Design and optimization of three-dimensional extrusion dies, using constraint optimization algorithm

Lebaal, Nadhir; Schmidt, Fabrice; Puissant, Stéphan

doi:10.1016/j.finel.2008.10.008

Cited by 48 publications

(28 citation statements)

References 14 publications

(21 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In order to discretize the streamfunction equations, we first discretize the momentum equations (3) and the curl operators in Eqs. (4) and (5). Let the linear system of the discretized momentum equations be:…”

Section: Discretization Of the Governing Equationsmentioning

confidence: 99%

“…Computational fluid dynamics (CFD) simulations can help understanding these instability phenomena and finding the solutions to eliminate them. Moreover, the development of reliable numerical simulations leads to the development of novel computer-aided design strategies in industrial production, using shape optimization algorithms and sensitivity analysis [5][6][7].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Numerical simulation of the planar extrudate swell of pseudoplastic and viscoelastic fluids with the streamfunction and the VOF methods

Comminal

Pimenta

Hattel

et al. 2018

Journal of Non-Newtonian Fluid Mechanics

View full text Add to dashboard Cite

. Numerical simulation of the planar extrudate swell of pseudoplastic and viscoelastic fluids with the streamfunction and the VOF methods. Journal of Non-Newtonian Fluid Mechanics, 252, 1-18. DOI: 10.1016/j.jnnfm.2017 A B S T R A C TWe present an Eulerian free-surface flow solver for incompressible pseudoplastic and viscoelastic non-Newtonian fluids. The free-surface flow solver is based on the streamfunction flow formulation and the volume-of-fluid method. The streamfunction solver computes the vector potential of a solenoidal velocity field, which ensures by construction the mass conservation of the solution, and removes the pressure unknown. Pseudoplastic liquids are modelled with a Carreau model. The viscoelastic fluids are governed by differential constitutive models reformulated with the log-conformation approach, in order to preserve the positive-definiteness of the conformation tensor, and to circumvent the high Weissenberg number problem. The volume fraction of the fluid is advected with a geometric conservative unsplit scheme that preserves a sharp interface representation. For the sake of comparison, we also implemented an algebraic advection scheme for the liquid volume fraction. The proposed numerical method is tested by simulating the planar extrudate swell with the Carreau, Oldroyd-B and Giesekus constitutive models. The swell ratio of the extrudates are compared with the data available in the literature, as well as with numerical simulations performed with the open-source rheoTool toolbox in OpenFOAM ® . While the simulations of the generalized Newtonian fluids achieved mesh independence for all the methods tested, the flow simulations of the viscoelastic fluids are more sensitive to mesh refinement and the choice of numerical scheme. Moreover, the simulations of Oldroyd-B fluid flows above a critical Weissenberg number are prone to artificial surface instabilities. These numerical artifacts are due to discretization errors within the Eulerian surface-capturing method. However, the numerical issues arise from the stress singularity at the die exit corner, and the unphysical predictions of the Oldroyd-B model in the skin layer of the extrudate after the die exit, where large extensional deformations occur.

show abstract

Section: Discretization Of the Governing Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical simulation of the planar extrudate swell of pseudoplastic and viscoelastic fluids with the streamfunction and the VOF methods

Comminal

Pimenta

Hattel

et al. 2018

Journal of Non-Newtonian Fluid Mechanics

View full text Add to dashboard Cite

show abstract

“…Kriging is an interpolation technique [14,15] From these outputs the unknown parameters α can be estimated: Where P is a vector including the value of p(x) evaluated at each of the design variables and R is the correlation matrix, which is composed of the correlation function evaluated at each possible combination of the points of design: …”

Section: Kriging Interpolationmentioning

confidence: 99%

Application of a response surface method to the optimal design of the wall temperature profiles in extrusion die

2009

Self Cite

View full text Add to dashboard Cite

A new approach to the optimal design of the die wall temperature profile in polymer extrusion processes is presented. In this approach, optimization of the design variables is conducted by a Response Surface Method (RSM) and the Sequential Quadratic Programming (SQP) algorithm. Design of experiment (DoE) needed for the construction of the response surface is used to evaluate the objective and the constraint functions on the basis of a finite element method (FEM). Two designs of experiments are used and the performances of the optimization results are compared with respect to efficiency and ability to obtain a global optimum. Typically, for extrusion die design, the objective function states that the average velocity across the die exit is uniform. Constraints are used to limit the pressure drop in the die. For this purpose, we optimize the wall temperature profile of a coat hanger die in a heterogeneous way, (i.e. the wall temperature may not be constant in the entire die). The melt temperature enables us to locally control the viscosity, which influences the flows in the various zones. The effect of the design variables in the objective and constraint functions is investigated using Taguchi method. The flow analysis results are then combined with an automatic optimization algorithm to provide a new profile of the die wall temperature distributions.

show abstract

“…: +86-451-86392501; fax: +86-451-86392522; e-mail address: hitlif@126.com [4] radically in the forming process and avoid the occurrence of defects [5]. Therefore the purpose of optimizing the technological parameters and the die design [6] to extrude metal can be achieved easily [7], which is also an effective way to improve the products quality and the mechanical properties.…”

Section: Introductionmentioning

confidence: 99%

Process analysis in mandrel extrusion of special-shaped aluminum alloys profile

Li¹,

He²,

Wang³

et al. 2021

View full text Add to dashboard Cite

In order to reveal abnormal shaped aluminum alloy law of needle piercing extrusion formation, setting the missile empennage as an example, this paper adopts the non-linear finite element to conduct the three-dimensional thermal simulation of abnormal shaped material law of needle piercing extrusion formation process and analyses systematically the influence of process law on temperature change, additional tensile stress and forming load. The results show that, in the range of low-speed extrusion, the billet's highest peak temperature shows a decreasing trend, and with the extrusion speed increasing, the decrease of highest peak temperature decreases, while the axial extra tensile stress on the mouth of model increases accordingly; the axis part of the mold's mouth is a high-temperature zone in the forming process, and with the axis center distance increasing, the temperature decreases gradually; and with the pressing reduction's increase, the gradient of temperature decreasing trend slows down gradually. This provides a theoretical basis to technical design of abnormal shaped material needle piercing extrusion formation and the metal distortion flow control. K e y w o r d s : mandrel extrusion, aluminum alloys profile, coupled thermal-mechanical numerical simulation

show abstract

Design and optimization of three-dimensional extrusion dies, using constraint optimization algorithm

Cited by 48 publications

References 14 publications

Numerical simulation of the planar extrudate swell of pseudoplastic and viscoelastic fluids with the streamfunction and the VOF methods

Numerical simulation of the planar extrudate swell of pseudoplastic and viscoelastic fluids with the streamfunction and the VOF methods

Application of a response surface method to the optimal design of the wall temperature profiles in extrusion die

Process analysis in mandrel extrusion of special-shaped aluminum alloys profile

Contact Info

Product

Resources

About