Effects of Forming Conditions of Roll Offset Method on Sectional Shape at the Corner of Square Steel Pipe +

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1 Materials Transactions, Vol. 54, No. 9 (2013) pp to The Japan Society for Technology of Plasticity Effects of Forming Conditions of Roll Offset Method on Sectional Shape at the Corner of Square Steel Pipe + Takuo Nagamachi 1, Takefumi Nakako 2 and Daisuke Nakamura 2 1 Institute of Technology and Science, University of Tokushima, Tokushima , Japan 2 Steel & Technology Development Laboratories, Nisshin Steel Co., Ltd., Sakai , Japan Square steel pipes are reshaped from welded round pipes by roll-forming. Effects of the roll diameter on the cross-sectional size of the square steel pipe were investigated by experimentation and three-dimensional finite element simulation. When the top roll diameter is greater than that of the side roll, then the width of a corner part of the formed pipe is greater than the height. The square steel pipe was formed by offsetting the small roll to the upstream side to make the width and height of a corner part equal. The offsetting result is affected by the longitudinal contact distance between a roll and a pipe. The geometric contact length and relative offset, the offsetting distance/geometric contact length, were defined. The optimum value of the relative offset was clarified, which increased with the expansion of the contact length of a top roll, the roll gap and the round pipe wall thickness. [doi: /matertrans.p-m ] (Received August 31, 2012; Accepted June 8, 2013; Published August 2, 2013) Keywords: roll forming, square steel pipe, roll diameter, offset, finite element (FE) simulation 1. Introduction Square steel pipes, normally produced by roll forming, are used widely as structural elements of buildings and machines. In the forming process, a roll set consisting of a top and bottom pair and a side pair, is generally arranged. Then several roll sets are connected tandemly. A circular pipe is pushed into the virtually square-shaped calibers of the center of the roll set. Bent corners and re-bent sides are formed in the cross section of the circular pipe. Finally the circular pipe is changed into a square pipe. On this subject, Kiuchi et al. 1) have conducted a series of experimental studies. To date Onoda et al. 2) reported an experimental investigation based on their numerical analyses. When designing a roll-forming machine for production of square steel pipes, the diameter of the paired top and bottom rolls is usually set as larger than that of the side roll pair. Thereby interference is avoided between the roll axes driven by electric motors. The authors have conducted experiments and FE simulations for top and bottom rolls with diameters larger than those of side rolls. 3) Results show the following: (1) the width of the formed pipe becomes smaller than its height, (2) it is therefore necessary to perform finish forming with a small increment of reduction to obtain a real square pipe, (3) the width of the corner is larger than its height, (4) offset forming in which roll pairs with smaller diameter are offset in the upstream direction is effective to produce pipes with equal width and height of the corner part. In this study, extended forming experiments and FE simulations are conducted to verify the results of offset forming in our previous report. We were able to ascertain the offset conditions to provide a sound corner shape are verified by examining the effect of the diameter ratio of top-bottom rolls to those of side one, reduction from circular pipe to square one and the initial thickness of the circular pipe, on relationship between amount of the offset and the geometry at the corner. 2. Experiment and Analysis Figure 1 presents a schematic view of the forming process used in this study. Hydraulic cylinder pushes the circular pipe into square-shaped roll calibers consisting of four roll sets. After passing roll sets, the square steel pipe is discharged finally. No rolls are driven in this process. Roll names and their dimensions are presented in Fig. 2 and Table 1. Rolls from A to D listed in the table have different diameters respectively. Three combinations of top and bottom rolls and side rolls, A-B, A-C and A-D, were investigated in a previous Fig. 1 Schematic illustration of forming processes. + This Paper was Originally Published in Japanese in J. JSTP 52 (2011) Fig. 2 Notations of roll dimensions.

