Plane Strain Forging—A Lower Upper Bound Approach

1975 ◽  
Vol 97 (1) ◽  
pp. 119-124 ◽  
Author(s):  
V. Nagpal ◽  
W. R. Clough
Keyword(s):  
Velocity Field ◽  
Process Parameters ◽  
Upper Bound ◽  
Dead Zone ◽  
Incompressible Material ◽  
Velocity Fields ◽  
Admissible Velocity ◽  
Special Cases ◽  
Rectangular Strip ◽  
General Velocity

A general kinematically admissible velocity field applicable to forging of a rectangular strip of a incompressible material is presented. Generalized shape of any dead zone, if assumed, can be obtained in terms of process parameters from this velocity field. Two different upper bound solutions for average forging pressure are obtained from simple velocity fields which are special cases of proposed general velocity field. Numerical results of the solutions show improvement over previous upper bound solutions published in literature over a certain range of process parameters.

General Kinematically Admissible Velocity Fields for Some Axisymmetric Metal Forming Problems

1974 ◽  
Vol 96 (4) ◽  
pp. 1197-1201 ◽  
Author(s):  
V. Nagpal
Keyword(s):  
Velocity Field ◽  
Plastic Zone ◽  
Metal Forming ◽  
Dead Zone ◽  
Incompressible Material ◽  
Velocity Fields ◽  
Admissible Velocity ◽  
Conical Die ◽  
General Velocity ◽  
Special Case

An approach for selecting general kinematically admissible velocity fields for an incompressible material from assumed shape of streamlines is outlined. Velocity field and generalized boundaries of plastic zone are obtained for axisymmetric extrusion of a rod through arbitrarily shaped die. For special case of conical die, the velocity field reduces to that presented by Stepanskii and Avitzur. General velocity field and boundary of dead zone, if assumed, for the problem of axisymmetric forging of cylindrical work-pieces are obtained. Other problems which can be treated are briefly discussed.

Upper Bound Solutions to Plane-Strain Extrusion Problems

1970 ◽  
Vol 92 (1) ◽  
pp. 158-164 ◽  
Author(s):  
P. C. T. Chen
Keyword(s):  
Plane Strain ◽  
Upper Bound ◽  
Material Properties ◽  
Incompressible Material ◽  
Velocity Fields ◽  
Deformation Pattern ◽  
Upper Bound Theorem ◽  
Admissible Velocity ◽  
Die Geometry ◽  
Bound Theorem

A method for selecting admissible velocity fields is presented for incompressible material. As illustrations, extrusion processes through three basic types of curved dies have been treated: cosine, elliptic, and hyperbolic. Upper-bound theorem is used in obtaining mean extrusion pressures and also in choosing the most suitable deformation pattern for extrusion through square dies. Effects of die geometry, friction, and material properties are discussed.

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.

An Upper Bound Solution for a Two-Layer Cylinder Subject to Compression and Twist

2007 ◽  
Vol 345-346 ◽  
pp. 37-40 ◽  
Author(s):  
Gow Yi Tzou ◽  
Sergei Alexandrov
Keyword(s):  
Velocity Field ◽  
Upper Bound ◽  
Additional Condition ◽  
Velocity Fields ◽  
Upper Bound Theorem ◽  
Predictive Capacity ◽  
Admissible Velocity ◽  
Bound Solution ◽  
Bound Theorem ◽  
Formal Requirements

The choice of a kinematically admissible velocity field has a great effect on the predictive capacity of upper bound solutions. It is always advantageous, in addition to the formal requirements of the upper bound theorem, to select a class of velocity fields satisfying some additional conditions that follow from the exact formulation of the problem. In the case of maximum friction law, such an additional condition is that the real velocity field is singular in the vicinity of the friction surface. In the present paper this additional condition is incorporated in the class of kinematically admissible velocity fields chosen for a theoretical analysis of two - layer cylinders subject to compression and twist. An effect of the angular velocity of the die on process parameters is emphasized and discussed.

A Generalized Velocity Field for Plane Strain Extrusion Through Arbitrarily Curved Dies

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
H. Haghighat ◽  
P. Amjadian
Keyword(s):  
Finite Element ◽  
Velocity Field ◽  
Angular Velocity ◽  
Plane Strain ◽  
Upper Bound ◽  
Velocity Fields ◽  
Finite Element Code ◽  
Admissible Velocity ◽  
Paper Plane ◽  
Good Agreement

In this paper, plane strain extrusion through arbitrarily curved dies is investigated analytically, numerically, and experimentally. Two kinematically admissible velocity fields based on assuming proportional angles, angular velocity field, and proportional distances from the midline in the deformation zone, sine velocity field, are developed for use in upper bound models. The relative average extrusion pressures for the two velocity fields are compared to each other and also with the velocity field of a reference for extrusion through a curved die. The results demonstrate that the angular velocity field is the best. Then, by using the developed analytical model, optimum die lengths which minimize the extrusion loads are determined for a streamlined die and also for a wedge shaped die. The corresponding results for those two die shapes are also determined by using the finite element code and by doing some experiments and are compared with upper bound results. These comparisons show a good agreement.

