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Optimization of open die forging of round shapes using FEM analysis
Journal of Materials Processing Technology 172 (2006) 88–95
Optimization of open die forging of round shapes using FEM analysis S.K. Choi a , M.S. Chun b , C.J. Van Tyne c , Y.H. Moon a,∗ a
Engineering Research Center for Net Shape and Die Manufacturing, Department of Mechanical Engineering, Pusan National University, San 30, Jangjeondong, Pusan 609-735, Republic of Korea b Research Institute of Industrial Science and Technology, Steel Processing Div., Pohang, Republic of Korea c Department of Metallurgical and Materials Engineering, Colorado School of Mines, Golden, CO 80401, USA Received 14 February 2005; received in revised form 26 April 2005; accepted 9 September 2005
Abstract A three-dimensional rigid-plastic finite element method (FEM) analysis has been performed to optimize an open die forging process in the production of circular shapes (i.e. round bars, spindles, rotors, etc.). In producing circular shapes by open die forging, it is difficult to achieve the optimal set of process parameters by trial and error within an industrial environment. In this study, the finite element method was used to analyze the practice of open die forging, focusing on the effects of feed rate and rotation angle for optimal forging pass design. The optimal combination of feed rate and rotation angle has been determined by quantifying the radius profile in the longitudinal direction and roundness of the product. From an analysis of the results, optimal process conditions are proposed for the production of circular shapes with good dimensional accuracy by open die forging. © 2005 Elsevier B.V. All rights reserved. Keywords: FEM; Open die forging; Round bar; Feed rate; Rotation angle
1. Introduction Open die forging is a metal forming process in which a workpiece is pressed between flat or simple contoured dies with a series of compressive blows [1–8]. The workpiece is manipulated and/or rotated between blows. Cylindrical steel components made in small quantities from large ingots, such as turbine rotors, spindles, or rolling mill rolls, are in great demand. In order to minimize subsequent machining, these large components require deformation to the approximate final geometry in an open die forging press. To achieve the required deformation, the open die forging process is used as the initial step in the manufacture of such large products. Open die forging reduces the cross section and increases the length of the workpiece by repetitive pressing and alternate rotation. The process is carried out incrementally; with only a part of the workpiece being deformed at each stage. The tooling for the press is a set of flat or curved dies, which can be produced economically. The tool sizes are quite small compared with the overall size of the forgings. Since only a portion of the workpiece is being deformed at any
∗
Corresponding author. E-mail address: [email protected] (Y.H. Moon).
0924-0136/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2005.09.010
one time the requisite forging loads are less than those needed to deform the entire workpiece. The reduced forging loads mean that a lower capacity machine can be used to produce a given part. The primary goal of such an incremental forging process is the compressing or upsetting of the material step-by-step until it reaches the final target shape. The quality of the open die forging depends on several controlling parameters; for example, die width, die configuration, die overlap, die stagger, ingot shape, temperature gradient, draft design, pass schedule, etc. There have been a number of studies in the past, which have modeled the open die forging process. Kiefer and Shah [6] analyzed the effect between die width ratio and height reduction for block ingot using flat dies. Based on the rigid-viscoplastic formulation, three-dimensional finite element analyses were performed by Park and Kobayashi [7]. Sun et al. [8] used simplified three-dimensional elements to analyze a three-bite flat bar forging under the assumption that the longitudinal velocity components of any material point were independent of the point’s coordinate in the transverse direction. The optimizations of hot forging process using a computer model which predicts flow and microstructure were also performed by Evans et al. [9,10] to further an understanding of the microstructural evolution during hot working. In the previous analyses of round billet forging, finite element simulation was successfully applied to optimize
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Table 1 Analysis condition
Feed rate (mm/rotation angle) Rotation angle (◦ )
Round forging step
Finish forging step
120, 150, 180, 200, 220 90, 120
50, 70, 90 45, 90, 120
Fig. 1. Cross sections for pass sequence from square billet to round bar.