2 1704 T. Nagamachi, T. Nakako and D. Nakamura Table 1 Path schedules. Table 2 Mechanical properties of round pipe. Roll gap Square pipe No. 1 process No. 2 process No. 3 process A/mm H 1 /mm r 1 /% H 2 /mm r 2 /% H 3 /mm r 3 /% Wall thickness: 2.11 mm Young s modules: GPa Poisson s ratio: 0.3 Yield stress: MPa n value: Flow stress: ¼ 468:4 ¾ 0:671 þ 387:9 MPa Reduction r i = (d 0 ¹ 2H i )/d 0 Roll dimension Process D Ti, D Si /mm No. i Roll-A Roll-B Roll-C Roll-D R/mm W/mm No No No ¹ Fig. 4 Notation representing corner shape of formed pipe. Fig. 3 Definition of geometrical contact length (L Ti, L Si ). study. 3) Two combinations of B-C and C-D are added for further examination of the effect of diameter ratio D Ti /D Si on the cross-sectional size at the corner. Here, geometric contact lengths are shown in Fig. 3 as a parameter representing diameter and configuration of rolls. These values at i-th process, L Ti and L Si, might be calculated using the following equations for top and bottom rolls and side rolls, respectively. s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi D 2 Ti L Ti ¼ D 2 Ti 2 2 H i 1 þ H i ð1þ s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi D 2 Si L Si ¼ D 2 Si 2 2 H i 1 þ H i ð2þ Nomenclature is presented in Fig. 2 and Table 1. For No. 1 process (i = 1), H i¹1 = H 0 = d 0 /2 (radius of the circular pipe). Table 2 presents mechanical properties obtained from tensile tests with a test piece. This is cut from a circular tube with the initial thickness t 0 of 2.11 mm, which is equivalent to a STK400 galvanized steel tube. The experimental apparatus places limits on experimental conditions mm on initial thickness t 0, 21.4% on reduction r i and 7.5 mm on offset Z oi. For conditions of t 0 heavier than 2.11 mm, r 3 larger than 23.3% and roll combinations except A-B, FE simulation is employed. This is conducted separately at each stand using a static implicit scheme applied to transient elasto-plastic analysis. Other details of the analysis are the same as those described in the previous report. 3) The domain for FE simulation is divided into hexahedral elements with eight nodes. Three elements are allocated in the thickness direction. The total number of elements is approximately 15,000 to 20,000 and 0.12 was assumed for the coefficient of Coulomb friction. Mechanical property of a circular pipe with initial thickness t 0 between 1.06 and 4.23 mm is assumed to be the same as that shown in Table 2. A general-purpose code of DEFORM-3D Ver. 6.1 was used for calculation. It took for 12 to 24 h in one forming stand on a PC with a Core 2, 3.0 GHz processor. 3. Results and Discussions 3.1 Influence of diameter ratio of top and bottom rolls to side rolls Although final dimensions of the cross-section that passed through three stands are important, the pipe that passed only the No. 1 stand and No. 1 and No. 2 stands were evaluated to make clear the effects of upstream deformations on crosssectional dimensions of the final product. The nomenclature for cross-sectional dimensions of the formed pipe is shown in Fig. 4. The peripheral part that made contact with the roll is defined as the side, and that which made no contact with it as the corner, while the boundary between these two parts as the shoulder. The width and the height of the corner (between two shoulders) are designated as s x and s y respectively; s a is the average of these two. Figure 5 demonstrates the average s a versus diameter ratio of top and bottom rolls to that of side rolls D Ti /D Si and Fig. 5 deviation of s y from s a,(s y ¹ s a )/s a. Ratio of the thickness to the outer diameter t 0 /d 0 is 3.9% and reduction r 3 is 19.6%. s a for every stand keeps almost constant for increasing D Ti /D Si. Whereas, (s y ¹ s a )/s a decreases with increasing D Ti /D Si and becomes negative, namely s x > s y for D Ti /D Si > 1.0. This status is expressed as corner droop. This occurrence can be explained by contact conditions between the pipe and the roll, 3) as follows. Because of the difference in roll diameters between the top and bottom pair and the side pair, lengths of longitudinal contact differ

3 Effects of Forming Conditions of Roll Offset Method on Sectional Shape at the Corner of Square Steel Pipe 1705 between two roll pairs. The longer contact length by the top and bottom rolls compared with that by side rolls causes the corner to shift from top to side. Then the shoulder of the top side goes away from the corner center and that of the side approaches it. Kondo et al. 4) described four-roll forming of wire and rods, whereby the longitudinal offset of axes of side roll pairs in the upstream direction (¹z direction) made the product wider horizontally. Considering the shift of the corner from top to side in our study as widening deformation by top and bottom rolls, suppression of the widening deformation and therefore the corner droop described above are