Analyzing the Bias in the Primal-Dual Upper Bound Method for Early Exercisable Derivatives: Bounds, Estimation and Removal

2014 ◽  
Author(s):  
Mark S. Joshi
Keyword(s):  
Upper Bound ◽  
Upper Bound Method ◽  
Primal Dual

An Analysis for Magnesium Alloy Curvature Products Formed by Staggered Extrusion (SE) Based on the Upper Bound Method

2021 ◽  
Author(s):  
Xi Jie Zhang ◽  
Feng Li ◽  
Ye Wang ◽  
Zi Yu Chen
Keyword(s):  
Magnesium Alloy ◽  
Upper Bound ◽  
Scientific Basis ◽  
Extrusion Ratio ◽  
Eccentricity Ratio ◽  
Fe Modelling ◽  
Upper Bound Method ◽  
Curvature Theory ◽  
Extruded Products ◽  
Good Agreement

Abstract Staggered extrusion (SE) is a new method to solve the bottleneck of traditional curvature products, such as long manufacturing cycle, many forming processes and difficult quality control. How to quantitatively control the curvature of extruded products is the key to implement this method. Herein, the upper bound method is used to calculate and analyze the power consumption of each characteristic zone in the SE process. The theoretical model of extrusion load and curvature is established. The results show that the staggered distance h has an important influence on the curvature κ. When the staggered distance h increases from 8 mm to 24 mm and other conditions remain unchanged, the curvature κ increases from 0.0546 to 0.1607. Any combination of the staggered distance h and the extrusion ratio λ corresponds to an eccentricity ratio ξ. The eccentricity ratio ξ decreases with the increase of the staggered distance h or the extrusion ratio λ. By comparison, it can be seen that the variation trend of the theoretical predicted value and the FE modelling in the steady-state extrusion stage is consistent. The experimental results are in good agreement with the curvature theory prediction model. These results provide a scientific basis for the formulation of the SE process and precisely controlling magnesium alloy curvature products.

Sign in / Sign up

Export Citation Format

Share Document