TPT November 2009

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126 November 2009 ›
Refer to Fig. 5 for setting boundary conditions.
 Figure 5: The setting of boundary conditions
3 Simulation results analysis
3.1 Analysis of equivalent strain
The distribution of strain and stress is different in the forming
process. The analysis of equivalent strain is used for the formed
tube section.
 Figure 6: The simulation of equivalent strain for 12mm x 1.8mm
Fig. 6 is an example for equivalent strain contour bands of simulation
results (12mm x 1.8mm).
3.2 Comparing between simulation results and ideal diagram
The red line is taken as the ideal
circle and the black line is the section
contour revieved from results of
simulation. Fig. 7 is a comparison
example for 12mm x 1.8mm tube.
 Figure 7 : A comparison example for
12mm x 1.8mm tube
3.3 Roundness error analysis
3.3.1 Roundness error
Compare with an ideal circle to decide if the formed tube section
is perfectly round or not. The evaluation of roundness error is the
procedure of comparing the actual contour of the measured tube
cross section with an ideal circle.
3.3.2 Evaluation method of roundness error
The currently used methods include the least square circle method,
minimum circumscribed circle method, maximum inscribing
circle method and minimal territory roundness method. The least
square circle method has statistics meaning that, although it
cannot eliminate influence caused by maximum error, it is a safer
method with limited actual measuring points; since the minimum
circumscribed circle method and maximum inscribing circle method
can describe positioning characteristics in the mating member as
close as possible, they have obvious using value; and the minimal
territory roundness method is a new good evaluating method. It can
not only obtain the minimum error evaluating result but also has
stable constraints to characteristics of the part. So it is an evaluating
method researched by modern measuring technology. Here the
minimal territory roundness method is adopted.
3.3.3 Evaluation roundness error
Using Matlab programming M-file is established and each point
value of radius is input. The distance between measured points and
circle centre is calculated so that the maximum error of roundness
can be given as seen in Table 3.
OD x t
(t/D=15%)
Error
(mm)
OD x t
(t/D=20%)
Error
(mm)
OD x t
(t/D=25%)
Error
(mm)
OD x t
(t/D=30%)
Error
(mm)
8 x 1.2 0.040 8 x 1.6 0.093 8 x 2 0.273 10 x 3 0.455
10 x 1.5 0.050 10 x 2 0.075 10 x 2.5 0.238
12 x 1.8 0.051 14 x 2.8 0.156 12 x 3 0.323
20 x 3 0.136 15 x 3 0.210 14 x 3.5 0.209
16 x 3.2 0.220
 Table 3: Roundness errors of welded tubes with various dimensions
Outside diameters and roundness error distribution of welded tubes
with various specifications is shown in Fig. 8.

Figure 8: Outside diameters
and roundness error
distribution of welded tubes
with various specifications
Roundness errors under the same OD (10mm) and different wall
thickness is shown in Fig. 9.

Figure 9: Errors of various
thickness/diameter ratio with
OD of 10mm
The fitted equation of the curve is δt=0.493-0.585 t +0.191 t2, where
δt is the dependent variable roundness error, and is the independent
variable wall thickness, the curve of δt changing along with t is the
right half of a second-degree parabola.
Roundness errors with various OD when the wall thickness is fixed
(3mm) are shown in Fig. 10.