General Kinematically Admissible Velocity Fields for Some Axisymmetric Metal Forming Problems

Abstract

An approach for selecting general kinematically admissible velocity fields for an incompressible material from assumed shape of streamlines is outlined. Velocity field and generalized boundaries of plastic zone are obtained for axisymmetric extrusion of a rod through arbitrarily shaped die. For special case of conical die, the velocity field reduces to that presented by Stepanskii and Avitzur. General velocity field and boundary of dead zone, if assumed, for the problem of axisymmetric forging of cylindrical work-pieces are obtained. Other problems which can be treated are briefly discussed.

Minimizing distortion during extrusion using adaptable dies

“…non-conical). Nagpal [10] further refined the upper bound approach to study alternative axisymmetric die shapes. In addition to conical dies, Chen and Ling [11] used the upper bound approach to study the flow through cosine, elliptic, and hyperbolic dies.…”

A general kinematically admissible velocity field for axisymmetric forging and its application to hollow disk forging

“…Several general kinematically admissible velocity fields for various forming processes have been proposed in [5,6,[11][12][13][14][15][16]. The fields proposed in [11,13] can be adopted to solve axisymmetric forging problems.…”

“…The fields proposed in [11,13] can be adopted to solve axisymmetric forging problems. The approach developed in [13] is to build up axisymmetric kinematically admissible velocity fields from regions in which the axial velocity is constant and the radial velocity is inversely proportional to the radius in a cylindrical coordinate system.…”

“…This approach has been adopted in [7] to study a radial forging process. A continu o us v e l o c i t y fi el d s a t i s f y i ng t he e q u a t i o n o f incompressibility has been built up in [11]. The associated power dissipation has not been found.…”

“…A possibility to introduce a rigid region near frictional interfaces has been mentioned, but no specific applications have been made. The velocity field proposed in [11] includes several other kinematically admissible velocity fields as special cases, for example those used in [17,18]. In these works, the associated power dissipation has been calculated.…”