Analysis of Combined Backward-Forward Extrusion

1976 ◽  
Vol 98 (2) ◽  
pp. 438-445 ◽  
Author(s):  
B. Avitzur ◽  
W. C. Hahn ◽  
M. Mori
Keyword(s):  
Upper Bound ◽  
Process Parameter ◽  
Total Power ◽  
Deformation Region ◽  
Forward Flow ◽  
Forward Extrusion ◽  
Combined Flow ◽  
Dependent Parameter ◽  
Independent Process

The upper bound approach is used to analyze combined backward-forward extrusion. The deformation region is divided into five zones separated by planer and cylindrical surfaces of velocity discontinuities. The internal power of deformation and shear and friction losses are computed individually and summed. The pseudo-independent process parameter is the backward rate of flow with respect to which the total power of deformation is optimized. The optimal backward rate of flow is assumed to be the actual one. Thus, the backward rate of flow becomes a dependent parameter to be studied through this analysis. Conditions covering backward rates of flow from zero to maximum are demonstrated graphically. Examples are given for which combined flow results and for which either only forward flow or only backward flow occur.

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.

Mechanical Solutions for Hot Forward Extrusion under Plane Strain Conditions by upper Bound Method

2008 ◽  
Vol 367 ◽  
pp. 201-208 ◽  
Author(s):  
Rosario Domingo ◽  
A.M. Camacho ◽  
E.M. Rubio Alvir ◽  
M.A. Sebastián
Keyword(s):  
Plane Strain ◽  
Upper Bound ◽  
Analytical Methods ◽  
Mechanical Parameters ◽  
Upper Bound Method ◽  
Zone Length ◽  
Forward Extrusion ◽  
Dead Metal Zone ◽  
Fractional Reduction ◽  
The Dead

This paper present a study focused on hot forward extrusion by upper bound method. In particular, hot forward extrusion of plates through square face dies under plane strain conditions. Slater defines the models used for large fractional reduction. Different models have been taken in account; they are dissimilar in relation to the dead metal zone (if covers or not the entire die face, partially or totally). Triangular rigid patterns of velocity discontinuities have been validated by analytical methods and a range of use for the selected configurations has been established. This methodology has been applied to other process with good results. Thus, the mechanical parameters analysed are fractional reduction, dead metal zone, length die and friction. Finally the calculation of the energy has been achieved by upper bound method. The results allow researching an optimisation of use of upper bound method in hot forward extrusion.

scholarly journals МОДЕЛЮВАННЯ ПРОЦЕСІВ КОМБІНОВАНОГО РАДІАЛЬНО-ПРЯМОГО ВИДАВЛЮВАННЯ СКЛАДНОПРОФІЛЬОВАНИХ ПОРОЖНИСТИХ ДЕТАЛЕЙ ІЗ ВИКОРИСТАННЯМ МЕТОДУ КІНЕМАТИЧНИХ МОДУЛІВ

2021 ◽  
Vol 146 (3) ◽  
pp. 69-78
Author(s):  
Н. С. Грудкіна
Keyword(s):  
Upper Bound ◽  
Defect Formation ◽  
Metal Flow ◽  
Relative Deformation ◽  
Complex Profile ◽  
Upper Bound Method ◽  
Factors Affecting ◽  
Forward Extrusion ◽  
Power Mode ◽  
Mathematical Relationships

Expanding the capabilities of the kinematic modules method to determine the value of the relative deformation pressure and shaping of a semi-finished product in the processes of combined radial-forward extrusion such as hollow parts with a complex profile. Obtaining calculated dependencies that will allow predicting compliance with the required dimensions of the part and assessing the possibility of defect formation. Upper bound method based on the method of kinematic modules is defined investigation of the main factors, affecting the power mode of deformation and features in the shaping of a semi-finished product in the processes of combined extrusion with several degrees of metal flow freedom Based on the upper bound method by using a kinematic module with two degrees of metal flow freedom is determined the value of the relative deformation pressure for make scheme of combined radial-forward extrusion such as hollow parts with a complex profile. The dependences of the increments in the semi-finished product that make it possible to analyze the influence of technological factors in the process of shaping and possible defect formation in the form of dimple are determined. The possibilities of the upper bound method by using kinematic modules with several degrees of metal flow freedom to assess the power mode and shaping of a semi-finished product in the processes of combined extrusion are determined. Significant influence of friction conditions and geometric parameters of the process the appearance of dimple in combined radial-forward extrusion such as hollow parts with a complex profile are considered. Mathematical relationships for calculating the value of the relative deformation pressure and increments of the semi-finished product in combined radial-forward extrusion such as hollow parts with a complex profile that will contribute to a more active introduction of combined extrusion processes in production are determined.

The Study of Distorted Grid Patterns for Flow-Through Conical Converging Dies by the Multi-triangular Velocity Field

1984 ◽  
Vol 106 (2) ◽  
pp. 150-160 ◽  
Author(s):  
J. Pan ◽  
W. Pachla ◽  
S. Rosenberry ◽  
B. Avitzur
Keyword(s):  
Velocity Field ◽  
Upper Bound ◽  
Cone Angle ◽  
Wire Drawing ◽  
Perfectly Plastic ◽  
Distorted Grid ◽  
Upper Bound Technique ◽  
Independent Process ◽  
Flow Through ◽  
Reduction In Area

A variety of velocity fields may be used to analyze the intermediate and final distorted grids for the so-called “flow-through” metal forming processes such as wire drawing, rolling, extrusion, etc. In this paper the triangular velocity field describes the flow of homogeneous, perfectly plastic Mises’ material through a conical converging die. The traditional triangular velocity field was treated and the solution extended. The shape of the distorted grids was uniquely determined by the minimization of the power (drawing or extrusion stresses) required to cause its distortion for a given set of independent process parameters, i.e., process geometry-reduction in area and semi-cone angle, and friction. Actual power (forming stress requirements) was estimated by the upper-bound technique. For the unitriangular velocity field, the power was minimized with respect to the shape of the workpiece (the shape of the triangle). For the multitriangular velocity field, the power was minimized with respect to the shape and the number of triangles. Further, the number of triangles was treated as a real number. Thus, the accurate lower upper-bound was found and the reasonable solution in predicting real distortion grid patterns was then obtained. The analysis determines the severity of the distortion as a function of process geometry and friction.

Criteria for the Prevention of Split Ends

1988 ◽  
Vol 110 (2) ◽  
pp. 162-172 ◽  
Author(s):  
Y. D. Zhu ◽  
B. Avitzur
Keyword(s):  
Rigid Body ◽  
Upper Bound ◽  
Strip Rolling ◽  
Deformation Region ◽  
Bound Solution ◽  
Upper Bound Solution ◽  
Perfectly Plastic ◽  
Rotational Motions ◽  
Split Ends

A criterion for the prevention of split ends (alligatoring) is expressed mathematically. This criteria, t0/R0>1.81×(t0/tf−1) is derived through the extension of an earlier upper bound solution for strip rolling of a perfectly plastic mises material. The treatment is based on the division of the deformation region to a series of triangles, undergoing rigid body rotational motions.

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