Prediction of Cutter-Workpiece Engagement for Five-Axis Ball-End Milling

Transcription

1 Materials Science Forum Online: ISSN: , Vols , pp doi: / Trans Tech Publications, Switzerland Prediction of Cutter-Workpiece Engagement for Five-Axis Ball-End Milling Ju Ganggang a, Song Qinghua b, Liu Zhanqiang c Key Laboratory of High Efficiency and Clean Mechanical Manufacture, Ministry of Education, School of Mechanical Engineering, Shandong University, Ji'nan, China a jugangg@qq.com, b ssinghua@sdu.edu.cn, c melius@sdu.edu.cn Keywords: Cutter-workpiece engagement; five-axis milling; lead angle; tilt angle Abstract. Five-axis ball-end milling technology is widely used in many industries such as aerospace, automotive and die-mold for complex surface machining. Despite recent advances in machining technology, productivity in five-axis ball-end milling is still limited due to the high cutting forces and stability. Moreover, cutting forces in machining is determined by extracting the cutter workpiece engagement (CWE) from the in-process workpiece. A discrete boundary representation method is developed. Cutter is firstly divided into disk elements along the tool axis. And in each disk element, boundary representation based exact Boolean method is introduced for extracting complex cutter-workpiece engagements at every cutter location due to its efficiency and speed over other discrete methods. Developed engagement model is proved to calculate complex engagement regions between tool and workpiece efficiently and accurately. Introduction Five-axis ball-end milling is mainly used in machining of complex surfaces [1]. Compared with three axis ball-end milling, there exists two additional parameters in five-axis ball-end milling, lead and tilt angles, which increase the accessibility and flexibility of the cutting process. Cutting forces is the most fundamental, and in many cases the most significant parameter limiting the improvement of the productivity of five-axis ball-end milling in machining operations. While, the cutting forces in five-axis ball-end milling is not available with the traditional method due to the variable surface of the workpiece and tool orientation. Moreover, cutting forces in machining is determined by extracting the cutter workpiece engagement (CWE) from the in-process workpiece. Due to the complexity of the contact condition, there are less work done on the extraction of CWE in five-axis ball-end milling than in three axis ball-end milling. In some early studies, Imani et al. [2] use two B-spline and one circular edge to determine the instantaneous in-cut segment to calculate the cutting forces. Bailey et al. [3] represent an algorithm to determine if points on the cutting edge are in cut with the workpiece to predict cutting forces. Larue et al. [4] presented a method to determine engagement boundaries between the tool and the workpiece for flank milling based on ACIS solid modeling environment. Ozturk et al. [5] proposed an analytical engagement criterion to determine the regions in cut with the workpiece in five-axis ball-end milling operations. Sadeghi et al. [6] determined cutting edge engagement for each tool rotational step using a solid modeler based ball-end milling process simulation. Kim et al. [7] determined the cutter contact area from the z- map of the surface geometry and current cutter location. Maeng et al. [8] updated z-map method to calculating the intersection points between workpiece and cutter. Aras [9] developed an analytical methodology for determining the shapes of the cutter swept envelopes based on a concept of twoparameter-family of sphere. Lazoglu et al. [10] introduced a boundary representation based exact Boolean method for extracting complex cutter-workpiece engagements at every cutter location point. The purpose of this paper is to propose a discrete boundary representation method to obtain the engagement regions between the tool and workpiece which is necessary for the calculation of the cutting forces in five-axis ball-end milling with changing lead and tilt angles. All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, (ID: , Pennsylvania State University, University Park, USA-05/03/16,08:47:23)

2 Materials Science Forum Vols Calculation of Engagement Domain In five-axis milling process, the cutter/workpiece engagement region does vary along the cutter path and in general, unless some specific and very simple workpiece geometry is machined, it is difficult to find an exact analytical representation for the engagement region. Chip load and force calculations are based on the cutter/workpiece engagements; therefore the output of the engagement model is very critical. The basic idea is mathematically removing the swept volume generated by cutter movements along the NC trajectory from the model of the raw stock, and thus obtaining inprocess or final machined workpiece. In this work, discrete boundary representation based method is developed to find the CWE. The tool movements are subtracted from the workpiece model by using Boolean operations in order to find the in-process machined surface. Coordinates frames. The position and orientation of the cutting tool and cutting parameters in five-axis milling can be determined by three coordinates systems [5] shown in Fig. 1(a). The first coordinate is called machine coordinate system (MCS) including X, Y, Z axes. The second one is a moving coordinate called process coordinate system (FCN). It consists of feed, cross-feed and surface normal axes which are represented by F, C and N, respectively and the origin of the FCN is the center of the ball-part of the cutting tool. Tool coordinate system (TCS) is the last coordinate made up of x, y, and z axes, the center of which is the center of the ball-part of the cutting tool as well. As a matter of fact, TCS is the rotated form of the FCN by the lead angle α and tilt angle β. The rotation process can be shown in Fig. 2. First of all, take F axis as the rotation axis, rotate the FCN clockwisely with the rotation angle β looked from the positive of F axis, the obtained coordinates called x y z coordinate. Then take the y axis as the rotation axis, rotate the x y z coordinate counterclockwisely with the rotation angle looked from the positive of y axis. The angle of γ can be calculated as γ = arctan(tanαcosβ). Finally the TCS is acquired. Definition of the lead and tilt angles are described in Fig. 1(b)(c). (a) (b) (c) Fig. 1 (a) Coordinate systems (b) Lead angle α (c) Tilt angle β Determination of Tool Location. The tool orientation, position, and process parameters are obtained from the CL file in the MCS. On the other hand, the lead and tilt angles are defined in the FCN. Therefore, the tool orientation in the CL file should be transformed into the FCN coordinates. Several motion commands such as GO TO, CIRCLE, and RAPID exist in a CL file. In fiveaxis machining of sculptured surfaces, tool traverses point to point on the surface by GO TO command whereas RAPID command specifies out of cut motions. The data following these commands provide the tool tip coordinates and the unit tool axis vector. A sample CL file section is shown in Fig.3. Fig. 2 Rotation process of FCN to TCS

