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.

FEM Analysis during Extrusion of Round-To-Pentagonal Sections through Converging Dies

2012 ◽  
Vol 500 ◽  
pp. 410-413
Author(s):  
Akshaya Kumar Rout ◽  
Kali Pada Maity
Keyword(s):  
Velocity Field ◽  
Stream Function ◽  
Function Method ◽  
Fem Analysis ◽  
Extrusion Process ◽  
Extrusion Pressure ◽  
Upper Bound Method ◽  
Die Profile ◽  
Deform 3D ◽  
Dual Stream Function

The linearly converging die plays a significant role in the extrusion process of section products in terms of reduction in extrusion load and improvement of product quality. With the help of upper bound method based on dual stream function method. Very few investigations have been reported when product and billet geometry are dissimilar using linear converging die. Dual stream function method is incapable of predicting kinematically admissible velocity field in the above case, SERR technique (Spatial Elementary Rigid Region) is the only alternative. In the present investigation, a reformulated SERR technique has been used to determine non-dimensional extrusion pressure and optimum die profile both for frictionless and friction conditions. SERR technique based on discontinuous velocity field is applicable for this case. In the present investigation, non-dimensional extrusion pressure and optimum die length has been determined for extrusion of pentagonal from round billet and the results are compared with the FEA results by using DEFORM 3D.

Direct Upper Bound Solution to Rectangular-to-Polygonal Extrusion Through Square Die

1999 ◽  
Vol 121 (2) ◽  
pp. 195-201 ◽  
Author(s):  
S. K. Sahoo ◽  
P. K. Kar ◽  
K. C. Singh
Keyword(s):  
Steady State ◽  
Velocity Field ◽  
Upper Bound ◽  
Velocity Fields ◽  
Extrusion Pressure ◽  
Admissible Velocity ◽  
Bound Solution ◽  
Upper Bound Solution ◽  
Aspect Ratios

This paper is concerned with an attempt to find an upper bound solution for the problems of steady-state extrusion of asymmetric polygonal section bars through rough square dies. A class of kinematically admissible velocity fields is examined, reformulating the SERR technique, to get the velocity field that gives the lowest upper bound. This velocity field is utilized to compute the non-dimensional average extrusion pressure at various area reductions for different billet aspect ratios.

A Three-Dimensional Upper Bound Elemental Technique for Forging Analysis

1996 ◽  
Vol 210 (4) ◽  
pp. 353-359 ◽  
Author(s):  
R S Lee ◽  
C T Kwan
Keyword(s):  
Velocity Field ◽  
Upper Bound ◽  
Metal Flow ◽  
Three Dimensional ◽  
Velocity Fields ◽  
Connecting Rod ◽  
Total Energy Consumption ◽  
Pure Lead ◽  
Forming Load ◽  
Theoretical Predictions

In this paper, two kinematically admissible velocity fields are derived for the proposed three-dimensional arbitrarily triangular and trapezoidal prismatic upper bound elemental technique (UBET) elements. These elements are applied to the portions between the circular shaped part and the straight rod part with three-dimensional metal flow in connecting rod forging, and then the capability of the proposed elements are shown. From the derived velocity fields, the upper bound loads on the upper die and the velocity field are determined by minimizing the total energy consumption with respect to some chosen parameters. Experiments with connecting rod forging were carried out with commercial pure lead billets at ambient temperature. The theoretical predictions of the forming load is in good agreement with the experimental results. It is shown that the proposed UBET elements in this work can effectively be used for the prediction of the forming load and velocity field in connecting rod forging.

Flow Characteristics Through Conical Converging Dies

1966 ◽  
Vol 88 (4) ◽  
pp. 410-419 ◽  
Author(s):  
B. Avitzur
Keyword(s):  
Velocity Field ◽  
Strain Rate ◽  
Effective Strain ◽  
Flow Characteristics ◽  
Published Data ◽  
Grid Pattern ◽  
Effective Strain Rate ◽  
Strain And Strain Rate ◽  
Distorted Grid ◽  
Flow Through

A velocity field is considered to describe flow through conical dies. The expected distorted grid pattern is studied. Strain and strain rate fields are analyzed. Effective strain and effective strain rate distributions and their averages are defined. Application to processes like drawing extrusion and hydrostatic extrusion is discussed. Analysis is compared with experimental published data.

On the Extrusion in Superplastic Conditions

1975 ◽  
Vol 97 (3) ◽  
pp. 1131-1135 ◽  
Author(s):  
A. Alto ◽  
G. Giorleo
Keyword(s):  
Velocity Field ◽  
Constitutive Equation ◽  
Strain Rate ◽  
Experimental Evidence ◽  
Upper Bound ◽  
Extrusion Pressure ◽  
Slab Method ◽  
Conical Die ◽  
Strain Rate Field ◽  
Superplastic Condition

In this paper the range within which the slab method is accurate enough to calculate the extrusion pressure in superplastic condition has been determined. A realistic velocity field, supported by experimental evidence, has been adopted. A strain rate field has been evaluated and an appropriate constitutive equation has been introduced. The slab method and the upper bound approach, here developed, have then been used to study the superplastic extrusion through a conical die. A comparison of the two solutions thus obtained has been carried out. It has been found that in any case the curves obtained using the slab method run higher than those obtained using the upper-bound approach. The analysis developed may be used to determine the range within the slab method is accurate enough for engineering purposes.

