Materials Transactions, Vol. 45, No. 4 (4) pp. 13 to 137 #4 The Japan Institute of Metals Effect of Pass Schedule on Cross-Sectional Shapes of Circular Seamless Pipes Reshaped into Square Shapes b Hot Roll Sizing Mill* Takuo Nagamachi 1, Yoshitomi Onoda, Eiji Wakamatsu, Takaaki Toooka 3, Takua Nagahama 4 and Nobuhiko Morioka 5 1 Department of Mechanical Engineering, Tokushima niversit, Tokushima 77-856, Japan Department of Mechanical Sstem Engineering, Yamanashi niversit, Yamanashi 4-8511, Japan 3 Steel Research Laborator, JFE Steel Corporation, Okaama 71-8511, Japan 4 Steel Research Laborator, JFE Steel Corporation, Aichi 475-8611, Japan 5 Chita Works JFE Steel Corporation, Aichi 475-8611, Japan A heav gauge square steel pipe is manufactured b a hot roll sizing process, in view of difficult in manufacturing such a pipe with sharp corners b cold roll forming. In this paper, the effect of pass schedule on a cross-sectional shape is discussed b referring to experimental measurements, and results calculated b the rigid-plastic finite element method. The experiment was carried out at the last step of the sizing process for seamless pipes. The corners of a product become sharper as the magnitude of total reduction increases. In the case of a two-roll tpe roller, the corner near the roll flange becomes sharper than the corner near the groove bottom. The hollow depth at the sides is small when the incremental reduction at each sizing stand is high at the earl reshaping stage with a large bending curvature (ðd =Þ=R i, R i : bending radius, D : initial external diameter of a circular seamless pipe) and low at the late reshaping stage with a small bending curvature. (Received August 7, 3; Accepted September 19, 3) Kewords: hot roll forming, tube forming, seamless pipe, heav gauge square pipe, rigid-plastic finite element method 1. Preface Square steel pipes are often used as pillars for low-rise to high-rise steel constructions. The are mainl cold-formed square steel pipes, which are produced b a roll forming sstem or a press forming sstem. The roll forming sstem continuousl reshapes ERW pipe into square steel pipes b tandem pass forming rolls. The press forming sstem forms a steel plate into a square cross-section or a pair of groove cross-sections and finishes the thus-produced intermediate products into a square steel pipe. Square steel pipes formed b these sstems are required to have high dimensional precision. The requisites of square steel pipes used for pillar and beam joints (connections) are a cross-sectional shape with a large flat area and small corners for high processabilit, and excellent flatness on the sides. In production of square steel pipe b the roll forming sstem, the corners can be reduced to some extent b increasing the amount of forming (reduction) with pass forming rolls. As the reduction is increased and the corners are made smaller, the corner walls become obviousl thicker, 1) work hardening progresses, and deformabilit (toughness) decreases. Excess reduction ma crack corners and disable forming. Since thick materials make the corner walls even thicker, the cold forming of thick-wall square steel pipes with small corners is known to be difficult. The work hardening of corners poses not onl a forming problem, but also a problem in earthquake resistance, because corners exhibit low plastic deformabilit. The thermal treatment of formed square steel pipes is a means of eliminating work hardening strain but involves man problems, including high cost and generation of *This Paper was Originall Published in Japanese in the Journal of JSTP, 43, () 988-99 lengthwise warpage. Bearing these problems in mind, the authors performed hot roll forming of circular pipes b heating to the recrstallization temperature or higher, and conducted an experiment on the reshaping of square steel pipes. This experiment was targeted at thick-wall pipes applicable to connections, which are reinforced b increasing the wall thickness. This report introduces the results of studing the effects of path schedules on the cross-sectional shapes of the corners and sides of hot-formed square steel pipes, b experimentation and simulation with rigid-plastic FEM.. Experiment and Calculation Methods In this stud, in a sizing mill at the seamless square pipe manufacturing process for the reshaping experiment on seamless square steel pipes, the last four of eight sizing roll stands were replaced with square-pipe forming rolls. Figure 1 shows a schematic illustration of the sizing mill used for the experiment. A preheated pipe was first reduced b the four pre-stage sizing mills of the sizing mill, and then reshaped into a square steel pipe b the four post-stage sizing rolls of the mill shown in Fig. 1. In this stud, two tpes of sizing rolls and square-pipe forming rolls are used; the top-bottom roll tpe and the side roll tpe. A circular pipe reduced b the sizing roll (side roll) of No. 4 sizing roll-stand has an oval shape whose vertical diameter (d ) is slightl greater than the horizontal diameter (d 1 ). In this stud, the mean external diameter (D ¼ ðd 1 þ d Þ=) of circular pipes is used as the circular-pipe external diameter. Of the square-pipe forming rolls, the topbottom roll tpe is emploed for No. 1 and No. 3 forming roll stands, and the side roll tpe is emploed for No. and No. 4 forming roll stands. Figure and Table 1 give the notations and dimensions of square-pipe forming rolls.
