To produce a wide range of steel pipes with high mechanical and performance characteristics, various methods of forming a tubular billet with a tool are used [1,2,3,4,5]. The tool design and forming pattern determine the geometry of tubular billets [6,7,8,9]. Longitudinally welded tubes of various standard dimensions and steel grades are often produced in electric-resistance welding (ERW) pipe mills using single- or multi-radius forming patterns.

Single-radius roll-pass designs are widely used in ERW pipe shops due to the simple manufacturing of the tool, simple tool manufacture process design (manufacturing and reconditioning of rolls), adjustment, and operation. A single-radius tool has disadvantages, however.

Our goal here is to develop multiradius forming patterns with straight and descending trajectories of the middle fibers of the workpiece and to assess the effectiveness of different patterns. They were tested for Dt × St ∅ 50 × 1.5 mm band TESA 30-50 tubes [10]. Double-radius forming patterns are most widely used in forming mills with different parameters such as:

– dependence of curvature on the length of the deformation zone;

– length of the deformation zone and interstand distance;

– trajectory shape and length for the middle fiber of the workpiece;

– longitudinal-strain fields of the workpiece.

The curvature changes in the following forming patterns were compared:

– two single-radius forming patterns, one with straight middle fiber and the other with descending middle fiber;

– two double-radius (MISiS) forming patterns, one with straight middle fiber and the other with descending middle fiber;

– two double-radius forming patterns with constant parameters (radius and bend angle) of the periphery and the central section of the workpiece formed at large radius gradually decreasing from stand to stand; with a straight middle fiber and a descending fiber.

Figure 1 shows forming flowers for the single-radius, double-radius roll-pass designs and the double-radius (MISiS) designs with straight and descending bending zones.

Fig. 1.
figure 1

Forming flowers for single-radius design (a, b); double-radius design (c, d); double-radius (MISiS) design (e, f) with straight (a, c, e) and descending (b, d, f) deformation zones.

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The length of the trajectories of workpiece fibers for the single-radius roll-pass design (Fig. 1a) with straight bending trajectory was determined [11]. Table 1 summarizes the lengths l33, l22, l11, l00 of the trajectories of fixed fibers for the single-radius roll-pass design with descending trajectory (Fig. 1b).

Table 1 Lengths of Trajectories of Fixed Fibers for Single-Radius Design with Descending Trajectory
Full size table

Figure 2 shows the strain fields for single-radius roll-pass designs with straight and descending trajectories of fixed fibers.

Fig. 2.
figure 2

Longitudinal-strain fields of a tubular billet for single-radius design: a, b — deformation of edge and bottom with straight trajectory (dashed line); c, d — deformation of edge and bottom with descending trajectory of fibers.

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The strain is maximum (0.0027) in the first open stand (OS) for the straight deformation zone. Then the longitudinal strain smoothly decreases to 0.0018 in the fourth open stand and then intensively decreases in the closed stands. If the deformation zone is descending, the strain increases to 0.0022 in the first four stands and then intensively decreases. The latter forming pattern is preferred because the total longitudinal strain decreases by 18.8%. The strain differences Δε for the open forming stands are given below:

Stand number

1

2

3

4

Δε

0.00122

0.000885

0.000351

– 0.0003

%

47.86

36.73

16.2

– 18.089

The length of the trajectories of workpiece fibers for the double-radius roll-pass design (Fig. 1c) with straight bending trajectory was determined [12]. Table 2 summarizes the lengths l33, l22, l11, l00 of the trajectories of fixed fibers for the double-radius roll-pass design with descending trajectory (Fig. 1d).

Table 2 Lengths of Trajectories of Three Fixed Fibers for Double-Radius Design with Descending Trajectory
Full size table

Figure 3 shows the strain fields for double-radius roll-pass designs with straight and descending trajectories of fibers.

Fig. 3.
figure 3

Longitudinal-strain fields of a tubular billet for double-radius design: a, b — deformation of edge and bottom with straight trajectory (dashed line); c, d — deformation of edge and bottom with descending trajectory of fibers.

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The longitudinal strain intensively increases to 0.0035 in the first open stand and then smoothly decreases to 0.0017 in the subsequent three stands. If the deformation zone is descending, the longitudinal strains are stable, varying within 4%, in the open stands.

The strain differences Δε for the open forming stands are given below:

Stand number

1

2

3

4

Δε

0.00127

0.001255

0.000364

– 0.000006

%

36.61

49.65

19.99

– 3.77

Table 3 summarizes the lengths l33, l22, l11, l00 of the trajectories of fixed fibers for the double-radius (MISiS) roll-pass design with descending trajectory (Fig. 1f). The trajectories of fixed fibers are equally spaced across the width, from the center to the edge of the strip.

Table 3 Lengths of Trajectory of Three Fixed Fibers for Double-Radius (MISiS) Roll-Pass Design with Descending Trajectory
Full size table

Figure 4 shows the strain fields for double-radius (MISiS) roll-pass design with straight and descending trajectories of fibers.

Fig. 4.
figure 4

Longitudinal-strain fields of a tubular billet for double-radius (MISiS) design: a, b — deformation of edge and bottom with straight trajectory (dashed line); c, d — deformation of edge and bottom with descending trajectory of fibers.

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If the deformation zone is straight, the longitudinal strains peak (0.0031) in the first and second stands and then intensively decrease in the closed stands. The major deformation occurs in the first two stands. If the deformation zone is descending, the strain varies from 0.0017 to 0.0022 in the open stands and then intensively decreases. The other forming pattern produces uniform bending of the workpiece in the open stands.

The strain differences Δε for the open forming stands are given below:

Stand number

1

2

3

4

Δε

0.00123

0.000852

0.000257

– 0.0002

%

41.47

27.66

10.88

– 12.34

Figure 5 compares the upper boundaries of longitudinal strains of the edges for the three roll-pass designs.

Fig. 5.
figure 5

Longitudinal-strain fields of a tubular billet with descending trajectory of fibers: a — single-radius design; b — double-radius design; c — double-radius (MISiS) design; d — deformation on bottom of tubular billet.

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The longitudinal strains of the edges for all the roll-pass designs exceed the proportional limit in the range (1.2–3.0)εt. This, however, does not affect buckling and edge displacement because the experiments [13,14,15] demonstrated that the safe range of longitudinal strains of the edges during quality forming is within 0.6–0.8% of the elastoplastic range. In this connection, the roll-pass designs can be arranged in the order of effectiveness as follows: double-radius (MISiS) design with descending trajectory; double-radius design with descending trajectory; single-radius design with descending trajectory; single-radius design with straight trajectory.

Conclusions

1. The forming pattern with descending middle fiber is the most effective in quality forming with a maximum longitudinal strain of 0.0022 in 4OS, 1OS, and 2OS.

Comparing the double-radius roll-pass designs with descending trajectory with the simplest single-radius design with straight trajectory shows that the longitudinal strains of the edges decrease by 18.5%, which indicates that the descending forming patterns are preferred.

Assessing the longitudinal-strain fields of the roll-pass designs, we can arrange them in the following order of effectiveness: double-radius (MISiS) design with descending trajectory; double-radius design with descending trajectory; single-radius design with descending trajectory; single-radius design with straight trajectory.

Multiradius roll-pass designs for a forming mill can be recommended for the production of longitudinally welded pipes of small and medium diameters in continuous electric-weld pipe mills.