Estimate of consumed energy at backward extrusion process by means of modelling approach

doi:10.1016/j.jmatprotec.2004.04.017

Journal of Materials Processing Technology

Volumes 153–154, 10 November 2004, Pages 907-912

https://doi.org/10.1016/j.jmatprotec.2004.04.017 Get rights and content

Abstract

In order to predict the consumed energy in backward extrusion process (on Al 99.5F7 specimens), the analytic (10 models), numerical, stochastic and experimental modelling of deformation work on the basis of multi-factorial experimental designs (by means of the rotatable design of experiments) was done. Thus, results of backward extrusion force versus punch motion with five different coefficients of friction and five different wall thicknesses were obtained. The most important factor contributing to the accuracy of modelling is the plastic curve of material, for that reason the experimental investigations (compression testing on specimens Ø $20 mm \times 20$ mm) were performed and results in form of Hollomon–Ludwik’s power law were obtained. Investigations in this paper were supported with: data processing system, measuring sensors and Lab View software. Experimental research of deformation work was done for both the checking and the verification of obtained results.

Introduction

Process of backward extrusion of axial-symmetric profiles, in comparison with deep drawing, has techno-economic advantages in spite of considerable investments in tools if deep drawing would be conducted in more steps [1]. For backward extrusion, it can be said that due to its material savings, different distributions of stresses in relation to similar processes, and increasingly reduced machining it has become one of the most promising manufacturing processes.

Problem is to determine the model type (analytic, stochastic or numerical) that describes the consumed energy (in the form of backward extrusion force versus punch motion) in backward extrusion process in the most accurate way in comparison with experiment. Because of that, 10 most common analytic models were examined. It is difficult, by means of analytic models, to determine the force of extrusion process exactly. Therefore, stochastic models especially provide wider possibilities in the solving of extrusion force [2].

It is useful to perform the stochastic modelling of the backward extrusion process before expensive manufacturing process. In this way, savings in process and tool improvements can be made at the start stage of process, before its establishing. When the parameters of process became better-understood, backward extrusion force by means of stochastic modelling can be determined. Thus, it is possible to find out the optimal force for this process.

Needs for the faster and cheaper solving of process are higher, therefore numerical modelling of process was performed. Experimental research for the checking and the verification of obtained results was done. All modelling and experiments were performed according to the rotatable design of experiments. Contribution and new in the paper are established stochastic model and the most accurate analytic model. According to authors’ knowledge, no one did the comparison.

Section snippets

Experimental design

Analytic, stochastic, numerical modelling and experimental investigations of backward extrusion were performed according to the rotatable design of experiments. This is an active experimental design which is the special form of central composition plan applying in the modelling and adaptive control in the processes with more variables. This plan, besides an applicative features, has the property of optimality, thus it is suitable for optimization of processes. The design contains a basic part 2^k

Analytic modelling

On the basis of different models (Dipper’s model, Siebel’s model, Storozev–Popov’s model, Tirosh’s model, Kudo’s model, Tarnovski’s model, Beisel’s model, Romanowski model, Hribar’s model and Anikin–Lukasin’s model) by means of different criteria of yielding with rotatable design of experiments the analytic modelling was derived [4]. According rotatable design of experiments the points of design have following features presented in Table 1, Table 2.

Regarding a grid element twisting (Fig. 1),

Stochastic modelling

Defining of stochastic model starts with identification of set of all process or system parameters (Fig. 3). Working out stochastic model is founded on the statistic processing of experimental data, when conditions are programmed according to the mathematical theory of experimental design (active experiment). That has been achieved by the change of input parameters determining the limit of varying in the conditions of real process. In this way, accurate mathematical model with minimal number of

Numerical modelling

In this analysis the model consisted of 600 axisymmetric quadrilateral elements with four nodes of reduced integration (TYPE=CAX4R). They are recommended as much more appropriate for such large plastic deformation that take place [8]. In backward extrusion during the material flow the element undergo a mesh distortion and that is the most important problem during the numerical analysis in a sever software. A problem is overcome with this type of elements and its interpolation functions. It was

Conclusions

Generally, the most accurate analytic model is Dipper’s model (at 1st and 13th point of design), then follows Anikin–Lukasin’s model (at 11th point), at these models there is the influence of friction, and Hribar’s at 3rd point, there is no the influence of friction. The best results in modelling were obtained by means of stochastic modelling, (at 4th, 5–10th, point of design) but disadvantage of this type of modelling is an expensive experiment. According to the experiment numerical modelling

Acknowledgements

The authors wish to express their gratitude to Dr. Karl Kuzman for his helpful comments, also for the use of equipment and resources during the period of this work. Special thanks for contributing to the paper with his knowledge in FEM to Dr. Zlatko Kampus and Dr. Miha Nastran. Also authors would like to thank TLM companies (Croatia, Sibenik), especially Ing. Zoran Bracic and Ing. Ivan Kostan, for materials used in the experiment.

References (9)

B. Barisic, M. Jurkovic, K. Kuzman, Numerical–experimental analysis of backward extrusion force, in: R. Cebalo, H....
M. Jurkovic, Mathematical Modeling and Optimization of Maching Processes, University of Rijeka Editions, Croatia,...
E.M. Mielnik, Metalworking Science and Engineering, McGraw-Hill Book Company Editions, USA,...
B. Barisic, Modeling approach for the determining of backward extrusion force, in: B. Katalinic (Ed.), Proceedings of...

There are more references available in the full text version of this article.

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