Prediction of geometric dimensions for cold forgings using the finite element method

Journal of Materials Processing Technology 189 (2007) 459 465 Prediction of geometric dimensions for cold forgings using the finite element method B.Y. Jun a, S.M. Kang b, M.C. Lee c, R.H. Park b, M.S. Joun b,d, a Technology Innovation Center of Gyeongsang National University, Gyeongsang National University, Jinju 660-701, Republic of Korea b School of Mechanical and Aerospace Engineering, Gyeongsang National University, Jinju 660-701, Republic of Korea c Department of Mechanical Engineering, Gyeongsang National University, Jinju 660-701, Republic of Korea d Research Center for Aircraft Parts Technology, Gyeongsang National University, Jinju 660-701, Republic of Korea Received 9 December 2005; received in revised form 21 December 2006; accepted 12 February 2007 Abstract In this paper, a practical approach for systematically estimating the geometric dimensions of cold forgings using the finite element method is presented. The forging process was simulated by a rigid-thermoplastic finite element method under the assumption that the dies and tools are rigid. Die structural and workpiece springback analyses were carried out using the information obtained from the forging simulation. The approach was applied to a test cold forging process. A comparison between predictions and measurements demonstrated that the proposed approach was acceptable for this application. 2007 Elsevier B.V. All rights reserved. Keywords: Cold forgings; Finite element method; Die structural analysis; Springback analysis 1. Introduction The practice of forging has constantly advanced over the years, especially during the recent mass production of mechanical parts that combine a low price with good quality. Without forging technology, the mass production of cars, home appliances, etc., would be impossible. Most mechanical parts need machining after forging or casting. However, this machining leads to increased manufacturing costs since it requires considerable processing time, an investment in equipment, and an increase in labor. Usually, the minimization of a machining process directly reduces the workpiece, labor, and machining costs, which eventually impact on the price competitiveness of the product. Consequently, various attempts to reduce the machining cost have been made. Forging has been one of the best solutions, and precision forging can now be used to achieve a dimensional accuracy of less than 10 m in net-shape manufacturing. Much progress has Corresponding author at: School of Mechanical and Aerospace Engineering, Gyeongsang National University, Gazwa-dong 900, Jinju-City, GyeongNam 660-701, Republic of Korea. Tel.: +82 55 751 5316; fax: +82 55 751 5316. E-mail address: msjoun@gsnu.ac.kr (M.S. Joun). been made in the production of special forging technologies, including the enclosed-die forming method, divided-flow forming method, backpressure forming method, and combined new forging method. The dimensions of forgings are dependent mostly on the elastic deformation of the die and tool, springback of the workpiece, and thermal contraction of the workpiece. Heat treatment can also lead to dimensional changes in forgings. This means that producing accurate predictions of geometric forging dimensions is a difficult task. Research on the elastic deformation of dies and tools has been attempted by a few researchers [1 8], but their results have only been applied to solve very restricted problems. In spite of the importance of precision forging, there have been very few applicable and systematic tools introduced that can predict the dimensions of forgings. Therefore, most process design engineers depend on traditional experience-based rules and trial-and-error approaches to meet dimensional accuracy targets, leading to an increase in the cost and time of the process development. The ability to predict the final dimensions of forgings is of great importance to meet dimensional accuracy requirements in precision forging. In this paper, a useful finite element-based approach for predicting the geometric dimensions of cold forgings is presented with an application example from a cold forging company. The 0924-0136/$ see front matter 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2007.02.030

