Analysis of the central cavity of axisymmetric forward extrusion by the upper bound approach

1992 ◽  
Vol 1 (3) ◽  
pp. 409-413 ◽  
Author(s):  
S. Wu ◽  
M. Li
Keyword(s):  
Upper Bound ◽  
Central Cavity ◽  
Forward Extrusion

Analysis of Combined Backward-Forward Extrusion

1976 ◽  
Vol 98 (2) ◽  
pp. 438-445 ◽  
Author(s):  
B. Avitzur ◽  
W. C. Hahn ◽  
M. Mori
Keyword(s):  
Upper Bound ◽  
Process Parameter ◽  
Total Power ◽  
Deformation Region ◽  
Forward Flow ◽  
Forward Extrusion ◽  
Combined Flow ◽  
Dependent Parameter ◽  
Independent Process

The upper bound approach is used to analyze combined backward-forward extrusion. The deformation region is divided into five zones separated by planer and cylindrical surfaces of velocity discontinuities. The internal power of deformation and shear and friction losses are computed individually and summed. The pseudo-independent process parameter is the backward rate of flow with respect to which the total power of deformation is optimized. The optimal backward rate of flow is assumed to be the actual one. Thus, the backward rate of flow becomes a dependent parameter to be studied through this analysis. Conditions covering backward rates of flow from zero to maximum are demonstrated graphically. Examples are given for which combined flow results and for which either only forward flow or only backward flow occur.

Mechanical Solutions for Hot Forward Extrusion under Plane Strain Conditions by upper Bound Method

2008 ◽  
Vol 367 ◽  
pp. 201-208 ◽  
Author(s):  
Rosario Domingo ◽  
A.M. Camacho ◽  
E.M. Rubio Alvir ◽  
M.A. Sebastián
Keyword(s):  
Plane Strain ◽  
Upper Bound ◽  
Analytical Methods ◽  
Mechanical Parameters ◽  
Upper Bound Method ◽  
Zone Length ◽  
Forward Extrusion ◽  
Dead Metal Zone ◽  
Fractional Reduction ◽  
The Dead

This paper present a study focused on hot forward extrusion by upper bound method. In particular, hot forward extrusion of plates through square face dies under plane strain conditions. Slater defines the models used for large fractional reduction. Different models have been taken in account; they are dissimilar in relation to the dead metal zone (if covers or not the entire die face, partially or totally). Triangular rigid patterns of velocity discontinuities have been validated by analytical methods and a range of use for the selected configurations has been established. This methodology has been applied to other process with good results. Thus, the mechanical parameters analysed are fractional reduction, dead metal zone, length die and friction. Finally the calculation of the energy has been achieved by upper bound method. The results allow researching an optimisation of use of upper bound method in hot forward extrusion.

scholarly journals МОДЕЛЮВАННЯ ПРОЦЕСІВ КОМБІНОВАНОГО РАДІАЛЬНО-ПРЯМОГО ВИДАВЛЮВАННЯ СКЛАДНОПРОФІЛЬОВАНИХ ПОРОЖНИСТИХ ДЕТАЛЕЙ ІЗ ВИКОРИСТАННЯМ МЕТОДУ КІНЕМАТИЧНИХ МОДУЛІВ

2021 ◽  
Vol 146 (3) ◽  
pp. 69-78
Author(s):  
Н. С. Грудкіна
Keyword(s):  
Upper Bound ◽  
Defect Formation ◽  
Metal Flow ◽  
Relative Deformation ◽  
Complex Profile ◽  
Upper Bound Method ◽  
Factors Affecting ◽  
Forward Extrusion ◽  
Power Mode ◽  
Mathematical Relationships