Effect of Pass Schedule on Cross-Sectional Shapes of Circular Seamless Pipes Reshaped into Square Shapes b Hot Roll Sizing Mill 133 Circular seamless pipe Top forming roll Flow of pipe Side forming roll Finished square pipe Initial mean external d 1 +d diameter D = d 1 Crosssectional view d x A No.4 sizing roll-stand No.1 forming roll-stand No. forming roll-stand No.3 forming roll-stand Bottom forming roll No.4 forming roll-stand A=5mm x Cross-sectional view z x Table Forming conditions. Case Forming Roll H i Reduction Temperature roll- No. /mm r i ¼ ln Hi of pipe stand i T/ C No. /% 1 1 143.4 11.9 885 1 133. 19.4 875 3 4 15. 5.7 865 1 1 143.4 11.9 885 3 133. 19.4 875 3 3 16. 4.7 865 4 4 15. 5.7 855 1 1 141.7 19.5 885 131.4 7. 875 3 3 16.4 3.9 865 4 4 15. 31.9 855 D Fig. 1 Schematic illustration of sizing mill emploed for the experiment. D i R ia R ib R i H i 45 No.i rolls (i =1~4) Fig. Notations of forming rolls. Reduction r i / % 4 35 3 5 15 1 5 1 3 4 Forming roll-stand No. (a) Transition of reduction (r i ) Relative bending curvature D /R i.4.3..1 15 5 3 11.9 r i / % 31.9 (b) Transition of relative bending curvature (D /R i ) Table 1 Dimensions of forming rolls. Fig. 3 Reduction schedule. Roll R i R ia R ib D i No. /mm /mm /mm /mm i 1 59. 193.3 349.6 147.1 19. 35.7 367.1 3 7961.4 19.8 349.4 4 1 19.8 348.6 Table lists the forming conditions. As Fig. shows, the distance between the center of the roll pass of No. i forming roll and the roll pass on the 45 line from the center to another is defined as H i and the forming ratio (reduction) is defined as r i ¼jlnðH i =D Þj. Figures 3(a) and (b) show the relative bending curvature transitions of reduction and roll pass. is a pass schedule set b referencing the actual cold square pipe reshaping process ) and uses three stages of stands and three sets of square-pipe forming rolls. uses four stages of stands and four sets of rolls. is a pass schedule where the reduction increments between the forming rolls of each set are almost uniform, and is a pass schedule where the reduction increments are gradual. However, the final reduction r 4 of 31.9% in is so great that product corners ma be cracked, or forming ma be impossible if each reduction r i is applied to cold forming as is. During square pipe reshaping, pipe temperature is maintained at 855 to 885 C. Table 3 lists the material tpes and cross-sectional shapes of pipes reduced b the sizing rolls. In this stud, two tpes of materials are used. Since the deformation resistance of STK49 b hot forming is not ver different from that of STK54 and the initial mean wall thickness does not differ greatl, the effects of differences in material and initial mean wall thickness are ignored. In addition to the forming experiment under each set of conditions, rigid-plastic FEM simulation is applied to the forming processes. The simulation is handled as a stationar analsis of single-stand forming. The actuall measured lengthwise velocit (. m/s) was used as a boundar condition for the pipe entr cross-section of No. 1 stand, and the velocit calculated at the pipe output cross-section of one step higher stand was used as a boundar condition for the pipe entr cross-sections of No. to No. 4 stands. The number of elements is about 4 per stand, and the coefficient of friction with the roll surface is.35. For the equation of pipe deformation resistance, the empirical equation of hot mean deformation resistance acquired b Yoshizaka et al. 3) is applied. Other calculation procedures and boundar condition setting methods are the same as for FEM simulation 4) of wall thickness increase behavior in the roll forming of a regular square pipe.
