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Vector model-based workpiece update in multi-axis milling by moving surface of revolution

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Abstract

This paper presents a parametric approach to updating workpiece surfaces in a virtual environment. The workpiece surfaces are represented by a series of discrete vectors, which may be orientated in different directions. The methodology is developed for multi-axis machining in which a tool can be arbitrarily oriented in space. The cutter is modeled as a surface of revolution, which is a canal surface formed by sweeping a sphere with varying radius along a spine curve. To define the tool swept envelope, the cutter surfaces are decomposed into a set of characteristic circles which are generated by a two-parameter family of spheres. Then, the grazing points, at which the discrete vectors can intersect the tool envelope, are obtained by considering the relationships between these circles and feed vector of the cutter. From this, the envelope-vector intersections are transformed into a single-variable function. Examples of this technique are generated for typical milling tools with both linear and circular spine curves. The vector/tool envelope intersection calculations for cutters with linear spine curves can be performed analytically. However, the intersection calculations for cutters having circular spine curves require solving a system of nonlinear equations. For this purpose, a root-finding analysis is developed for guaranteeing the root(s) in the given interval. Finally, to improve the efficiency when updating the workpiece, a vector localization scheme is developed based on the Axis-aligned Bounding Box method.

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References

  1. Voelcker H. B, Hunt W. A. Role of solid modeling in machining-process modeling and NC verification. SAE Preprints 1981; n: 810195, 10p.

  2. Wang WP (1988) Solid modeling for optimizing metal removal of three-dimensional NC end milling. J Manuf Syst 7(1):57–65

    Article  Google Scholar 

  3. Spence AD, Altintas YA (1994) Solid modeler-based milling process simulation and planning system. J of Eng for Ind, Transactions of the ASME 116(1):61–69

    Article  Google Scholar 

  4. El Mounayri H, Spence AD, Elbestawi MA (1998) Milling process simulation—a generic solid modeler based paradigm. Journal of Manufacturing Science and Engineering, Transactions of the ASME 120(2):213–221

    Article  Google Scholar 

  5. Gupta SK, Saini SK, Brent WS, Yao Z (2005) Geometric algorithms for computing cutter engagement functions in 2.5D milling operations. Comput-Aided Des 37:1469–1480

    Article  Google Scholar 

  6. Yip-Hoi D, Huang X (2006) Cutter/Workpiece engagement feature extraction from solid models for end milling. Journal of Manufacturing Science and Engineering, Transactions of the ASME 128(1):249–260

    Article  Google Scholar 

  7. Aras E, Yip-Hoi D. (2008) Geometric Modeling of Cutter/Workpiece engagements in three-axis milling using polyhedral representations. Journal of Computing and Information Science in Engineering, Transactions of the ASME 8(3).

  8. Jerard RB, Drysdale RL, Hauck KE, Schaudt B, Magewick J (1989) Methods for detecting errors in numerically controlled machining of sculptured surfaces. Computer Graphics and Applications, IEEE 9(1):26–39

    Article  Google Scholar 

  9. Chappel IT (1983) The use of vectors to simulate material removed by numerically controlled milling. Comput-Aided Des 15(3):156–158

    Article  Google Scholar 

  10. Oliver JH, Goodman ED (1986) Color graphic verification of N/C milling programs for sculptured surface parts. First Symposium on Integrated Intelligent Manufacturing ASME

  11. Wang WP, Wang KK (1986) Real-time verification of multi-axis NC programs with raster graphics. IEEE Proc. Int'l Conf. Robotics and Automation, CS Press; 166-171.

  12. Wang WP, Wang KK (1986) Geometric modeling for swept volume of moving solids. CG&A 6(12):8–17

    Google Scholar 

  13. Van Hook T (1986) Real-time shaded NC milling display. Computer Graphics (Proc SIGGRAPH) 20(4):15–20

    Article  Google Scholar 

  14. Atherton P, Earl C, Fred C. (1987) A graphical simulation system for dynamic five-axis NC verification. Proc. Auto fact. SME (2-1 to 2-12).

