Optimization of spinning parameters of 20/316L bimetal composite tube based on orthogonal test

2.1 Build finite element model

The size of the carbon steel base tube is Φ 89×4.5mm and 316L liner size is Φ 79.2×1 mm. The gap between base and liner tube is 0.4mm. The embedding quantity δ is 0.14 mm, orientation Angle β (the centerline of the roller and liner axis Angle) is 2.5^∘, the feed rate f (axial feed roller speed/angular velocity) is 0.3. The three-dimensional simulation model of the bimetallic clad pipe is shown as the Figure 1.

Figure 1

3D model of bimetallic clad pipe formed by spinning

2.2 Defining the load and boundary conditions

In the spinning process of the composite tube, the liner should be flanged and fixed on the base tube. Therefore, the displacement/Angle constraint mode is adopted when defining boundary conditions. U2 = 0 is defined at the end of the liner and base tube. The axial loading speed defined as v2 = 18.84mm/s, the rotating speed n = 600r/min and the amplitude curve of smooth step is introduced for loading.

2.3 Contact mode and mesh division

Applying the method of surface to surface contact between the outer wall of the liner and the inner wall of the base tube and assuming the inner wall of the base tube as the main contact surface and the outer wall of the liner as the slave contact surface simulated the forming process. The surface to surface contact method was also adopted between the roller and the inner wall of the liner inner wall, and the roller as the main contact surface and the inner wall of the liner as the slave contact surface. The finite slip was introduced in each contact pair and the motion contact as the mechanical constraint. The C3D8R hexahedron unit was employed to mesh the liner and base tube, the liner was divided into 94000 hexahedron units and 79000 hexahedron units for the base tube was divided. Because of the shear load, the grid distortion may occur in the liner and base tube and it seriously affects the analytical accuracy, misconvergence and even interrupts the program. The usage of the ALE adaptive grid control prevents the occurrence of this phenomenon.

3.1 Equivalent plastic strain analyses

The equivalent plastic strain (PEEQ) of the base tube and liner in the stable spinning stage of the composite tube was shown in Figure 2:

Figure 2

Plastic strain of base tube and lined tube

The material hardening model was used to calculate the accumulated plastic strain, and the PEEQ can be used to express the accumulated plastic strain. According to the shear failure criterion, the material failure may happen when the PEEQ reached above 1.0. Figure 2 (a) showed that the equivalent plastic strain of the base tube was almost close to zero. It can be considered that the base tube was always within the elastic range during the forming process, the theoretical calculation with multiple tube spinning forming and the actual production safety requirements were consistent. The liner would be plastic deformation because of its large deformation. As it can be seen from Figure 2 (b) of the equivalent plastic strain distribution of the liner, plastic deformation occurred in the liner, and the maximum PEEQ was 0.2279, which didn’t exceed 1.0, so the material didn’t fail due to large deformation.

3.2 Residual contact pressure and torque

Residual contact pressure is the main index for the quality of composite tube. Under the condition of the base tube being in plastic deformation and the liner being well, the greater the residual contact pressure between the liner and the base tube, the better the quality of the composite tube. Figure 3 showed the distribution of the average residual contact pressure obtained along the uniformly selected path along the inner wall of the base tube. It can be seen that the residual contact pressure of each path was inconsistent, and the average residual contact pressure of each path was 8.20MPa.Metal accumulation formed by uneven metal-flowing in the forming process would lead to uneven residual contact pressure. In practical production, physical defects, such as small concave anti-bulge on inner wall of base tube or outer wall of liner, would also lead to uneven distribution of contact pressure between liner and base tube.

Figure 3

Residual contact pressure between lined tube and base tube

The torque distribution of the composite tube in spinning process was shown in Figure 4. The forming process went through three stages: in the initial spinning stage, the spinning mold came into contacting with the liner, the metal-flowing started to increase, the contact pressure also increased gradually, and the torque increased with time. In the stable spinning stage, the roller was in full contact with the liner, and the metal-flowing and contact pressure tended to be stable, so the torque fluctuated in a small range and tended to be stable. Spinning unloading stage, spinning roller and liner separated gradually, contact pressure reduced and torque also reduced to zero. The average torque of the entire spinning process was 3943.69 N·m.

Figure 4

Torque

4.1 Range analysis

The range analysis method can estimate the influence of various factors on the test results. The larger the range R value is, the greater the influence of the corresponding factors will be. Therefore, the influence of each factor on the test evaluation index can be ensured by the size of the range R value, and the better level of each factor can be ensured according to the size of the k value, so as to determine the optimal level combination.

From Table 3, The range analysis of the four factors on the residual contact pressure was RA>RC>RD>RB, which meant that the embedding amount exerted the greatest influence on the residual contact pressure, followed by the leading Angle, the feed rate, and the liner and base tube clearance, respectively. The four factors of A, B, C and D respectively gained the maximum residual contact pressure at the level of A4, B3, C5 and D5, so the corresponding optimal spinning process parameter was A4B3C5D5.

It can be seen from table 4 that the range analysis of torque by the four factors was RA>RC>RB>RD. It was also basically consistent with the range analysis results of residual contact pressure. The embedding amount and steering Angle had a large influence on the residual contact pressure and torque, and the gap between liner and base tube and the feed rate f had a low influence on them. The minimum torque was obtained at the level of A1, B1, C1 and D5, so the optimal process parameter should be A1B1C1D5. Overall consideration of torque and the <CJ/T 192-2004 lined stainless-steel tube> standard for the requirement of the residual contact pressure, the optimal parameter combination was acquired at A4B3C1D5.

4.2 Comparison of optimized and unoptimized results

The optimized parameters were used for numerical simulation and compared with unoptimized results. The differences between them were shown in Figure 5 and Figure 6.

Figure 5

Residual contact pressure

Figure 6

Torque

From Figure 5 (b), it can be seen that the range of residual contact pressure was form 8.4 MPa to 10 MPa, which was smaller than unoptimized results and the quality of the tube was more stable. The average residual contact pressure was 9.19 MPa, nearly 1 MPa higher than unoptimized results. From the Figure 6 (b), the average torque was 3783.61N·m, 160N·m less than unoptimized results.

5.1 Pull-out test

The holes on both ends of the specimen were clamped by the jacket on the material testing machine. One end was fixed and the other end could be moving. The testing machine applied tension to the removable jacket and pulled it out according to the standard of <CJ/T 192-2004 lined stainless-steel tube>. The force corresponding to the displacement of the liner and the base tube under the action of tension was the binding force F at the interface of the liner and the base tube separation, from the formula P_rc = F/πμD_iH, where D_i: inner diameter of the liner base tube of the composite tube. H: effective binding length of composite tube sample. Friction coefficient of liner and base tube, μ = 0.21.

5.2 Experimental scheme

According to the influence factor of residual contact pressure and the limitation of test conditions, four groups of tests were conducted, as shown in Table 5. The test parameters in the test table were selected according to the orthogonal test and test conditions.

5.3 Experimental results

From Figure 8, the residual contact pressure by simulating was not much different from the experimental value, with the mutual error of about 15%, under the acceptable range of engineering, because the simulated value was obtained under the assumption of the liner and base tube being ideal, and it would cause the simulated value larger than the test value. Moreover, the concave resistance, bending, uneven wall thickness and poor cleaning of liner and base tube during the actual forming of composite tube would reduce the residual contact stress.

Figure 8

The comparison of residual contact pressure