Swept surface determination for five-axis numerical control machining

Abstract This paper presents a closed-form solution of the swept profile of a generalized cutter in five-axis numerical control (NC) machining. The machine configurations and tool movements defined in NC programs are considered to model the true machine tool trajectory, which includes the linearly translational and rotational movements. Based on the machine tool trajectory and the cutter geometry, the cutter’s instantaneous swept profile is determined. By integrating the intermediate swept profiles, the cutter’s swept envelope can be constructed and applied to NC verification. The proposed method provides the explicit solution of the swept profile of a generalized cutter, which is important but not possible in the existing methods for five-axis NC verification. The computer implementations show that the approach developed is superior to the traditional methods.

[1]  Sanjay G. Dhande,et al.  Geometric Modeling of Manufacturing Processes Using Symbolic and Computational Conjugate Geometry , 1995 .

[2]  K. K. Wang,et al.  Geometric Modeling for Swept Volume of Moving Solids , 1986, IEEE Computer Graphics and Applications.

[3]  Byoung Kyu Choi,et al.  Modeling the surface swept by a generalized cutter for NC verification , 1998, Comput. Aided Des..

[4]  Walter Rubio,et al.  Calculation of tool paths for a torus mill on free-form surfaces on five-axis machines with detection and elimination of interference , 1998 .

[5]  Sanjeev Bedi,et al.  Swept volumes of toroidal cutters using generating curves , 1998 .

[6]  Takahiro Watanabe,et al.  Generation of 5-Axis Control Collision-Free Tool Path and Postprocessing for NC Data , 1992 .

[7]  Ming C. Leu,et al.  The sweep-envelope differential equation algorithm and its application to NC machining verification , 1997, Comput. Aided Des..

[8]  Irvin H. Kral.  Numerical Control Programming in Apt , 1986 .

[9]  Yuan-Shin Lee,et al.  A shape-generating approach for multi-axis machining G-buffer models , 1999, Comput. Aided Des..

[10]  M. Leu,et al.  Analysis of Swept Volume via Lie Groups and Differential Equations , 1992 .

[11]  Sanjeev Bedi,et al.  Surface swept by a toroidal cutter during 5-axis machining , 2001, Comput. Aided Des..

[12]  Russell H. Taylor,et al.  Planning and execution of straight line manipulator trajectories , 1979 .

[13]  Suk-Hwan Suh,et al.  Flank milling of ruled surfaces by the additional-axis machining method , 1999 .

[14]  G. W. Vickers,et al.  Ball-Mills Versus End-Mills for Curved Surface Machining , 1989 .

[15]  Karim Abdel-Malek,et al.  Geometric representation of the swept volume using Jacobian rank-deficiency conditions , 1997, Comput. Aided Des..

[16]  Robert B. Jerard,et al.  5-axis Machining of Sculptured Surfaces with a Flat-end Cutter , 1994, Comput. Aided Des..

[17]  Yuan-Shin Lee.  Mathematical modelling using different endmills and tool placement problems for 4- and 5-axis NC complex surface machining , 1998 .

[18]  Robert B. Jerard,et al.  Methods for detecting errors in numerically controlled machining of sculptured surfaces , 1989, IEEE Computer Graphics and Applications.

[19]  Daniel D. Frey,et al.  Swept Envelopes of Cutting Tools in Integrated Machine and Workpiece Error Budgeting , 1997 .