A General Velocity Field for Shape Rolling of a V-Sectioned Sheet

1999 ◽  
Vol 122 (1) ◽  
pp. 227-234 ◽  
Author(s):  
Yeong-Maw Hwang ◽  
Hung-Jiun Lin ◽  
J. R. Chen
Keyword(s):  
Plastic Deformation ◽  
Velocity Field ◽  
Rolled Product ◽  
Deformation Behavior ◽  
Thickness Reduction ◽  
Shape Rolling ◽  
Admissible Velocity ◽  
Plastic Deformation Behavior ◽  
Roll Gap ◽  
General Velocity

A general kinematically admissible velocity field has been proposed in this work to examine the plastic deformation behavior of the sheet at the roll gap during shape rolling of a V-sectioned sheet. This velocity field is employed to examine the geometry of the rolled product, which are effected by various rolling conditions such as the sizes of the raw sheet and the vacancy, thickness reduction, etc. Furthermore, experiments on cold shape rolling of aluminum sheet have also been conducted. The rolling forces and the shape of the rolled product were measured to compare with the analytical values. Through the comparisons between them, the validity of this newly proposed velocity field was verified. [S1087-1357(00)71301-3]

Analysis of Strip Rolling by the Upper Bound Approach

1987 ◽  
Vol 109 (4) ◽  
pp. 338-346 ◽  
Author(s):  
B. Avitzur ◽  
W. Gordon ◽  
S. Talbert
Keyword(s):  
Velocity Field ◽  
Rigid Body ◽  
Upper Bound ◽  
Velocity Fields ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Total Power ◽  
Strip Rolling ◽  
Upper Bound Technique ◽  
Independent Process

The process of strip rolling is analyzed using the upper bound technique. Two triangular velocity fields, one with triangles in linear rigid body motion and the other with triangles in rotational rigid body motion, are developed. The total power is determined as a function of the four independent process parameters (relative thickness, reduction, friction and net front-back tension). The results of these two velocity fields are compared with the established solution from Avitzur’s velocity field of continuous deformation. Upon establishing the validity of the triangular velocity field as an approach to the strip rolling problem, recommendations are suggested on how this approach can be used to study the split end or alligatoring defect.

An Arbitrarily Inclined Triangular UBET Element and Its Application to Combined Forging

1985 ◽  
Vol 107 (2) ◽  
pp. 134-140 ◽  
Author(s):  
D. Y. Yang ◽  
J. H. Kim ◽  
C. K. Lim
Keyword(s):  
Velocity Field ◽  
Room Temperature ◽  
Field Experiments ◽  
Velocity Fields ◽  
Admissible Velocity ◽  
Forming Load ◽  
Theoretical Predictions ◽  
Triangular Elements ◽  
Al 2024 ◽  
Good Agreement

A kinematically admissible velocity field is derived for a proposed arbitrarily inclined triangular UBET element. The method is applied to combined forging to show the flexibility of application. From the derived velocity fields upper-bound loads on the punch and deformed configurations are determined by optimizing some given parameters related with geometry and velocity field. Experiments on combined forging are carried out with annealed Al-2024 billets at room temperature for several punch shapes. The theoretical predictions both in the forming load and deformed configuration are in good agreement with the experimental results. It is shown that arbitrarily inclined triangular elements proposed in this work can effectively be used for the prediction of the forming load and deformation in combined forging and can be applied to other forming processes with flexibility.

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.

Upper-Bound Solutions of Axisymmetric Forming Problems—I

1964 ◽  
Vol 86 (2) ◽  
pp. 122-126 ◽  
Author(s):  
Shiro Kobayashi
Keyword(s):  
Upper Bound ◽  
Velocity Fields ◽  
Curved Surfaces ◽  
Admissible Velocity ◽  
Extended Treatment ◽  
Discontinuity Surfaces ◽  
Cylindrical Parts ◽  
Conical Surfaces

The Kudo method for obtaining average pressures in some axisymmetric forming problems by the use of velocity fields having conical surfaces as discontinuity surfaces is reviewed in the paper. Following this it is shown that the extended treatment of admissible velocity fields is possible if the conical surfaces suggested by Kudo are replaced by curved surfaces. The application of these velocity fields to forming problems is then illustrated by simple examples of compression of cylindrical parts, and the improved upper bound to forming pressures is obtained.

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