350 Tran Duc Tang VCM2012 Tính toán các tọa độ máy và hậu xử lý cho máy phay CNC 5 trục Calculation of machine coordinates and postprocessor for 5-Axis CNC milling machine Tran Duc Tang Military Technical Academy, e-Mail: tangtd@gmail.com Tóm tắt Chức năng chính của bộ hậu xử lý cho máy CNC 5 trục là đọc dữ liệu đường chạy dao (các vị trí dao cắt)- được tạo bởi các hệ thống CAD/CAM và chuyển dữ liệu này sang hệ thống tọa độ của máy. Bài báo này trình bày một phương pháp tính toán các tọa độ của máy từ hệ thống tọa độ của phôi và xây dựng bộ hậu xử lý cho máy phay CNC 5 trục. Dựa trên phương pháp tính toán đã đề xuất, tác giả đã xây dựng một mô đun phần mềm hậu xử lý trên nền windows bằng ngôn ngữ lập trình Visual Basic. Lấy mô hình máy phay CNC 5 trục kiểu hai trục quay trên bàn gá phôi làm ví dụ để mô phỏng và kiểm tra tính đúng đắn của phương pháp tính toán bằng phần mềm VERICUT ® . Kết quả kiểm tra chỉ ra rằng phần mềm hậu xử lý đáng tin cậy và phương pháp tính toán đã đề xuất có thể áp dụng cho các kiểu cấu hình máy CNC khác nhau. Abstract: The main function of the 5-axis CNC machine postprocessor is reading data from cutter location data prepared by general purpose CAD/CAM systems and converting these data to machine coordinate system. This paper presents a method of calculation of the machine coordinate system (from the workpiece coordinate system) and a postprocessor for 5-axis CNC milling machine. A windows-based postprocessor module written by Visual Basic was developed according to the presented calculation method. A 5-axis CNC milling machine tool with two rotary axes on the table is constructed and vefified by VERICUT ® software to demonstrate and validate the proposed method. The result shows that the software is reliable and the proposed method can be applied to any types of 5-axis CNC machine configuration. Keywords: Postprocessor, 5-axis CNC machine, Inverse Kinematics, NC Simulation, CAD/CAM. Abbreviations CAD Computer-Aided Design CAM Computer-Aided Manufacturing NC Numerical Control CNC Computer Numerical Control CL Cutter Location MCS Machine Coordinate System WCS Workpiece Coordinate System 1. Introduction A 5-axis machine means a machine with five degrees of freedom: three translatory movements (X, Y, Z) and two rotational movements AB, AC, or BC. The 5-axis machine is similar to two cooperating robots, one robot carrying the workpiece and one robot carrying the tool. The 5- axis CNC machines have proved their advantages in the accurate and fast machining of complex parts such as impellers, mold/die, and others. However, the generation of an NC program for 5- axis machine needs a postprocessor. The postprocessor is the interface that links the CAM systems and CNC machines. It converts CL data to machine code. Concretely, NC postprocessor converts the machine independent CL data (x, y, z, i, j, k) into a machine specific NC program (X, Y, Z, A, B) or (X, Y, Z, A, C) or (X, Y, Z, B, C) depending on the machine configuration. The toolpath which is generated by the CAD/CAM system is provided in a machine independent format (called the CL data). The CL data gives the successive tool positions in a coordinate system fixed to the workpiece. The workpiece is fixed and the tool does all movements. This CL data approximates the workpiece geometry with a certain tolerance which has to be provided to the CAD/CAM system by the part programmer before the generation of the CL data. This CL data must be transformed to the machine coordinates. In 5- axis machine tool the postprocessor is highly Tuyển tập công trình Hội nghị Cơ điện tử toàn quốc lần thứ 6 351 Mã bài: 78 complex because the simultaneous linear and rotary motions occur. Various studies have address the issue of developing postprocessor for 5-axis machine tools. Bohez [1] classified the CNC machines into three main types based on the location of the rotary axes: (i) 5-axis machine tool with two rotary axes