134 T. Nagamachi et al. Table 3 Materials and cross-sectional dimensions of tested circular pipes. Forming Initial Initial mean conditions Carbon mean external t Material content wall d D 1 /mm d /mm diameter Case Reduction /mass% thickness D ¼ d 1 þ d /% r 4 /% t /mm /mm 1 5.7 STK49.16.8 318.5 38. 33.3 6.4 31.9 STK54. 1.3 338.3 35.4 344.4 6. O, V : Contact point adjacent, S to and Corner-, Pipe formed b No.1 rolls Q respectivel Q 18 V, Pipe formed b No. rolls, Finished pipe t ρo V A δ : Depth of hollow 16 Circular pipe ρi Corner- W 14 External profile External profile Internal profile 1 ρ S O1 1 45 ρ I1 Q 1 1 x Corner- Cross-section of t 1 8 formed pipe S 1, S : Size of and Corner-, respectivel 6 t 1, t : Wall thickness at point Q 1 and Q, respectivel Internal profile ρo1, ρo : Radius of external curvature at point Q 1 4 and Q, respectivel ρi1, ρi : Radius of internal curvature at point Q 1 and Q, respectivel Q 1 Fig. 4 Notations representing cross-sectional shape of formed pipe. 4 6 8 1 1 14 16 18 x / mm / mm 3. Results and Discussion 3.1 Cross-sectional shape of corner Figure 4 shows notations for the cross-sectional shape of a pipe formed b the forming rolls of each set. is an x- axis corner (flange position of the top-bottom roll and throat position of the side roll) and Corner- is a -axis corner (throat position of the top-bottom roll and flange position of the side roll). Points and V represent the contacts points (shoulders) of and Corner- with adjacent forming rolls. Figure 5 shows the transition of the cross-sectional shape of a pipe formed b No. i forming rolls in. The crosssectional shape shows one-quarter of the area. With regard to the circular pipe of, the side was bent back in the vertical and horizontal directions and the corners were bent b No. 1, No., and No. 4 forming rolls into a square steel pipe. With regard to a pipe formed b No. 1 forming roll, x is 166.8 mm outside the center of ( at point Q 1 in the figure). The x value is 7.6 mm greater than the d 1 = value of the circular pipe, meaning that a rather large bulge is produced at the center of Corner 1 ib forming with No. 1 forming roll. Outside the center of Corner- ( at point Q in the figure), is 164.6 mm and not greatl different from the d = value of the circular pipe, indicating no large bulge outside. shows a similar tendenc. This is attributable to the following reasons: No. 1 forming roll in this stud is a top-bottom roll. On the pipe external surface at contact point Fig. 5 Transition of cross-sectional shape of pipe formed b No. i forming rolls in. Roll profile V V Corner- Pipe being formed b rolls Formed pipe O Top forming roll P P : Contact point P v v s V R F V R : Peripheral velocit x of roll at point P v : Velocit of pipe at point P v s : Sliding velocit at point P F : Frictional force Bottom forming roll Fig. 6 Schematic illustration of directions of frictional force acting on pipe being formed b No. 1 forming rolls. P between the pipe and the forming roll, sliding (sliding velocit v s ) from the flange position toward the throat position is generated against the roll surface in the x cross section as shown in Fig. 6. Thus, frictional force F from the throat position toward the flange position acts on the external surface of the pipe. This frictional force produces a pass filling effect for and an opposite effect for Corner-. The external bulge of seems to become greater than
Effect of Pass Schedule on Cross-Sectional Shapes of Circular Seamless Pipes Reshaped into Square Shapes b Hot Roll Sizing Mill 135 /mm 18 16 14 1 1 8 6 4 4 6 8 1 1 14 16 18 x /mm Fig. 7 V Internal profile,, r 4 =5.7%,, r 4 =5.7%,, r 4 =31.9% Finished pipe External profile Cross-sectional shapes of finished square pipes. that of Corner-. On the pipe external surface in almost all contact areas, a sliding velocit from the flange position toward the throat position is generated against the roll surface in the x cross section, as confirmed b simulation-based calculation results. When a side roll is formed b No. forming roll, the bulges of and Corner- show the opposite tendenc. In shown in Fig. 5, the x- coordinate of at Q 1 is smaller than the x-coordinate of at Q 1, and the -coordinate coordinate of at Q is greater than the -coordinate of at Q. Figure 7 shows the measured cross-sectional shapes of products in the cases. Figures 8(a), (b), (c), and (d) show the effects of reduction (r 4 ) on the measured values of the relative size of each corner (, Corner-) on the wall thickness of the circular pipe t (S 1 =t, S =t ), the relative radius of external