the shape of anvil and pass schedule in preventing the forging cracks [11,12]. For the analysis in this paper, three-dimensional rigid-plastic finite element method (FEM) was performed for a given tooling in order to optimize the open die forging operation such as feed rate and rotational angle for the proper pass schedule and dimensional precision. Fig. 1 shows the billet cross section for a pass sequence from a square billet to a round bar. The pass sequence is roughly square to octagon to round, where reduction ratio only varies every second pass. A square is forged to a rectangular section with a given height reduction, turned 90◦ and then forged again with the same reduction and same bite ratio, producing a new square cross section of smaller size. The newly obtained square bar is then forged into an octagonal bar, which is an intermediate shape between square and round. Finally, the round bar is produced in successive passes by deforming the octagonal bar. The octagonal bar has a greater cross sectional area than the final round bar. The round bar is finished in a round-contoured die during the finishing passes. Fig. 2 shows the overall forging sequence from a square billet to a round bar. To make a round bar in open die forging, the most important step from a product quality perspective is from octagon to round. Hence, in this study, three-dimensional rigid-plastic finite element analysis was used to optimize the open die forging of an octagonal bar into a round bar. A commercially available threedimensional finite element code, DEFORM-3D, was used for the analysis. The focus is on the effects of feed rate and rotation
Fig. 3. The initial mesh of octagonal bar.
angle for optimal forging pass design. The radius profile in the longitudinal direction and roundness of the bar are used to determine the quality of the product. Various combinations of feed rates and rotation angles were simulated, with the radius profile and roundness determined after the simulation was complete. From the results, forging conditions are proposed for making a round bar with good dimensional accuracy. 2. Finite element analysis 2.1. Analysis conditions Table 1 shows the analysis conditions to study the effect of open die forging parameters on the quality of a round product. 2.2. Workpiece and mesh system For comparison with operational results, the geometry and material properties of the workpiece were supplied by a commercial forge. Fig. 3 shows the meshed geometry of the octagonal bar, and the convergence tolerance was used in the calculations. Due to symmetric geometry and boundary conditions, only one-half (or sometimes one-quarter) of the workpiece is considered in the computations. Table 2 shows the material properties Table 2 Input values for FE analysis
Fig. 2. Overall forging sequence from square billet to round bar.
Thermal conductivity (W/m K) Heat capacity (N/mm2 ◦ C) Convective heat transfer coefficient (N/s mm ◦ C) Shear friction constant Temperature (◦ C)
24.3–24.7 3.588 0.004 0.3 1000
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Fig. 4. Schematic drawing of dies with round bar.
of the AISI-H13 used for the workpiece. The experimentally obtained deformation resistance, Km , as a function of strain and temperature for the H13 workpiece is: 10052 0.14294 Km = (0.009128ε ) exp (1) kg/mm2 T where ε is the effective plastic strain and T is the temperature in K. The heat flow from the workpiece to the environment was simplified as convective losses with a higher value of the convective heat transfer coefficient to account for radiation losses. 2.3. Die configurations Fig. 4 shows a schematic of the round-contoured die (anvil) used in the simulations. The loading was applied by specifying constant velocities for the upper and the lower dies. The workpiece was deformed through surface contact between the die and workpiece. 3. Results and discussion
diameter is larger than 250 mm, the reduction amount necessary to achieve the target diameter of 250 mm will be larger, and it can be determined by Eq. (2). Fig. 6(a) shows the reduction obtained from the finite element method to make a round bar having 250 mm diameter, from the octagonal bar with an inscribed circle diameter of 250 mm. The reduction has been determined when the round die completely touches the surface of deforming octagon. For the initial stage (i.e. feed = 0 mm), the octagonal bar is forged down 11 mm, turned 90◦ and forged down again 22 mm, turned 90◦ again and forged down 17 mm, then finally, it is turned 90◦ and forged down 6 mm. Then, the octagonal bar is axially moved (fed forward) 150 mm, and forged again with rotation through the four 90◦ rotations. The discrepancy between the value of 20.6 mm reduction calculated by Eq. (2), and the various reductions at each pass obtained from finite element analysis, is due mainly to the incremental nature of the open die forging process. Only part of the workpiece is deformed at each stage. Since the die width is small compared with the overall length of the octagonal bar, the spread and the non-uniform deformation in prior reduction passes directly influence the subsequent passes.
