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Journal of Materials Processing Technology 113 (2001) 774±778

A parametric study on forming length in roll forming

Sukmoo Hong, Seungyoon Lee, Naksoo Kim*

Department of Mechanical Engineering, Sogang University, Shinsoo-dong, Mapo-gu, Seoul 121-742, South Korea

Abstract A simulation program has been developed in order to examine the roll forming process. The program is based on the three-dimensional ?nite element analysis of shape and roll forming under kinematically steady-state condition. In this study, the forming length of the strip in the roll forming process was estimated in consideration of some factors such as material properties, strip thickness, roll diameter, roll velocity, and the deformation of the material that in?uence the forming length decisively. The sensitivity of the forming length to these factors was considered, and the interaction between factors that affect the forming length was considered also. To verify the reliability of the simulation program, the simulated results for longitudinal strain were compared with experimental results available in the literature. It was concluded that the work-hardening exponent plays a major role in the forming length of the pre-deformed strip. # 2001 Elsevier Science B.V. All rights reserved.

Keywords: Rigid±plastic ?nite element method; Roll forming; Forming length; Longitudinal strain; Work-hardening exponent

1. Introduction Roll forming is known as a highly productive method for the production of pro?les or welded tubes and pipes. However, since it is relatively poorly understood, industrial practice has been largely restricted to empiricism and heuristic rules. To solve these problems and to improve the effectiveness of process design, a simulation program has been developed. Kiuchi and Koudobashi [1,2] performed a comprehensive theoretical study of the forming of a circular section by assuming the streamline of a strip as a sinusoidal curve. Jimma and his co-workers [3,4] have taken a more practical approach and have been successful in explaining some salient features of the roll forming of simple sections. With regard to the roll schedule for some sections Ona et al. [6] have suggested an empirical approach based on the experience of a particular company. At the same time Bhattacharyya and Panton [5] have adopted a semi-empirical approach and by minimizing the total energy have produced an expression for predicting the deformation length of a channel section. The concept has also been extended to predict the roll separating force [7]. In the roll forming process, the material is formed by rotating rolls that are arranged in a sequence. The material to be formed has a resistance against bending caused by its stiffness and material properties. Therefore, the starting

*

Corresponding author.

deformation point will not be the same for different materials. The distance between the ?rst deformation point and the center of the next pair of rolls is called the forming length. In the forming length, the strip deforms plastically and plastic deformation has an in?uence on a variety of variables, such as a thickness of the strip, the width of the bending angle, the material properties, the bend radius of the exit section, and the conditions of the entrance. After determining the bending angle, the bend radius of the exit section, and the conditions of the entrance, only the thickness of the strip and the material properties have an in?uence on the important variables determined by the formability and the forming length. To realize an improved product without defects from the current roll forming line, it is necessary to change the roll design, such as the forming length and the roll stand distance. When the roll horizontal distance is too long compared to the forming length, spring-back will occur. On the other hand, when the distance is too short, buckling will occur. Therefore, the roll horizontal distance considering the forming length. However, most of the process designs depend on the designer's experience. The trial-and-error method would lead to the wasting of a large amount of material and time. Recently, to obtain exact and effective solutions in metal forming processes, the ?nite element method has been most helpful and productive. Accordingly, the ?nite element method can help in making a decision on the important process variables and to know the tendency about the defects

0924-0136/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 0 1 3 6 ( 0 1 ) 0 0 7 1 1 - 7

S. Hong et al. / Journal of Materials Processing Technology 113 (2001) 774±778

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in the roll forming process. In this paper, a roll forming simulation program based on the ?nite element method was developed and veri?ed for its reliability, and the important parameters are studied. 2. Theory 2.1. Rigid±plastic ?nite element method The basic formulations of the rigid±plastic ?nite element method have been well described by Kobayashi et al. [8]. Here, only the governing equations, boundary conditions and some basic relations are summarized. 1. Equilibrium equations: sij;j ? 0 vi ? v? i in V in Su ; ti ? ti? in Sf (1) (2) 2. Boundary conditions: 3. Constitutive equation: _ 3 H e s 2 s ij _ _ _ where ? ?2 eij eij ?1=2 and s ? ?3 sHij sHij ?1=2 . e 3 2 4. Compatibility: _ eij ? _ eij ? 1 ?vi;j ? vj;i ? 2 5. Incompressibility: _ ekk ? 0 6. Yield function and ?ow stress: q????? s H _ e e f ? J2 ? p??? and s ? s?; ; T? 3 7. Constant friction factor model: s f ? m p??? 3 (7) (5) (3)

