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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...
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This study aims the modeling and simulation of the direct extrusion process and determination of optimal process parameters using Finite Element Method (FEM) and Artificial Neural Network (ANN) cooperatively. First, the die set has been designed for direct extrusion of an aluminum rod and its numerical simulation has been prepared by mean of ABAQUS...
Citations
... Wu et al. [13] also developed a one-dimensional model that takes into account the effect of temperature variation and its effect on flow uniformity. In another study, Lebaal et al. [14] optimized the wall temperature profile of a coat-hanger extrusion die. By changing wall temperature, viscosity of the fluid in the vicinity of the wall can be changed and consequently flow rate can be manipulated. ...
In the design of coat hanger extrusion dies, the main objective is to provide a uniform flow rate at the die exit. Previously, a multi-rheology isothermal method model for coat hanger extrusion dies was developed to reach this objective. Polymer melts in extrusion dies commonly experience high shear rates. Viscous dissipation rooted by high shear rate may lead to significant temperature differences across the die. Due to temperature-dependency of viscosity, temperature differences may lead to nonuniform flow rates, which may significantly affect the flow rate at the die exit. As a result, a new design method is proposed to take into account the effects of temperature and viscous dissipation in the design of coat hanger dies. Although more non-Newtonian fluid rheology models can be adapted in the proposed study, as demonstration, temperature-dependent power-law and Carreau–Yasuda models are adapted in this study. Performances are compared with our isothermal method published earlier. In addition, the novel nonisothermal method is comprehensively examined where the effect of viscous dissipation is studied through Brinkman number of extrusion die. It is demonstrated that, for a low Brinkman number, both isothermal and nonisothermal design give similar flow uniformity level. However, for higher Brinkman numbers, the proposed nonisothermal method produces a design with more desirable velocity uniformity level along with a maximum improvement of 5.24% over the isothermal method. In addition, dependency of flow field on temperature, due to temperature-dependent viscosity, is studied, and it is demonstrated that fully-developed velocity profile changes as temperature increases along the flow channel. Moreover, the effect of the temperature sensitivity parameter in temperature-dependent non-Newtonian models is considered. It is demonstrated that the temperature boundary condition with the Biot number of 1.0 gives adequate results for lower values of the temperature sensitivity parameter.
... The substitution of Equations (10) and (11) in Equation (7) gives the following equation of the radius: ...
In the polymer sheet processing industry, the primary objective when designing a coat-hanger die is to achieve a uniform velocity distribution at the exit of the extrusion die outlet. This velocity distribution depends on the internal flow channels of the die, rheological parameters and extrusion process conditions. As a result, coat-hanger dies are often designed for each polymer based on its individual rheological data and other conditions. A multi-rheology method based on a flow network model and the Winter–Fritz equation is proposed and implemented for the calculation, design and optimization of flat sheeting polymer extrusion dies. This method provides a fast and accurate algorithm to obtain die design geometries with constant wall-shear rates and optimal outlet velocity distributions. The geometric design when complemented and validated with fluid flow simulations could be applied for multi-rheological fluid models such as the power-law, Carreau–Yasuda and Cross. This method is applied to sheet dies with both circular- and rectangular-shaped manifolds for several rheological fluids. The designed geometrical parameters are obtained, and the associated fluid simulations are performed to demonstrate its favorable applicability without being limited to only the power-law rheology. The two such designed dies exhibit 32.9 and 21.5 percent improvement in flow uniformity compared to the previous methods for dies with circular and rectangular manifolds, respectively.
... Increased velocity in a given section will thicken corresponding cross-section of the product due to higher volumetric flow and elongational strain rate. The melt temperature fluctuation affects the material viscosity, density, process stability, extrusion output rate and quality of the extruded product [7]. ...
Coat-hanger dies are widely used in the extrusion of polymer sheets and films. However, when designing the flat film/sheet extrusion dies manufacturing companies still facing difficulties in achieving the flow uniformity of the polymer melt. This affects the product quality and tool life. This study examines the existing extrusion die design which is used in in the industry in Kazakhstan for polypropylene sheet production and proposes better geometry of a die. These die geometries will be tested for flow uniformity in terms of velocity and pressure at the outlet.
... Evolutionary algorithms, gradient based methods and approximation approaches are among most commonly used methods for various material forming optimization problems [26][27][28][29]. Several works have to approach the study of the effects of parameterized and the optimization with the design of experiments. ...
This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the author's institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: http://www.elsevier.com/authorsrights A B S T R A C T The present study deals with the improvement of the Friction Stir Welding process, through the prediction of the optimal operating conditions, necessary for welding typical Aluminum-Lithium alloy material AA2195-T8. An optimization strategy coupled with 3D transient heat transfer computation were used to improve the FSW process parameters such as welding velocity, tool rotation velocity, tool diameter and applied force. The optimization procedure is based on three criteria: the control of the maximum temperature during FSW; the minimization of the Heat Affected Zone (HAZ) length and finally the reduction of the total welding energy. The obtained optimal parameters have given an ideal welding temperature in the workpiece, thereby ensuring good welding quality, gain in energy consumption and decrease both the welding time and the HAZ length.
... Response surface modeling is frequently used for extruder processes, see for instance Lebaal et al. (2010) and Formela and Bogucki (2014). Extrusion of plastic and cereals have much in common, and response surface modeling for cereal extrusion is described by Kowalski et al. (2016). ...
Many complex processes have a low degree of automation, and oftentimes important quality information is only available hours or even days after the production is completed. This article shows how multivariate design and response surface modeling were applied to a lay-At plastic hose extrusion process in a full-scale experiment. Clear quantitative relationships were found, which to a large degree match existing qualitative process understanding. For instance, it was quantified how adhesion improves with increased extrusion screw speed and extrusion head temperature. The results can readily be used to inform the operators in real-Time of important quality parameters of the hose currently under production. The clear results also indicate that increased process automation is achievable.