3.1. Determination of reduction amount The amount of reduction (r) to forge the octagonal bar into round bar can be approximately determined by: r=
S − D0 cos(22.5◦ )
(2)
where S is diameter of inscribed circle within the octagon, and D0 is target diameter. Fig. 5 shows the inscribed circle for an octagonal cross sectional shape. To make a round bar with a 250 mm diameter, the reduction amount calculated by Eq. (2) is 20.6 mm for an octagon with an inscribed circle of diameter of 250 mm. If the inscribed circle
Fig. 5. Cross section of octagonal bar.
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Fig. 7. Round forged shape for 150 mm feed rate.
For the best coordination between the press and the manipulator, it is important to know that a bar being squeezed between the two flat dies not only spreads and elongates in width, but also elongates in length. The manipulator feed rate, or bite, is an important factor in all calculations used to analyze the forging process. The feed rate must be kept within close tolerances to ensure that the pre-calculation of the spread is correct.
Fig. 6. Minimum reduction to make round bar having 250 mm diameter (a) round forging and (b) finish forging.
Fig. 6(b) shows the reduction obtained from finite element method for finish forging of a round forged bar with a 250 mm diameter. The reduction was determined when the round die completely touches the surface of the deforming octagon. For the initial stage (i.e. feed = 0 mm), the octagonal bar is forged down 6 mm, turned 45◦ and forged down again 10 mm, turned 45◦ again and forged down 9 mm and finally turned 45◦ and forged down 3 mm. The octagon is axially moved (fed forward) 70 mm and forged again with the three rotations. Similar to the round forging shown in Fig. 6(a), the reductions in the finish forging are also influenced by the prior reduction due to the spread and non-uniform deformation, but the reduction amounts are smaller than those of round forging. The optimal reduction amount for round forging must be determined after considering the effects of non-uniform deformation during the prior passes. 3.2. Effect of feed rate Fig. 7 shows the shape of a partially forged octagonal bar into a round bar. Fig. 7 shows examples of deformed products at 150 mm feed interval, with a 90◦ rotation between each feed step.
Fig. 8. (a) Radius profile in longitudinal direction and (b) radius variance for round forging.
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Fig. 8(a) shows the radius profile in the longitudinal direction at various feed rates, with a 90◦ rotation after each step for the round forging sequence. As the figure shows, the profiles in the initially forged zone are similar regardless of the feed rates, while the variation in radius in the longitudinal direction increases with the feed rate. Fig. 8(b) shows the variation of the radius in the longitudinal direction that has been quantitatively calculated. As Fig. 8(b) shows, the variance for 120 and 150 mm feed rates are similar, while for a feed rate of more than 180 mm, the variance increases significantly. Therefore, to have a high quality forging at high productivity, a 150 mm feed rate is desirable. A more general expression for the desirable feed rate is 0.6 times the target diameter of the round bar. Fig. 9(a) shows the radius profile in the longitudinal direction for various feed rates, with 45◦ rotation between each step for the finish forging sequence. The variance of the radius in the longitudinal direction is shown in Fig. 9(b). As seen in the figure, the variation in radius increases with feeding rate, but the level of variance for the finish forging is significantly lower than the round forging. 3.3. Effect of rotation angle Figs. 10 and 11 both show the cross sectional shape change as a function of rotation angle during the round bar forging. Figs. 10 and 11 also give examples of the deformed shapes at 90◦ and 120◦ rotation angles, respectively. The roundness of the final bar is strongly dependent on the rotation angle. The roundness for both 90◦ and 120◦ rotation angles have been determined. Fig. 12 shows the roundness obtained for the 90◦ rotation angle.
Fig. 9. (a) Radius profile in longitudinal direction and (b) radius variance for finish forging.
Fig. 10. Deformation shape with rotation angle: (a) 0◦ open, (b) 0◦ forging, (c) 90◦ open and (d) 90◦ forging.