curvature ( O1 =t, O =t ), and relative radius of internal curvature ( I1 =t, I =t ) at the center of each corner, along with the increasing rate of wall thickness (T 1, T ). The relationship between reduction and the cross-sectional shape of a product corner is as follows. At the shoulder positions (points and V) of a product whose r 4 is as great as 31.9% the r 4 value is small as shown in Fig. 7. Compared with those of a product whose r 4 is as small as 5.7%, the positions are closer to the centers of the respective corners ( and Corner-). With regard to the product of r 4 ¼ 31:9%, the external surface at the center of each corner is bulged further outward. In other words, the S 1 =t, S =t, O1 =t, O =t, I1 =t, and I =t values of each corner become small in inverse proportion to the r 4 value, as shown in Figs. 8(a), (b), and (c). The relative size of r 4 ¼ 31:9% reaches S 1 =t ¼ :7 and S =t ¼ :75 (S 1 =A ¼ :6 and S =A ¼ :64 for product width A ¼ 5 mm). When a thick-wall circular pipe whose t =D is 6% is reshaped into a square steel pipe b cold forming, the empiricall determined limit is S 1 =t ; S =t ; :9. This confirms the superiorit of hot forming. As Fig. 8(d) shows, the T 1 and T values of each corner become great in proportion to the r 4 value. With the peripheral strain at the center of the product corner calculated S 1 S t t, I t ρ ρ I1 t, 1.4 1. 1..8.6.7.6.5.4 S 1 t S t O t O1 t, T 1, T / % 1.9 1.8 b rigid-plastic FEM shown in Fig. 9, this behavior of wall thickness increase can be explained as follows. The corner size and the internal and external curvature radii at the center 1.6 1.4 1..4 1.. 5 6 8 3 3.9 5 6 8 3 3 Reduction r 4 / % Reduction r 4 / % (a) Relative size of corner (b) Relative radius of (S 1 /t, S /t ) external curvature ( ρ O1 /t, ρo/t ) ρ ρ ρi1 ρi.3 t t T 1 =ln t 1 ( t ). 15 t T =ln( t ).1 1 5 6 8 3 3 5 6 8 3 3 Reduction r 4 / % Reduction r 4 / % (c) Relative radius of internal (d) Increasing rate of wall curvature ( ρ I1 /t, ρi/t ) thickness (T 1, T ) 4 35 3 5 ρo1 t ρ T 1 T O t Fig. 8 Effect of reduction (r 4 ) on cross-sectional shape of corner pipe of finished square pipe. Peripheral strain ε p.5 -.1 -. -.3 External Corner- Internal Peripheral strain ε mp, ε bp.5..15.1.5 -.5 -.1 -.4 -.15 Calculated -. -.5 b rigidplastic FEM -.5 εmp -.55 5 6 8 3 3 -.3 5 6 8 3 3 Reduction r 4 / % Reduction r 4 / % (a) Peripheral strain ( ε p ) (b) Peripheral strain ( ε mp, εbp) ( ε mp : Membrane strain, εbp : Bending strain ) ε bp εbp > Outer laer Calculated b rigid-plastic FEM Fig. 9 Effect of reduction (r 4 ) on peripheral strain (" p, " mp, " bp ) at center of corner of finished pipe.
136 T. Nagamachi et al. of the corner of the product of r 4 ¼ 31:9% are rather small as compared with those of the product of r 4 ¼ 5:7% (see Figs. 8(a) to (c)). As Fig. 9(a) shows, the absolute value of the peripheral strain " p (shrinkage strain) inside the product of r 4 ¼ 31:9% where the peripheral shrinkage strain b bending and the shrinkage strain b reduction overlap becomes rather high as compared with that of the product of r 4 ¼ 5:7%. As Fig. 9(b) shows, the absolute value of peripheral membrane strain " mp (shrinkage strain) also becomes rather high. In other words, mainl these great peripheral shrinkage strains increase the wall thickness at the corner center. Meanwhile, the product of r 4 ¼ 31:9% has a higher peripheral bending strain " bp than the product of r 4 ¼ 5:7%. This is related to the internal and external curvature radii being small at the corner center of the product of r 4 ¼ 31:9%. With regard to the difference in the number of stands used in where three stages of forming roll stands and three sets of square-pipe forming rolls are used, apparentl S 1 =t is smaller than S =t, O1 =t is smaller than O =t, I1 =t is smaller than I =t, and T 1 is greater than T, as indicated b and in Fig. 8. This is probabl attributable to the reason given in Fig. 6; i.e., in two sets of top-bottom rolls and one set of side rolls are used. In, where two sets of top-bottom rolls and two sets of side rolls are used, the differences in values between and Corner- are smaller than those of as indicated b and in Fig. 9. 3. Side cross-sectional shape Figure 1 shows the effect of incremental reduction (r 4 ) b No. 4 (finishing) forming roll on the relative depth of / 1 - δ A.6.5.4.3..1 4 6 7 r 4 / % Fig. 1 Effect of incremental reduction (r 4 ) at last reshaping stage on relative depth of hollow (=A) at side of finished square pipe (r 4 ¼ r 4 r in, r 4 ¼ r 4 r 3 in ). Fig. 11 Calculated 3-dimensional shapes and contact areas.
