided into twocategories: lathe-based and mill-based 1. Manymachine tool builders, such as Mazak 2 and DeckelMaho 3, have developed the commercial millturnmachines. The lathe-based configuration is a lathewith a milling head and a powered turret living thatcan perform milling operations. The mill-based con-figuration is based on a machining centre that allowsfor turning operations when the spindle is locked,and a rotary table can perform the high-speed rota-tion by the motor. This study aims at the numericalcontrol (NC) code generation for the lathe-based con-figuration shown in Fig. 1. The machine tool modelMT200S manufactured by Yeong Chin Machinery4 has five axis motions (X, Y, Z, C, and B axes).Compared with conventional lathe-based millturnmachines with X, Z, and C axes, the additional Yand B axes facilitate off-centre and compound angleoperations 5. Since linear and rotary movementsfor this configuration are non-orthogonal, generatingthe part program manually is almost impossible.Although some commercial software systems existfor this machine tool type, such as FeatureCAM 6and PartMaker 7, they remain expensive. Con-versely, an advanced controller, such as a Fanuc*Corresponding author: Department of Mechanical and Com-puter Aided Engineering, National Formosa University, 64Wen-Hua Road, Huwei, Yunlin 632, Taiwan, Republic of China.email: chshe.twSHORT COMMUNICATION741JEM1098SC ? IMechE 2008Proc. IMechE Vol. 222 Part B: J. Engineering Manufacture18i-TB, is frequently used to allow users to inputorthogonal axis motion commands. However, thesecontrollers are also expensive.The interface, called a postprocessor, should bedeveloped to convert cutter location data (CL) gener-ated by the general commercial computer-aideddesign (CAD)/computer-aided manufacturing (CAM)system into the NC data dedicated for a millturnmachine. However, current multi-axis postprocessormethods primarily deal with orthogonal configura-tions 8, 9. Studies have rarely investigated non-orthogonal configurations to the best of the presentauthors knowledge. Yang 10 and Lin 11 developeda postprocessor for the MT200S millturn machinetoolusingDenavitandHartenberg (DH)notion.How-ever,inclinedanglesarefixed,i.e.a?30?andb45?.To generalize the postprocessor method, inclinedangles in this study are variable. Complete analyticalequations for NC data are obtained through a form-shaping function matrix and inverse kinematics.Moreover, an obliquecoordinate transformationmatrix should be used since the linear and rotarymovements of a machine tool are nonorthogonal. AC window-based postprocessor system was devel-oped based on the proposed algorithm. Solid cuttingsimulation software confirms the feasibility of theproposed algorithm.2POSTPROCESSOR FOR THE MACHINE TOOL2.1Determination of form-shaping functionmatrix by forward kinematicsMachine tools can be considered as a chain con-nected links with joints. To manipulate the positionand orientation of the cutting tool and the machinetool, a homogeneous transformation matrix can beused to define the geometric relationship betweentwo adjacent links connected through a point. Thetranslation matrix, Trans, and the rotation matrix,Rot, using Pauls notation 12 are introduced inthis study. Figure 1 shows the schematic diagram ofa millturn machine tool with a C-axis rotary tableand a B-axis rotary head. Movements of the linearaxes (X, Y, and Z) are non-orthogonal and the direc-tions of the axes can be defined by two angles, aand b. Assume that the system ObaseXbaseYbaseZbaseis the orthogonal coordinate system, where a isdefined as the angle between axes Xbaseand X, andb is defined as the angle between axes Ybaseand Y.Positive rotation of a and b is in the direction toadvance a right-hand screw in the Ybaseand Xbaseaxis direction. Coordinate systems OwXwYwZwandOtXtYtZtshown in Fig. 2 are attached to the workpieceand the cutting tool, respectively. Offset vectorLxiLyjLzk is determined from origin Owto thepivot point of the C axis. The term Ltis the distancedetermined from the pivot point of the B axis to thecutter tip centre.Since the structural elements of the machine toolconsist of a linear table, machine bed, rotary table,rotary head, and the cutting tool, the generatingmotion of the machine tool, which determines itsdesigned characteristics, is referred to as the form-shaping function 13, which can be characterizedsequentially starting from the workpiece and endingat the cutting tool. Mathematically, the form-shapingfunction of this machine tool can be expressed asfollowsTransLx;Ly;Lz Rotz;?fz Trans0;0;PzRotx;b Trans0;Py;0 Rotx;?b Rotz;aTransPx;0;0 Roty;fy Roty;90?001000?Lt1266437751where Px, Py, Pzdenote the relative translation dis-tances of the X, Y, Z tables, respectively. Terms fzZ, ZbaseXbaseXBCYbaseYFig. 1Configuration of MT200S millturn machine toolFig. 