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Fig. 11. Deformation shape with rotation angle: (a) 0◦ open, (b) 0◦ forging, (c) 120◦ open and (d) 120◦ forging.
As Fig. 12 shows, the original octagonal shape is changed to a round shape with successive passes. To investigate the effect of rotation angle on the roundness of the round bar, the variance of radius for 90◦ and 120◦ rotation angles are compared in Fig. 13. In Fig. 13, the roundness of the 90◦ rotation angle is better than that of 120◦ . The poor roundness for the 120◦ rotation angle is primarily caused by the non-symmetric deformation as Fig. 11 shows. Hence, a 90◦ rotation angle is deemed to be most desirable for the round forging sequence. For the finish forging, the roundness for 45◦ , 90◦ and 120◦ rotation angles have been determined. Fig. 14 shows the roundness obtained with a 45◦ rotation angle.
Fig. 12. (a) Quarter section of round bar and (b) radius profile for 90◦ rotation angle for round forging.
Fig. 13. Radius variances at different rotation angles during round forging.
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Fig. 14. (a) Cross section and (b) radius profile for 45◦ rotation angle for finish forging.
To investigate the effect of rotation angle during finish forging on the roundness of the final bar, the variance of radius for 45◦ , 90◦ and 120◦ rotation angles are compared. Fig. 15 shows the variance of radius for 45◦ , 90◦ and 120◦ rotation angles during the finish forging. The variance of a 90◦ rotation angle after five passes is higher than that of 45◦ and 120◦ rotation angles, because the radially bulged area can be effectively forged down during the successive passes. For both 45◦ and 120◦ rotation angles, there is no significant change in radius variance after the fourth pass. These results indicate that a four-pass sequence is enough to finish forge the bar, if either a 45◦ and 120◦ rotation angle is used. The results from the FEM study have been implemented within the control logic of the computerized process control program in a commercial forge shop for the production of round bars. Since the implementation of the results, the productivity of good quality round bars has increased. This increase in productivity and increase in quality indicates the industrial significance of the results from the study and also provides an indirect validation of the FEM analysis results. The flow chart for the implemented control logic in the computer control program is shown in Fig. 16.
Fig. 16. Optimum pass control in round bar.
4. Conclusions A three-dimensional rigid-plastic finite element method was used to model and optimize the open die forging process for making round bars. The significant findings of the study are summarized as follows: (1) The optimal reduction amount for the round forging sequence must be determined with consideration of the effect of non-uniform deformation during prior passes. (2) The radius variance in the longitudinal direction increases with feed rate. The optimal feed rate is 0.6 times the target diameter of the round bar. This optimal feed rate balances forging productivity and the quality of the product. (3) Symmetric deformations at 90◦ rotation angles provide good roundness for the round bar forging process. (4) For the finish forging sequence, 45◦ or 120◦ rotation angles with four-passes are found to produce sufficient roundness in the bar with a minimal number of passes. References
Fig. 15. Radius variances for different rotation angles during finish forging.
[1] K. Tamura, J. Tajima, Optimisation of open die forging condition and tool design, Ironmaking Steelmaking 30 (5) (2000) 405–412. [2] S.P. Dudra, Y.T. Im, Analysis of void closure in open die forging, Int. J. Mac. Tools Manuf. 30 (1990) 65–75. [3] Zhao, G. Wang, R.V. Grandhi, Die cavity design of near flashless forging process using FEM-based backward simulation, J. Mater. Process. Technol. 121 (2002) 173–181.
S.K. Choi et al. / Journal of Materials Processing Technology 172 (2006) 88–95 [4] L. Capan, O. Baran, Calculation method of the press force in a round shaped closed-die forging based on similarities to indirect extrusion, J. Mater. Process. Technol. 102 (2000) 230–233. [5] T. Robert, Die forging stress determination: a dimensional analysis approach, J. Manuf. Sci. Eng. 123 (2001) 416–419. [6] B.V. Kiefer, K.N. Shah, Three-dimensional simulation of open-die press forging, J. Eng. Mater. Technol. (Trans. ASME) 112 (1990) 477–486. [7] J.J. Park, S. Kobayashi, Three dimensional finite element analysis of block forging, Int. J. Mech. Sci. 26 (1984) 165–176. [8] J.X. Sun, G.J. Li, S. Kobayashi, Analysis of spread in flat tool forging by the finite element method, in: Proceedings of 11th North American Research Conference, NAMRI-SME, Dearborn, MI, USA, 1983, pp. 224–231.