on the machine table; (ii) 5-axis machine tool with two rotary axes on the tool spindle; and (iii) 5- axis machine tool with a rotary table and a rotary tool spindle. Kruth et al. [2] developed an integration of NC-postprocessor and NC- simulation. This intergration makes it possible to exploit fully the capacibilities of the NC- postprocessor, the NC-simulation package and the 5-axis milling machine. Lee and She [4] presented an analytical methodology to develop a postprocessor for three typical 5-axis machine tools. Jung et al. [5] proposed algorithm for NC- postprocessing for 5-axis milling machine of table- rotating/tilting type. The spindle-tilting type 5-axis machine tool with a nutating head has developed by She and Chang [6]. The table-tilting type 5-axis machine tool with nutating table has presented by Sorby [7]. In [7] Sorby presented an algorithm for calculating the inverse kinematics of 5-axis machines close to singular configurations. A postprocessor for 5-axis machine tool with nutating head and table configuration has also developed by She and Huang [9]. This paper presents a method of calculation of machine coordinates based on the coordinate transformation to yield the analytical equation of NC data, and a postprocessor for 5-aixs CNC machine. A postprocessor software for 5-axis machine DMU 70eVolution is also developed to validate the NC data generated by proposed method. In addition, the generated NC data are verified using the solid cutting software VERICUT ® [10]. 2. Calculation of machine coordiantes The CAD/CAM system normally calculates the tool coordinates in a reference system attached to the workpiece (WCS), these are cutter location (x, y, z) and orienation (i, j, k). The machine however needs to be programmed in a reference system fixed to the machine (MCS), these are three linear motions (X, Y, Z) and two rotary motions (A, B) or (A, C) or (B, C). Therefore, the machine coordinates need to be calculated based on the input data of the workpiece coordate (CL data). This can be done by the geometry transformation from the WCS to the MCS. In this paper, to demonstrate for the proposed method, a 5-axis with two rotary axes on the table - DMU 70 eVolution (Fig.1) is used. In order to calculate the coordinate (X, Y, Z, B, C) of the machine from the CL data (x, y, z, i, j, k) we have defined additional coordinate systems at some joints. These reference systems are defined in such away that the transformation from workpiece coordinates to machine coordinates can be done in simple steps. These intermediate reference systems are shown as in Fig.2 and the transformation matrices are calculated as follows: O 0 (x 0 y 0 z 0 ) is located in the center of the table surface C, when B = C = 0 0 . z 0 -axis coincides with the C-axis centerline. O 1 (x 1 y 1 z 1 ) is obtained by rotating (x 0 y 0 z 0 ) around z 0 at an angle C. The transformation matrix is written as: 1 0 cos sin 0 0 sin cos 0 0 0 0 1 0 0 0 0 1 C C C C T (1) O 2 (x 2 y 2 z 2 ) is obtained by translating (x 1 y 1 z 1 ) at a distance d along z 0 . The transformation matrix is written as: 2 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 T d (2) Fig. 1 5-axis machine tool-DMU 70 eVolution [1] 352 Tran Duc Tang VCM2012 Z T 45 ° C B d t z t y t O 3, 4 z 3, 4 y 2, 5 y 2, 5 z 2, 3, 4, 5 O 0, 1, 6 O y 0, 6 0, 6 z Fig. 2 Intermediate reference coordinate systems O 3 (x 3 y 3 z 3 ) is obtained by rotating (x 2 y 2 z 2 ) around x 2 at an angle +45 0 . The transformation matrix is written as: 0 0 3 2 0 0 1 0 0 0 0 cos45 sin 45 0 0 sin 45 cos45 0 0 0 0 1 T (3) O 4 (x 4 y 4 z 4 ) is obtained by rotating (x 3 y 3 z 3 ) around z 3 at an angle B. The transformation matrix is written as: 4 3 cos sin 0 0 sin cos 0 0 0 0 1 0 0 0 0 1 B B B B T (4) O 5 (x 5 y 5 z 5 ) is obtained by rotating (x 4 y 4 z 4 ) around x 4 at an angle -45 0 . The transformation matrix is written as: 0 0 5 4 0 0 1 0 0 0 0 cos45 sin 45 0 0 