  15. Choi B.K., Jerard R.B. (1998). Sculptured surface machining: Theory and Applications. Kluwer Academic Publishers

  16. Fussel BK, Jerard RB, Hemmet JG (2003) Modeling of cutting geometry and forces for 5-axis sculptured surface machining. Comput-Aided Des 35:333–346

    Article  Google Scholar 

  17. Chung YC, Park JW, Shin H, Choi BK (1998) Modeling the surface swept by a generalized cutter for NC verification. Comput-Aided Des 30(8):587–594

    Article  MATH  Google Scholar 

  18. Baek N, Maeng SR, Shin SY, Choi BK (2003) A Z-map update method for linearly moving tools. Comput-Aided Des 35:995–1009

    Article  Google Scholar 

  19. Baek N, Maeng SR, Shin SY, Choi BK (2004) A fast NC simulation method for circularly moving tools in the Z-map environment. Proceeding of the Geometric Modeling and Processing

  20. Jerard RB, Hussaini SZ, Drysdale RL, Schaudt B (1989) "Approximate Methods for Simulation and Verification of Numerically Controlled Machining Programs", The Visual Computer, vol. 5, no. 6

  21. Drysdale RL, Jerard RB, Schaudt B, Hauck K (1989) Discrete simulation of NC machining. Algorithmica Special Issue on Computational Geometry 4(1):33–60

    MATH  MathSciNet  Google Scholar 

  22. Quinn J (1993) Accurate verification of five-axis numerically controlled machining. PhD Thesis, Department of Computer Science, Dartmouth College, Tech Report PCS-TR93-191

  23. Chen CZ, Dong Z, Vickers WG (2003) Automated surface subdivision and toolpath generation for 3½½ axis CNC machining of sculptured parts. Computers in Industry 50:319–331

    Article  Google Scholar 

  24. Peternell M, Pottmann H (1997) Computing rational parameterizations of canal surfaces. Journal of Symbolic Computation 23:255–266

    Article  MATH  MathSciNet  Google Scholar 

  25. Aras E (2009) Generating cutter swept envelopes in five-axis milling by two-parameter families of spheres. Comput-Aided Des 41(2):95–105

    Article  Google Scholar 

  26. Frey DD, Otto KN, Pflager W (1997) Swept envelopes of cutting tools in integrated machine and workpiece error budgeting. Ann CIRP 46(1):475–480

    Article  Google Scholar 

  27. Wang WP, Wang KK (1986) Geometric modeling for swept volume of moving solids. IEEE Comput Graph Appl 6(12):8–17

    Article  Google Scholar 

  28. Blackmore D, Leu MC, Wang LP (1997) The sweep-envelope differential equation algorithm and its application to NC-machining verification. Comput-Aided Des 29(9):629–637

    Article  Google Scholar 

  29. William HP, Saul AT, William TV, Brian PF (2007) Numerical Recipes 3rd Edn. The Art of Scientific Computing

  30. Jung WP, Yang HS, Yun CC (2005) Hybrid cutting simulation via discrete vector model. Comput-Aided Des 37:419–430

    Article  Google Scholar 

  31. You CF, Chu CH (1997) Toolpath verification in five-axis machining of sculptured surfaces. Int J Adv Manuf Technol 13(4):248–255

    Article  Google Scholar 

  32. Ericson C (2005) Real-time collision detection. The Morgan Kaufmann Series in Interactive 3-D Technology

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Authors and Affiliations

  1. Department of Mechanical Engineering, King Saud University, P.O. Box 800, Riyadh, 11421, Kingdom of Saudi Arabia

    Eyyup Aras

  2. Department of Mechanical Engineering, The University of British Columbia, Vancouver, BC, Canada, V6T 1Z4

    Hsi-Yung Feng

Authors
  1. Eyyup Aras
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  2. Hsi-Yung Feng
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Correspondence to Eyyup Aras.

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Aras, E., Feng, HY. Vector model-based workpiece update in multi-axis milling by moving surface of revolution. Int J Adv Manuf Technol 52, 913–927 (2011). https://doi.org/10.1007/s00170-010-2799-8

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  • DOI: https://doi.org/10.1007/s00170-010-2799-8

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