Abstract
Computational numerical simulation has been largely applied in the design and analysis of metal forming processes. Extrusion is one of the main forming processes largely applied in the manufacturing of metallic products or parts. Historically, the Finite Element Method (FEM) has been applied for decades in metal extrusion analysis. However, recently in the academy, there is a trend to use the Finite Volume Method (FVM), because literature suggests that metal flow by extrusion can be analyzed by the flow formulation. Thus, metal flow can be modelled as an incompressible viscous fluid. The MacCormack Method is commonly used to simulate compressible fluid flow by the FVM. However, metal extrusion does not present state equations to calculate the pressure, and therefore, a velocity-pressure coupling method is necessary to obtain consistent velocity and pressure fields. This work proposes a new numerical scheme to obtain information about metal flow in the extrusion process along the steady state. The governing equations were discretized by FVM, using the Explicit MacCormack Method to structured and collocated mesh. The SIMPLE Method was applied to attain pressure-velocity coupling. This new numerical scheme was applied to analyze forward extrusion of lead. The metal extrusion velocity fields were calculated with a fast convergence and presented a good agreement with analytical and experimental results obtained from literature.
Highlights
In the academic and industrial environments, numerical simulation is an unquestionable reality
Considering incompressible fluid flow and metal flow, both cases are governed by conservation law equations, those are second order partial differential equations (PDEs) and can be represented by Generic Transport Equation [2,4,10,13], which has four parts, being: transient term, convective term, diffusive term and source term [4,6]
As metal forming flow is governed by Conservations Differential Equations, this work proposes to use the MacCormack method to solve the governing equations of metal flow in forward extrusion, considering the velocities discontinuities at the entrance and at the exit of the deformation zone [15]
Summary
In the academic and industrial environments, numerical simulation is an unquestionable reality. In metal forming processes, the flow formulation considers the metal similar to an incompressible viscous fluid [15, 17], which was and still is analyzed numerically by Finite Volume Method (FVM) [4]. Considering incompressible fluid flow and metal flow, both cases are governed by conservation law equations (mass, momentum and energy), those are second order partial differential equations (PDEs) and can be represented by Generic Transport Equation [2,4,10,13], which has four parts, being: transient term, convective term, diffusive term and source term [4,6] Each one of these terms represents the physical behavior of the phenomena and these behaviors are a mix of elliptic, parabolic and hyperbolic behavior [4, 10]. As metal forming flow is governed by Conservations Differential Equations, this work proposes to use the MacCormack method to solve the governing equations of metal flow in forward extrusion, considering the velocities discontinuities at the entrance and at the exit of the deformation zone [15]
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