TPT November 2009

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. 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. 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)

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

 Figure 8 : Outside diameters and roundness error

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.

distribution of welded tubes with various specifications Roundness errors under the same OD (10mm) and different wall thickness is shown in Fig. 9.

 Figure 7 : A comparison example for 12mm x 1.8mm tube

3.3 Roundness error analysis 3.3.1 Roundness error

 Figure 9 : Errors of various thickness/diameter ratio with OD of 10mm

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

The fitted equation of the curve is δ t

=0.493-0.585 t +0.191 t 2 , where

δ t is the dependent variable roundness error, and is the independent variable wall thickness, the curve of δ t 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.

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N ovember 2009

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