0
TECHNICAL PAPERS

Optimal Process Planning for Laser Forming of Doubly Curved Shapes

[+] Author and Article Information
Chao Liu, Y. Lawrence Yao

Department of Mechanical Engineering, Columbia University, New York, NY 10027

Vijay Srinivasan

IBM Corporation, White Plains, NY 10604

J. Manuf. Sci. Eng 126(1), 1-9 (Mar 18, 2004) (9 pages) doi:10.1115/1.1643077 History: Received May 01, 2003; Online March 18, 2004
Copyright © 2004 by ASME
Your Session has timed out. Please sign back in to continue.

References

Ueda,  K., Murakawa,  H., Rashwan,  A. M., Okumoto,  Y., and Kamichika,  R., 1994, “Development of Computer-aided Process Planning System for Plate Bending by Line Heating (Report 1)-Relation Between Final Form of Plate and Inherent Strain,” J. Ship Prod., 10(1), pp. 59–67.
Jang,  C. D., and Moon,  S. C., 1998, “An Algorithm to Determine Heating Lines for Plate Forming by Line Heating Method,” J. Ship Prod., 14(4), pp. 238–245.
Shimizu, H., 1997, “A Heating Process Algorithm for Metal Forming by a Moving Heat Source,” M.S. thesis, M.I.T.
Yu,  G., Patrikalakis,  N. M., and Maekawa,  T., 2000, “Optimal Development of Doubly Curved Surfaces,” Computer Aided Geometric Design, 17, pp. 545–577.
Liu, C., and Yao, Y. L., 2002, “Optimal and Robust Design of Laser Forming Process,” Trans. NAMRC XXX, 2002, pp. 39–46.
Cheng, J., and Yao, Y. L., 2001, “Process Synthesis of Laser Forming by Genetic Algorithms,” Proceedings of ICALEO 2001, Section D 604.
Ventsel, E., and Krauthammer, T., 2001, Thin Plates and Shells, Marcel Dekker Publishing Company, New York.
Mortenson, M., 1985, Geometric Modeling, John Wiley & Sons, New York.
Lipschultz, M., 1969, Theory and Problems of Differential Geometry, McGraw-Hill.
Numerical Algorithms Group, 2000, NAG C Library Manual, Chapter 4, Mark 5, Oxford, England.
Vollertsen, F., 1994, “Mechanisms and Models for Laser Forming.” Laser Assisted Net Shape Engineering, Proceedings of the LANE’94, Vol. 1, Meisenbach Bamberg, pp. 345–360.
Struik, D. J., 1950, Lectures on Classical Differential Geometry, Addison-Wesley, Cambridge, MA.
Dahlquist, G., and Bjorck, A., 1974, Numerical Method, Prentice-Hall, Englewood Cliffs, NJ.

Figures

Grahic Jump Location
Desired pillow shape (also note the shape along the u-direction curves higher than that along the v-direction)
Grahic Jump Location
Outline of the process planning scheme
Grahic Jump Location
Doubly curved surface, its planar development and the strain definition
Grahic Jump Location
Strains along principal curvature directions on the pillow shape (the segment length represents the strain magnitude and the segment orientation represents the strain direction)
Grahic Jump Location
Strains along principal curvature directions on the saddle shape (the segment length represents the strain magnitude and the segment orientation represents the strain direction)
Grahic Jump Location
Planar developed shape of the pillow case (distortion from the original parametric space D:(u,v)∊[0,1] is magnified by a factor of 5 for viewing clarity)
Grahic Jump Location
Planar developed shape of the saddle case (distortion from the original parametric space D:(u,v)∊[0,1] is magnified by a factor of 5 for viewing clarity)
Grahic Jump Location
Comparison between desired and reconstructed shapes of the pillow case (the difference between the two surfaces is multiplied by 5 for viewing clarity)
Grahic Jump Location
Comparison between desired and reconstructed shapes of the saddle case (the difference between the two surfaces is multiplied by 5 for viewing clarity)
Grahic Jump Location
Strains along the principal curvature directions on the planar developed shape of the pillow case (the segment length represents the strain magnitude and the segment orientation represents the strain direction)
Grahic Jump Location
Strains along the principal curvature directions on the planar developed shape of the saddle case (the segment length represents the strain magnitude and the segment orientation represents the strain direction)
Grahic Jump Location
Magnitude of principal curvatures of the pillow shape showing that all the principal curvatures have negative values
Grahic Jump Location
Magnitude of principal curvatures of the saddle shape showing that they have both positive and negative values
Grahic Jump Location
Typical simulation results showing temperature and compressive plastic strain rise do not go beyond the extent of laser beam size (beam diameter is 4 mm, scanning path at y=0 mm, square 1010 steel plate of 80 by 80 by 0.89 mm) 5
Grahic Jump Location
Optimal planning of laser paths (shown in line segments) and heating condition (power shown in watts and scanning speed shown in numbers with unit of mm/s) for the pillow shape. A quarter of a 80 by 80 by 0.89 mm plate is shown due to symmetry. Material is 1010 steel. Beam spot size is 6 mm. Shown in background are strains.
Grahic Jump Location
Optimal planning of laser paths (shown in lines) and heating condition (power shown in watts and scanning speed shown in numbers with unit of mm/s) for the saddle shape. Only a quarter of the paths/condition is shown due to symmetry. Material is 1010 steel. Beam spot size is 6 mm. The dotted line represents a scanning path on the opposite side of the plate and other paths on the opposite side (similar to the ones on the side shown) are not shown for viewing clarity.
Grahic Jump Location
Average principal in-plane strain vs. power and velocity from FEM analysis. The average is carried out over the laser beam radius (beam diameter is 4 mm, square 1010 steel plate of 80 by 80 by 0.89 mm) 6.
Grahic Jump Location
Laser formed pillow and saddle shapes using the process plans shown in Figs. 15 and 16, respectively (1010 steel plate of 80 by 80 by 0.89 nm, beam diameter is 4 mm)
Grahic Jump Location
Comparison of desired and measured shapes of the pillow case (an array of 7 by 7 points measured by CMM)
Grahic Jump Location
Comparison of desired and measured shapes of the saddle case (an array of 7 by 7 points measured by CMM)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In