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The computer simulation of cold-roll-forming using FE methods and applied real time re-meshing techniques
Journal of Materials Processing Technology 142 (2003) 102–111
The computer simulation of cold-roll-forming using FE methods and applied real time re-meshing techniques A. Alsamhan a,∗ , P. Hartely b , I. Pillinger b b
a Mechanical Engineering Department, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia School of Manufacturing and Mechanical Engineering, The University of Birmingham, Edgbaston, Birmingham B15 2TT, UK
Received 26 October 2000; received in revised form 26 October 2000; accepted 17 February 2003
Abstract Cold-roll-forming (CRF) is an important sheet metal forming process. However, product design procedures, in terms of rolls design and rolls pass schedule, remains more an art than science. Finite element (FE) computer simulation can be used to predict the deformation and final product geometry, hence, reduce the design time and cost. The main objective of this work is to develop a FE models to simulate the CRF process, and to predict membrane strain distributions. The model was used to simulate CRF of a trapezoidal channel section, and the simulation results were compared to publish experiments. Two models were investigated in this paper, simulating strip rolling with friction was investigated using two FE models. The first model involves closing the rolls over the undeformed stock to predict the initial deformed mesh, as a first stage, followed by rolling, as a second stage. The second model involved a rolling simulation with a pre-deformed mesh until the deformation was fully developed. Furthermore, to decrease the computation time and to continue the rolling simulation, a technique using dual meshes and re-meshing was applied to simulate roll-forming trapezoidal channel section. © 2003 Elsevier Science B.V. All rights reserved. Keywords: Cold-roll-forming; FE models; Computer simulation
1. Introduction Cold-roll-forming (CRF) is an important sheet metal forming process and is used widely to manufacture long sheet metal products with a constant cross-section thickness. The design procedure for CRF products, roll pass sequences and forming rolls remains more an art than a science. Therefore, to reduce the process development efforts and forming defects, which result in improper process design, finite element (FE) computer simulation can be used to predict strain distributions and final geometry of cold-roll-formed products. Due to the complicated deformation of the CRF process, it was found that most of the FE models described in the literature are based on three approaches. The first two approaches are based on simulating strip rolling without friction, while the third approach is based on simulating strip bending between the forming stands. The first approach, the initial deformation shape, is obtained by pressing the deformed rolls towards the undeformed strip followed by pulling the strip longitudinally from the strip leading edge ∗
Corresponding author.
through the roll gaps of the forming stands [1–3]. The second approach involves predicting the deformation by pulling an undeformed strip, from the leading edge, through the roll gaps of deformed roll sets of the forming stands [4,5]. The third approach, is based on predicting the deformation between the forming stands, without simulating the strip rolling and starting from undeformed stock [6]. This approach involves predicting the deformation by applying nodal linear displacements on the nodes located at the channel flange edge of each forming stand. Nodal constraints, through mesh thickness, are imposed on the web nodes located at the forming stand centre line plane. Hence, rolling simulations approaches, and therefore mesh movement, are forced using the longitudinal displacements (without friction) applied at the strip leading edge. The main objective of the present work is to develop a FE model to simulate the CRF process and to predict membrane strain distributions. To support the model, it was decided to simulate CRF of a trapezoidal channel section and the simulation results were compared to publish experiments [7], for the same channel geometry. To fulfil the rolling simulation and to reduce the computational time, the previous developed a technique using dual meshes and real time
0924-0136/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0924-0136(03)00468-0
A. Alsamhan et al. / Journal of Materials Processing Technology 142 (2003) 102–111
re-meshing [8] was adopted and applied in conjunction with the utilised EPFEP3 program [9], to simulate trapezoidal channel roll forming. Furthermore, in the present computer simulation friction was considered on the contact boundary surfaces.
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Table 1 The coefficients of the constitutive material equation of the EPFEP3 program hp0 (MPa)
hp1 (MPa)
hp2
hp3 (MPa)
hp4
hp5
ε0
60.0
139.467
0.00602
322.6
−23.423
−0.05
0.705
2. Experimental work and computational techniques Fig. 1 illustrates the channel section and forming rolls dimensions used in experimental work. The strip material used in the experimental work of reference [7] was bright mild steel JISG 3141 SPEEN-50 with yield strength of 160 MPa. It was found that the mild steel AISI 1006 is the closest material property sited in the literatures [7,10], which was used in the developed FE model. The Poisson’s ratio was specified as 0.34 and the Young’s modules as 190 GPa. The flow stress–strain curve of AISI 1006 is obtained from Altan [11] and given (in SI units) as (σ¯ = σy + Kεn ), where σ¯ is the stress, ε the plastic strain, σ y the yield stress 160 MPa, K the material constant 613.8 MPa, and exponent n = 0.31. The constitutive material equation employed by the EPFEP3 program uses logarithmic and exponential functions to model material strain-hardening behaviour at the room temperature
and given as follows:
εp + hp2 y(εp ) = hp0 + hp1 ln hp2 + hp3 exp(hp4 (εp − hp5 )) y(εp ) = Y(εp ) +
dY(ε0 ) (εp − ε0 ) dεp
for εp ≤ 1.0 for εp > 1.0
(1) (2)
The coefficients of the logarithmic function (hp0 , hp1 and hp2 ) and the exponential function (hp3 , hp4 and hp5 ) were obtained through trial and error procedure [10], and are given in Table 1. Fig. 2 illustrates the strain-hardening behaviour of the two material equations. The figure illustrates that there is 20% error in the stress calculation resulting from inaccuracy in the fitted flow curve. The longitudinal membrane strain distribution experiments, at channel flange edge (located 1.5 mm from the edge) and web centre are selected for the purpose of comparison with the predicted FE results. In the experimental work, the membrane strain is obtained by averaging the surface strain values on the top and bottom of the sheet metal [7]. Where strain gauges were bounded on the upper and lower surfaces of the strip to measure the surfaces strains. The membrane strain distribution experiments [7] on the channel flange edge and the web centre for a single forming stand (fold angle 20◦ ), were compared to the predicted FE results. The membrane strain values in FE model, were calculated at element nodes then averaged at the element centroid. The utilised FE code is the EPFEP3 program [9]. It is a 3D implicit elastic–plastic FE program, developed initially to deal with bulk metal forming analysis by Pillinger [9]. The EPFEP3 program has proved successful for modelling metal forming processes, such as boundary surface and friction layer techniques [15]. All the computer simulations presented in this research, were executed on HP 400 Apollo workstations, with 32MB of memory and 600MB of hard drive capacity for the data storage.
