The control of each individual bend and overall process is presented in Part 1 of the paper. In Part 2 of the paper, statistical methods are used to analyze and improve 3-D tube bending accuracy. The relationship between bending process error and tube geometry error is obtained with Monte Carlo simulation. For the same tube tolerance requirement, the required process tolerance varies in a large range based on tube geometry. Among the three bending errors: bend angle, bend plane and distance between bends, bend angle error has the largest influence on tube error. For a tube with multiple bends, the overall tube geometry error can be minimized by intentionally modifying the nominal values of the bends to be made based on the errors in the existing bends. The required modification of the bending commands is calculated with an adaptive bend correction algorithm.

Issue Section:
Technical Papers
Keywords:
forming processes, manufacturing processes, bending, mechanical variables control, Monte Carlo methods, statistical analysis, tolerance analysis
Topics:
Errors, Geometry, Tolerance analysis, Algorithms, Tube bending, Simulation
1.
Wang
,
W. C.
, and
Stelson
,
K. A.
,
1991
, “
Computer Aided Manufacturing for Three-dimensional Tube Bending with On-line Springback Compensation
,”
Trans. North Am. Manufact. Res. Inst. SME
,
19
, pp.
70
–
76
.
2.
Li, H. Z., and Stelson, K. A., 1994, “Modeling of Thin-Walled Tube Bending at Large Deformation,” Proceedings of the First S.M. Wu Symposium on Manufacturing Science, 1, pp. 237–246.
3.
von Karman
,
T. H.
,
1911
, “
Uber die Formanderung dunnwandiger rohre insbesonders federnder Ausgleichrohre
,”
Zeits VDI
,
55
, pp.
1889
–
1895
.
4.
Den Hartog, J. P., 1952, Advanced Strength of Materials, McGraw-Hill, New York, pp. 234–245.
5.
Li
,
H. Z.
,
Fagerson
,
R.
, and
Stelson
,
K. A.
,
1994
, “
A Method of Adaptive Control of Rotary Draw Thin-walled Tube Bending with Springback Compensation
,”
Trans. North Am. Manufact. Res. Inst. SME
,
22
, pp.
25
–
28
.
6.
Pan
,
K.
, and
Stelson
,
K. A.
,
1995
, “
On the Plastic Deformation of a Tube During Bending
,”
ASME J. Eng. Ind.
,
117
, pp.
494
–
500
.
7.
Bauer
,
D.
, and
Khodayari
,
G.
,
1992
, “
In-process Compensation of Tube Springback During Bending
,”
Baender Bleche Rohre
,
33
, No.
7
, pp.
27
–
37
.
8.
Sabine
,
J.
,
1993
, “
Material Properties in Bending Tube
,”
Tube International
,
12
, No. 52,
January
, pp.
34
–
36
.
9.
Wang
,
Y.
,
Gupta
,
S.
,
Hulting
,
F.
, and
Fussell
,
P. S.
,
1998
, “
Manufactured Part Modeling for Characterization of Geometric Errors of Automotive SpaceFrames Extrusions
,”
ASME J. Manuf. Sci. Eng.
,
120
, No. 3,
August
, pp.
523
–
531
.
10.
Decker
,
K. M.
,
1991
, “
The Monte Carlo Method in Science and Engineering: Theory and Application
,”
Comput. Methods Appl. Mech. Eng.
,
89
, pp.
463
–
483
.
11.
Taylor, B. N., and Kuyatt, C. E., 1994, “Guideline for Evaluating and Expressing the Uncertainty of NIST Measurement Results,” NIST Technical Note 1297.
12.
Montgomery, D. C., and Peck, E. A., 1982, Introduction to Linear Regression Analysis, Wiley, New York.
13.
Lou, H., and Stelson, K. A., 1996, “Relating Process and Product Tolerance for Three-Dimensional Tube Bending,” Proceedings of the Second S.M. Wu Symposium on Manufacturing Science, 1, pp. 78–82.
14.
Stelson
,
K. A.
, and
Lou
,
H.
,
1995
, “
Tolerance Analysis of Three-dimensional Tube Bending: Worst Case and Statistical Methods
,”
Trans. North Am. Manufact. Res. Inst. SME
,
23
, pp.
293
–
298
.
Copyright © 2001
 by ASME
You do not currently have access to this content.