sin 45 cos45 0 0 0 0 1 T (5) O 6 (x 6 y 6 z 6 ) is obtained by translating (x 5 y 5 z 5 ) at a distance -d along z 5 . The transformation matrix is written as: 6 5 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 T d (6) O w (x w y w z w ) is obtained by translating (x 6 y 6 z 6 ) along the offset vector x y z L i L j L k from the workpiece origin O w to the rotary C-axis. The transformation matrix is written as: 10 1 0 0 0 0 1 0 0 0 0 1 6 z y x w L L L T (7) O t (x t y t z t ) is machine coordinate system fixed to the tool spindle tip. The transformation matrix is written as: 0 1 0 0 0 1 0 0 0 1 0 0 0 1 t X Y T Z (8) The coordinate tranformation matrix from WCS to the MCS (tool’s coordinates: X, Y, Z, B, C) is: t TTTTTTT w T t w T 0 0 1 1 2 2 3 3 4 4 5 5 6 6 (9) Because 1 n m m n T T , therefore, equation (9) can be expressed as: t TTTTTTT w T t w T 0 1 0 2 1 3 2 4 3 5 4 6 56 1111111 (10) Use of equations (1)-(8) and substitute into (10), the solution for t w T can be found. The CL data generated by CAM system are the cutter location (x, y, z) and orientation (i, j, k) defined in WCS. The CL vector (E) can be expressed as: 1 0 0 1 0 0 0 0 0 1 i x j y E k z (11) And the machine coordinates for a given CL data can be found with the equation: t w E T (12) or 0 0 0 0 1 0 0 1 0 1 t w i x j y T k z (13) Solving equations (1) - (13), the solutions for X, Y, Z, B, C can found: arccos(2 1) B k (14) 2 2 ( 1) 2( ) tan 2( ) ( 1) k i k k j C a k k i k j (15) Tuyển tập công trình Hội nghị Cơ điện tử toàn quốc lần thứ 6 353 Mã bài: 78 )( ) (sin cos )( ) 2 ( ) 2 2 2 (cos cos sin sin cos sin 2 2 2 sin sin 2 x L C B y L x y z L z X C B C B C B B d B (16) ) 2 1 2 1 [ cos sin sin (1 cos )]( ) [ sin sinh cos (1 cos )]( 2 2 2 2 1 (cos 1)( ) (cos 1) 2 X z y Y C B C B x L C B C B y L B z L B d (17) ) ) 2 1 2 1 [ cos sin sin (cos 1)]( [ sin sin cos (cos 1)]( 2 2 2 2 1 (cos 1)( ) 2 z T T x y Z C B C B x L C B C B y L B z L d d Z WhereZ isthetoollength (18) Based on the above calculation method the equations to generate NC data for other types of 5- axis machine tools can be determined also. 3. Software implementation and verification To confirm the feasibility of the presented machine coordinates calculation method, a window-based postprocessor for 5-axis with two rotary axes on the table has been developed under the Windows XP environment in Visual Basic programming language. A solid cutting simulation is also performed by VERICUT ® software to validate the correctness of the proposed method. The user interface of the developed postprocessor is shown in Fig.3. The user can enter relevant parameters, e.g. tool length, the distance (d) from the C table to the intersection of B and C-axis, the offset vector (L x , L y , L z ) from the workpiece origin to the C-axis. The CL file is opened by selecting the "File\Open" menu or clicking the Open icon on the toolbar and the CL data is displayed in the left below window corner. The NC data are generated by selecting the "Run\Start" menu or clicking the Run icon on the toolbar and the NC data is displayed in the right below window corner. The generated NC file is saved by selecting “File\Save” menu or clicking the Save icon (Fig.3). To demonstrate and confirm the correctness of the NC data generated by the proposed postprocessor, an air-compressor turbine blade (Fig.4) was used. The CL data are firstly generated by the commercial CAD/CAM system (Pro/engineer). These CL data are then inputed into the proposed postprocessor to generate NC data. Finally, the generated NC data are verified by VERICUT © software with the model of 5-axis machine DMU 70 eVolution is constructed in the software enviroment (Fig.5). The results shows that the cutting simulation of the CL data (Fig.6) and generated NC data (Fig.7) are the same. Therefore, the calculated machine coordiantes from the CL data by the proposed method and postprocessor is correct. 