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.

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.

Construction of unwinding equation of motion for thin cable in spherical coordinate system

2017 ◽  
Vol 232 (7) ◽  
pp. 1208-1220
Author(s):  
Kun-Woo Kim ◽  
Jae-Wook Lee ◽  
Jin-Seok Jang ◽  
Joo-Young Oh ◽  
Ji-Heon Kang ◽  
...  
Keyword(s):  
Coordinate System ◽  
Open System ◽  
Control Volume ◽  
Transient State ◽  
Equation Of Motion ◽  
Spherical Coordinate System ◽  
Coordinate Systems ◽  
Spherical Coordinate ◽  
Cylindrical Coordinate ◽  
Engineering Problems

The transient-state unwinding equation of motion for a thin cable can be derived by using Hamilton’s principle for an open system, which can consider the mass change produced by the unwinding velocity in a control volume. In general, most engineering problems can be analyzed in Cartesian, cylindrical, and spherical coordinate systems. In the field of unwinding dynamics, until now, only Cartesian and cylindrical coordinate systems have been used. A spherical coordinate system has not been used because of the complexity of derivatives. Therefore, in this study, the unwinding motion of a thin cable was analyzed using a spherical coordinate system in both water and air, and the results were compared with the results in Cartesian and cylindrical coordinate systems. The unwinding motions in the spherical, Cartesian, and cylindrical coordinate systems were nearly same in both water and air. The error related to the total length was within 0.5% in water, and the error related to the maximum balloon radius was also within 0.5 % in air. Therefore, it can be concluded that it is possible to solve the transient-state unwinding equation of motion in a spherical coordinate system.

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.

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.

Comparison Considerations Toward Investigating the Factors of Load and Age Group on the Maximum Reach Envelope

2020 ◽  
pp. 001872082096501
Author(s):  
Heather Johnston ◽  
Colleen Dewis ◽  
John Kozey
Keyword(s):  
Coordinate System ◽  
Three Dimensional ◽  
Spherical Coordinate System ◽  
Upper Body ◽  
Group Differences ◽  
Anthropometric Measures ◽  
Younger Adults ◽  
Present Measurement ◽  
Spherical Coordinate ◽  
Cylindrical Coordinate

Objective The objectives were to compare cylindrical and spherical coordinate representations of the maximum reach envelope (MRE) and apply these to a comparison of age and load on the MRE. Background The MRE is a useful measurement in the design of workstations and quantifying functional capability of the upper body. As a dynamic measure, there are human factors that impact the size, shape, and boundaries of the MRE. Method Three-dimensional reach measures were recorded using a computerized potentiometric system for anthropometric measures (CPSAM) on two adult groups (aged 18–25 years and 35–70 years). Reach trials were performed holding .0, .5, and 1 kg. Results Three-dimensional Cartesian coordinates were transformed into cylindrical ( r, θ , Z) and spherical ( r, θ, ϕ) coordinates. Median reach distance vectors were calculated for 54 panels within the MRE as created by incremented banding of the respective coordinate systems. Reach distance and reach area were compared between the two groups and the loaded conditions using a spherical coordinate system. Both younger adults and unloaded condition produced greater reach distances and reach areas. Conclusions Where a cylindrical coordinate system may reflect absolute reference for design, a normalized spherical coordinate system may better reflect functional range of motion and better compare individual and group differences. Age and load are both factors that impact the MRE. Application These findings present measurement considerations for use in human reach investigation and design.

Optimal Design and Structural Precision Analysis for a Spherical Coordinate System 3D Scanner Guiding Device

2014 ◽  
Vol 705 ◽  
pp. 164-168
Author(s):  
Sang Wook Park ◽  
Hee Young Maeng ◽  
Ju Wook Park
Keyword(s):  
Optimal Design ◽  
Data Collection ◽  
Reverse Engineering ◽  
Coordinate System ◽  
Fem Analysis ◽  
Spherical Coordinate System ◽  
3D Scanner ◽  
Spherical Coordinate ◽  
Overall Performance ◽  
Improved Design

Recently, automatic 3D scanning devices are commonly researched and developed for better productivity of the reverse engineering fields. In this paper, a 3D scanner utilizing a spherical coordinate system was designed and analyzed using FEM analysis. The system was designed for optimal performance, high precision, minimal deflection, and speed of data collection. FEM analysis allowed us to properly design the system to achieve these goals, with focus on the deflection of the cantilever arm. Results of the FEM analysis and figures showing the apparatus design are provided. Successive prototypes are shown to increase in overall performance and reliability through improved design and analysis.

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