A Three-Dimensional Upper Bound Elemental Technique for Forging Analysis

1996 ◽  
Vol 210 (4) ◽  
pp. 353-359 ◽  
Author(s):  
R S Lee ◽  
C T Kwan
Keyword(s):  
Velocity Field ◽  
Upper Bound ◽  
Metal Flow ◽  
Three Dimensional ◽  
Velocity Fields ◽  
Connecting Rod ◽  
Total Energy Consumption ◽  
Pure Lead ◽  
Forming Load ◽  
Theoretical Predictions

In this paper, two kinematically admissible velocity fields are derived for the proposed three-dimensional arbitrarily triangular and trapezoidal prismatic upper bound elemental technique (UBET) elements. These elements are applied to the portions between the circular shaped part and the straight rod part with three-dimensional metal flow in connecting rod forging, and then the capability of the proposed elements are shown. From the derived velocity fields, the upper bound loads on the upper die and the velocity field are determined by minimizing the total energy consumption with respect to some chosen parameters. Experiments with connecting rod forging were carried out with commercial pure lead billets at ambient temperature. The theoretical predictions of the forming load is in good agreement with the experimental results. It is shown that the proposed UBET elements in this work can effectively be used for the prediction of the forming load and velocity field in connecting rod forging.

An Arbitrarily Inclined Triangular UBET Element and Its Application to Combined Forging

1985 ◽  
Vol 107 (2) ◽  
pp. 134-140 ◽  
Author(s):  
D. Y. Yang ◽  
J. H. Kim ◽  
C. K. Lim
Keyword(s):  
Velocity Field ◽  
Room Temperature ◽  
Field Experiments ◽  
Velocity Fields ◽  
Admissible Velocity ◽  
Forming Load ◽  
Theoretical Predictions ◽  
Triangular Elements ◽  
Al 2024 ◽  
Good Agreement

A kinematically admissible velocity field is derived for a proposed arbitrarily inclined triangular UBET element. The method is applied to combined forging to show the flexibility of application. From the derived velocity fields upper-bound loads on the punch and deformed configurations are determined by optimizing some given parameters related with geometry and velocity field. Experiments on combined forging are carried out with annealed Al-2024 billets at room temperature for several punch shapes. The theoretical predictions both in the forming load and deformed configuration are in good agreement with the experimental results. It is shown that arbitrarily inclined triangular elements proposed in this work can effectively be used for the prediction of the forming load and deformation in combined forging and can be applied to other forming processes with flexibility.

An Analysis of Three-Dimensional Upset Forging of Regular Polygonal Blocks by Using the Upper-Bound Method

1987 ◽  
Vol 109 (2) ◽  
pp. 155-160 ◽  
Author(s):  
D. Y. Yang ◽  
J. H. Kim
Keyword(s):  
Velocity Field ◽  
Upper Bound ◽  
Pure Copper ◽  
Three Dimensional ◽  
Total Power ◽  
Total Power Consumption ◽  
Upset Forging ◽  
Theoretical Predictions ◽  
Forging Load ◽  
Good Agreement

A simple kinematically admissible velocity field for three-dimensional deformation in upset forging of regular polygonal blocks is proposed which takes into account the sidewise spread as well as the bulging along thickness. From the proposed velocity field the upper-bound load and the deformed configuration are determined by minimizing the total power consumption with respect to three chosen parameters. Experiments are carried out with annealed commercially pure copper at room temperature for different thicknesses, billet shapes and lubrication conditions. The theoretical predictions both in the forging load and the deformed configuration are in good agreement with the experimental results. It is thus shown that the velocity field proposed in this work can be conveniently used for the prediction of the forging load and deformation in the upset forging of regular polygonal blocks.

scholarly journals Improved convergence and stability properties in a three-dimensional higher-order ice sheet model

2011 ◽  
Vol 4 (3) ◽  
pp. 1569-1610
Author(s):  
J. J. Fürst ◽  
O. Rybak ◽  
H. Goelzer ◽  
B. De Smedt ◽  
P. de Groen ◽  
...  
Keyword(s):  
Velocity Field ◽  
Finite Difference ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Higher Order ◽  
Velocity Fields ◽  
Force Balance ◽  
Staggered Grid ◽  
Comparison Results ◽  
Resultant Velocity