460 B.Y. Jun et al. / Journal of Materials Processing Technology 189 (2007) 459 465 elastic deformation of the die, springback of the workpiece, and thermal contraction of the workpiece are considered in the proposed approach. 2. Methodology It is impossible to take into account all the factors and correlations when predicting the geometric dimensions of forgings. Consequently, some minor factors must be neglected in order to obtain engineering solutions. All parameters that affect the geometric dimensions of forgings may be more or less coupled, but most research studies neglect these correlations to obtain engineering solutions, as is the case in this study. A rigid-thermoplastic finite element method was employed. The dies and tools were assumed to be rigid in the forging simulation [9]. The simulation results, including force, temperature, and stress information, were employed to analyse the elastic deformation of the die and tool, and springback of the workpiece due to the release of mechanical and thermal loads. We assumed that the forming and thermal loads were removed instantly from the workpiece after forging and that the workpiece behaved elastically and isotropically. To predict the geometry of the workpiece, we added the elastic deformation of the die and tool to the springback of the workpiece, which were calculated independently. The concept explained above is shown in Fig. 1. Fig. 1(a) gives the geometry of the product, which was obtained from a forging simulation under the rigid-die assumption, where P is a point on the workpiece in the figure. Fig. 1(b) describes the die deformation, where d 1 in the figure is the displacement of the workpiece point P due to the die deformation. Fig. 1(c) shows the springback of the workpiece due to the removal of the forming and thermal loads, where d 2 in the figure is the displacement of workpiece point P due to the springback. In Fig. 1(d), the displacement d of point P is calculated by adding d 1 to d 2. 3. Theoretical background Fig. 2 shows a conceptual diagram of a contact problem between two objects. The objects have the same normal vector n i along the contacting interface. If the normal vector points outwards from the object, its corresponding boundary is denoted as Γ c + and the opposite boundary is denoted as Γc. Here, Γ c indicates both Γ c + and Γc. Under the assumption that the interface obeys the law of Coulomb friction, the geometrical and mechanical boundary conditions on Γ c are formulated as follows. In the normal direction: u +c n = u c n if σ n +c = σn c < 0 (1) σ n +c = 0 if u +c n u c n < 0 (2) In the tangential direction: σ t +c = σ t +c = μ σ +c (u c t u +c t ) n u c t u +c t if u c t u +c t (3) Fig. 1. Basic approach used to estimate the geometric dimensions of cold forgings: (a) results of the forging simulation, (b) elastic deformation of the die, (c) springback of the workpiece, and (d) final geometry of the product.

B.Y. Jun et al. / Journal of Materials Processing Technology 189 (2007) 459 465 461 + β t (u +c t Γ ct u c t )(δu +c t δu c t )dγ σ t +c δu +c t dγ = 0 (7) Γ cs where Γ cn ( Γ c ) is the mechanically contacting boundary on which σ n +c < 0, Γ cs and Γ ct (Γ cn = Γ ct Γ cs ) are the boundaries governed by Eqs. (3) and (4), respectively, and β n and β t are large positive constants whose physical meanings can be expressed as: σ n +c = β n (u +c n u c n ) (8) σ t +c = β t (u +c t u c t ) (9) The die is assumed to be linear-elastic and isotropic. In this case, the stress strain relationship can be expressed as: σ ij = E 1 + ν ε νe ij + (1 + ν)(1 2ν) ε kkδ ij αe 1 2ν Tδ ij (10) where E, ν, and α are Young s modulus, Poisson s ratio, and the coefficient of thermal expansion, respectively, T the temperature difference, and δ ij is the Kronecker delta. Here, α may differ from direction to direction as well as from position to position [8]. Detailed solution schemes have been presented and proven in Ref. [8]. Fig. 2. Conceptual diagram of a contact problem: (a) problem description and (b) contact surface. u c t = u +c t if σ +c t <μ σ +c n (4) where μ is the coefficient of Coulomb friction and the subscripts n and t denote the n-component and t-component, respectively, in the local coordinate system shown in Fig. 2. Superscripts +c and c in the stress and velocity components specify their related values at Γ c + and Γc, respectively. For example: u +c n = u i n i, σ n +c = σ ij n i n j on Γ c + (5) u c n = u i n i, σn c = σ ij n i n j on Γc (6) where u i is the displacement vector and σ ij is the stress tensor. Note that n i on Γ c + points outwards from the object while n i on Γc points inwards from the other object. Eqs. (3) and (4) imply that the tangential stress is governed by the law of Coulomb friction if sliding takes place along the interface. The contacting interface is considered to be a no-slip region if the tangential stress is less than μ σ n. Using a penalty method, one can imbed Eqs. (1) and (4) into the virtual work principle as follows: σ ij δε ij dω f i δu i dω t i δu i dγ Γ ti Ω + β n (u +c n Γ cn Ω u c n )(δu+c n δu c n )dγ 4. Application example 4.1. Test cold forging process Fig. 3 describes the cold forging process sequence that was selected as a test for the proposed geometrical estimation approach. This process is quite simple, as shown in the Fig. 3. Forging sequence of the selected test example: (a) first stage and (b) second stage.