Expanding the capabilities of the kinematic modules method to determine the value of the relative deformation pressure and shaping of a semi-finished product in the processes of combined radial-forward extrusion such as hollow parts with a complex profile. Obtaining calculated dependencies that will allow predicting compliance with the required dimensions of the part and assessing the possibility of defect formation. Upper bound method based on the method of kinematic modules is defined investigation of the main factors, affecting the power mode of deformation and features in the shaping of a semi-finished product in the processes of combined extrusion with several degrees of metal flow freedom Based on the upper bound method by using a kinematic module with two degrees of metal flow freedom is determined the value of the relative deformation pressure for make scheme of combined radial-forward extrusion such as hollow parts with a complex profile. The dependences of the increments in the semi-finished product that make it possible to analyze the influence of technological factors in the process of shaping and possible defect formation in the form of dimple are determined. The possibilities of the upper bound method by using kinematic modules with several degrees of metal flow freedom to assess the power mode and shaping of a semi-finished product in the processes of combined extrusion are determined. Significant influence of friction conditions and geometric parameters of the process the appearance of dimple in combined radial-forward extrusion such as hollow parts with a complex profile are considered. Mathematical relationships for calculating the value of the relative deformation pressure and increments of the semi-finished product in combined radial-forward extrusion such as hollow parts with a complex profile that will contribute to a more active introduction of combined extrusion processes in production are determined.

Upper-bound analysis of square-die forward extrusion

1996 ◽  
Vol 62 (1-3) ◽  
pp. 242-248 ◽  
Author(s):  
D.K. Kim ◽  
J.R. Cho ◽  
W.B. Bae ◽  
Y.H. Kim
Keyword(s):  
Upper Bound ◽  
Upper Bound Analysis ◽  
Forward Extrusion ◽  
Bound Analysis

scholarly journals Analysis of power parameters of combined three-direction deformation of parts with flange

2021 ◽  
Vol 49 (2) ◽  
pp. 344-355
Author(s):  
Leila Aliieva ◽  
Oleg Markov ◽  
Igramotdin Aliiev ◽  
Natalia Hrudkina ◽  
Vladymyr Levchenko ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Upper Bound ◽  
Metal Flow ◽  
Calculation Scheme ◽  
Power Method ◽  
The Finite Element Method ◽  
Forward Extrusion ◽  
Prevailing Direction ◽  
Experimental Values

The upper bound power method is used to simulate the process of combined radial-backward-forward extrusion of hollow parts of the "cup with flange and branch pieces" type from a continuous workpiece. The calculation scheme with autonomous deformation zones is used, which contains modules with an inclined boundary and the condition for the equality of powers acting on both sides of the intermediate hard zone is accepted. This made it possible to more accurately determine the power regime and the prevailing direction of the metal flow, which is necessary to assess the character of the forming of the part. The comparison of theoretical and experimental values of the deformation pressures and the flow velocities with each other, as well as with the results obtained by the finite element method shows the feasibility of using the obtained functions for technological calculations of power parameters and evaluating of part forming.

A New Formulation of Generalized Velocity Field for Axisymmetric Forward Extrusion Through Arbitrarily Curved Dies

1987 ◽  
Vol 109 (2) ◽  
pp. 161-168 ◽  
Author(s):  
D. Y. Yang ◽  
C. H. Han
Keyword(s):  
Velocity Field ◽  
Upper Bound ◽  
Effective Strain ◽  
Extrusion Pressure ◽  
Grid Pattern ◽  
Forward Extrusion ◽  
Area Reduction ◽  
Theoretical Predictions ◽  
Die Profile ◽  
New Formulation

A new analytic method is proposd for estimating the extrusion pressure, the final effective strain of the extruded billet, and the grid distortion patterns in axisymmetric forward extrusion through arbitrarily curved dies. A generalized kinematically admissible velocity field is derived to formulate an upper-bound solution. The corresponding upper-bound extrusion pressure is then obtained by optimizing the process parameters. The effects of area reduction, frictional condition, die length, and the die profile are discussed in relation to the extrusion pressure, the distorted grid pattern, and distribution of the final effective strain on the cross-section of the extruded billet. In the computation a biquadratic polynomial is chosen for the die profile. The work-hardening effect is incorporated in the formulation. Experiments are carried out for AISI 4140 steel billets at room temperature. The theoretical predictions both in the extrusion load and deformed configuration are in excellent agreement with the experimental results and the results computed by the finite element method.

Sign in / Sign up

Export Citation Format

Share Document