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.

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.

Nonisothermal Axisymmetric Forging

1986 ◽  
Vol 108 (4) ◽  
pp. 288-294 ◽  
Author(s):  
P. Dadras ◽  
P. R. Burte
Keyword(s):  
Thermal Analysis ◽  
Upper Bound ◽  
Total Power ◽  
Homogeneous State ◽  
Field Equations ◽  
Strain And Strain Rate ◽  
Upset Forging ◽  
Theoretical Predictions ◽  
Temperature Strain ◽  
Recorded Temperature

An approximate solution for nonisothermal upset forging is presented. A finite difference thermal analysis and an upper-bound deformation solution are used for this purpose. The thermal analysis is for a homogeneous state of strain, it ignores deformation heating, but accounts for all modes of heat flow during the transfer of the billet to the tooling and throughout the deformation. The upper-bound solution is based on admissible velocity field equations, the recorded temperature data from the thermal analysis, and constitutive equations for temperature, strain, and strain rate-dependence of flow stress. The size of the chilled zone is determined by minimization of total power for the deformation process. Theoretical predictions for load-displacement behavior and the size of the chilled zone are compared with the experimental results for 304 stainless and AISI 1042 steels.

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.

Studies on the Three-Dimensional Temperature Transients in the Canine Prostate During Transurethral Microwave Thermal Therapy

2000 ◽  
Vol 122 (4) ◽  
pp. 372-379 ◽  
Author(s):  
Jing Liu ◽  
Liang Zhu ◽  
Lisa X. Xu
Keyword(s):  
Three Dimensional ◽  
Blood Perfusion ◽  
Thermal Therapy ◽  
Bioheat Transfer ◽  
Target Tissue ◽  
Urethral Wall ◽  
Theoretical Predictions ◽  
Closed Form Analytical Solution ◽  
Good Agreement

Thermal therapy of benign prostatic hyperplasia requires accurate prediction of the temperature distribution induced by the heating within the prostatic tissue. In this study, the Pennes bioheat transfer equation was used to model the transient heat transfer inside the canine prostate during transurethral microwave thermal therapy. Incorporating the specific absorption rate of microwave energy in tissue, a closed-form analytical solution was obtained. Good agreement was found between the theoretical predictions and in-vivo experimental results. Effects of blood perfusion and the cooling at the urethral wall on the temperature rise were investigated within the prostate during heating. The peak intraprostatic temperatures attained by application of 5, 10, or 15 W microwave power were predicted to be 38°C,41°C, and 44°C. Results from this study will help optimize the thermal dose that can be applied to target tissue during the therapy. [S0148-0731(00)01004-9]

Backward Extrusion of Internally Shaped Tubes From Round Billets

1984 ◽  
Vol 106 (2) ◽  
pp. 143-149 ◽  
Author(s):  
D. Y. Yang ◽  
C. H. Han
Keyword(s):  
Pure Aluminum ◽  
Three Dimensional ◽  
Mapping Function ◽  
Velocity Transformation ◽  
Backward Extrusion ◽  
Commercially Pure ◽  
Theoretical Predictions ◽  
Experimental Values ◽  
Punch Pressure ◽  
Good Agreement

An analytical method is proposed for estimating the steady-state punch pressure for three-dimensional backward extrusion (or piercing) of complicated internally shaped tubes from circular billets. A kinematically admissible velocity field is derived to formulate an upper-bound solution using velocity transformation and mapping function. The configuration of deforming boundary surfaces are determined by minimizing the extrusion power with respect to some chosen parameters. Experiments are carried out with commercially pure aluminum billets for internally shaped tubes at various reductions of area by using different sizes of shaped punches, such as square and regular hexagons. It is shown that the theoretical predictions for extrusion load are in good agreement with the experimental values.

A General Formulation for Hydroforming of Arbitrarily-Shaped Boxes and Its Application to Hydroforming of an Elliptic-Circular Box

1998 ◽  
Vol 120 (3) ◽  
pp. 481-488 ◽  
Author(s):  
T. S. Noh ◽  
D. Y. Yang
Keyword(s):  
Velocity Field ◽  
Fluid Pressure ◽  
Frictional Coefficient ◽  
Total Power ◽  
Thickness Variation ◽  
Pressure Curve ◽  
Bound Solution ◽  
Total Power Consumption ◽  
Uniform Wall ◽  
Blank Size