462 B.Y. Jun et al. / Journal of Materials Processing Technology 189 (2007) 459 465 Fig. 5. Predicted metal flow lines. Fig. 4. Design of the die set. figure, and thus appropriate for such a test. The process is composed of two cold forging stages. The workpiece was SCM420H, which was annealed before each forging stage. The detailed design of the die and tool geometry employed in the second stage is shown in Fig. 4. The die insert was shrink fitted by a 400 C temperature difference and all the die parts were made of SKD11. Before forging, the die geometry was measured with a precision coordinate measuring machine. This measured geometry was used in the simulation to determine the basic information required to predict the geometric dimensions of the forging. Two cases with t = 5.0 and 4.6 mm, defined in Fig. 3, were considered. The process conditions and material properties used in the simulation are given in Table 1. The thermal properties of the workpiece and die/tool, and the thermal process conditions used in the simulation can be found in Ref. [10]. Since the simulation results of the two cases were nearly the same, only the results of the t = 4.6 mm case are given in Figs. 5 7. Fig. 5 shows the metal flow lines and Fig. 6 shows the traction vectors for which the maximum normal component was 2330 MPa. Fig. 7 shows the temperature distributions, just after forming in Fig. 7(a) and 10 s later in Fig. 7(b). These reveal that the workpiece temperature had risen by an average of 58 C. The traction vectors were used for the deformation analysis of the die as well as the springback analysis of the workpiece, while the temperature distribution was used for the thermal contraction analysis of the workpiece. In this study, the effect of the temperature rise of the die on the material was neglected. 4.2. Die deformation analysis The die structure is shown in Fig. 4. The material properties of the die parts are given in Table 2. Fig. 8 shows the finite element model with boundary conditions that was used for the die structural analysis. The deformation-enlarged configuration of the die structure is given in Fig. 9 with the nodal displacements multiplied by 10. The effective stress distributions are shown in Fig. 10. Table 1 Material properties and process conditions for the cold forging process simulation Flow stress, σ (MPa) 745.3 ε 0.2 Coefficient of Coulomb friction, μ 0.1 Coefficient of thermal expansion, α (/ C) 1.2 10 5 Initial temperature of material ( C) 20 Initial temperature of die ( C) 20 Fig. 6. Stress vectors (MPa).

B.Y. Jun et al. / Journal of Materials Processing Technology 189 (2007) 459 465 463 Fig. 9. Deformation of the die set due to the forming load and shrink fit (Nodal displacements are enlarged 10 times.). 4.3. Springback of the workpiece Fig. 7. Temperature distribution ( C) (a) at the end of the stroke and (b) 10 s after forming. Information used for the analysis of the springback due to the release of mechanical and thermal loads is given in Table 3. The analysis results are given in Fig. 11 with the nodal displacements multiplied by 10. 4.4. Comparison of analysis results with measurements Radial displacements at points P, Q, and R on the workpiece and points P, Q, and R on the die, shown in Fig. 12, were used to compare the analysis results with measurements. The distances measured from the central line to the points P, Q, and R before forming were 22.976, 22.976, and 22.975 mm, respectively. The analyzed and measured results are summarized in Table 4 for t = 4.6 mm and in Table 5 for t = 5.0 mm. When t = 4.6 mm, the predicted radial displacement of point Q due to the springback and thermal contraction of the workpiece was 0.011 mm Table 2 Material properties and process conditions for the die parts Modulus of elasticity, E (GPa) 220 Poisson s ratio, ν 0.3 Coefficient of Coulomb friction, μ 0.1 Coefficient of thermal expansion, α (/ C) 1.2 10 5 Table 3 Material properties and process conditions for the springback of the workpiece Fig. 8. Finite element model for the die structural analysis. Modulus of elasticity, E (GPa) 210 Poisson s ratio, ν 0.3 Coefficient of thermal expansion, α (/ C) 1.2 10 5

464 B.Y. Jun et al. / Journal of Materials Processing Technology 189 (2007) 459 465 Fig. 10. Effective stress distributions (MPa). Fig. 12. Test points selected for comparison in the radial direction: (a) workpiece and (b) die. Fig. 11. Springback of the workpiece due to mechanical and thermal loads (Nodal displacements are enlarged 10 times.). and the predicted radial displacement of the point due to the die deformation was 0.072 mm. Thus, the related point of the workpiece moved outwards by 0.083 mm so that the predicted dimension of the forging was 0.083 mm greater than that of the die. The difference between the radius of the die and workpiece in the measurements taken at point Q was 0.058 mm, yielding a prediction error of approximately 30%. The errors at points P and R, calculated in the same manner, were 38% and 8%, respectively. As shown in Table 5, the results of the t = 5.0 mm case were nearly the same. The same procedures were applied to investigate the accuracy of the proposed geometric estimation approach in the axial direction. The difference y between the two points A and B shown in Fig. 13 was obtained for both the predictions and measurements. The prediction considered the springback, thermal contraction of the workpiece, and deformation of the die (see Fig. 14). The results are summarized and compared in Table 6. Table 4 Comparison of the predicted radial displacements against measured values for t = 4.6 mm P Q R Deformation of die, d 1 (mm) 0.061 0.072 0.067 Springback of material, d 2 (mm) 0.015 0.011 0.003 Prediction, d = d 1 + d 2 (mm) 0.076 0.083 0.070 Measurement, a (mm) 0.047 0.058 0.076 d/a (%) 62 70 108 Table 5 Comparison of the predicted radial displacements against measured values for t = 5.0 mm P Q R Deformation of die, d 1 (mm) 0.059 0.076 0.060 Springback of material, d 2 (mm) 0.016 0.015 0.004 Prediction, d = d 1 + d 2 (mm) 0.075 0.091 0.064 Measurement, a (mm) 0.050 0.061 0.065 d/a (%) 67 67 101