expected by offsetting side rolls to the upstream direction. In our previous study, 3) experiments and FE simulation for roll combinations of A-B, A-C and A-D were conducted. The effectiveness of side rolls offsetting was confirmed to form products that have a corner with the equal width to the height. In the current study adding some more combinations of rolls, additional FE simulations were conducted. Fig. 5 Relationship between ratio of roll diameter and corner shape of pipe formed by No. i rolls (t 0 /d 0 = 3.9%, r 1 = 12.2%, r 2 = 17.1%, r 3 = 19.6%); Average of height s y and width s x of corner, Deviation of height s y to average s a of corner. Figure 6 shows the corner deviation (s y ¹ s a )/s a versus side roll offsetting Z oi for No. 1 stand. Side roll offsetting Z oi shows the longitudinal distance between the center of top and bottom rolls and that of side rolls, and is presented in Fig. 2. Figure 6 shows that (s y ¹ s a )/s a approaches zero with increasing Z oi. Therefore, the corner droop is balanced. However, too much offsetting of Z o1 causes results with (s y ¹ s a )/s a > 0 and therefore s x < s y, which means an inverse corner droop. To balance corner droop, (s y ¹ s a )/ s a = 0, Z o1 of 6.2 mm is found for D T1 /D S1 = 2.0, the roll combination of A-C and marked by. For combinations B-D, marked by, Z o1 is 4.0 mm for the same value of D T1 /D S For a combination of smaller rolls such as B-D, the longitudinal contact length for top and bottom rolls is short and widening deformation of pipe occurs in the adjacent region to the roll center. This fact might explain the smaller offsetting of side rolls to suppress widening deformation. Relative offset Z o1 /L a1 is introduced to normalize the offset, where L a1 is the average of geometrical contact length between the pipe and the roll denoted by L T1 and L S1, which was defined respectively in eqs. (1) and (2). The relationship between (s y ¹ s a )/s a and Z o1 /L a1 is shown in Fig. 6. L T1 /L S1 is shown in the same figure as a parameter representing the roll combination. This figure suggests that, Z o1 /L a1 that makes (s y ¹ s a )/s a zero becomes larger as L T1 / L S1 is increased. One might find the optimum offset balancing corner droop uniquely for any combination of rolls by making use of the geometrical contact length. Figure 7 shows (s y ¹ s a )/s a of pipes after successive offset forming by stands No. 1 and No. 2. Results for roll combinations of B-C, C-D and B-D are shown. Because the reduction increment at No. 3 finishing process is quite small, pipe shape after No. 3 process marked by, shows little difference in that after No. 2 process, marked by, as shown in Figs. 5 and 5. This fact suggests that forming work should be made only by No. 1 and 2 stands to obtain products with small droop. Fig. 6 Effect of ratio of roll diameter on relationship between offset and deviation of corner shape of pipe formed by No. 1 rolls (t 0 /d 0 = 3.9l%, r 1 = 12.2%, simulation results); (s y ¹ s a )/s a vs. Z o1 (s y ¹ s a )/s a vs. Z o1 /L a1.

4 1706 T. Nagamachi, T. Nakako and D. Nakamura (c) Fig. 7 Effect of offset Z o1 on relationship between offset Z o2 and deviation of corner shape of pipe formed by No. 2 rolls (t 0 /d 0 = 3.91%, r 1 = 12.2%, r 2 = 17.1%, simulation results); L T2 /L S2 = 1.14 L T2 /L S2 = 1.23 (c) L T2 /L S2 = Fig. 9 Effect of reduction r 1 on relationship between ratio of roll diameter and corner shape of pipe formed by No. l rolls (t 0 /d 0 = 3.91%); Average of height s y and width s x of corner Deviation of height s y to average s a of corner. Fig. 8 Effect of ratio of geometrical contact length on offset of rolls in case of becoming s y ¹ s a = 0(t 0 /d 0 = 3.91%, r 1 = 12.2%, r 2 = 17.1%). Several combinations of offset at No. 1 and 2 stands eliminating corner droop are possible for roll diameter ratios of, top-bottom rolls and side rolls, as shown in Fig. 7. Figure 8 summarizes combinations obtained from 7 types of experiments and 127 types of FE simulations. 3.2 Effect of reduction The effect of reduction from a circular pipe to a square one on sectional dimensions of formed pipes is discussed, for 3.9% with ratio of thickness to outer diameter of circular pipe t 0 /d 0, and 19.6, 21.4 and 23.3% with final reduction r 3. Figure 9 demonstrates effects of reduction r 1 on relationship between s a and D Ti /D Si and that between (s y ¹ s a )/s a and D Ti /D Si for No. 1 process. In Fig. 9, s a is almost constant with increasing D Ti /D Si, but it decreases rapidly with increasing r 1 for the fixed D Ti /D Si. In Fig. 9, (s y ¹ s a )/s a is decreased with increasing D Ti /D Si, but this is nearly kept constant with varying r 1 for the fixed D Ti /D Si. These results are the same in the real product. With increasing r 1,(s y ¹ s a )/s a is nearly kept constant, but s a is decreased rapidly. This means that actual difference between height and width of