3. Description of the rolling simulation models with friction
Fig. 1. Channel dimensions (mm) and forming rolls as given in experiment [7].
Two FE models, were investigated based on simulating the strip rolling with friction. These models include process modelling by closing the rolls over the sheet metal,
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A. Alsamhan et al. / Journal of Materials Processing Technology 142 (2003) 102–111
Fig. 2. Actual and curve-fit flow (stress–strain) curves for plastic strain range from 0 to 0.1 [10].
followed by rolling and process modelling by commencing rolling simulation on a pre-deformed sheet metal strip, respectively. In both cases, the computer simulation was carried out for single forming stand, with fold angle of 20◦ and strip length of 146 mm span. Due to symmetry, only one half of the strip and the forming rolls were modelled. For example, half of the strip width (15 mm) was used as strip width of the FE mesh, and nodal constraint conditions along the width direction, were applied along the span length, in the plan of the symmetry. The upper roll was modelled as cylindrical boundary surfaces, while the lower forming roll was modelled as single tool consisting of two boundary surfaces (cylindrical and conical types). The cylindrical type was modelled in the channel web region, while the conical type was modelled in the channel flange region. Generally, friction factors in sheet metal forming processes can be measured experimentally, using special testing devices mounted on standard tensile machines [12–14]. The friction layer in the EPFEP3 program is transitory and uses the friction factor [15], to imitate different lubricants. Due to lack of information on the experiments conducted mainly the frictional conditions, it was decided to specify a friction factor of m = 0.5, that provides stable contact between rolls and FE mesh, during the rolling simulation. Maintaining this contact during the rolling simulation is important, for the effectiveness of the friction layer technique that assists mesh movement, along the rolling direction. In the first FE model, the upper roll was displaced incrementally toward the lower forming roll, while the undeformed FE mesh in between (as pressing stage) was used to predict the deformed mesh. Applying rotational displacements (rolling increments) was followed on the upper and lower rolls. In the second model, the pressing stage was eliminated and strip-rolling simulation was carried out from the beginning, on a created pre-deformed mesh.
4. Discussion of preliminary simulation results Initially a coarse longitudinal elements, were used in the FE mesh generation mainly in roll gap area, however, it was found later, that fine longitudinal elements are required for predicting stable rolling simulation, using friction layer technique [15]. Furthermore, and in order to increase the efficiency of rolling simulation, roll penetration in the FE mesh was further increased to allow more elements in contact with boundary surfaces, in the rolls gap. Moreover, its was also found decreasing rolling increments is very important to predict stable and efficient rolling simulation. The simulation results for the first pressing stage, showed unstable numerical computation, when a fine mesh was used in the deformation zone, in the area near roll gap. However, stable numerical computations were observed, for the second rolling stage after mesh refinement, increasing the roll penetration and decreasing rolling increments. For this reason the pressing stage was eliminated, and rolling simulation was carried out from the beginning on a pre-deformed mesh through the second FE model. Two approaches for determining the initial mesh shape, were investigated using the second FE model. The first of which involved creating the FE mesh assuming a linear deformation between the rolling stands. The second approach, involved creating the FE mesh using the bend angle curve, based on the geometric restrictions imposed by the lower roll [16]. It was found that the application of the second method is more realistic and practical, especially when the friction layer technique was involved. This is because the latter method provides wide contact area between the mesh and the lower side roll, which is essential in the effectiveness of the friction layer technique. Finally, it was concluded that these techniques need more computational time, to reach the fully developed membrane strain distributions. Re-meshing
A. Alsamhan et al. / Journal of Materials Processing Technology 142 (2003) 102–111
was therefore introduced to address these problems. Details of these preliminary simulation results can be found in reference [10]. Dual mesh and real time re-meshing was developed by the authors [8] to address these problems. It was found that compete simulation can be obtained and the computational time could also be, saved using this technique on a benchmark FE model.