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[9] C.A. Dandre, S.M. Roberts, R.W. Evans, R.C. Reed, Microstructural evolution of Inconel718 during ingot breakdown: process modeling and validation, Mater. Sci. Technol. 16 (2000) 15–25. [10] R.W. Evans, Modelling of the hot-working of high performance alloys, Key Eng. Mater. 77–78 (1993) 227–400. [11] K. Yamamoto, Forging technique to prevent cracks in the long round bar analyzed by FEM, in: Proceedings of 13th International Forgemasters Meeting: Advances in Heavy Forgings, vol. 1, 1997, pp. 115– 132. [12] K. Tamura, J. Tajima, Y. Fukutome, Optimisation of spiral forging process design for ensuring dimensional precision of forged round billets by three dimensional rigid-plastic finite element analysis, Ironmaking Steelmaking 30 (2003) 240–248.
Optimization of open die forging of round shapes using FEM analysis S.K. Choi a , M.S. Chun b , C.J. Van Tyne c , Y.H. Moon a,∗ a
Engineering Research Center for Net Shape and Die Manufacturing, Department of Mechanical Engineering, Pusan National University, San 30, Jangjeondong, Pusan 609-735, Republic of Korea b Research Institute of Industrial Science and Technology, Steel Processing Div., Pohang, Republic of Korea c Department of Metallurgical and Materials Engineering, Colorado School of Mines, Golden, CO 80401, USA Received 14 February 2005; received in revised form 26 April 2005; accepted 9 September 2005
Abstract A three-dimensional rigid-plastic finite element method (FEM) analysis has been performed to optimize an open die forging process in the production of circular shapes (i.e. round bars, spindles, rotors, etc.). In producing circular shapes by open die forging, it is difficult to achieve the optimal set of process parameters by trial and error within an industrial environment. In this study, the finite element method was used to analyze the practice of open die forging, focusing on the effects of feed rate and rotation angle for optimal forging pass design. The optimal combination of feed rate and rotation angle has been determined by quantifying the radius profile in the longitudinal direction and roundness of the product. From an analysis of the results, optimal process conditions are proposed for the production of circular shapes with good dimensional accuracy by open die forging. © 2005 Elsevier B.V. All rights reserved. Keywords: FEM; Open die forging; Round bar; Feed rate; Rotation angle
1. Introduction Open die forging is a metal forming process in which a workpiece is pressed between flat or simple contoured dies with a series of compressive blows [1–8]. The workpiece is manipulated and/or rotated between blows. Cylindrical steel components made in small quantities from large ingots, such as turbine rotors, spindles, or rolling mill rolls, are in great demand. In order to minimize subsequent machining, these large components require deformation to the approximate final geometry in an open die forging press. To achieve the required deformation, the open die forging process is used as the initial step in the manufacture of such large products. Open die forging reduces the cross section and increases the length of the workpiece by repetitive pressing and alternate rotation. The process is carried out incrementally; with only a part of the workpiece being deformed at each stage. The tooling for the press is a set of flat or curved dies, which can be produced economically. The tool sizes are quite small compared with the overall size of the forgings. Since only a portion of the workpiece is being deformed at any
∗
Corresponding author. E-mail address: [email protected] (Y.H. Moon).