the corner s y ¹ s a (= s y /2 ¹ s x /2) is decreased rapidly with increasing r 1. For small difference of s y ¹ s a, a small offset might eliminate the corner droop. The effect of reduction r 1 on the relationship between Z o1 /L a1 and (s y ¹ s a )/s a for No. 1 process is presented in Fig. 10. Inferring from results presented in Fig. 9, Z o1 /L a1 that makes (s y ¹ s a )/s a zero is decreased with increasing r 1 in every combination of rolls. Figure 11 summarizes those combinations of offset at No. 1 and 2 stands eliminating corner droop. These have been found from 14 types of experiments and 139 types of FE simulations. As reduction becomes larger, corner droop can be eliminated with smaller Z o1 and Z o Effect of initial pipe thickness The effect of the initial thickness on sectional dimensions of formed pipes is discussed, for 19.6% in reduction r 3 with 2.0, 3.9, 5.9 and 7.8% in ratio of the thickness to the outer diameter of circular pipe t 0 /d 0. Figure 12 demonstrates effects of t 0 /d 0 on relationship between s a and D Ti /D Si and that between (s y ¹ s a )/s a and

5 Effects of Forming Conditions of Roll Offset Method on Sectional Shape at the Corner of Square Steel Pipe 1707 (c) Fig. 10 Effect of reduction r 1 on relationship between offset Z o1 and deviation of corner shape of pipe formed by No. l rolls (t 0 /d 0 = 3.9l%); L T1 /L S1 = 1.27 L T1 /L S1 = 1.43 (c) L T1 /L S1 = (c) Fig. 12 Effect of wall thickness t 0 on relationship between ratio of roll diameter and corner shape of pipe formed by No. 1 rolls (r 1 = 12.2%); Average of height s y and width s x of corner Deviation of height s y to average s a of corner. Fig. 11 Effect of reduction r i on offset of rolls in case of becoming s y ¹ s a = 0(t 0 /d 0 = 3.9l%); L Ti /L Si = 1.27 L Ti /L Si = 1.43 (c) L Ti / L Si = D Ti /D Si for No. 1 stand. In Fig. 12, s a is almost constant with increasing D Ti /D Si, but s a is increased rapidly with t 0 /d 0 for the fixed D Ti /D Si. Whereas in Fig. 12, (s y ¹ s a )/s a is decreased with increasing D Ti /D Si. Clear effect is not found for varied t 0 /d 0 for the fixed D Ti /D Si. Even with increasing t 0 /d 0,(s y ¹ s a )/s a is nearly kept constant but s a is increased rapidly. In brief, actual difference s y ¹ s a (= s y /2 ¹ s x /2) is increased rapidly with increasing t 0 /d 0. For large difference of s y ¹ s a, large offset might be necessary to eliminate the corner droop. The effect of ratio of thickness to outer diameter t 0 /d 0 on the relationship between Z o1 /L a1 and (s y ¹ s a )/s a for No. 1 stand is presented in Fig. 13. As expected from Fig. 12, Z o1 / L a1 that makes (s y ¹ s a )/s a zero is increased together with increasing t 0 /d 0 in every combination of rolls examined in through (c). However, for the condition with the largest ratios of 1.77 for L T1 /L S1 and 7.8% for t 0 /d 0 in Fig. 13(c), (s y ¹ s a )/s a was not zero even by a considerable large offset. The corner droop on this condition can not be a eliminated. Figure 14 summarizes combinations of offsets at No. 1 and 2 processes for eliminating corner droop. These have been found from 7 kinds of experiments and 261 kinds of FE simulations. The larger the ratio of thickness to outer diameter is, the larger offset is necessary to eliminate corner droop. In Fig. 14(c) for L T1 /L S1 = 1.77, offsets to eliminate corner droop can not been found for pipes with heavier thicknesses t 0 /d and 7.8%. 4. Conclusions (1) Corner droop can be reduced by offsetting side rolls. This depends on the longitudinal contact length of top and bottom rolls. (2) Defining the geometrical contact length by normalizing the offset by the defined contact length, it is possible to find the optimum offset uniquely for forming conditions.

6 1708 T. Nagamachi, T. Nakako and D. Nakamura (c) Fig. 13 Effect of wall thickness t 0 on relationship between offset Z o1 and deviation of corner shape of pipe formed by No. 1 rolls (r 1 = 12.2%); L T1 /L S1 = 1.27 L T1 /L S1 = 1.43 (c) L T1 /L S1 = (c) Fig. 14 Effect of wall thickness t 0 on offset of rolls in case of becoming s y ¹ s a = 0(r 3 = 19.6%); L Ti /L Si = 1.27 L Ti /L Si = 1.43 (c) L Ti /L Si = (3) The relative offset to eliminate the corner droop is made clear for many forming conditions. The larger the ratio of geometrical contact length of top and bottom rolls to that of side rolls is, the larger the offset becomes. The larger the reduction from the circular pipe to the square one is, the smaller it becomes. The heavier the ratio of thickness to the outer diameter of the circular pipe is, again the larger it becomes. REFERENCES 1) M. Kiuchi, K. Shintani and M. Tozawa: J. JSTP 21 (1980) (in Japanese). 2) Y. Onoda, T. Nagamachi and T. Sugiyama: J. JSTP 36 (1995) (in Japanese). 3) T. Nagamachi, T. Nakako and D. Nakamura: Mater. Trans. 52 (2011) ) H. Kondo, R. Takeda, K. Ohmori and N. Kunita: Kawasaki Steel GIHO 28 (1996) (in Japanese).