Effect of Pass Schedule on Cross-Sectional Shapes of Circular Seamless Pipes Reshaped into Square Shapes b Hot Roll Sizing Mill 137 bp / 1 - Peripheral bending strain ε -1.8 εbp < Outer laer -. -. Calculated b -.4 rigid-plastic FEM -.6 -.8-3. -3. -3.4-3.6 1 15 5 3 3 Reduction r i / % Fig. 1 Transition of peripheral bending strain (" bp ) at point W shown in Fig. 4. hollow (=A) versus product width A at the side center (point W in Fig. 4) of the product. In, where the r 4 value is as large as 6.3% and the incremental reduction is uniform, a large hollow was generated on the side of the product reshaped b a pass schedule. In contrast, a rather small hollow was generated on the side of the product in where the r 4 value is as small as 1.% and the incremental reduction is gradual. With the pipe and forming roll contact status calculated b rigid-plastic FEM shown in Fig. 11 and the peripheral bending strain at the side center shown in Fig. 1, the differences between the hollows can be explained as follows. As Fig. 11(a) shows, the pipe and forming roll contact can be seen in an area ver close to a shoulder near the central position (dot-dash line in the figure) of each forming roll but not at the side center in. In other words, the pipe external surface of the side center at this position is awa from the roll pass and does not match the pass profile. In forming b No. 1 and No. forming rolls, the roll passes are formed from arcs of radii R 1 and R, and even a side center deviation from a roll pass does not generate a hollow. In forming b No. 4 (finishing) forming roll of R 4 =, however, a side center deviation from a roll pass appears as a hollow. In, the absolute value of bending strain at the side center increases rapidl at r i ¼ 19:4% or more, as shown in Fig. 1, indicating the excess bend-back deformation of the side b the No. 4 forming roll. In of r 4 ¼ 31:9%, the pipe and forming roll contact can be seen at the side center in an area rather closer to the respective centers of No. 3 and No. 4 (finishing) forming rolls than in as shown in Fig. 11(b). of r 4 ¼ 5:7% shows a similar tendenc. As Fig. 1 shows, the absolute values of these side-center bending strains increase more slowl in than in. Kiuchi et al. 5) reported that a hollow will be generated on the side if the bend-back information is not adequate when a shoulder that had received peripheral bending deformation from forming at the previous stage is newl incorporated into the side. Cold forming ma clear a side hollow generated during forming if the corner deformed b bending springs back after forming. Hot forming, however, tends to generate a side hollow, because spring-back hardl occurs after forming. Considering these results, adopting a gradual pass schedule ma be rather effective for improving a side hollow. 4. Conclusion (1) A thick-wall circular pipe of initial wall thickness/initial external size = 6.4% could be reshaped b hot roll forming into a square steel pipe with rather small corners of corner size/initial wall thickness =.7 to.75 (corner size/ product width =.6 to.64). The wall at the center of a corner became 8 to 3% thick. () As the total reduction increases, corner size and the internal and external curvature radii of the product become smaller and the wall thickness increase rate become greater. (3) Adopting a pass schedule of gradual incremental reduction greatl alleviates the problem of a side hollow. REFERENCES 1) Y. Onoda, T. Nagamachi and S. Kimura: J. JSTP 33 (199) 573 578. (in Japanese) ) F. Liu, Y. Onoda, T. Nagamachi, S. Kimura and T. Kitawaki: J. JSTP 38 (1997) 199 113. (in Japanese) 3) K. Misaka and T. Yoshimoto: J. JSTP 8 (1967) 414 4. (in Japanese) 4) Y. Onoda, T. Nagamachi and T. Sugiama: Proc. 7th Int. Conf. on Numerical Methods in Industrial Forming Process (NMIFORM 1), ed. b K. Mori, (Toohashi, Japan) pp. 583 589. 5) M. Kiuchi, K. Shintani and M. Tozawa: J. JSTP 1 (198) 339 346. (in Japanese)