Criteria for the Prevention of Split Ends

1988 ◽  
Vol 110 (2) ◽  
pp. 162-172 ◽  
Author(s):  
Y. D. Zhu ◽  
B. Avitzur
Keyword(s):  
Rigid Body ◽  
Upper Bound ◽  
Strip Rolling ◽  
Deformation Region ◽  
Bound Solution ◽  
Upper Bound Solution ◽  
Perfectly Plastic ◽  
Rotational Motions ◽  
Split Ends

A criterion for the prevention of split ends (alligatoring) is expressed mathematically. This criteria, t0/R0>1.81×(t0/tf−1) is derived through the extension of an earlier upper bound solution for strip rolling of a perfectly plastic mises material. The treatment is based on the division of the deformation region to a series of triangles, undergoing rigid body rotational motions.

An Upper Bound Solution for Upsetting of Two-Layer Cylinder

2006 ◽  
Vol 505-507 ◽  
pp. 1303-1308 ◽  
Author(s):  
Gow Yi Tzou ◽  
Sergei Alexandrov
Keyword(s):  
Velocity Field ◽  
Upper Bound ◽  
Limit Load ◽  
Equivalent Strain ◽  
Industrial Applications ◽  
Upper Bound Theorem ◽  
Bound Solution ◽  
Upper Bound Solution ◽  
Perfectly Plastic ◽  
Plastic Materials

An upper bound solution for axisymmetric upsetting of two-layer cylinder made of rigid perfectly plastic materials is provided. An important feature of the solution is that the kinematically admissible velocity field, in addition to the necessary requirements of the upper bound theorem, satisfies the frictional boundary condition in stresses, the maximum friction law. The latter is archived by introducing a singular velocity field such that the equivalent strain rate approaches infinity at the friction surface. The dependence of the upper bound limit load on geometric parameters and the ratio of the yield stresses of the two materials is analyzed. The solution can be used in industrial applications for evaluating the load required to deform two-layer cylinders.

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.

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