Analysis of Plastic Flow Through Inclined Planes in Plane Strain

1967 ◽  
Vol 89 (2) ◽  
pp. 361-375 ◽  
Author(s):  
B. Avitzur ◽  
J. Fueyo ◽  
J. Thompson
Keyword(s):  
Velocity Field ◽  
Strain Rate ◽  
Dead Zone ◽  
Effective Strain ◽  
Grid Pattern ◽  
Independent Variables ◽  
Strain And Strain Rate ◽  
Distorted Grid ◽  
Flow Through ◽  
Inclined Planes

A wide strip of thickness t0 is pulled or extruded through inclined planes converging with semiangle α and exit gap tf. While passing through the die, the thickness of the strip changes from t0 to tf, its length increases, but no change occurs in its width. A kinematically admissible velocity field is assumed to describe the flow. The expected distorted grid pattern is studied. Strain and strain rate fields are analyzed. Effective strain and effective strain rate distributions and their averages are defined. The same velocity field is utilized to obtain an upper-bound solution for the drawing and extrusion forces. Maximum reductions possible are predicted and the optimal included angle between the planes, required to minimize the forces, is evaluated. Formation and prevention of a dead zone are indicated. The analytical results are compared with other solutions and with published experimental data, where the independent variables are: Thicknesses t0 and tf, semiangle of the die α, friction (m), and flow stress of the material.

Upper Bound Analysis of Axisymmetric, Closed-Die Forgings

1981 ◽  
Vol 103 (1) ◽  
pp. 109-112 ◽  
Author(s):  
P. Dadras
Keyword(s):  
Velocity Field ◽  
Upper Bound ◽  
Deformation Zone ◽  
Admissible Velocity ◽  
Upper Bound Analysis ◽  
Die Forging ◽  
Closed Die Forging ◽  
Theoretical Predictions ◽  
Experimental Values ◽  
Bound Analysis

A kinematically admissible velocity field for axisymmetric closed die forging is proposed. The forging power and load are calculated and compared with experimental values. It is found that the theoretical predictions give estimates that are substantially higher than actual loads and powers. Also, the effect of different parameters on the height and shape of the deformation zone is investigated and it is shown that the height is independent of flash thickness and length. The angle of convergence of flow from the die to the flash decreases as the flash thickness is increased.

An Analysis of Three-Dimensional Upset Forging of Regular Polygonal Blocks by Using the Upper-Bound Method

1987 ◽  
Vol 109 (2) ◽  
pp. 155-160 ◽  
Author(s):  
D. Y. Yang ◽  
J. H. Kim
Keyword(s):  
Velocity Field ◽  
Upper Bound ◽  
Pure Copper ◽  
Three Dimensional ◽  
Total Power ◽  
Total Power Consumption ◽  
Upset Forging ◽  
Theoretical Predictions ◽  
Forging Load ◽  
Good Agreement

A simple kinematically admissible velocity field for three-dimensional deformation in upset forging of regular polygonal blocks is proposed which takes into account the sidewise spread as well as the bulging along thickness. From the proposed velocity field the upper-bound load and the deformed configuration are determined by minimizing the total power consumption with respect to three chosen parameters. Experiments are carried out with annealed commercially pure copper at room temperature for different thicknesses, billet shapes and lubrication conditions. The theoretical predictions both in the forging load and the deformed configuration are in good agreement with the experimental results. It is thus shown that the velocity field proposed in this work can be conveniently used for the prediction of the forging load and deformation in the upset forging of regular polygonal blocks.

An Analytical study of Optimal Die Design of Elliptic Tube

2013 ◽  
Vol 1 (1) ◽  
pp. 43-59
Author(s):  
Muthanna H. S.
Keyword(s):  
Friction Factor ◽  
Upper Bound ◽  
Die Design ◽  
Relative Deformation ◽  
Area Reduction ◽  
Variable Friction ◽  
Die Profile ◽  
Upper Bound Technique ◽  
New Equation ◽  
Reduction Of Area

In this study, die profile of the elliptic tube extrusion is analysis to predict the optimum die design by using upper bound theory. Developed manner in determining the relative extrusion power by dividing the extrusion die for different sector and calculate the relative deformation power of each sector under different condition which are reduction of area, friction factor and relative die length. The study predicts a new equation for determining the optimum die length with taking in the count the effects of those variables.  The surface of the die is generated by an envelope of straight lines drawn from the points on the perimeter at the entry section to corresponding points at exist of the die. An upper bound technique based on the kinematically admissible velocity field is used to determine the forming stress. A complex program built in Visual Fortran V5.0 used to calculate relative extrusion power with variable friction factor (relative optimum extrusion power for values of  reduction area are changed from 52.6% at area reduction equals to 0.15 to 82.8% at area reduction equals to 0.4). ANSYS program is used to compare the behavior and values of  relative extrusion stress for  optimum relative die length at constant reduction of area (R.A.=25%). The results are compared with other papers theoretical and experimental results are found to be in a very good agreement.

Radial Flow Velocity Field for Predicting Upper-Bound Solutions for Plane Strain Extrusion

1968 ◽  
Vol 90 (1) ◽  
pp. 45-50
Author(s):  
R. G. Fenton
Keyword(s):  
Velocity Field ◽  
Flow Field ◽  
Flow Velocity ◽  
Plane Strain ◽  
Upper Bound ◽  
Radial Flow ◽  
Flow Velocity Field ◽  
Wide Range ◽  
Ram Pressure ◽  
Considerable Range

The upper bound of the average ram pressure, based on an assumed radial flow velocity field, is derived for plane strain extrusion. Ram pressures are calculated for a complete range of reduction ratios and die angles, considering a wide range of frictional conditions. Results are compared with upper-bound ram pressures obtained by considering velocity fields other than the radial flow field, and it is shown that for a considerable range of reduction ratios and die angles, the radial flow field yields better upper bounds for the average ram pressure.

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