3 256 High Speed Machining VI Fig. 3 An example obtaining the CL file Tool Swept Volume. NC verification kernel gives all of the cut points while tool is moving from one CL point to the other CL point. This yields that cut points have to be trimmed before the engagement region is determined. Schematic illustration of a ball-end mill sweep is shown in Fig.4(a). Possible engagement domain of the cutter lies in the front side of the tool swept volume. Tool motion in 5-axis machining also includes an arbitrary rotation and this effect must be taken into account if swept volume of the conical part of the cutter is in cut, on the other hand in freeform surface machining distance and angular rotation between is relatively small, therefore instead of applying exact 5-axis tool motion swept volume is modeled assuming 3+2 axis tool motion. Then, the contact patch surface between the tool and workpiece can be extracted as illustrated in Fig. 4(b). (a) (b) Fig. 4 (a) Tool swept volume (b) Contact patch Calculation of Engagement Regions. Once the in-process workpiece is obtained for each cutter location (CL) point, the contact patch surface between the tool and workpiece can be extracted. Then, the resulting 3D contact surface, as illustrated in Fig. 4, is projected to the plane perpendicular to the cutter axis. The cutter is discretized into slices along the tool axis. In order to perform force calculation for each slice, the engagement domain is determined. The engagement domain is the combination of start and exit angles of each discrete disc located on the cutter. The next step is to assign the start and exit angles to each respective projected disc by intersecting the discs with the boundaries of the contact patch in plane, as shown in Fig.5. (a) (b) Fig. 5 (a) Discretized cutting tool (b) Start and exit angles of the discretized element

4 Materials Science Forum Vols Sample Results The procedure described above is implemented in the Parasolid kernel. Engagement regions with two different combinations of lead (15º and 60º) and tilt (15º and 0º) angles are shown in Fig. 6 as the examples for instantaneous CWE model outputs. It is seen in this figure that the engagement is sphere surface (single contact) in the case lead=15º and tilt=15º (Fig. 6a, c). However, in the case lead=60º and tilt=0º, engagement is combinations (multiple contacts) of sphere surface and conical surface (Fig. 6a, c). (a) (b) (c) (d) Fig. 6 (a) Contact patch(lead=15º, tilt=15º) (b) Contact patch(lead=60º, tilt=0º) (c) Immersion angles(lead=15º, tilt=15º) (d) Immersion angles(lead=60º, tilt=0º) Therefore, one of the advantages of this newly developed boundary representation based engagement domain calculation method over the existing techniques is that the new method allows determining complex engagement domains (multiple contacts) regions precisely. Precise determination of the engagement regions naturally helps to enhance the force predictions. Moreover, the newly developed boundary representation based CWE model is very fast. Conclusions Five-axis ball-end milling technology is widely used in many industries such as aerospace, automotive and die-mold for complex surface machining. Cutting forces in machining is determined by extracting the CWE from the in-process workpiece. Due to variable tool axis orientation, free form surfaces of workpiece and tool geometry, engagement regions between the tool and the workpiece all along the tool path are very complex and irregular. A novel boundary representation method is used for determining the complex cutter-workpiece engagements. The developed engagement model provides an efficient and accurate solution for extracting the information on contact region at CL points from the in-process workpiece. Another distinctive point of the developed model is that it allows especially for multi-stage process simulations including roughing, semi-finishing and finishing. Acknowledgements The authors are grateful to the financial supports of the National Natural Science Foundation of China (no ), the Research Award fund for Outstanding Young Scientists of Shandong Province (no. BS2013ZZ013), and Major National Science and Technology Project (no. 2014ZX ).

5 258 High Speed Machining VI References [1] J.P. Davim, Machining of complex sculptured surfaces, Springer, New York, [2] B.M. Imani, M.H. Sadeghi, M.A. Elbestawi, International Journal of Machine Tools and Manufacture, 38 (1998): [3] T. Bailey, T.I. El-Wardany, P. Fitzpatrick, M.A. Elbestawi, Journal of manufacturing science and engineering, 124 (2002): [4] A. Larue, Y. Altintas, International Journal of Machine Tools and Manufacture, 45 (2005): [5] E. Ozturk, E. Budak, Machining Science and Technology, 11 (2007): [6] M.H. Sadeghi, H. Haghighat, M.A. Elbestawi, International Journal of Advanced Manufacture Technology, 22 (2003): [7] G.M. Kim, P.J. Cho, C.N, Chu, International Journal of Machine Tools and Manufacture, 40 (2000): [8] S.R. Maeng, N. Baek, S.Y. Shin, B.K. Choi, Computer-Aided Design, 35 (2003): [9] E. Aras, Cutter-workpiece engagement identification in multi-axis milling, dissertation, The University of British Columbia, [10] I. Lazoglu, Y. Boz, H. Erdim, CIRP Annals-Manufacturing Technology, 60 (2011):

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