The Upper-Bound Solution as Applied to Three-Dimensional Extrusion and Piercing Problems

1962 ◽  
Vol 84 (4) ◽  
pp. 397-404 ◽  
Author(s):  
C. T. Yang
Keyword(s):  
Experimental Data ◽  
Upper Bound ◽  
Close Agreement ◽  
Three Dimensional ◽  
Slight Modification ◽  
Graphical Solution ◽  
Bound Solution ◽  
Upper Bound Solution ◽  
Region Approach ◽  
Good Agreement

The upper-bound solution for plane-strain problems is modified and applied to three-dimensional extrusion and piercing. Johnson’s graphical solution is used to solve axisymmetric, eccentric, and two-bar extrusion problems of a lead billet. Kudo’s unit-deforming region approach is employed to solve cylindrical piercing problems of six nonferrous metals. The analytical extrusion pressure is compared with Frisch and Thomsen’s experimental data. A reasonably close agreement is obtained in the first two cases. The calculated piercing pressure is compared with the experimental results of Fukui, et al. A remarkably good agreement is observed for all six cases. Therefore the upper-bound solution after slight modification can be extended to three-dimensional problems in extrusion and piercing. A general conclusion for extending the upper-bound approach to all forming operations cannot be drawn until further study is done along this line.

A Control Strategy and Upper Bound Solution for Non-Flat Tool Open Die Forging Automation

1999 ◽  
Author(s):  
T. J. Nye
Keyword(s):  
Control Strategy ◽  
Upper Bound ◽  
Sequence Generation ◽  
Bound Solution ◽  
Upper Bound Solution ◽  
Die Forging ◽  
Strategy Model ◽  
Model Predictions ◽  
Open Die Forging ◽  
Good Agreement

Abstract The open die forging process can provide a number of benefits if its costs can be made competitive through automation. This paper describes a control strategy for automated open die forging forming sequence generation. An upper bound solution for forging with radiused tools is developed, along with a method for using this solution to estimate forming results, a necessary component of the control strategy. Model predictions are compared to physical experimental data using plasticine, and show good agreement.

An Upper Bound Solution Analysis of Equal Channel Angular Pressing

2005 ◽  
Vol 23 ◽  
pp. 109-112
Author(s):  
Wei Wei ◽  
Guang Chen
Keyword(s):  
Equal Channel Angular Pressing ◽  
Upper Bound ◽  
Maximum Load ◽  
Equivalent Strain ◽  
Bound Solution ◽  
Upper Bound Solution ◽  
Angular Pressing ◽  
Good Agreement

The purpose of this study is to obtain an upper bound solution of ECAP at 0 = ψ and φ=90 deg, which aims at analysis of the relations between ECAP upper bound pressure and the die angles of φ and ψ. The results show that the value of pressing load and the equivalent strain, e ε , decreases as the angle ψ increases at φ=90 deg, but the equivalent strain, e ε , decreases rapidly and no less than 0.90. The measured maximum load required for ECAP is in good agreement with the values obtained from the upper bound solution.

APPLICATION OF A NEW HAMILTONIAN OF INTERACTION TO THREE-DIMENSIONAL STRUCTURES

2004 ◽  
Vol 18 (09) ◽  
pp. 1351-1368
Author(s):  
ANDREI DOLOCAN ◽  
VOICU OCTAVIAN DOLOCAN ◽  
VOICU DOLOCAN
Keyword(s):  
Experimental Data ◽  
Cohesive Energy ◽  
Noble Gases ◽  
Three Dimensional ◽  
The Other ◽  
Ionic Crystals ◽  
Coupling Constant ◽  
Good Agreement

Using a new Hamiltonian of interaction we have calculated the cohesive energy in three-dimensional structures. We have found the news dependences of this energy on the distance between the atoms. The obtained results are in a good agreement with experimental data in ionic, covalent and noble gases crystals. The coupling constant γ between the interacting field and the atoms is somewhat smaller than unity in ionic crystals and is some larger than unity in covalent and noble gases crystals. The formulae found by us are general and may be applied, also, to the other types of interactions, for example, gravitational interactions.

Sign in / Sign up

Export Citation Format

Share Document