Iranian Journal of Mechanical Engineering Transactions of ISME

Iranian Journal of Mechanical Engineering Transactions of ISME

A new velocity field for analysis of rod drawing process through curved dies

Authors
Mohammad mehdi Mahdavi
Heshmat allah Haghighat
10.30506/ijmep.2021.109219.1590
Abstract
In this paper, a new velocity field and the upper bound solution of rod drawing process through
arbitrarily curved dies are presented. In analysis, the inlet and outlet shear boundaries of
deformation zone have been assumed as flexible exponential curves. By using the continuity of
material flow and the geometry of the die, mathematical equation of flow curve for each particle
in deformation zone, is defined. By minimizing the required total power with respect to the
shapes of the inlet and outlet shear boundaries, the drawing force has been determined.
The rod drawing process is also simulated by using the finite element code, DEFORM. The
analytical results have been compared with finite element data and the theoretical results
obtained from a classic solution to illustrate the validity of the proposed upper bound solution.
These comparisons show a good agreement. It was found that the proposed approach can result
in lower upper bound predictions while comparing with the results of previous work.
Keywords
Rod drawing
curved die
Velocity field
Upper bound method

Subjects

[1] Avitzur, B., “Analysis of Wire Drawing and Extrusion through Conical Dies of Small Cone Angle”, ASME Journal of Engineering for Industry, Vol. 85, pp. 89-96, (1963).
[2] Avitzur, B., “Analysis of Wire Drawing and Extrusion through Conical Dies of Large Cone Angle”, ASME Journal of Engineering for Industry, Vol. 86, pp. 305-316, (1964).
[3] Chen, C.T., and Ling, F.F., “Upper Bound Solutions to Axisymmetric Extrusion Problems”, International Journal of Mechanical Sciences, Vol. 10, pp. 863-879, (1968).
[4] Nagpal, V., “General Kinematically Admissible Velocity Fields for some Axisymmetric Metal Forming Problems”, ASME Journal of Engineering for Industry, Vol. 96, pp. 1197-1201, (1974).
[5] Oh S.I., Chen, C.C., and Kobayashi, S., “Ductile Fracture in Axisymmetric Extrusion and Drawing-Part I: Deformation Mechanics of Extrusion and Drawing Metal”, ASME Journal of Engineering for Industry, Vol. 101, pp. 36-44, (1979).
[6] Liu, T.S., and Chung, N.L., “Extrusion Analysis and Workability Prediction using Finite Element Method”, Composite Structures, Vol. 36, pp. 369-377, (1990).
[7] Yang, D.Y., Han, C.H., and Lee, B.C., “The use of Generalized Deformation Boundaries for the Analysis of Axisymmetric Extrusion through Curved Dies”, International Journal of Mechanical Sciences, Vol. 27, pp. 653-663, (1985).
[8] Yang, D.Y., and Han C.H., “A New Formulation of Generalized Velocity Field for Axisymmetric Forward Extrusion through Arbitrarily Curved Dies”, ASME Journal of Engineering for Industry, Vol. 109, pp. 161-168, (1987).
[9] Peng, D.S., “An Upper Bound Analysis of the Geometric Shape of the Deformation Zone in Rod Extrusion”, Journal of Material Processing Technology, Vol. 21, pp. 303-311, (1989).
[10] Chevalier, L., “Prediction of Defects in Metal Forming: Application to Wire Drawing”, Journal of Materials Processing Technology, Vol. 32, pp.145-153, (1992).
[11] Zhao, D.W., Zhao, H.J., and Wang, G.D., “Curvilinear Integral of the Velocity Field of Drawing and Extrusion through Elliptic Die Profile”, Transactions of Nonferrous Metals Society of China, Vol. 5, pp. 79-83, (1995).
