Upper-Bound Solutions of Some Axisymmetric Cold Forging Problems

1971 ◽  
Vol 93 (4) ◽  
pp. 1134-1144 ◽  
Author(s):  
J. Y. Liu
Keyword(s):  
Velocity Field ◽  
Upper Bound ◽  
Cylindrical Surface ◽  
Numerical Results ◽  
Cold Forging ◽  
Current Analysis ◽  
Physical Boundary ◽  
Free Cylindrical Surface

A new velocity field for the forging of some cylindrical workpieces is presented taking into account the bulging of the free cylindrical surface during deformation. The velocity field is more realistic than that proposed by Avitzur in that the physical boundary and continuity conditions are satisfied. Numerical results indicate that the current analysis improves upon previous solutions published in the literature.

Radial Flow Velocity Field for Predicting Upper-Bound Solutions for Plane Strain Extrusion

1968 ◽  
Vol 90 (1) ◽  
pp. 45-50
Author(s):  
R. G. Fenton
Keyword(s):  
Velocity Field ◽  
Flow Field ◽  
Flow Velocity ◽  
Plane Strain ◽  
Upper Bound ◽  
Radial Flow ◽  
Flow Velocity Field ◽  
Wide Range ◽  
Ram Pressure ◽  
Considerable Range

The upper bound of the average ram pressure, based on an assumed radial flow velocity field, is derived for plane strain extrusion. Ram pressures are calculated for a complete range of reduction ratios and die angles, considering a wide range of frictional conditions. Results are compared with upper-bound ram pressures obtained by considering velocity fields other than the radial flow field, and it is shown that for a considerable range of reduction ratios and die angles, the radial flow field yields better upper bounds for the average ram pressure.

A Yield Criterion of Porous Materials With Anisotropy Caused by Geometry or Distribution of Pores

1991 ◽  
Vol 113 (4) ◽  
pp. 425-429 ◽  
Author(s):  
T. Hisatsune ◽  
T. Tabata ◽  
S. Masaki
Keyword(s):  
Velocity Field ◽  
Porous Materials ◽  
Upper Bound ◽  
Volume Fraction ◽  
Yield Criterion ◽  
Longitudinal Direction ◽  
Axisymmetric Deformation ◽  
The Other ◽  
The Matrix ◽  
Spherical Cells

Axisymmetric deformation of anisotropic porous materials caused by geometry of pores or by distribution of pores is analyzed. Two models of the materials are proposed: one consists of spherical cells each of which has a concentric ellipsoidal pore; and the other consists of ellipsoidal cells each of which has a concentric spherical pore. The velocity field in the matrix is assumed and the upper bound approach is attempted. Yield criteria are expressed as ellipses on the σm σ3 plane which are longer in longitudinal direction with increasing anisotropy and smaller with increasing volume fraction of the pore. Furthermore, the axes rotate about the origin at an angle α from the σm-axis, while the axis for isotropic porous materials is on the σm-axis.

scholarly journals Upper-bound solutions for face stability of circular tunnel in purely cohesive soil using continuous rotational velocity field

2018 ◽  
Vol 58 (6) ◽  
pp. 1511-1525
Author(s):  
Wantao Ding ◽  
Keqi Liu ◽  
Lewen Zhang ◽  
Peihe Shi ◽  
Mingjiang Li ◽  
...  
Keyword(s):  
Velocity Field ◽  
Upper Bound ◽  
Rotational Velocity ◽  
Cohesive Soil ◽  
Circular Tunnel ◽  
Face Stability

scholarly journals Tracking Control for Quad-Rotor Using Velocity Field and Obstacle Avoidance Based on Hydrodynamics

Electronics ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 233
Author(s):  
Julián Rascón-Enríquez ◽  
Luis Arturo García-Delgado ◽  
José R. Noriega ◽  
Alejandro García-Juárez ◽  
Eduardo S. Espinoza
Keyword(s):  
Velocity Field ◽  
Path Planning ◽  
Obstacle Avoidance ◽  
Tracking Control ◽  
Numerical Results ◽  
Recursive Method ◽  
Field Technique ◽  
Navigation Control ◽  
Total Velocity

In this work, the problem of navigation control of a quad-rotor, which includes path planning (to a desired trajectory with obstacle avoidance) and tracking control, is addressed. Path planning is achieved by means of the velocity field technique, since this method generates smooth trajectories that are suitable for this kind of vehicles. We propose a recursive method for the composition of the total velocity reference. In order to achieve a good tracking of the generated references, a saturated controller is used, namely, nested saturation. It is demonstrated that the velocity reference can be tracked with a reduction in the order of the controller, from four to three saturators, which simplifies the implementation. Numerical results show that a correct tracking could be guaranteed.

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.

Uncoupled Wave Systems and Dispersion in an Infinite Solid Cylinder

1989 ◽  
Vol 56 (2) ◽  
pp. 347-355 ◽  
Author(s):  
Yoon Young Kim
Keyword(s):  
Cylindrical Surface ◽  
Wave Motion ◽  
Fourier Number ◽  
Large Wave ◽  
Surface Conditions ◽  
Asymptotic Nature ◽  
Wave Numbers ◽  
Complex Wave ◽  
Insight Into ◽  
Free Cylindrical Surface

In this study, it is shown that there exist uncoupled wave systems for general non-axisymmetric wave propagation in an infinite isotropic cylinder. Two cylindrical surface conditions corresponding to the uncoupled wave systems are discussed. The solutions of the uncoupled wave systems are shown to provide proper bounds of Pochhammer’s equation for a free cylindrical surface. The bounds, which are easy to construct for any Fourier number in the circumferential direction, can be used to trace the branches of Pochhammer’s equation. They also give insight into the modal composition of the branches of Pochhammer’s equation at and between the intersections of the bounds. More refined dispersion relations of Pochhammer’s equation are possible through an asymptotic analysis of the itersections of the branches of Pochhammer’s equation with one family of the bounds. The asymptotic nature of wave motion corresponding to large wave numbers, imaginary or complex, for Pochhammer’s equation is studied. The wave motion is asymptotically equivoluminal for large imaginary wave numbers, and is characterized by coupled dilatation and shear for large complex wave numbers.

Stability of fibers near a free cylindrical surface

1988 ◽  
Vol 24 (10) ◽  
pp. 939-944 ◽  
Author(s):  
A. N. Guz' ◽  
Yu. N. Lapusta
Keyword(s):  
Cylindrical Surface ◽  
Free Cylindrical Surface

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.

Study of the Injection Upsetting of Metals

1973 ◽  
Vol 15 (6) ◽  
pp. 410-421 ◽  
Author(s):  
B. Parsons ◽  
P. R. Milner ◽  
B. N. Cole
Keyword(s):  
Velocity Field ◽  
Upper Bound ◽  
Work Hardening ◽  
Plastic Material ◽  
Pure Aluminium ◽  
Rigid Plastic ◽  
Cylindrical Billet ◽  
Rigid Plastic Material ◽  
Slab Stress ◽  
Punch Pressure

The punch pressure required to injection upset a cylindrical billet of an isotropic, non-work-hardening, rigid–plastic material is derived using an upper bound (velocity field) technique and by a ‘slab’ stress analysis. A method for applying the theory to the injection upsetting of work-hardening materials is evolved and the validity of this application is demonstrated by the results of experiments using pure aluminium, an aluminium alloy and copper.

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