Abstract. We present a novel finite difference implementation of a three-dimensional higher-order ice sheet model that performs well both in terms of convergence rate and numerical stability. In order to achieve these benefits the discretisation of the governing force balance equation makes extensive use of information on staggered grid points. Using the same iterative solver, an existing discretisation that operates exclusively on the regular grid serves as a reference. Participation in the ISMIP-HOM benchmark indicates that both discretisations are capable of reproducing the higher-order model inter-comparison results. This allows a direct comparison not only of the resultant velocity fields but also of the solver's convergence behaviour which holds main differences. First and foremost, the new finite difference scheme facilitates convergence by a factor of up to 7 and 2.6 in average. In addition to this decrease in computational costs, the precision for the resultant velocity field can be chosen higher in the novel finite difference implementation. For high precisions, the old discretisation experiences difficulties to converge due to large variation in the velocity fields of consecutive Picard iterations. Finally, changing discretisation prevents build-up of local field irregularites that occasionally cause divergence of the solution for the reference discretisation. The improved behaviour makes the new discretisation more reliable for extensive application to real ice geometries. Higher precision and robust numerics are crucial in time dependent applications since numerical oscillations in the velocity field of subsequent time steps are attenuated and divergence of the solution is prevented. Transient applications also benefit from the increased computational efficiency.

Analysis of Strip Rolling by the Upper Bound Approach

1987 ◽  
Vol 109 (4) ◽  
pp. 338-346 ◽  
Author(s):  
B. Avitzur ◽  
W. Gordon ◽  
S. Talbert
Keyword(s):  
Velocity Field ◽  
Rigid Body ◽  
Upper Bound ◽  
Velocity Fields ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Total Power ◽  
Strip Rolling ◽  
Upper Bound Technique ◽  
Independent Process

The process of strip rolling is analyzed using the upper bound technique. Two triangular velocity fields, one with triangles in linear rigid body motion and the other with triangles in rotational rigid body motion, are developed. The total power is determined as a function of the four independent process parameters (relative thickness, reduction, friction and net front-back tension). The results of these two velocity fields are compared with the established solution from Avitzur’s velocity field of continuous deformation. Upon establishing the validity of the triangular velocity field as an approach to the strip rolling problem, recommendations are suggested on how this approach can be used to study the split end or alligatoring defect.

Direct Upper Bound Solution to Rectangular-to-Polygonal Extrusion Through Square Die

1999 ◽  
Vol 121 (2) ◽  
pp. 195-201 ◽  
Author(s):  
S. K. Sahoo ◽  
P. K. Kar ◽  
K. C. Singh
Keyword(s):  
Steady State ◽  
Velocity Field ◽  
Upper Bound ◽  
Velocity Fields ◽  
Extrusion Pressure ◽  
Admissible Velocity ◽  
Bound Solution ◽  
Upper Bound Solution ◽  
Aspect Ratios

This paper is concerned with an attempt to find an upper bound solution for the problems of steady-state extrusion of asymmetric polygonal section bars through rough square dies. A class of kinematically admissible velocity fields is examined, reformulating the SERR technique, to get the velocity field that gives the lowest upper bound. This velocity field is utilized to compute the non-dimensional average extrusion pressure at various area reductions for different billet aspect ratios.

An Upper Bound Solution for a Two-Layer Cylinder Subject to Compression and Twist

2007 ◽  
Vol 345-346 ◽  
pp. 37-40 ◽  
Author(s):  
Gow Yi Tzou ◽  
Sergei Alexandrov
Keyword(s):  
Velocity Field ◽  
Upper Bound ◽  
Additional Condition ◽  
Velocity Fields ◽  
Upper Bound Theorem ◽  
Predictive Capacity ◽  
Admissible Velocity ◽  
Bound Solution ◽  
Bound Theorem ◽  
Formal Requirements

The choice of a kinematically admissible velocity field has a great effect on the predictive capacity of upper bound solutions. It is always advantageous, in addition to the formal requirements of the upper bound theorem, to select a class of velocity fields satisfying some additional conditions that follow from the exact formulation of the problem. In the case of maximum friction law, such an additional condition is that the real velocity field is singular in the vicinity of the friction surface. In the present paper this additional condition is incorporated in the class of kinematically admissible velocity fields chosen for a theoretical analysis of two - layer cylinders subject to compression and twist. An effect of the angular velocity of the die on process parameters is emphasized and discussed.