354 Tran Duc Tang VCM2012 Fig.3 Interactive user interface of the proposed postprocessor Fig.4 Air-compressor turbine blade and 3D model Fig.5 Setting simulation and verification in VERICUT® with DMU 70 eVolution 5-axis machine Tuyển tập công trình Hội nghị Cơ điện tử toàn quốc lần thứ 6 355 Mã bài: 78 Fig.6 Cutting result by CL data Fig.7 Cutting result by generated NC data 4. Conclusion This paper has presented a postprocessor methodology for 5-axis machine tool with two rotary axes on the table. The calculation of the machine coordinates is determined by the homogeneous coordinate transformation matrix, forward and inverse kinematics. The generated NC data are verified using the solid cutting software VERICUT ® . The result confirms the correctness of the proposed method and postprocessor. The proposed methodology can be applied to other types of 5-axis machine. Acknowledgement This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant No. 107.04.2011.09. The author would like to thank for their support for this research. References [1] Bohez, E. L. J.: Five-axis milling machine tool kinematics chain design and analysis. International Journal of Machine Tools & Manufacture 42 (2002), p505-520. [2] Kruth, J.P. and Kelwais, P.: NC-Processing and NC-Simulation for Five-Axis Milling Operations with Automatic Collision Avoidance. Proceeding of the International Manufacturing Engineering Conference, 1996. [3] Nagasaka, M.; Takeuchi, Y.: Generalized postprocessor for five-axis control machining based on form shape function. Journal of the Japan Society for Precision Engineering 62 (11), 1996, p1607-1611. [4] Lee, R S. and She, S H.: Developing a Postprocessor for Three Types of Five-Axis Machine Tool. International Journal of Advanced Manufacturing Technology 13, 1997, p658-665 [5] Jung, Y.H.; Lee, D.W.; Kim, J.S.; Mok, H.S.: NC Postprocessor for 5-axis milling machine of table-rotating/tilting type. Journal of Materials Processing Technology 130-131, 2002, p641-646 [6] She, C H.; Chang, C C.: Development of a Five-Axis Post-processor System with A Nutating Head. Journal of Materials Processing Technology 187-188, 2007, p60-64 [7] Knut Sorby: Inverse Kinematics of Five- Axis Machines Near Singular Configurations. International Journal of Machine Tools & Manufacture 47, 2007, p299-306 [8] She, C.H.; Le, R.S.: A postprocessor based on the kinematics model for general five- axis mahine tools. SME Journal of Manufacturing Process 2 (2), 2000, p131- 141. [9] She, C H.; Huang, Z T.: Postprocessor Development of A Five-Axis Machine Tool with Nutating Head and Table Configuration. International Journal of Advanced Manufacturing Technology 38, 2008, p728-740. [10] VERICUT ® V6.2 User manual, URL: http://www.cgtech.com 356 Tran Duc Tang VCM2012 Tran Duc Tang is currently an Assistant Professor in the Aerospace Technology and Equipments at the Militaty Technical Academy, Hanoi, Vietnam. He received his PhD and M.Eng in Design and Manufacturing Engineering from Asian Institute of Technology (AIT) - Thailand in 2007 and 2002, respectively. He is teaching the courses of advanced manufacturing processes, CAD/CAM/CAE, FMS, multi-axis machine tools. His research interests are five-axis machining, CAD/CAE/CAM/CNC, modeling of FMS by PetriNet, reverse engineering, rapid prototyping, NC simulation & programming, and Computer Graphics. His email address is: tangtd@mta.edu.vn or tangtd@gmail.com . này trình bày một phương pháp tính toán các tọa độ của máy từ hệ thống tọa độ của phôi và xây dựng bộ hậu xử lý cho máy phay CNC 5 trục. Dựa trên phương pháp tính toán đã đề xuất, tác giả đã xây. 350 Tran Duc Tang VCM2 012 Tính toán các tọa độ máy và hậu xử lý cho máy phay CNC 5 trục Calculation of machine coordinates and postprocessor. năng chính của bộ hậu xử lý cho máy CNC 5 trục là đọc dữ liệu đường chạy dao (các vị trí dao cắt)- được tạo bởi các hệ thống CAD/CAM và chuyển dữ liệu này sang hệ thống tọa độ của máy. Bài báo này