5. CRF computer simulation using dual mesh and re-meshing FE model In this section, the application of the dual mesh FE model is applied to the simulation of CRF of a trapezoidal chan-
105
nel section, for a single forming stand with a 20◦ fold angle. Three FE models were investigated. For all cases, the FE mesh was set up for a single pass, using the bend angle curve based on roll geometric restrictions of the lower side roll [16]. In the beginning of the computer simulation, vertical constraint conditions were applied on the nodes located along the mesh trailing edge, to represent the guiding model. Next, the nodes located at the channel flange length only (along the mesh trailing edge), were unconstrained. Fig. 3 illustrates the general set up of the computational mesh and the forming rolls. To save computational time, half of the model was considered, as shown in Fig. 3. Table 2 illustrates the general configuration of the FE models. Refining the fine
Fig. 3. General configuration of the computational mesh and boundary surfaces utilised with dual mesh FE models 1, 2 and 3.
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Table 2 General configuration and computational parameters of the dual mesh FE models Model
Computational time (min) (EPFEP3)
Transfer time (CRF program) (min)
Number of the utilised nodes and elements
Rolling increment (◦ )
1 2 3
3.053 3.38 3.4
5.4 6.79 15.57
16082 × 7300 (fine mesh), 858 × 380 (computational mesh) 40172 × 18250, 990 × 440 44400 × 20339, 1464 × 660
0.01 0.01 0.0005
Fig. 4. Variation of the computational mesh configuration and boundary surface contact area during re-meshing phases for FE model 1, for increments 1, 999 (8.975 mm) and 2499 (22.45 mm).
A. Alsamhan et al. / Journal of Materials Processing Technology 142 (2003) 102–111
Fig. 5. Generalised plastic strain contours of the re-meshed computational mesh given for increments 1, 1999 and 2499 for FE model 1.
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mesh is the main difference between model 1 and model 2; it was 0.2 mm longitudinal length for model 1 compare to 0.08 mm in model 2. This was adopted to decrease the roll penetration, hence minimising the mesh thinning, and also maintaining more fine longitudinal elements in the roll gap, for efficient rolling simulation. Roll penetration was 3.5 m in model 1 compared to 0.25 m in model 2. Furthermore, rolling increment was decreased from 0.01◦ in models 1 and 2, to 0.0005◦ in model 3, to investigate maintaining the
mesh-roll contact on the side roll, conical roll, during the rolling simulation.
6. Simulation results and discussions The computer simulation was carried out for nearly 2500 fixed rolling increments using FE model 1, which is equivalent to longitudinal strip displacement of 22.45 mm. It was
Fig. 6. Generalised plastic strain contours of the re-meshed computational mesh given for increments 1, 1499 and 1899, for FE model 2.
A. Alsamhan et al. / Journal of Materials Processing Technology 142 (2003) 102–111
found that, the total computational time is 8.5 min (3.1 min computational time plus 5.4 min transfer time), for each rolling increment. Fig. 4 illustrates the deformed computational mesh for the increments 1, 999 (8.98 mm), and 2499 (22.5 mm) which is equivalent to the quoted total rolling displacements in mm. The figure illustrates the mesh-roll contact areas (the dark shaded element faces) and the variation in the computational mesh configuration during the re-meshing phases. The mesh-roll contact was maintained during the rolling simulation at the element faces located at the channel web area (dark shaded areas in Fig. 4). Hence,
109
a stable numerical computation was obtained and a forward movement of the mesh through the roll gap was produced. Fig. 5 illustrates the generalised plastic strain contours of the computational mesh for the rolling increments 1, 1999 and 2499. It can be seen that plastic strains are concentrated along the channel web rolling area, which is not the case in actual CRF. The larger generalised plastic strain at the channel web area can be attributed to high roll penetration in the FE mesh. This results in a thickness reduction, which is not found in CRF processes. This will also affect, the proper prediction of the membrane strain at the channel web
Fig. 7. Membrane strain distributions as (a) channel flange edge, and (b) channel web centre for different rolling increments given for FE model 2.