Analysis of a Turbulent Propeller Inflow

2003 ◽  
Vol 125 (3) ◽  
pp. 533-542 ◽  
Author(s):  
Stephen A. Huyer ◽  
Stephen R. Snarski
Keyword(s):  
Boundary Layer ◽  
Velocity Field ◽  
Three Dimensional ◽  
Velocity Fields ◽  
Autocorrelation Analysis ◽  
Mean Velocity ◽  
Turbulent Inflow ◽  
Turbulent Flow Structure ◽  
Induced Velocity ◽  
Insight Into

The unsteady turbulent inflow into a swirl-inducing stator upstream of propeller (SISUP) propeller is presented. The upstream stators and hull boundary layer generate a complex, three-dimensional inflow that was measured using x-wire anemometry. High resolution measurements consisting of 12 locations in the radial direction and 600 in the circumferential direction yielded mean velocity and rms turbulent quantities for a total of 7200 points. The axial, radial, and circumferential velocity fields were thus measured. This enabled the induced velocity due to the stator wakes, the induced velocity due to the propeller, and the turbulent hull boundary layer to be characterized. To assist in decoupling the effects on the velocity field due to the stator and propeller, a potential flow computation of the swirl component was used. Spectra and autocorrelation analysis of the inflow velocity field were used to estimate the integral length scale and lend further insight into the turbulent flow structure. These data can be used to validate computational fluid dynamics codes and assist in developing of turbulent inflow models.

An Approximate Three-Dimensional Metal Flow Analysis for Shape Rolling

1988 ◽  
Vol 110 (3) ◽  
pp. 223-231 ◽  
Author(s):  
Kevin F. Kennedy
Keyword(s):  
Velocity Field ◽  
Metal Flow ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Energy Dissipation Rate ◽  
Shape Rolling ◽  
Perfectly Plastic ◽  
Deformation Problem ◽  
Rod Rolling

An approximate three-dimensional metal flow analysis for shape rolling is developed. The analysis, which is presently applicable to rod rolling, is based on an upper-bound approach in which an iterative numerical procedure is used to minimize the energy dissipation rate to obtain kinematically admissible velocity field solutions of the rolling problem. Once the velocity field and the final shape of the plastically deforming body are known, then elementary stress analysis techniques are used to determine the force related aspects of the rolling problem. It is assumed that the rolled material is rigid perfectly plastic, and only the purely mechanical aspects of the metal deformation problem in rolling are considered assuming isothermal conditions. The analysis shows good agreement with elongation and roll separating force measurements in the hot rolling of mild carbon steel for a variety of workpiece and roll cross-section geometries commonly used in rod rolling.

Analysis of Tube Extrusion

1970 ◽  
Vol 92 (2) ◽  
pp. 403-410 ◽  
Author(s):  
H. S. Mehta ◽  
A. H. Shabaik ◽  
Shiro Kobayashi
Keyword(s):  
Velocity Field ◽  
Velocity Fields ◽  
The Other ◽  
Stress Distributions ◽  
Pure Lead ◽  
Admissible Velocity ◽  
Tube Extrusion ◽  
Commercially Pure ◽  
Superplastic Alloy ◽  
Good Agreement

Two solutions for the detailed mechanics of tube extrusion are presented. One is based on the theoretical velocity field, and the other on the flow field observed experimentally. The theoretical solution makes use of admissible velocity fields containing no velocity discontinuities. Experimental flow patterns are obtained for commercially pure lead and a superplastic alloy of the eutectic of lead and tin. The two solutions are compared in terms of velocity components, grid distortions, and strain and stress distributions, and very good agreement between the two solutions is revealed.

Generalized Framework for Three-Dimensional Upper Bound Limit Analysis in a Tresca Material

2003 ◽  
Vol 70 (1) ◽  
pp. 91-100 ◽  
Author(s):  
A. M. Puzrin ◽  
M. F. Randolph
Keyword(s):  
Upper Bound ◽  
Limit Analysis ◽  
Three Dimensional ◽  
Analytical Form ◽  
Velocity Fields ◽  
Coordinate Transformations ◽  
Incompressibility Condition ◽  
Standard Procedures ◽  
Generalized Framework ◽  
Upper Bound Limit Analysis

A new method is proposed for deriving kinematically admissible velocity fields (KAVFs) for three-dimensional upper bound limit analyses in a Tresca material using coordinate transformations. The method allows the incompressibility condition to be satisfied simply by imposing certain requirements on the analytical form of velocity magnitudes. This allows for new classes of velocity fields to be derived solely using standard procedures. These new classes of fields include: KAVFs with new streamline shapes; new planar but non-plane-strain KAVFs; new radial but nonaxisymmetric KAVFs. The method allows the expression of local dissipation of plastic work in any field to be derived in a closed form. The proposed method makes an attempt to expand the applicability of three-dimensional upper bound limit analysis by introducing more realistic shapes of KAVFs, while maintaining simplicity and clear engineering meaning.

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