Int J Mater Form (2010) Vol. 3 Suppl 1:295–298 DOI 10.1007/s12289-010-0765-5 © Springer-Verlag France 2010

NUMERICAL ANALYSES OF TUBE HYDROFORMING PROBLEM USING ARTIFICIAL NEURAL NETWORKS T. Belhadj1, F. Abbassi 1, S. Mistou 2, A. Zghal 1 1

URMSSDT- ESST Tunis, 5 Avenue Taha Hussein, BP, 56, Bâb Manara, 1008 Tunisia 2 CMAO-LGP-ENIT/Université de Toulouse, France

ABSTRACT: The hydroforming process is characterized in these recent years by the remarkable development to compare with other processes manufacturing such as deep drawing and bending... Hydroforming is a reliable process that improves the resistance and rigidity of parts with the geometrical and dimensional tolerances allowing for lower costs tool and therefore an overall cost of manufacturing reduced. The success of hydroforming process requires the control simultaneously of various parameters such as used material properties, thickness, internal pressure,... In this paper, we introduce our model based in a neural approach (ANN) compared to the numerical simulation and experimental results. This method allows a better thickness distribution during Tee extrusion tube hydroforming process (THF) and the optimization of the final part geometry. A multilayer’s neural networks (MNN) program is used to control the tube wall thickness variation, so the loading paths (axial feeding and the internal pressure) are used like inputs for our networks, the thickness is the output. KEYWORDS: Tube Hydroforming THF, Artificial Neural Networks ANN,

1 INTRODUCTION Technological and the current scientific progress in the field of simulation and numerical prototyping explain the great revolution which characterized the field of the optimization and the control of the processes of hydroforming and the big demand of the industrial and automobile sector in particular of the hydroforming parts. Contrary to the others forming processes such as stamping and forging which generally use tools, tube hydroforming THF is a process which applies an internal pressure to lead to more complex forms with an increased resistance and at reduced cost. In hydroforming, the initial thickness, the internal pressure and tooling design (die holders, dies, inserts, punches, sealing systems...) on a warp-tube are parameters which can predict feasibility to deform or not a part. The effects of these various parameters can be studied while varying the geometry (dimensions) or the conditions of loading. Such an optimized loading can be obtained by the use of the techniques of analysis (numerical and analytical modelling) to avoid certain defects in the deformed tube as the fracture, wrinkling, bursting, etc and to be in the safety and working region. ____________________

* T. Belhadj: ESSTT, 5 Avenue Taha Hussein BP 56-1008 – Bab Manara – Tunisia, +21621124508, +21671391166 [email protected]

Figure 1 show tow parts obtained by tube hydroforming: (a) part with typical fracture, (b) successful part

(a)

(b)

Figure 1: Example hydroformed parts in THF

Many subjects of research tried to propose solutions to optimize the distribution thicknesses according to loading. The Artificial Neuronal Networks ANN is now among the most means used to describe the behaviour and the manufacturing processes of the tube hydroforming (THF). M.A. Karkoub [1], developed a model to predict the amount of deformation caused by hydroforming using random neural networks (RNN).

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A model based on the network abductive which consists to decompose a complex system in simpler subsystems grouped into several layers using polynomial functional nodes and the FEM is employed by Lin and Kwan [2] to predict an acceptable product on T-shape tube hydroforming process. The contribution of this paper is the application of an original neural network technique to predict the thickness distribution in Tube Hydroforming process (THF) according the loading parameters. This paper is made in three step: the first step is devoted to the preparation of a training base which will be used in the following step for the training of neural network. Finally we finish by a real case study to validate our neuronal model.

2 NEURAL NETWORK Inspired by the structure of the human brain, artificial neural networks have been widely applied to fields such as pattern recognition, optimization, coding, control, etc., because of their ability to solve cumbersome or intractable problems by learning directly from data. Today, the artificial neural network was used and integrated in many different field such industrial, military, financial… seeing their efficacy and fidelity. In our case, we will apply a multilayer’s neural network (MNN) to predict the thickness of hydroformed parts. 2.1 TRAINING OF NEURAL NETWORK (NN) Generally, the training of NN is a phase of development of the network of neurons, whose behaviours of the network are modified until obtaining desired behaviours. In this phase it is necessary to well choose the rules and An adequate choice of neural network structure is very important factor to have good results, the choice of the function and training algorithm, the choice of the hidden layers number ... are all factors that directly affect neural network performance. The MatLab toolbox was used like software for the programming (training, generalization…etc) of the neural networks (NN) and the back-propagation like a training algorithm. The back-propagation consists in optimization of the connection weights of the network which were initialized by going up layer by layer, of the output layer towards the input layer in order to minimize the TMSE (Training Means Square Error) given by the Equation [1] calculated in the output S, see Equation [2]. The Training Means Square Error is given as: 1