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centre near and in the roll gap. Roll penetration must be selected minimum to predict accurate deformation. However, the efficient rolling simulation can be obtained when more element faces in contact with upper and lower roll, which can be achieved by increasing the roll penetration in the FE mesh. Decreasing the roll penetration and increasing number of the longitudinal element faces in contact, with upper and lower rolls can be achieved by refining the fine elements in the roll gap. The computer simulation was executed for 1899 fixed rolling, which equivalent to 17.1 mm rolling displacement using model 2. It was found that 3.4 min was required to execute one rolling increment, while 6.8 min was the transfer time between the dual meshes. Hence, the total computational time was 10.2 min per each rolling increment. The computer simulation with model 2, shows stable numerical computation and smooth predicted deformation. The generalised plastic strain contours of the computational mesh during re-meshing are shown in Fig. 6, for increments 1, 1499 (13.5 mm) and 1899 (17.1 mm) for model 2. Unlike the results of model 1, the maximum plastic strain is concentrated at the bend zone and along the rolling direction, which is the case in actual CRF process. Furthermore, the predicted plastic strain at the channel flange edge, and along rolling direction, can be attributed to the longitudinal stretching and bending along rolling direction. The predicted membrane strain distributions at the channel flange edge and the web centre, for different rolling increments, are shown in Fig. 7a and b, respectively (for model 2). The predicted membrane strain distribution, at channel flange edge (Fig. 7a) shows similar trends as the experimental work up to a strip distance of 134 mm. The predicted peak membrane strain is smaller than the experimental measured strain, and shifted left from the position of the experimental peak value by 12 mm. The predicted strain distribution shows, some disturbances near and after roll centre line (see the strain distribution in Fig. 7a after 134 mm strip distance). The predicted membrane strain distribution, at the web centre shows a similar trend to the experiment for up to a strip distance of 141 mm (see Fig. 7b). The predicted strain distribution shows, disturbances near and after the roll centre line mainly after a strip distance of 144 mm. The rolling increment was decreased significantly form 0.01◦ , in models 1 and 2, to 0.0005◦ , in model 3. In the beginning of the computer simulation, in the first increment, very wide contact area was found, however, during the computer simulation this contact area gradually becomes narrow and ineffective, to continue rolling with friction and eventually the contact was lost. Hence, predicting accurate membrane strain distributions becomes difficult with FE models use rolling with friction (mainly friction layer technique [16]). In general, the total simulation time using either model 1 or 2, is very high, and impractical from an industrial point of view. For example, executing 2500 increments using model 1 requires approximately 400 h, which is very high and totally impractical for the industry. This can be attributed mainly
due to the utilisation of low speed computers and low speed data storage. Using a high-speed computer and quick access storage hardware do significantly decrease the computation time by 60 times.
7. Conclusions From the simulation results of the dual mesh and remeshing FE model, it can be concluded that the FE model introduced is an efficient technique and can be used to model and simulate CRF processes. This is because the deformation history, such as the geometric information, strains and stresses are maintained in the fine mesh. In general the simulation results illustrate satisfactory results compared to the practical CRF process. The accuracy of the results is a function of the selected configurations of the computational mesh, especially in the main deformation zones, and the refined elements in the fine mesh.
References [1] S. Geyer, Process simulation for profile rolling, The MARC News Letter, MARC Analysis Research Corp., January 1993, pp. 6–11. [2] S. Geyer, N. Stricker, Neue Perspektiven fur die Umformtechnik. 5. Umformtechnisches Kolloquium, Institute for Production Technology, University of Darmstadt, Germany, 1994, p. 16.1. [3] F. Heislitz, H. Livatyali, M.A. Ahmetoglu, Simulation of roll forming process with the 3-D FEM code PAM-STAMP, J. Mater. Process. Technol. 59 (1996) 59–67. [4] N. Rebelo, J.C. Nagtegaal, L.M. Taylor, Comparison of implicit finite-element methods in the simulation of metal forming processes, in: Numerical Methods in Industrial Forming Processes, Chenot, Wood & Zienkiewicz, 1992, pp. 99–108. [5] C.K. McClure, H. Li, Roll forming simulation using finite-element analysis, Manuf. Rev. 8 (1995) 114. [6] R.S. Senanayake, I.M. Cole, S. Thiruvarudchelvan, The application of computational and experimental techniques to metal deformation in cold-roll-forming, J. Mater. Process. Technol. 45 (1994) 155–160. [7] K.F. Chiang, Cold roll forming, M.Sc. Thesis, Mechanical Engineering Department, University of Auckland, August 1984. [8] A. Alsamhan, I. Pillinger, P. Hartely, The development of real time re-meshing technique for simulating cold-roll-forming using FE methods, in press. [9] I. Pillinger, The prediction of metal flow and properties in threedimensional forging using the finite-element method, Ph.D. Thesis, School of Manufacturing and Mechanical Engineering, The University of Birmingham, 1984. [10] A. Alsamhan, The development of finite-element models and re-meshing techniques in the computer simulation of cold-rollforming, Ph.D. Thesis, School of Manufacturing and Mechanical Engineering, The University of Birmingham, 1999. [11] T. Altan, F.W. Boulger, J.R. Becker, N. Akgerman, H.J. Henning, Forging equipment, material and practices, Battle Columbus Laboratories, Metal Working Division, Air Force Material Laboratory, Wright-Patterson Air Force Base, October 1973. [12] Y. Kong, Y. Sun, X. Wang, Development of new friction test device in sheet forming, in: A. Altan (Ed.), Proceedings of the Fifth ICTP, vol. 2, Columbus, OH, USA, 7–10 October 1996, pp. 835–838. [13] X. Wang, J. Duncan, M. Devenpeck, Punch friction test for sheet metal forming, J. Appl. Metalwork. 3, 3.
A. Alsamhan et al. / Journal of Materials Processing Technology 142 (2003) 102–111 [14] W. Wang, R. Wagoner, Realistic friction test in sheet forming, in: Proceedings of the Fourth ICTP, 1993, pp. 1495–1500. [15] G.W. Rowe, C.E.N. Sturgess, P. Hartley, I. Pillinger, Finite-element Plasticity and Metal Forming Analysis, Cambridge University Press, Cambridge, 1991.