A general kinematically admissible velocity field is suggested for the upper-bound solution of hydroforming of arbitrarily-shaped boxes. The suggested formulation is then applied to hydroforming of an elliptic-circular box. From the proposed velocity field, the fluid pressure vs. punch stroke relationship to render uniform thickness and the deformed configuration are determined by minimizing the total power consumption with respect to some chosen parameters. Experiments are carried out in the hydroforming press according to the computed pressure vs. punch stroke curve. The assumption of uniform wall thickness is confirmed by measuring the thickness variation. The effects of various process parameters including blank size, work-hardening exponent and frictional coefficient on the pressure curve are analyzed and discussed. It is thus shown that the proposed method of analysis in the present study can be effectively used for hydroforming of arbitrarily shaped boxes.

Experimental Study of Propeller-Induced Vibratory Pressures on Simple Surfaces and Correlation With Theoretical Predictions

1964 ◽  
Vol 8 (05) ◽  
pp. 15-28
Author(s):  
J. P. Breslin ◽  
T. Kowalski
Keyword(s):  
Free Space ◽  
Three Dimensional ◽  
Theoretical Treatment ◽  
Plate Boundaries ◽  
Practical Application ◽  
Finite Area ◽  
Experimental Procedure ◽  
Theoretical Predictions ◽  
Pressure Changes ◽  
Good Agreement

Vibratory pressures exerted on cylindrical and flat-plate boundaries due to a model propeller were measured at three advance coefficients. A number of "free-space" measurements also were made. All measurements were made by driving a propeller past fixed pressure gages. This method yielded curves of pressure changes which are entirely free from background noise. The magnitudes of the free-space pressures were found to be larger than one half the corresponding magnitudes measured by gages mounted flush in a large plate at equal clearances from the propeller. By postulating that the finite area of the gage diaphragm produces a partial image of the propeller (and hence a larger pressure than that in free space) an experimental procedure was devised for correcting for this finite-area effect yielding results in good agreement with theory. A theoretical treatment of this effect of finite gage size is given in Appendix 2. The decay of maximum amplitudes of vibrating pressures is shown by means of three-dimensional plots. The pressures were found to become vanishingly small within approximately one propeller diameter fore and aft of the center of the propeller. The comparison with theoretically calculated pressures and forces gives very close agreement for free-space pressures and reasonable agreement for forces on a cylindrical surface. The agreement of both pressures and forces with theory is excellent for operation near the design advance ratio. A strong plea is made for further experiments with ship models in an effort to develop design criteria for practical application.

A Simplified Method of Using Four-Hole Probes to Measure Three-Dimensional Flow Fields

1985 ◽  
Vol 107 (1) ◽  
pp. 31-35 ◽  
Author(s):  
N. Sitaram ◽  
A. L. Treaster
Keyword(s):  
Flat Plate ◽  
Three Dimensional ◽  
Flow Fields ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Application Procedure ◽  
Simplified Method ◽  
Theoretical Predictions ◽  
Gradient Effects ◽  
Good Agreement

A simplified method of using four-hole probes to measure three-dimensional flow-fields is presented. This method is similar to an existing calibration and application procedure used for five-hole probes. The new method is demonstrated for two four-hole probes of different geometry. These four-hole probes and a five-hole probe are used to measure the turbulent boundary layer on a flat plate. The results from the three probes are in good agreement with theoretical predictions. The major discrepancies occur near the surface of the flat plate and are attributed to wall vicinity and velocity gradient effects.

scholarly journals Energy spectrum in the dissipation range of fluid turbulence

1997 ◽  
Vol 57 (1) ◽  
pp. 195-201 ◽  
Author(s):  
D. O. MARTÍNEZ ◽  
S. CHEN ◽  
G. D. DOOLEN ◽  
R. H. KRAICHNAN ◽  
L.-P. WANG ◽  
...  
Keyword(s):  
Energy Spectrum ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Fluid Turbulence ◽  
Theoretical Predictions ◽  
Dissipation Range ◽  
Good Agreement

High-resolution, direct numerical simulations of three-dimensional incompressible Navier–Stokes equations are carried out to study the energy spectrum in the dissipation range. An energy spectrum of the form A(k/kd)α exp[−βk/kd] is confirmed. The possible values of the parameters α and β, as well as their dependence on Reynolds numbers and length scales, are investigated, showing good agreement with recent theoretical predictions. A ‘bottleneck’-type effect is reported at k/kd≈4, exhibiting a possible transition from near-dissipation to far-dissipation.

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