... This space reduction can be used with any search strategy in order to minimize J(x). Gradient based approaches including BFGS (Broyden-Fletcher-Goldfarb-Shanno) and SQP (sequential quadratic programming) algorithm are among one of the earlier methods used in a non-linear optimization problem [28,29]. In this paper, the SQP algorithm was used to solve the identification problem and search of optimal parameters. ...
The simulative prediction of material behaviour in forming processes necessitates a
precise determination of the material parameters. The present work focusses on the
modelling of the isostatic part of the flow stress using a flow curve with an analytical
suppression of the influence of friction and an adequate analytical law. The
experimental data are obtained from isothermal upsetting tests with various upsetting
ratios. The different ratios are based on a variation of the height of the sample,
remaining the diameter constant. For the proposed flow stress law five parameters are
identified. In order to decrease the number of function evaluations, a new reduction
model method based on both analytical and sequential quadratic programming (SQP)
algorithms is developed and applied to identify flow stress law parameters. A
comparison with traditional SQP algorithm is also done. A 3D finite element model is
built in order to simulate a side pressing test and an experimental validation is done. As
numerical results fit very well experimental data, the proposed model achieves a
precise prediction of the flow behaviour. The identification of the other parts of the
model (i.e. dependencies on strain-rate and temperature) are conducted in further
works.
... The large solution space, lack of gradient or other analytical information and use of simulation all suggest that search optimization methods would be most appropriate for optimizing tool paths. In order to decrease the evaluation number of the objective and constraint functions we use in this work response surface method [16]. This method consists in the construction of an approximate expression of the objective and constraint functions starting from a limited number of evaluations of the real functions. ...
a b s t r a c t Incremental sheet forming (ISF) process is based on localized plastic deformation in a thin sheet metal blank. It consists to deform progressively and locally the sheet metal using spherical forming tool controlled by a CNC machine-tool. Although it is a slow process compared to conventional forming technique such as stamping. The cost reduction linked to the fact that punches and dies are avoided which makes it a very attractive process for small batch production and rapid prototyping. However, ISF process depends strongly on the forming tool path which influences greatly the part geometry and sheet thickness dis-tribution. A homogeneous thickness distribution requires a rigorous optimization of the parameter settings, and an optimal parameterization of the forming strategy. This paper shows an optimization procedure tested for a given forming strategy, in order to reduce the manufacturing time and homogenize thickness distribution of an asymmetric part. The optimal forming strategy was determined by finite element analyses (FEA) in combi-nation with response surface method (RMS) and sequential quadratic programming (SQP) algorithm. Ó 2012 Elsevier B.V. All rights reserved.
Plastic profile extrusion – a manufacturing process for continuous profiles with fixed cross section – requires a complex and iterative design process to prevent deformations and residual stresses in the final product. The central task is to ensure a uniform material velocity at the outlet. To this end, not only the geometry of the flow decisively influences the quality of the outflow, but also the temperature profile along the flow channel wall. It is exactly here that this work contributes by presenting a novel design approach for extrusion dies that will allow for optimal temperature profiles. The core of this approach is the composition of the extrusion die through microstructures. The optimal shape and distribution of these microstructures is determined via shape optimization. The corresponding optimization procedure is the main topic of this paper. Special emphasis is placed on the definition of a suitable, low-dimensional shape parameterization. The proposed design-framework is then applied to two numerical test cases with varying complexity.
Bearing design is a major issue in controlling material flow and producing high-quality extruded products. Adjusting the bearing length is often performed using costly trial and error approaches in the extrusion industry. This is true even when using finite element analysis. The purpose of this study is to optimize the bearing length of forward extrusion dies using an analytical approach for metal extruded sections. This method is based on a generalized kinematically admissible velocity field to obtain uniform velocity at the die exit. The deformation zone contains the dead metal zone (DMZ) and bearing channel which is assumed to be non-linear. Based on this assumption, a new formulation was developed to define the geometry of the deformation zone. The response surface methodology was employed to optimize the relative extrusion pressure, deviation of the mean value for the velocity at die exit, and subsequently the bearing length for the extrusion die. Using this theoretical method, extrusion of rectangular and L and T-shaped sections was investigated and compared to previous work. Physical modelling experiments and finite element simulations were carried out to validate the suggested analytical method. The proposed analytical method gave a unique answer for the required bearing design in a few seconds contrary to finite element method which required many timely and costly trials. This method would be useful for die designers to get the appropriate bearing length.
The new method presented in this paper falls into the category of sampling methods and model management in the optimization process of surrogate related methods. This method was introduced in order to reach the global optimum with a limited number of computer experiments. During these developments, the Particle Swarm Optimization (PSO) was used as a smart sampling tool to construct the metamodel. These methods with their stochastic nature can also overcome the problems of local minima.
In order to improve the efficiency and accuracy of the metamodel (Kriging), a knowledge database with smart sampling methods has been integrated into the optimization model management, to avoid unnecessary finite elements calculations and enrich the collection (sampling) in each optimization iteration. This method makes it possible to reduce the sampling size and at the same time increases the accuracy of the metamodel.
For validation of the developed method, different benchmark functions were chosen in terms of features and has successfully then minimized. Finally, a practical engineering optimization problem for polymer extrusion was implemented with suggested Kriging Swarm Optimization algorithm (KSO). In this procedure, the Finite Element Analysis (FEA) was combined for simulation procedures to resolve non-isothermal non-Newtonian flow. Polymer extrusion results were applied for gathering information from design space samples and Kriging.