[12] Lu, Y.H., and Lo, S.W., “An Advanced Model of Designing Controlled Strain Rate Dies for Axisymmetric Extrusion”, Journal of Materials Engineering Performance, Vol. 8, pp. 51-60, (1999).
[13] Luis, C.J., Leon, J., and Luri, R., “Comparison Between Finite Element Method and Analytical Methods for Studying Wire Drawing Processes”, Journal of Materials Processing Technology, Vol. 164-165, pp. 1218-1225, (2005).
[14] Ponalagusamy, R., Narayanasamy, R., and Srinivasan P., “Design and Development of Streamlined Extrusion Dies: A Bezier Curve Approach”, Journal of Materials Processing Technology, Vol. 161, pp. 375-380, (2005).
[15] Chen, D.C., and Huang, J.Y., “Design of Brass Alloy Drawing Process using Taguchi Method”, Materials Science Engineering, Vol. 464, pp. 135-140, (2007).
[16] Gordon, W.A., Van Tyne, C.J., and Moon, Y.H., “Axisymmetric Extrusion through Adaptable Dies-Part I: Flexible Velocity Fields and Power Terms”, International Journal of Mechanical Sciences, Vol. 49, pp. 86-95, (2007).
[17] Gordon, W.A., Van Tyne, C.J., and Moon Y.H., “Axisymmetric Extrusion through Adaptable Dies-Part II: Comparison of Velocity Fields”, International Journal of Mechanical Sciences, Vol. 49, pp. 96-103, (2007).
[18] Gordon, W.A., Van Tyne, C.J., and Moon, Y.H., “Axisymmetric Extrusion through Adaptable Dies-Part III: Minimum Pressure Streamlined Die Shapes”, International Journal of Mechanical Sciences, Vol. 49, pp. 104-115, (2007).
[19] Panteghini, A., and Genna, F., “An Engineering Analytical Approach to the Design of Cold Wire Drawing Processes for Strain-hardening Materials”, International Journal of Material Forming, Vol. 3, pp. 279-289, (2010).
[20] Rubio Alvir, E.M., Sebastian Perez, M.A., and Sanz, L., “A Mechanical Solutions for Drawing Processes under Plane Strain Conditions by the Upper Bound Method”, Journal of Materials Processing Technology, Vol. 143-144, pp. 539-545, (2003).
[21] Gonzalez Rojas, H.A., Calvet, J.V., and Bubnovich, V.I., “A New Analytical Solution for Prediction of Forward Tension in the Drawing Process”, Journal of Materials Processing Technology, Vol. 198, pp. 93-98, (2008).
[22] Rubio Alvir, E.M., Mariin, M., Domingo, R., and Sebastian Perez, M., “Analysis of Plate Drawing Processes by the Upper Bound Method using Theoretical Work-hardening Materials”, International Journal of Advanced Manufacturing Technology, Vol. 40, pp. 261-269, (2009).
[23] Panteghini, A., “An Analytical Solution for the Estimation of the Drawing Force in Three Dimensional Plate Drawing Processes”, International Journal of Mechanical Sciences, Vol. 84, pp. 147-157, (2014).
[24] Zhang, S.H., Chen, X.D., Zhou, J., and Zhao, D.W., “Upper Bound Analysis of Wire Drawing through a Twin Parabolic Die”, Meccanica, Vol. 51, pp. 2099-2110, (2016).
[25] Parghazeh, A., and Haghighat, H., “Prediction of Central Bursting Defects in Rod Extrusion Process with the Method of Upper Bound”, Transactions of Nonferrous Metals Society of China, Vol. 26, No. 11, pp. 2892-2899, (2016).
[26] Haghighat, H., and Mahdavi, M.M., “On the Optimum Die Angle in Rod Drawing Process Considering Strain-hardening Effect of Material”, Iranian Journal of Mechanical Engineering Transaction of ISME, Vol. 20, No. 1, pp. 113-128, (2019)
[27] Balaji, P.A., Sundararajan, T., and Lal, G.K., “Viscoplastic Deformation Analysis and Extrusion Die Design by FEM”, ASME Journal of Applied Mechanics, Vol. 58, pp. 644- 650, (1991).

  • Receive Date 08 June 2019
  • Revise Date 27 February 2020
  • Accept Date 19 June 2021