0924-0136/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2005.09.010
one time the requisite forging loads are less than those needed to deform the entire workpiece. The reduced forging loads mean that a lower capacity machine can be used to produce a given part. The primary goal of such an incremental forging process is the compressing or upsetting of the material step-by-step until it reaches the final target shape. The quality of the open die forging depends on several controlling parameters; for example, die width, die configuration, die overlap, die stagger, ingot shape, temperature gradient, draft design, pass schedule, etc. There have been a number of studies in the past, which have modeled the open die forging process. Kiefer and Shah [6] analyzed the effect between die width ratio and height reduction for block ingot using flat dies. Based on the rigid-viscoplastic formulation, three-dimensional finite element analyses were performed by Park and Kobayashi [7]. Sun et al. [8] used simplified three-dimensional elements to analyze a three-bite flat bar forging under the assumption that the longitudinal velocity components of any material point were independent of the point’s coordinate in the transverse direction. The optimizations of hot forging process using a computer model which predicts flow and microstructure were also performed by Evans et al. [9,10] to further an understanding of the microstructural evolution during hot working. In the previous analyses of round billet forging, finite element simulation was successfully applied to optimize
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Table 1 Analysis condition
Feed rate (mm/rotation angle) Rotation angle (◦ )
Round forging step
Finish forging step
120, 150, 180, 200, 220 90, 120
50, 70, 90 45, 90, 120
Fig. 1. Cross sections for pass sequence from square billet to round bar.
the shape of anvil and pass schedule in preventing the forging cracks [11,12]. For the analysis in this paper, three-dimensional rigid-plastic finite element method (FEM) was performed for a given tooling in order to optimize the open die forging operation such as feed rate and rotational angle for the proper pass schedule and dimensional precision. Fig. 1 shows the billet cross section for a pass sequence from a square billet to a round bar. The pass sequence is roughly square to octagon to round, where reduction ratio only varies every second pass. A square is forged to a rectangular section with a given height reduction, turned 90◦ and then forged again with the same reduction and same bite ratio, producing a new square cross section of smaller size. The newly obtained square bar is then forged into an octagonal bar, which is an intermediate shape between square and round. Finally, the round bar is produced in successive passes by deforming the octagonal bar. The octagonal bar has a greater cross sectional area than the final round bar. The round bar is finished in a round-contoured die during the finishing passes. Fig. 2 shows the overall forging sequence from a square billet to a round bar. To make a round bar in open die forging, the most important step from a product quality perspective is from octagon to round. Hence, in this study, three-dimensional rigid-plastic finite element analysis was used to optimize the open die forging of an octagonal bar into a round bar. A commercially available threedimensional finite element code, DEFORM-3D, was used for the analysis. The focus is on the effects of feed rate and rotation
Fig. 3. The initial mesh of octagonal bar.
angle for optimal forging pass design. The radius profile in the longitudinal direction and roundness of the bar are used to determine the quality of the product. Various combinations of feed rates and rotation angles were simulated, with the radius profile and roundness determined after the simulation was complete. From the results, forging conditions are proposed for making a round bar with good dimensional accuracy. 2. Finite element analysis 2.1. Analysis conditions Table 1 shows the analysis conditions to study the effect of open die forging parameters on the quality of a round product. 2.2. Workpiece and mesh system For comparison with operational results, the geometry and material properties of the workpiece were supplied by a commercial forge. Fig. 3 shows the meshed geometry of the octagonal bar, and the convergence tolerance was used in the calculations. Due to symmetric geometry and boundary conditions, only one-half (or sometimes one-quarter) of the workpiece is considered in the computations. Table 2 shows the material properties Table 2 Input values for FE analysis
Fig. 2. Overall forging sequence from square billet to round bar.
Thermal conductivity (W/m K) Heat capacity (N/mm2 ◦ C) Convective heat transfer coefficient (N/s mm ◦ C) Shear friction constant Temperature (◦ C)
24.3–24.7 3.588 0.004 0.3 1000
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Fig. 4. Schematic drawing of dies with round bar.