B.Y. Jun et al. / Journal of Materials Processing Technology 189 (2007) 459 465 465 The differences between the predictions and measurements were less than 9%. 5. Conclusions Fig. 13. Definition of y. In this paper, a systematic approach for predicting the geometric dimensions of cold forgings was proposed. The approach employed a rigid-thermoplastic finite element method to simulate the forging and an elastic finite element method to model both the elastic deformation of the die and provide a springback analysis of the workpiece. Both the mechanical and thermal loads were considered in the springback analysis. The mechanical load was applied due to the elastic unloading of the forming load while the thermal load was applied due to the cooling of the increased forging temperature to room temperature. All of the results were superposed to yield the final dimensions of the cold forged product. The predictions were compared with measurements and results were qualitatively very close. With the support of experience, the proposed approach can be a useful tool for process design in precision cold forging. Acknowledgement This work was supported by the K-MEM R&D Cluster Project of Kyongnam Province in Korea. References Fig. 14. Test points for comparison in the axial direction: (a) workpiece and (b) die. Table 6 Comparison of predicted vs. measured axial displacements t = 4.6 mm t = 5.0 mm Deformation of die, y S (mm) 0.115 0.110 Springback of material, y D (mm) 0.058 0.058 Prediction, A = y S + y D (mm) 0.173 0.156 Measurement, B (mm) 0.170 0.170 (B/A) 100 (%) 98 109 [1] U. Engel, M. Hansel, FEM-simulation of fatigue crack growth in cold forging dies, in: Advanced Technology of Plasticity 1990: Proceedings of the 3rd International Conference on Technology of Plasticity, vol. 1, Kyoto, Japan, 1990, pp. 355 360. [2] Z. Xing-hua, Finite element analysis of container and accuracy control of extrusion products, in: Advanced Technology of Plasticity 1990: Proceedings of the 3rd International Conference on Technology of Plasticity, vol. 1, Kyoto, Japan, 1990, pp. 343 348. [3] K. Lange, A. Hettig, M. Knoerr, Increasing tool life in cold forging through advanced design and tool manufacturing techniques, J. Mater. Process. Technol. 35 (1992) 495 513. [4] K.F. Hoffmann, K. Lange, Computation of the elastic expansion and stresses in cold extrusion dies with non-axisymmetric inner shape, Trans. NAMRI/SME 17 (1989) 71 78. [5] S. Takahashi, C.A. Brebbia, Forging die stress analysis using boundary element method, in: Advanced Technology of Plasticity 1990: Proceedings of the 3rd International Conference on Technology of Plasticity, vol. 1, Kyoto, Japan, 1990, pp. 203 210. [6] Y. Ochial, R. Wadabayashi, Application of boundary element method to cold forging die design, in: Advanced Technology of Plasticity 1987: Proceedings of the 2nd International Conference on Technology of Plasticity, vol. 1, Stuttgart, Germany, 1987, pp. 37 42. [7] M. Fu, B. Shang, Stress analysis of the precision forging die for a bevel gear and its optimal design using the boundary-element method, J. Mater. Process. Technol. 53 (1995) 511 520. [8] M.S. Joun, M.C. Lee, J.M. Park, Finite element analysis of prestressed die set in cold forging, Int. J. Mach. Tools Manuf. 42 (2002) 1214 1222. [9] M.S. Joun, M.C. Lee, Quadrilateral finite-element generation and mesh quality control for metal forming simulation, Int. J. Numer. Methods Eng. 40 (1997) 4059 4075. [10] M.S. Joun, H.K. Moon, R. Shivpuri, Automatic simulation of a sequence of hot-former forging processes by a rigid-thermoviscoplastic finite element method, J. Eng. Mater. Technol. Trans. ASME 120 (1998) 291 296.