A general thermal modeling and control methodology for thermal processing of layered materials for rapid prototyping technologies is established in this article. An analytical multivariable model of lumped temperature outputs generated by heat inputs on a surface grid is developed, based on Green’s function and state-space descriptions. The few independent parameters needed in such a linearized formulation are experimentally identified, and their time-variability reflects the heat transfer nonlinearities and process disturbances. A robust controller with thermal feedback is designed by pole placement methods, to obtain a specified dynamic temperature field yielding the desired material structure and properties. The regulated thermal processing is optimized in real time by proper heat source power modulation and torch guidance through a simulated annealing strategy. Its performance is tested on both the computer model and a laboratory station, using robotically guided plasma-arc cutting and infrared thermal sensing, in regulating the sensitized zone during blanking of an elementary contour pattern on stainless steel.

Issue Section:
Research Papers
Topics:
Cutting, Manufacturing, Temperature, Heat, Blanking (Metalworking), Computers, Control equipment, Control modeling, Electric arcs, Feedback, Heat transfer, Pole placement, Rapid prototyping, Simulated annealing, Stainless steel
1.
Amon, C. H., Finger, S., Prinz, F. B., and Weiss, L. E., 1994, “Modeling Novel Manufacturing Processes,” Manuf. Sci. & Engineering, ASME PED Vol. 68–2, Chicago, II, pp. 535–546.
2.
Astrom, K. J., and Wittenmark, B., 1995, Computer-Controlled Systems, 3rd Edition, Prentice-Hall, Englewood Cliffs, NJ.
3.
Bourell, D. L., Crawford, R. H., Marcus, H. L., Beaman, J. J., and Barlow, J. W., 1994, “Selective Laser Sintering of Metals,” Manuf. Sci. & Engineering, ASME PED Vol. 68–1, Chicago, II, pp. 519–528.
4.
Carslaw, H. S., and Jaeger, J. C., 1959, Conduction of Heat in Solids, 2nd edition, Oxford Press, London, UK.
5.
Chartoff, R. P., Briore, B., Klosterman, D. A., and Pak, S. S., 1996, “Composite Tooling via Laminated Object Manufacturing,” Proc. 28th Intl. SAMPE Tech. Conf., v. 28, pp. 1048–1055.
6.
Chin, B. A., Madsen, N. H., and Goodling, J. S., 1983, “Infrared Thermography for Sensing the Arc Welding Process,” Welding Journal (September), pp. 227s–234s.
7.
Danforth
S. C.
,
1995
, “
Fused Deposition of Ceramics
,”
Materials Technology
, v.
10
(
7–8
), pp.
144
–
146
.
8.
Doumanidis
C. C.
, and
Hardt
D. E.
,
1990
, “
Simultaneous In-Process Control of Heat-Affected Zone and Cooling Rate During Arc Welding
,”
Welding Journal
, Vol.
69
/
5
, pp.
186s–196s
186s–196s
.
9.
Doumanidis
C. C.
,
1997
, “
Simulation for Control of Sequential and Scanned Thermal Processing
,”
Intl. Journal of Modelling and Simulation
, Vol.
17
/
3
, p.
169
–
177
.
10.
Duff, I. S., and Stewart, D. J., 1979,“Sparse Matrix Proceedings,” SIAM, Philadelphia PA.
11.
Eagar
T. W.
, and
Tsai
N. S.
,
1983
, “
Temperature Fields Reproduced by Traveling Distributed Heat Source
,”
Welding Journal
,
62
(
12
), pp.
346s–355s
346s–355s
.
12.
Einerson, C. J., Smartt, H. B., Johnson, J. A., and Taylor, P. L., 1992, “Development of an Intelligent System for Cooling Rate and Fill Control in GMAW,” ASM Conf on Trends in Welding Research, Gatlinburg TN, pp. 853–858.
13.
Goldak, J., 1988,“Modeling Thermal Stresses and Distortions in Welds,” Trends in Welding Research, ASM Intl., Gatlinburg, TN, pp. 71–82.
14.
Hartwig, G., 1997, “Rapid 3D Modelers,” Design Engineering, March 1997, pp. 37–44.
15.
Hibbitt
H. D.
, and
Marcal
P. V.
,
1973
, “
A Numerical Thermomechanical Model of the Welding and Subsequent Loading of a Fabricated Structure
,”
Computers & Structures
,
3
/
5
, pp.
1145
–
1174
.
16.
Kailath, T., 1980, “Linear Systems,” Prentice-Hall, Englewood Cliffs, NJ.
17.
Kalpakjian, S., 1995, Manufacturing Engineering and Technology, 3rd edition, Addison-Wesley, Reading, MA.
18.
Karlsson, L., and Lindgren, L. E., 1991, “Combined Heat and Stress-Strain Calculations,” Modeling of Casting, Welding and Advanced Solidification Processes, V, TMS, pp. 187–202.
19.
Kirckpatrick
S.
,
1984
, “
Simulated Annealing
,”
J. of Statistical Physics
, Vol.
34
, pp.
975
–
981
.
20.
Kwak, Y. M., and Doumanidis, C. C., 1998, “Thermo-Geometrical Design Models for SFF with Material Transfer,” 3rd ASME Design for Manufacturing Conf., Atlanta, GA, DETC/DFM-5720.
21.
Marquis, B. P., and Doumanidis, C. C., 1993, “Distributed-Parameter Simulation of the Scan Welding Process,” IASTED Conf. on Modelling & Simulation, Pittsburgh PA, pp. 146–149.
22.
Metropolis
N.
,
Rosenbluth
A. & M.
, and
Teller
A. & E.
,
1953
, “
Simulated Annealing Methods for Global Optimization
,”
Journal of Chemical Physics
,
21
, 1953, p.
1087
–
1092
.
23.
Miyachi, H., 1989, “In-Process Control of Root Gap Changes During Butt Welding,” Ph.D. Thesis, Dept. of Mechanical Engineering, MIT, Cambridge MA.
24.
Nelder
J. A.
, and
Mead
R.
,
1964
, “
A Simplex Method for Function Minimization
,”
Computer Journal
,
7
, pp.
89
–
97
.
25.
Orme, M. E., and Huang, C., 1995, “Thermal Design Parameters Critical to the Development of Solid Freeform Fabrication of Structural Materials with Controlled Nano-Liter Droplets,” Proc. Solid Freeform Fabrication Symposium, Austin, TX, pp. 88–95.
26.
Schmitendorf, W. E., and Barmish, B. R., 1985, “Guaranteed Asymptotic Stability for Systems with Constant Disturbances,” Proceedings of American Control Conference, Boston MA.
27.
Stratasys, 1991, “Fast, Precise, Safe Prototype with FDM,” Proc. Solid Freeform Fabrication Symposium, Austin, TX, pp. 115–122.
28.
Tekriwal, P., and Mazumder, J., 1991, “Transient and Residual Thermal Stress-Strain Analysis of Arc Welding Processes,” Modeling of Welding, Casting and Advanced Solidification Processes, V, TMS, pp. 211–218.
29.
Thermal Dynamics, 1986, Plasma Cutting Handbook, Doc. #300-2090, St. Louis, MO.
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