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[16] S.M. Panton, S.D. Zhu, J.L. Duncan, Geometric constraints on the forming path in roll forming channel sections, in: Proceedings of the Institution of Mechanical Engineers, J. Eng. Manuf. 206 (1992) 113–118.
The computer simulation of cold-roll-forming using FE methods and applied real time re-meshing techniques A. Alsamhan a,∗ , P. Hartely b , I. Pillinger b b
a Mechanical Engineering Department, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia School of Manufacturing and Mechanical Engineering, The University of Birmingham, Edgbaston, Birmingham B15 2TT, UK
Received 26 October 2000; received in revised form 26 October 2000; accepted 17 February 2003
Abstract Cold-roll-forming (CRF) is an important sheet metal forming process. However, product design procedures, in terms of rolls design and rolls pass schedule, remains more an art than science. Finite element (FE) computer simulation can be used to predict the deformation and final product geometry, hence, reduce the design time and cost. The main objective of this work is to develop a FE models to simulate the CRF process, and to predict membrane strain distributions. The model was used to simulate CRF of a trapezoidal channel section, and the simulation results were compared to publish experiments. Two models were investigated in this paper, simulating strip rolling with friction was investigated using two FE models. The first model involves closing the rolls over the undeformed stock to predict the initial deformed mesh, as a first stage, followed by rolling, as a second stage. The second model involved a rolling simulation with a pre-deformed mesh until the deformation was fully developed. Furthermore, to decrease the computation time and to continue the rolling simulation, a technique using dual meshes and re-meshing was applied to simulate roll-forming trapezoidal channel section. © 2003 Elsevier Science B.V. All rights reserved. Keywords: Cold-roll-forming; FE models; Computer simulation
1. Introduction Cold-roll-forming (CRF) is an important sheet metal forming process and is used widely to manufacture long sheet metal products with a constant cross-section thickness. The design procedure for CRF products, roll pass sequences and forming rolls remains more an art than a science. Therefore, to reduce the process development efforts and forming defects, which result in improper process design, finite element (FE) computer simulation can be used to predict strain distributions and final geometry of cold-roll-formed products. Due to the complicated deformation of the CRF process, it was found that most of the FE models described in the literature are based on three approaches. The first two approaches are based on simulating strip rolling without friction, while the third approach is based on simulating strip bending between the forming stands. The first approach, the initial deformation shape, is obtained by pressing the deformed rolls towards the undeformed strip followed by pulling the strip longitudinally from the strip leading edge ∗
Corresponding author.
through the roll gaps of the forming stands [1–3]. The second approach involves predicting the deformation by pulling an undeformed strip, from the leading edge, through the roll gaps of deformed roll sets of the forming stands [4,5]. The third approach, is based on predicting the deformation between the forming stands, without simulating the strip rolling and starting from undeformed stock [6]. This approach involves predicting the deformation by applying nodal linear displacements on the nodes located at the channel flange edge of each forming stand. Nodal constraints, through mesh thickness, are imposed on the web nodes located at the forming stand centre line plane. Hence, rolling simulations approaches, and therefore mesh movement, are forced using the longitudinal displacements (without friction) applied at the strip leading edge. The main objective of the present work is to develop a FE model to simulate the CRF process and to predict membrane strain distributions. To support the model, it was decided to simulate CRF of a trapezoidal channel section and the simulation results were compared to publish experiments [7], for the same channel geometry. To fulfil the rolling simulation and to reduce the computational time, the previous developed a technique using dual meshes and real time
0924-0136/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0924-0136(03)00468-0
A. Alsamhan et al. / Journal of Materials Processing Technology 142 (2003) 102–111
re-meshing [8] was adopted and applied in conjunction with the utilised EPFEP3 program [9], to simulate trapezoidal channel roll forming. Furthermore, in the present computer simulation friction was considered on the contact boundary surfaces.
103
Table 1 The coefficients of the constitutive material equation of the EPFEP3 program hp0 (MPa)
hp1 (MPa)
hp2
hp3 (MPa)
hp4
hp5
ε0
60.0
139.467
0.00602
322.6
−23.423
−0.05
0.705
2. Experimental work and computational techniques Fig. 1 illustrates the channel section and forming rolls dimensions used in experimental work. The strip material used in the experimental work of reference [7] was bright mild steel JISG 3141 SPEEN-50 with yield strength of 160 MPa. It was found that the mild steel AISI 1006 is the closest material property sited in the literatures [7,10], which was used in the developed FE model. The Poisson’s ratio was specified as 0.34 and the Young’s modules as 190 GPa. The flow stress–strain curve of AISI 1006 is obtained from Altan [11] and given (in SI units) as (σ¯ = σy + Kεn ), where σ¯ is the stress, ε the plastic strain, σ y the yield stress 160 MPa, K the material constant 613.8 MPa, and exponent n = 0.31. The constitutive material equation employed by the EPFEP3 program uses logarithmic and exponential functions to model material strain-hardening behaviour at the room temperature
and given as follows:
εp + hp2 y(εp ) = hp0 + hp1 ln hp2 + hp3 exp(hp4 (εp − hp5 )) y(εp ) = Y(εp ) +
dY(ε0 ) (εp − ε0 ) dεp
for εp ≤ 1.0 for εp > 1.0
(1) (2)
The coefficients of the logarithmic function (hp0 , hp1 and hp2 ) and the exponential function (hp3 , hp4 and hp5 ) were obtained through trial and error procedure [10], and are given in Table 1. Fig. 2 illustrates the strain-hardening behaviour of the two material equations. The figure illustrates that there is 20% error in the stress calculation resulting from inaccuracy in the fitted flow curve. The longitudinal membrane strain distribution experiments, at channel flange edge (located 1.5 mm from the edge) and web centre are selected for the purpose of comparison with the predicted FE results. In the experimental work, the membrane strain is obtained by averaging the surface strain values on the top and bottom of the sheet metal [7]. Where strain gauges were bounded on the upper and lower surfaces of the strip to measure the surfaces strains. The membrane strain distribution experiments [7] on the channel flange edge and the web centre for a single forming stand (fold angle 20◦ ), were compared to the predicted FE results. The membrane strain values in FE model, were calculated at element nodes then averaged at the element centroid. The utilised FE code is the EPFEP3 program [9]. It is a 3D implicit elastic–plastic FE program, developed initially to deal with bulk metal forming analysis by Pillinger [9]. The EPFEP3 program has proved successful for modelling metal forming processes, such as boundary surface and friction layer techniques [15]. All the computer simulations presented in this research, were executed on HP 400 Apollo workstations, with 32MB of memory and 600MB of hard drive capacity for the data storage.
