7.6.1 Formulation of the Problem

Let us consider now a mathematical model for hot tube extrusion, taking into account the influence of the working speed, when melted glass is used as a lubricant. We consider the problem of being stationary and isothermal. The working speed is considered variable during the process but for a certain magnitude of this velocity it is assumed that it is maintained constant for certain time interval so that during this time the process is considered stationary . Therefore, the variation of the working speed is described by a set of stationary cases (Cleja-Tigoiu and Cristescu [1985]).

The extrusion problem considered with classical plasticity theory was considered by many authors. We mention here only Avitzur [1968], Blazynski [1976], Maneghin et al. [1980], Medvedev et al. [1980], Hartley [1971], etc. to mention just a few.

The cylindrical billet of annular cross-section with outer radius R ₁, inner radius R ₃ and length l is pushed out from a cylindrical container using a ram which is moving with the speed ? ₀ (Fig. 7.6.1). In the interior of the billet a cylindrical plug of radius R ₃ and moving together with the ram is used to control the final inner radius of the tube. In front of the billet, between the billet and container, is placed a glass ring which at the beginning of the process melts and forms a dead zone which during the extrusion process is an extrusion...