of the AISI-H13 used for the workpiece. The experimentally obtained deformation resistance, Km , as a function of strain and temperature for the H13 workpiece is: 10052 0.14294 Km = (0.009128ε ) exp (1) kg/mm2 T where ε is the effective plastic strain and T is the temperature in K. The heat flow from the workpiece to the environment was simplified as convective losses with a higher value of the convective heat transfer coefficient to account for radiation losses. 2.3. Die configurations Fig. 4 shows a schematic of the round-contoured die (anvil) used in the simulations. The loading was applied by specifying constant velocities for the upper and the lower dies. The workpiece was deformed through surface contact between the die and workpiece. 3. Results and discussion
diameter is larger than 250 mm, the reduction amount necessary to achieve the target diameter of 250 mm will be larger, and it can be determined by Eq. (2). Fig. 6(a) shows the reduction obtained from the finite element method to make a round bar having 250 mm diameter, from the octagonal bar with an inscribed circle diameter of 250 mm. The reduction has been determined when the round die completely touches the surface of deforming octagon. For the initial stage (i.e. feed = 0 mm), the octagonal bar is forged down 11 mm, turned 90◦ and forged down again 22 mm, turned 90◦ again and forged down 17 mm, then finally, it is turned 90◦ and forged down 6 mm. Then, the octagonal bar is axially moved (fed forward) 150 mm, and forged again with rotation through the four 90◦ rotations. The discrepancy between the value of 20.6 mm reduction calculated by Eq. (2), and the various reductions at each pass obtained from finite element analysis, is due mainly to the incremental nature of the open die forging process. Only part of the workpiece is deformed at each stage. Since the die width is small compared with the overall length of the octagonal bar, the spread and the non-uniform deformation in prior reduction passes directly influence the subsequent passes.
3.1. Determination of reduction amount The amount of reduction (r) to forge the octagonal bar into round bar can be approximately determined by: r=
S − D0 cos(22.5◦ )
(2)
where S is diameter of inscribed circle within the octagon, and D0 is target diameter. Fig. 5 shows the inscribed circle for an octagonal cross sectional shape. To make a round bar with a 250 mm diameter, the reduction amount calculated by Eq. (2) is 20.6 mm for an octagon with an inscribed circle of diameter of 250 mm. If the inscribed circle
Fig. 5. Cross section of octagonal bar.
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Fig. 7. Round forged shape for 150 mm feed rate.
For the best coordination between the press and the manipulator, it is important to know that a bar being squeezed between the two flat dies not only spreads and elongates in width, but also elongates in length. The manipulator feed rate, or bite, is an important factor in all calculations used to analyze the forging process. The feed rate must be kept within close tolerances to ensure that the pre-calculation of the spread is correct.
Fig. 6. Minimum reduction to make round bar having 250 mm diameter (a) round forging and (b) finish forging.
Fig. 6(b) shows the reduction obtained from finite element method for finish forging of a round forged bar with a 250 mm diameter. The reduction was determined when the round die completely touches the surface of the deforming octagon. For the initial stage (i.e. feed = 0 mm), the octagonal bar is forged down 6 mm, turned 45◦ and forged down again 10 mm, turned 45◦ again and forged down 9 mm and finally turned 45◦ and forged down 3 mm. The octagon is axially moved (fed forward) 70 mm and forged again with the three rotations. Similar to the round forging shown in Fig. 6(a), the reductions in the finish forging are also influenced by the prior reduction due to the spread and non-uniform deformation, but the reduction amounts are smaller than those of round forging. The optimal reduction amount for round forging must be determined after considering the effects of non-uniform deformation during the prior passes. 3.2. Effect of feed rate Fig. 7 shows the shape of a partially forged octagonal bar into a round bar. Fig. 7 shows examples of deformed products at 150 mm feed interval, with a 90◦ rotation between each feed step.
Fig. 8. (a) Radius profile in longitudinal direction and (b) radius variance for round forging.