3. Description of the rolling simulation models with friction
Fig. 1. Channel dimensions (mm) and forming rolls as given in experiment [7].
Two FE models, were investigated based on simulating the strip rolling with friction. These models include process modelling by closing the rolls over the sheet metal,
104
A. Alsamhan et al. / Journal of Materials Processing Technology 142 (2003) 102–111
Fig. 2. Actual and curve-fit flow (stress–strain) curves for plastic strain range from 0 to 0.1 [10].
followed by rolling and process modelling by commencing rolling simulation on a pre-deformed sheet metal strip, respectively. In both cases, the computer simulation was carried out for single forming stand, with fold angle of 20◦ and strip length of 146 mm span. Due to symmetry, only one half of the strip and the forming rolls were modelled. For example, half of the strip width (15 mm) was used as strip width of the FE mesh, and nodal constraint conditions along the width direction, were applied along the span length, in the plan of the symmetry. The upper roll was modelled as cylindrical boundary surfaces, while the lower forming roll was modelled as single tool consisting of two boundary surfaces (cylindrical and conical types). The cylindrical type was modelled in the channel web region, while the conical type was modelled in the channel flange region. Generally, friction factors in sheet metal forming processes can be measured experimentally, using special testing devices mounted on standard tensile machines [12–14]. The friction layer in the EPFEP3 program is transitory and uses the friction factor [15], to imitate different lubricants. Due to lack of information on the experiments conducted mainly the frictional conditions, it was decided to specify a friction factor of m = 0.5, that provides stable contact between rolls and FE mesh, during the rolling simulation. Maintaining this contact during the rolling simulation is important, for the effectiveness of the friction layer technique that assists mesh movement, along the rolling direction. In the first FE model, the upper roll was displaced incrementally toward the lower forming roll, while the undeformed FE mesh in between (as pressing stage) was used to predict the deformed mesh. Applying rotational displacements (rolling increments) was followed on the upper and lower rolls. In the second model, the pressing stage was eliminated and strip-rolling simulation was carried out from the beginning, on a created pre-deformed mesh.
4. Discussion of preliminary simulation results Initially a coarse longitudinal elements, were used in the FE mesh generation mainly in roll gap area, however, it was found later, that fine longitudinal elements are required for predicting stable rolling simulation, using friction layer technique [15]. Furthermore, and in order to increase the efficiency of rolling simulation, roll penetration in the FE mesh was further increased to allow more elements in contact with boundary surfaces, in the rolls gap. Moreover, its was also found decreasing rolling increments is very important to predict stable and efficient rolling simulation. The simulation results for the first pressing stage, showed unstable numerical computation, when a fine mesh was used in the deformation zone, in the area near roll gap. However, stable numerical computations were observed, for the second rolling stage after mesh refinement, increasing the roll penetration and decreasing rolling increments. For this reason the pressing stage was eliminated, and rolling simulation was carried out from the beginning on a pre-deformed mesh through the second FE model. Two approaches for determining the initial mesh shape, were investigated using the second FE model. The first of which involved creating the FE mesh assuming a linear deformation between the rolling stands. The second approach, involved creating the FE mesh using the bend angle curve, based on the geometric restrictions imposed by the lower roll [16]. It was found that the application of the second method is more realistic and practical, especially when the friction layer technique was involved. This is because the latter method provides wide contact area between the mesh and the lower side roll, which is essential in the effectiveness of the friction layer technique. Finally, it was concluded that these techniques need more computational time, to reach the fully developed membrane strain distributions. Re-meshing
A. Alsamhan et al. / Journal of Materials Processing Technology 142 (2003) 102–111
was therefore introduced to address these problems. Details of these preliminary simulation results can be found in reference [10]. Dual mesh and real time re-meshing was developed by the authors [8] to address these problems. It was found that compete simulation can be obtained and the computational time could also be, saved using this technique on a benchmark FE model.