the cross-section of the strip perpendicular to the rolling direction by approximating a ``generalized'' plane-strain condition. The generalized plain-strain condition allows a uniform strain in the perpendicular direction to the plane. The basic assumption of two-dimensional is that the longitudinal velocity or strain-rate is uniform over any crosssection perpendicular to the rolling direction, which means a plane remains as a plane during deformation. The threedimensional FEM simulation starts with the geometry and boundary conditions determined by two-dimensional FEM simulation. With the velocity calculated by three-dimensional FEM, the geometry can be updated. When the boundary conditions are not changed after updating (kinematically steady-state is achieved), the simulation will stop. The friction force per unit area is assumed to be acting on the strip with a constant amount, e.g. a constant friction factor is used. The direction of the friction force vector at a material point is opposite to the direction of the relative velocity at the contacting roll surface. The three-dimensional geometry of the roll and strip interface is considered and the total external force including friction and pressure in the rolling direction can be calculated. Fig. 1 shows a ?ow

(4)

(6)

The boundary value problem described by Eqs. (1) and (2) can be formulated into a weak form. By applying Eqs. (3)± (5) to the weak form, the following is obtained. Z Z Z 2s _ e _ e (8) e d_ dV ? K ekk d_ kk dV ? ti? dvi dS ? 0 _ ij ij e V 3 V Sf where incompressibility is imposed by the penalty constant K (a very large positive constant). The ?ow stress (6) and the friction condition (7) are given as input to the computer program. 2.2. Numerical algorithm The roll forming process can be numerically simulated by the two-dimensional rigid±plastic ?nite element method in

Fig. 1. Flow chart of the algorithm.

776

S. Hong et al. / Journal of Materials Processing Technology 113 (2001) 774±778

chart of the overall procedure for numerical simulation of the roll forming [9,10]. The ?nite element simulation program (COPRA FEA-RF) using the combined two-dimensional- and three-dimensional-algorithm is integrated into a user-friendly graphics oriented pre/post-processor. The program can be used in Windows and Windows-NT. Therefore, the users can utilize the program in personal computers. 3. Modeling of the roll-forming process 3.1. Program veri?cation The example presented in this study is a U-channel forming process that is composed of three passes, and each roll stand has a bending angle of 308, 608, and 908 in Fig. 2. In the channel process, ?nding the minimum of the longitudinal strain from the proper roll stand distance and roll gap can help to exclude defects such as buckling and bowing. The experimental data of this process are published by Darm [11]. The material properties and the process conditions are shown in Table 1. Among them, a friction coef?cient is properly assumed. The rolls illustrated in Fig. 3 were used in the simulation.

Fig. 4. Simulation results of the three pass U-channel forming process.

The velocity ?eld along the strip line can be calculated and the longitudinal strain of rolling can be determined with the simulation program. The simulation results were compared with the experimental results Fig. 4 shows perspective view of the process obtained by the simulation. Fig. 5 shows the longitudinal strain distribution of the exit section for pass No. 3. As shown in Fig. 6, the experimental data are the

Fig. 2. Section pro?le.

Table 1 Conditions of simulation Material Initial strip thickness Initial width Roll velocity Flow stress (MPa) Friction coefficient AISI 1015 4.0 mm 236.0 mm 0.1 m/s s ? 617:2?1:292 ? 104 ? ?0:143 e 0.2 (assumed) Fig. 5. Distribution of longitudinal strain for pass No. 3.

Fig. 3. Roll pro?les: (a) pass No. 1; (b) pass No. 2; (c) pass No. 3.

Fig. 6. Distribution of longitudinal strains.