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Fig. 8(a) shows the radius profile in the longitudinal direction at various feed rates, with a 90◦ rotation after each step for the round forging sequence. As the figure shows, the profiles in the initially forged zone are similar regardless of the feed rates, while the variation in radius in the longitudinal direction increases with the feed rate. Fig. 8(b) shows the variation of the radius in the longitudinal direction that has been quantitatively calculated. As Fig. 8(b) shows, the variance for 120 and 150 mm feed rates are similar, while for a feed rate of more than 180 mm, the variance increases significantly. Therefore, to have a high quality forging at high productivity, a 150 mm feed rate is desirable. A more general expression for the desirable feed rate is 0.6 times the target diameter of the round bar. Fig. 9(a) shows the radius profile in the longitudinal direction for various feed rates, with 45◦ rotation between each step for the finish forging sequence. The variance of the radius in the longitudinal direction is shown in Fig. 9(b). As seen in the figure, the variation in radius increases with feeding rate, but the level of variance for the finish forging is significantly lower than the round forging. 3.3. Effect of rotation angle Figs. 10 and 11 both show the cross sectional shape change as a function of rotation angle during the round bar forging. Figs. 10 and 11 also give examples of the deformed shapes at 90◦ and 120◦ rotation angles, respectively. The roundness of the final bar is strongly dependent on the rotation angle. The roundness for both 90◦ and 120◦ rotation angles have been determined. Fig. 12 shows the roundness obtained for the 90◦ rotation angle.
Fig. 9. (a) Radius profile in longitudinal direction and (b) radius variance for finish forging.
Fig. 10. Deformation shape with rotation angle: (a) 0◦ open, (b) 0◦ forging, (c) 90◦ open and (d) 90◦ forging.
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Fig. 11. Deformation shape with rotation angle: (a) 0◦ open, (b) 0◦ forging, (c) 120◦ open and (d) 120◦ forging.
As Fig. 12 shows, the original octagonal shape is changed to a round shape with successive passes. To investigate the effect of rotation angle on the roundness of the round bar, the variance of radius for 90◦ and 120◦ rotation angles are compared in Fig. 13. In Fig. 13, the roundness of the 90◦ rotation angle is better than that of 120◦ . The poor roundness for the 120◦ rotation angle is primarily caused by the non-symmetric deformation as Fig. 11 shows. Hence, a 90◦ rotation angle is deemed to be most desirable for the round forging sequence. For the finish forging, the roundness for 45◦ , 90◦ and 120◦ rotation angles have been determined. Fig. 14 shows the roundness obtained with a 45◦ rotation angle.
Fig. 12. (a) Quarter section of round bar and (b) radius profile for 90◦ rotation angle for round forging.
Fig. 13. Radius variances at different rotation angles during round forging.
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Fig. 14. (a) Cross section and (b) radius profile for 45◦ rotation angle for finish forging.
To investigate the effect of rotation angle during finish forging on the roundness of the final bar, the variance of radius for 45◦ , 90◦ and 120◦ rotation angles are compared. Fig. 15 shows the variance of radius for 45◦ , 90◦ and 120◦ rotation angles during the finish forging. The variance of a 90◦ rotation angle after five passes is higher than that of 45◦ and 120◦ rotation angles, because the radially bulged area can be effectively forged down during the successive passes. For both 45◦ and 120◦ rotation angles, there is no significant change in radius variance after the fourth pass. These results indicate that a four-pass sequence is enough to finish forge the bar, if either a 45◦ and 120◦ rotation angle is used. The results from the FEM study have been implemented within the control logic of the computerized process control program in a commercial forge shop for the production of round bars. Since the implementation of the results, the productivity of good quality round bars has increased. This increase in productivity and increase in quality indicates the industrial significance of the results from the study and also provides an indirect validation of the FEM analysis results. The flow chart for the implemented control logic in the computer control program is shown in Fig. 16.
Fig. 16. Optimum pass control in round bar.
4. Conclusions A three-dimensional rigid-plastic finite element method was used to model and optimize the open die forging process for making round bars. The significant findings of the study are summarized as follows: (1) The optimal reduction amount for the round forging sequence must be determined with consideration of the effect of non-uniform deformation during prior passes. (2) The radius variance in the longitudinal direction increases with feed rate. The optimal feed rate is 0.6 times the target diameter of the round bar. This optimal feed rate balances forging productivity and the quality of the product. (3) Symmetric deformations at 90◦ rotation angles provide good roundness for the round bar forging process. (4) For the finish forging sequence, 45◦ or 120◦ rotation angles with four-passes are found to produce sufficient roundness in the bar with a minimal number of passes. References
Fig. 15. Radius variances for different rotation angles during finish forging.
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