5. CRF computer simulation using dual mesh and re-meshing FE model In this section, the application of the dual mesh FE model is applied to the simulation of CRF of a trapezoidal chan-
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nel section, for a single forming stand with a 20◦ fold angle. Three FE models were investigated. For all cases, the FE mesh was set up for a single pass, using the bend angle curve based on roll geometric restrictions of the lower side roll [16]. In the beginning of the computer simulation, vertical constraint conditions were applied on the nodes located along the mesh trailing edge, to represent the guiding model. Next, the nodes located at the channel flange length only (along the mesh trailing edge), were unconstrained. Fig. 3 illustrates the general set up of the computational mesh and the forming rolls. To save computational time, half of the model was considered, as shown in Fig. 3. Table 2 illustrates the general configuration of the FE models. Refining the fine
Fig. 3. General configuration of the computational mesh and boundary surfaces utilised with dual mesh FE models 1, 2 and 3.
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Table 2 General configuration and computational parameters of the dual mesh FE models Model
Computational time (min) (EPFEP3)
Transfer time (CRF program) (min)
Number of the utilised nodes and elements
Rolling increment (◦ )
1 2 3
3.053 3.38 3.4
5.4 6.79 15.57
16082 × 7300 (fine mesh), 858 × 380 (computational mesh) 40172 × 18250, 990 × 440 44400 × 20339, 1464 × 660
0.01 0.01 0.0005
Fig. 4. Variation of the computational mesh configuration and boundary surface contact area during re-meshing phases for FE model 1, for increments 1, 999 (8.975 mm) and 2499 (22.45 mm).
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Fig. 5. Generalised plastic strain contours of the re-meshed computational mesh given for increments 1, 1999 and 2499 for FE model 1.
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mesh is the main difference between model 1 and model 2; it was 0.2 mm longitudinal length for model 1 compare to 0.08 mm in model 2. This was adopted to decrease the roll penetration, hence minimising the mesh thinning, and also maintaining more fine longitudinal elements in the roll gap, for efficient rolling simulation. Roll penetration was 3.5 m in model 1 compared to 0.25 m in model 2. Furthermore, rolling increment was decreased from 0.01◦ in models 1 and 2, to 0.0005◦ in model 3, to investigate maintaining the
mesh-roll contact on the side roll, conical roll, during the rolling simulation.
6. Simulation results and discussions The computer simulation was carried out for nearly 2500 fixed rolling increments using FE model 1, which is equivalent to longitudinal strip displacement of 22.45 mm. It was
Fig. 6. Generalised plastic strain contours of the re-meshed computational mesh given for increments 1, 1499 and 1899, for FE model 2.
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found that, the total computational time is 8.5 min (3.1 min computational time plus 5.4 min transfer time), for each rolling increment. Fig. 4 illustrates the deformed computational mesh for the increments 1, 999 (8.98 mm), and 2499 (22.5 mm) which is equivalent to the quoted total rolling displacements in mm. The figure illustrates the mesh-roll contact areas (the dark shaded element faces) and the variation in the computational mesh configuration during the re-meshing phases. The mesh-roll contact was maintained during the rolling simulation at the element faces located at the channel web area (dark shaded areas in Fig. 4). Hence,
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a stable numerical computation was obtained and a forward movement of the mesh through the roll gap was produced. Fig. 5 illustrates the generalised plastic strain contours of the computational mesh for the rolling increments 1, 1999 and 2499. It can be seen that plastic strains are concentrated along the channel web rolling area, which is not the case in actual CRF. The larger generalised plastic strain at the channel web area can be attributed to high roll penetration in the FE mesh. This results in a thickness reduction, which is not found in CRF processes. This will also affect, the proper prediction of the membrane strain at the channel web
Fig. 7. Membrane strain distributions as (a) channel flange edge, and (b) channel web centre for different rolling increments given for FE model 2.
