Limit Analysis of Hollow Disk Forging—Part 1: Upper Bound

1978 ◽  
Vol 100 (3) ◽  
pp. 340-344 ◽  
Author(s):  
B. Avitzur ◽  
F. Sauerwine
Keyword(s):  
Velocity Field ◽  
Upper Bound ◽  
Limit Analysis ◽  
Friction Stress ◽  
Average Pressure ◽  
Admissible Velocity ◽  
Disk Interface ◽  
Upper Bound Analysis ◽  
Bound Analysis

An upper bound analysis for hollow disk forging is presented. Flow is described by a kinematically admissible velocity field which accounts for bulging of the inner and outer surfaces. The friction stress is assumed to be constant across the entire platen-hollow disk interface. Analytical predictions include the relative neutral radius, a bulge parameter and the relative average pressure all in terms of friction and hollow disk geometry. An improvement is observed over previous parallel velocity field solutions.

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.

Disk and Strip Forging with Side-surface Foldover—Part 1: Velocity Field and Upper-Bound Analysis

1978 ◽  
Vol 100 (4) ◽  
pp. 421-427 ◽  
Author(s):  
B. Avitzur ◽  
R. A. Kohser
Keyword(s):  
Velocity Field ◽  
Upper Bound ◽  
Plastic Material ◽  
Relative Size ◽  
Side Surface ◽  
Friction Material ◽  
Material Strength ◽  
Upper Bound Analysis ◽  
Zone Ii ◽  
Bound Analysis

With the assumptions of a Mises’ rigid, perfectly-plastic material and constant shear stress friction prevailing between the forge platens and deforming solid, the upper-bound analysis technique was applied to the upset forging of rectangular strip and solid cylindrical disks in an effort to incorporate the combined phenomena of bluge and fold. A two-zone velocity field was proposed for each geometry with Zone I occupying the interior volume and Zone II, the region near the free-surface periphery. The velocity field in Zone I was chosen as the exponential cusp-type used successfully in several previous analyses. Zone II was represented by a velocity field compatible with a foldover phenomenon and kinematically admissible with respect to boundary conditions and compatibility with Zone I. Solutions based on the above assumptions provide the forging pressure as a function of specimen geometry, interface friction, material strength, rate of bulge formation and relative size of Zone II. Minimization with respect to the last two variables provides the optimum rate of barreling or bulging and determines the degree of foldover expected.

Optimized Upper Bound Analysis of Axisymmetric Extrusion Using Spherical Velocity Field

2005 ◽  
Vol 128 (1) ◽  
pp. 4-10 ◽  
Author(s):  
Der-Form Chang ◽  
Jyhwen Wang
Keyword(s):  
Velocity Field ◽  
Coordinate System ◽  
Upper Bound ◽  
Spherical Coordinate System ◽  
Modeling Technique ◽  
Coordinate Systems ◽  
Spherical Coordinate ◽  
Die Geometry ◽  
Upper Bound Analysis ◽  
Bound Analysis

This paper presents an upper bound approach to analyze axisymmetric extrusion processes. A cylindrical and a spherical coordinate system are defined to represent the die geometry and the velocity field, respectively. For various curved dies, minimized upper bound results can be obtained by relating these two coordinate systems. Based on this modeling technique, the effects of die geometry, reduction ratio, and friction are investigated. Axisymmetric extrusion through various curved dies can be easily optimized with the proposed methodology.

Upper-Bound Analysis

Metal Forming ◽  
2012 ◽  
pp. 110-127
Author(s):  
William F. Hosford ◽  
Robert M. Caddell
Keyword(s):  
Upper Bound ◽  
Upper Bound Analysis ◽  
Bound Analysis
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