TMSE = 2 ∑𝑝𝑝𝑖𝑖=𝑝𝑝 ∑𝑘𝑘𝑘𝑘=1(𝑠𝑠𝑖𝑖𝑖𝑖 − 𝑜𝑜𝑖𝑖𝑖𝑖 )2

Where Sik is the desired output (numerical value), Oik the output of the current model, p represents the total number of layers and “k” is the output nodes number. S = Ft . X

(2)

Ft = 1+𝑒𝑒 −𝑋𝑋

1

(3)

𝑋𝑋 = ∑ 𝑤𝑤(𝑖𝑖) . 𝐶𝐶(𝑖𝑖) + 𝑏𝑏

(4)

X represents the input of a second layer which will be the balanced sum of the outputs values of the preceding neuron with a term of bias b (Equation 4)

For a ANN composed by N neurons which the first layer noted C1, C2…, CN and N weights noted w(1), w(2)…, w(N), the term of input X can be determined by equation (4):

Our neural network NN has as inputs the axial load Fa , used to force material into the die cavity and to seal it, and the internal pressure Pi and like outputs the thickness of the formed tube. The internal pressure required during THF process is related to many factors such as material work hardening, material feeding, die friction, irregular geometry, and small corner radii [6]. In our work, we used the equation (5) and (6) to calculate the values of Pi and Fa which will be injected in the numerical model of THF process developed under Abaqus code.

𝑃𝑃𝑖𝑖 =

𝜎𝜎𝑠𝑠 𝑡𝑡 𝑟𝑟

𝐹𝐹𝑎𝑎 = 𝑃𝑃𝑖𝑖 𝐴𝐴

(5) (6)

Where 𝜎𝜎s is the elastic limit of material (ANSI 304), “t0” is the initial thickness of the tube, “r” is the radius of the internal diameter of the tube and “A” is the projected component surface.

(1) Figure 2: Die shape and loading in tube forming process

297

298 0

4 CONCLUSIONS

10

-1

10

-2

10

-3

10

0

10

20

30

40

50

60

70

80

90

100

Figure 6: Example of TMSE Table 3: Example of ANN results compared to Abaqus code which (Faxial=450 N and Pi=15 MPa)

t / t0

P1

P2

P3

P4

P5

Abaqus code.

1.15727

1.00772

1.09154

0.951804

0.833403

ANN

1.1598

1.0324

1.0928

0.93853

0.66288

In the table 3 we show a good correlation between the multilayer’s neural networks (MLANN) results of the thickness variation and the results obtained from the numerical modelling under Abaqus. We see that the thickness values for points P1, P2, P3 and P4 are very close then for the point P5, one notes a difference between the two results. The variation thickness in this zone is very sensitive to the variation of the input parameters, we proposes to improve the training algorithms or to make a base of training especially at this zone based on a numerical experimental design. 3.3 «ANN_THF» interface A MatLab interface «ANN_THF» has been designed to facilitate the implementation and the use of the defined ANN. It allows users to manipulate the network parameters and the direct display of results.

Figure 7: «ANN_THF» GUI

In this paper, a new method of thickness prediction in the tube T-shape finished parts has been suggested. This method is based on the Artificial Neural Network (ANN) and the results of the FEM. In hydroforming, analyzing thinning, thickening, strain and stress distribution on a deformed tube can predict feasibility of forming for a specific part. But to select the parameters of the tube forming process and predict the thickness variations in deformed shape require several simulation tests. For that we develop the “ANN-THF” tool to training the result extracted from the simulation results using multilayer’sartificial neural network. The occurrence of instabilities depends predominantly on the process control selected for the forming loads Fa and the internal pressure Pi.

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