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centre near and in the roll gap. Roll penetration must be selected minimum to predict accurate deformation. However, the efficient rolling simulation can be obtained when more element faces in contact with upper and lower roll, which can be achieved by increasing the roll penetration in the FE mesh. Decreasing the roll penetration and increasing number of the longitudinal element faces in contact, with upper and lower rolls can be achieved by refining the fine elements in the roll gap. The computer simulation was executed for 1899 fixed rolling, which equivalent to 17.1 mm rolling displacement using model 2. It was found that 3.4 min was required to execute one rolling increment, while 6.8 min was the transfer time between the dual meshes. Hence, the total computational time was 10.2 min per each rolling increment. The computer simulation with model 2, shows stable numerical computation and smooth predicted deformation. The generalised plastic strain contours of the computational mesh during re-meshing are shown in Fig. 6, for increments 1, 1499 (13.5 mm) and 1899 (17.1 mm) for model 2. Unlike the results of model 1, the maximum plastic strain is concentrated at the bend zone and along the rolling direction, which is the case in actual CRF process. Furthermore, the predicted plastic strain at the channel flange edge, and along rolling direction, can be attributed to the longitudinal stretching and bending along rolling direction. The predicted membrane strain distributions at the channel flange edge and the web centre, for different rolling increments, are shown in Fig. 7a and b, respectively (for model 2). The predicted membrane strain distribution, at channel flange edge (Fig. 7a) shows similar trends as the experimental work up to a strip distance of 134 mm. The predicted peak membrane strain is smaller than the experimental measured strain, and shifted left from the position of the experimental peak value by 12 mm. The predicted strain distribution shows, some disturbances near and after roll centre line (see the strain distribution in Fig. 7a after 134 mm strip distance). The predicted membrane strain distribution, at the web centre shows a similar trend to the experiment for up to a strip distance of 141 mm (see Fig. 7b). The predicted strain distribution shows, disturbances near and after the roll centre line mainly after a strip distance of 144 mm. The rolling increment was decreased significantly form 0.01◦ , in models 1 and 2, to 0.0005◦ , in model 3. In the beginning of the computer simulation, in the first increment, very wide contact area was found, however, during the computer simulation this contact area gradually becomes narrow and ineffective, to continue rolling with friction and eventually the contact was lost. Hence, predicting accurate membrane strain distributions becomes difficult with FE models use rolling with friction (mainly friction layer technique [16]). In general, the total simulation time using either model 1 or 2, is very high, and impractical from an industrial point of view. For example, executing 2500 increments using model 1 requires approximately 400 h, which is very high and totally impractical for the industry. This can be attributed mainly
due to the utilisation of low speed computers and low speed data storage. Using a high-speed computer and quick access storage hardware do significantly decrease the computation time by 60 times.
7. Conclusions From the simulation results of the dual mesh and remeshing FE model, it can be concluded that the FE model introduced is an efficient technique and can be used to model and simulate CRF processes. This is because the deformation history, such as the geometric information, strains and stresses are maintained in the fine mesh. In general the simulation results illustrate satisfactory results compared to the practical CRF process. The accuracy of the results is a function of the selected configurations of the computational mesh, especially in the main deformation zones, and the refined elements in the fine mesh.
References [1] S. Geyer, Process simulation for profile rolling, The MARC News Letter, MARC Analysis Research Corp., January 1993, pp. 6–11. [2] S. Geyer, N. Stricker, Neue Perspektiven fur die Umformtechnik. 5. Umformtechnisches Kolloquium, Institute for Production Technology, University of Darmstadt, Germany, 1994, p. 16.1. [3] F. Heislitz, H. Livatyali, M.A. Ahmetoglu, Simulation of roll forming process with the 3-D FEM code PAM-STAMP, J. Mater. Process. Technol. 59 (1996) 59–67. [4] N. Rebelo, J.C. Nagtegaal, L.M. Taylor, Comparison of implicit finite-element methods in the simulation of metal forming processes, in: Numerical Methods in Industrial Forming Processes, Chenot, Wood & Zienkiewicz, 1992, pp. 99–108. [5] C.K. McClure, H. Li, Roll forming simulation using finite-element analysis, Manuf. Rev. 8 (1995) 114. [6] R.S. Senanayake, I.M. Cole, S. Thiruvarudchelvan, The application of computational and experimental techniques to metal deformation in cold-roll-forming, J. Mater. Process. Technol. 45 (1994) 155–160. [7] K.F. Chiang, Cold roll forming, M.Sc. Thesis, Mechanical Engineering Department, University of Auckland, August 1984. [8] A. Alsamhan, I. Pillinger, P. Hartely, The development of real time re-meshing technique for simulating cold-roll-forming using FE methods, in press. [9] I. Pillinger, The prediction of metal flow and properties in threedimensional forging using the finite-element method, Ph.D. Thesis, School of Manufacturing and Mechanical Engineering, The University of Birmingham, 1984. [10] A. Alsamhan, The development of finite-element models and re-meshing techniques in the computer simulation of cold-rollforming, Ph.D. Thesis, School of Manufacturing and Mechanical Engineering, The University of Birmingham, 1999. [11] T. Altan, F.W. Boulger, J.R. Becker, N. Akgerman, H.J. Henning, Forging equipment, material and practices, Battle Columbus Laboratories, Metal Working Division, Air Force Material Laboratory, Wright-Patterson Air Force Base, October 1973. [12] Y. Kong, Y. Sun, X. Wang, Development of new friction test device in sheet forming, in: A. Altan (Ed.), Proceedings of the Fifth ICTP, vol. 2, Columbus, OH, USA, 7–10 October 1996, pp. 835–838. [13] X. Wang, J. Duncan, M. Devenpeck, Punch friction test for sheet metal forming, J. Appl. Metalwork. 3, 3.
A. Alsamhan et al. / Journal of Materials Processing Technology 142 (2003) 102–111 [14] W. Wang, R. Wagoner, Realistic friction test in sheet forming, in: Proceedings of the Fourth ICTP, 1993, pp. 1495–1500. [15] G.W. Rowe, C.E.N. Sturgess, P. Hartley, I. Pillinger, Finite-element Plasticity and Metal Forming Analysis, Cambridge University Press, Cambridge, 1991.
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[16] S.M. Panton, S.D. Zhu, J.L. Duncan, Geometric constraints on the forming path in roll forming channel sections, in: Proceedings of the Institution of Mechanical Engineers, J. Eng. Manuf. 206 (1992) 113–118.