S. Hong et al. / Journal of Materials Processing Technology 113 (2001) 774±778

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Fig. 7. The direction of rolling and the location of strain measurement.

longitudinal strain of a streamline 1.5 cm away from the edge (from A to AH in Fig. 7). The simulation results are in good agreement with the experimental results on the whole. In simulation, only the deformation areas are considered, the tensions in front of and behind the deformation area not being considered. The simulation results are in good agreement with the experiment in pass No. 1 but there are increasing errors in passes 2 and 3. 3.2. Result and discussion of the parametric study The forming length is in?uenced by the thickness, the material properties, the roll diameter, the deformation rate of the strip, and the angular velocity of the roll. When the longitudinal strain exceeds the yield point buckling may occur. The parametric variables, work-hardening coef?cient and thickness, are studied and the results are shown in Figs. 8 and 9. As shown in Fig. 8, it can be con?rmed that the larger is the work-hardening coef?cient, the greater is the forming length. In general, the metal strip hardens as the plastic strain increases, especially during a cold working process such as roll forming. Also, one important tendency in most metal strips is that the slope of the strain±stress curve decreases as

Fig. 9. In?uence of strip thickness on the forming length.

the strip experiences larger plastic strain. In other words, the metal strip becomes rigid and the work-hardening exponent, n, decreases. At the same time, an annealed strip with little accumulated plastic strain has a large value of n. From the numerical simulation result, it was concluded that the highly work-hardened metal strip has a shorter forming length, while an annealed strip has a longer one. If the forming length is short for a given roll geometry, then the maximum longitudinal strain in the strip becomes large, making it dif?cult to produce defect-free products. Therefore, a highly work-hardened strip is hard to roll-form compared with an annealed strip, which has been frequently reported by roll formers. In Fig. 9, the change of the strip thickness is seen to have only a slight in?uence on the forming length. For the same roll gap, the strip thickness has only a slight effect on the forming length, but the longitudinal strain is different for a thinner strip with increasing bend radius. Therefore, operators can select the strip, estimate the proper forming length, and must exclude defects by regulating the roll stand distance. The currently decided forming length can be utilized as a minimum of the roll stand distance, and if the roll stand distance is greater than the forming length, there will be a spring-back or buckling problem. With the roll stand distance decreasing, buckling will take place easily, whilst with a greater roll stand distance, the more spring-back may occur. Therefore, spring-back and buckling are important in determining the roll stand distance. Through the simulation program, the important parameters are determined by taking into account the forming length and roll stand distance. 4. Conclusion and future work Through the study, the following are concluded. 1. Through the rigid±plastic ?nite element method, the roll forming process can be effectively analyzed.

Fig. 8. In?uence of the work-hardening coef?cient on the forming length.

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S. Hong et al. / Journal of Materials Processing Technology 113 (2001) 774±778 [2] M. Kiuchi, T. Koudobashi, Proceedings of the Third International Conference on Rotary Metal Working Process, Kyoto, 1984, p. 423. [3] T. Jimma, H. Ona, Proceedings of the 21st International MTDR Conference, 1980, p. 63. [4] H. Ona, T. Jimma, N. Fukoya, J. Mech. Working Technol. 8 (1983) 273. [5] D. Bhattacharyya, S.M. Panton, Research and Computer-aided Design in Cold Roll Forming, Academic Press/Pergamon Press, New York/Oxford, 1989. [6] H. Ona, T. Jimma, H. Kozono, Adv. Technol. Plasticity 1 (1984) 508. [7] D. Bhattacharyya, P.D. Smith, C.H. Yee, I.F. Collins, J. Mech. Working Technol. 9 (1984) 181. [8] S. Kobayashi, S.I. Oh, T. Altan, Metal Forming and the Finite Element Method, Oxford University Press, Oxford, 1989. [9] N. Kim, S.I. Oh, Ann. CIRP 48 (1) (1999) 235. [10] S.M. Hong, N. Kim, Trans. Proceedings of the Spring Conference. Korean Soc. Technol. Plasticity (1999) 207. [11] K. Darm, Determination of longitudinal strains in roll forming of standard section in a multi-stand machine, Institute for Production Technology, Germany, 1989.

2. The work-hardening exponent, n, has a most signi?cant effect on the forming length. It should be taken into account for other strips with the same pro?le of rolls. 3. The above simulation results can be utilized in the real roll forming industry. This is done either by choosing adequate metal strips, which do not yield high longitudinal strains, or by modifying the process parameters, such as the roll design. If not only above process variables but also spring-back and buckling are considered in the ?nite element analysis, it will be useful to make an estimation of the reasonable roll stand distance, the formability, and the defects of the rollformed products. References

[1] M. Kiuchi, Analytical study on cold roll forming process, Report of the Inst. of Ind. Sci., No. 23, University of Tokyo, 1973.

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