2Coordinate systems and parameters742Chen-Hua She and Chih-Wei HungProc. IMechE Vol. 222 Part B: J. Engineering ManufactureJEM1098SC ? IMechE 2008and fyrepresent rotational angles for the rotary tableand rotary head, respectively. Equation (1) describesthe form-shaping function matrix of this machinetool, and joint parameters Px, Py, Pz, fz, and fymustbe determined.2.2Determination of NC databy inverse kinematicsMost current CAD/CAM systems generate CL dataexpressed in the following matrix formKQ01?KxKyKz0QxQyQz1266437752where Kx, Ky, and Kzare directional cosines of thevector of tool orientation K, and Qx, Qy, and Qzarethe components of the position vector of the centreposition of the tool tip, Q. Once the CL data matrixis obtained, three linear motions plus two rotarymotions can be determined by inverse kinematicstransformation.Equating the CL data matrix in equation (2) and theform-shaping function matrix in equation (1) leads tothe following equationsKxKyKz026643775cosacosfz sinasinfzcosfysinacosfz?cosasinfzcosfy?sinfy0266437753QxQyQz126643775PxcosfzcosasinfzsinaPysinfzcosb?LtcosfzcosasinfzsinacosfyLxPxcosfzsina?sinfzcosaPycosfzcosbLtsinfzcosa?cosfzsinacosfyLyPysinbPzLtsinfyLz1266666666437777777754Therefore, joint angles fzand fycan be obtained asfollowsB fy arcsin?Kz5C fz arctan2Kxsina?Kycosa?cosfy;Kxcosa Kysina?cosfy6where arctan 2(y,x) is the function that returns ang-les in the range of ?p6u6p by examining the signsof both y and x 12.Furthermore, three unknowns, Px, Py, and Pz, can besolved using linear equations. Notably, Px, Py, and Pzare not the actual NC data expressions. The NC datain the orthogonal coordinate system are obtainedusing equation (4) under the condition fyfz0, and QxQyQz1?T XbaseYbaseZbase1?Tsince the program coordinate system is coincidentwith the workpiece coordinate system. This leads toXbaseYbaseZbase126643775Pxcosa?LtcosaLxPxsinaPycosb?LtsinaLyPysinbPzLz126643775Qx?Lxcosfz?Qy?LysinfzLtcosfy?1cosaLxQx?LxsinfzQy?LycosfzLtcosfy?1sinaLyQz?Lz?LtsinfyLz1266666666437777777757Since the desired axis command of linear move-ments of the machine tool is along the non-orthogonaldirection,anobliquecoordinatetransformationmatrix 14 describing the relationship between theorthogonal and non-orthogonal coordinate systemsmustbe used.Thetransformationcanbe expressedasXbaseYbaseZbase126643775cosa000sinacosb000sinb10000126643775XYZ126643775X cosaX sina Y cosbY sinb Z1266437758Consequently, the desired NC code data of linearaxis are obtained using equations (7) and (8), andexpressed as followsXYZ126643775secaQx?Lxcosfz?Qy?LysinfzLtcosfy?1cosa Lx?secbf?Qx?Lxtana Qy?Ly?cosfz Qx?Lx Qy?Lytana?sinfz?Lxtana Lyg?tanbf?Qx?Lxtana Qy?Ly?cosfz Qx?Lx Qy?Lytana?sinfz?Lxtana Lyg Qz?Lz?Ltsinfy Lz12666666666666666643777777777777777759Notably, the derived analytical equation for NCdata is a general form that can be reduced to theorthogonal configuration. When angles are set at ab0, equation (9) agrees with the table/spindle-tilting configuration presented in the current authorsprevious research 8.Development of multi-axis numerical control program for millturn machine743JEM1098SC ? IMechE 2008Proc. IMechE Vol. 222 Part B: J. Engineering Manufacture3SOFTWARE IMPLEMENTATIONAND VERIFICATIONA window-based postprocessor system written inBorland C Builder and OpenGL programming lan-guages was developed to confirm the feasibility of theproposed algorithm. Figure 3 shows the screenshot ofthe system execution dialogue. The user can use themouse button to rotate and zoom in on the surfacemodel of the machine tool, and the Animate buttonto animate dynamically the machine tool. The relevantparameters, such as offset vector from the workpieceorigin to the rotary axis, set length from the tool tip tothegaugeplane,andthedistancefromthegaugeplaneto the pivot point of rotary axis, are required for NCmachining. Additionally, the targetCLdata are openedby clicking the File button and the NC data are gener-ated accordingly by clicking the OK button.The generated NC data are further verified usingthe solid cutting simulation software VERICUT?15.Fig. 3Screenshot of system execution dialogueFig. 4Screenshot of VERICUT verification744Chen-Hua She and Chih-Wei HungProc. IMechE Vol. 222 Part B: J. Engineering ManufactureJEM1098SC ? IMechE 2008A millturn machine tool is constructed in thesoftware environment by importing the STL file.Figure 4 presents the VERICUT component tree. Thistree indicates that the offset vector LxiLyjLzk is?10i?20j?130k and the distance from the gaugeplane to the pivot point of rotary axis is 158.92mm.Moreover, the set length from the tool tip to thegauge plane in the tool library is 75mm. Once theconfiguration process is completed, the software sys-tem reads the NC data to perform the cutting action.Additionally, the system outputs the transformed CLdata, which can be double-checked with original CLdata. The results reveal that the developed postpro-cessor method is accurate and extremely reliable.4CONCLUSIONThis work presents a postprocessor method for themillturn machine tool with non-orthogonal axes tothe machine coordinate system. The complete ana-lytical equations of NC data were derived by the ho-mogeneous coordinate transformation matrix andinverse kinematics. The derived NC data equation isa general form for this machine tool type. The feasi-bility of the proposed postprocessor methodologywas confirmed by the commercial solid cutting soft-ware. The proposed algorithm can also be appliedto various millturn machine tool configurations.ACKNOWLEDGEMENTThe authors are grateful to the National ScienceCouncil of Taiwan for supporting this research undergrant NSC 95-2221-E-150-101.REFERENCES1 Capes, P. You turn it while I mill it. Metalworking Prod.Mag.,2003,June, availablefrom URL:http:/www.2 Mazak, available from URL: .3 Deckel Maho, available from URL: http:/www.dmg.4 Yeong