Analytical expression of the swept surface of a rotary cutter using the envelope theory of sphere congruence

Journal of Manufacturing Science and Engineering

Volumn 131, Issue 4, 2009, Pages 0410171-0410177

  Zhu, Li Min ^a   Zhang, Xiao Ming ^a   Zheng, Gang ^a   Ding, Han ^a  

^a SHANGHAI JIAO TONG UNIVERSITY   (China)

Author keywords

Envelope; Multi axis NC machining; Rotary cutter; Sphere congruence; Swept volume; Tool path optimization

Indexed keywords

CUTTING TOOLS;

ENVELOPE; NC-MACHINING; ROTARY CUTTERS; SWEPT VOLUME; TOOL PATH OPTIMIZATION;

SPHERES;

EID: 77955295254     PISSN: 10871357     EISSN: 15288935     Source Type: Journal    
DOI: 10.1115/1.3168443     Document Type: Article

References (26)

1. Chiou, C. J., and Lee, Y. S., 2005, "Optimal Tool Orientation for Five-Axis Too-End Machining by Swept Envelope Approach," ASME J. Manuf. Sci. Eng., 127(4), pp. 810-818.
2. Chiou, C. J., 2004, "Accurate Tool Position for Five-Axis Ruled Surface Machining by Swept Envelope Approach," Comput.-Aided Des., 36 (10), pp. 967-974.
3. Lartigue, C., Duc, E., and Affouard, A., 2003, "Tool Path Deformation in 5-Axis Flank Milling Using Envelope Surface," Comput.-Aided Des., 35 (4), pp. 375-382.
4. Wang, W. P., and Wang, K. K., 1986, "Geometric Modeling for Swept Volume of Moving Solids," IEEE Comput. Graphics Appl., 6 (12), pp. 8-17.
5. Abdel-Malek, K., and Yeh, H. J., 1997, "Geometric Representation of the Swept Volume Using Jacobian Rank-Deficiency Conditions," Comput.-Aided Des., 29 (6), pp. 457-468.
6. Abdel-Malek, K., Seaman, W., and Yeh, H. J., 2001, "NC Verification of Up to 5 Axis Machining Processes Using Manifold Stratification," ASME J. Manuf. Sci. Eng., 123 (1), pp. 99-109.
7. Blackmore, D., Leu, M. C., and Wang, L. P., 1997, "The Sweep-Envelope Differential Equation Algorithm and Its Application to NC-Machining Verification," Comput.-Aided Des., 29 (9), pp. 629-637.
8. Leu, M. C., Wang, L. P., and Blackmore, D., 1997, "A Verification Program for 5-Axis NC Machining With General APT Tools," CIRP Ann., 46 (1), pp. 419- 424.
9. Leu, M. C., Wang, L. P., and Blackmore, D., 1998, "Simulation of NC Machining With Cutter Deflection by Modeling Deformed Swept Volume," CIRP Ann., 47 (1), pp. 441-446.
10. Hu, Z. J., and Ling, Z. K., 1996, "Swept Volumes Generated by the Natural Quadric Surfaces," Comput. Graphics, 20 (2), pp. 263-274.
11. Jüttler, B., and Wagner, M. G., 1996, "Computer-Aided Design With Spatial Rational B-Spline Motions," ASME J. Mech. Des., 118 (2), pp. 193-201.
12. Xia, J., and Ge, Q. J., 2001, "On the Exact Representation of the Boundary Surfaces of the Swept Volume of a Cylinder Undergoing Rational Bezier and B-Spline Motions," ASME J. Mech. Des., 123 (2), pp. 261-265.
13. Chung, Y. C., Park, J. W., Shin, H., and Choi, B. K., 1998, "Modeling the Surface Swept by a Generalized Cutter for NC-Verification," Comput.-Aided Des., 30 (8), pp. 587-593.
14. Roth, D., Bedi, S., Ismail, F., and Mann, S., 2001, "Surface Swept by a Toroidal Cutter During 5-Axis Machining," Comput.-Aided Des., 33 (1), pp. 57- 63.
15. Mann, S., and Bedi, S., 2002, "Generalization of the Imprint Method to General Surfaces of Revolution for NC Machining," Comput.-Aided Des., 34 (5), pp. 373-378.
16. Chiou, C. J., and Lee, Y. S., 2002, "Swept Surface Determination for Five-Axis Numerical Control Machining," Int. J. Mach. Tools Manuf., 42 (14), pp. 1497-1507.
17. Weinert, K., Du, S. J., Damm, P., and Stautner, M., 2004, "Swept Volume Generation for the Simulation of Machining Processes," Int. J. Mach. Tools Manuf., 44 (6), pp. 617-628.
18. Du, S. J., Surmann, T., Webber, O., and Weinert, K., 2005, "Formulating Swept Profiles for Five-Axis Tool Motions," Int. J. Mach. Tools Manuf., 45 (7-8), pp. 849-861.
19. Zhu, L. M., Zheng, G., and Ding, H., 2009, "Formulating the Swept Envelope of Rotary Cutter Undergoing General Spatial Motion for Multi-Axis NC Machining," Int. J. Mach. Tools Manuf., 49 (2), pp. 199-202.
20. Aras, E., 2009, "Generating Cutter Swept Envelopes in Five-Axis Milling by Two-Parameter Families of Spheres," Comput.-Aided Des., 41 (2), pp. 95-105.
21. Bianchi, L., 1927, Lezioni di Geometria Differenziale, 3rd ed., Nicola Zanichelli Editore, Bologna.
22. Yoshizawa, S., Belyaev, A., and Seidel, H. P., 2007, "Skeleton-Based Variational Mesh Deformations," Comput. Graph. Forum, 26 (3), pp. 255-264.
23. Xu, Z. Q., Feng, R. Z., and Sun, J. G., 2006, "Analytic and Algebraic Properties of Canal Surfaces," J. Comput. Appl. Math., 195 (1-2), pp. 220-228.
24. Pigel, L., and Tiller, W., 1995, The NURBS Book, Springer, Berlin.
25. Lee, K., Seong, J. K., Kim, K. J., and Hong, S. J., 2007, "Minimum Distance Between Two Sphere-Swept Surface," Comput.-Aided Des., 39 (6), pp. 452- 459.
26. Sarkar, B., and Menq, C. H., 1991, "Parameter Optimization in Approximating Curves and Surfaces to Measurement Data," Comput. Aided Geom. Des., 8 (4), pp. 267-290.