Prediction of metal wire behavior using genetic programming

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Abstract

Dimensional stability of forming processes is becoming very important in the modern manufacture. It is particularly in mass manufacture that technological systems have to be most reliable and accurate. Growing market demands are pushing the manufacturing engineers towards process optimization in order to achieve high machinery efficiency and reduce manufacturing costs. Predicting the process behavior is an important precondition for having it improved. The paper presents the use of genetic programming for forecasting the wire geometry after forming. The obtained results are the basis for later optimization of forming processes.

Introduction

Dimensional accuracy and geometrical stability of products are two of the major problems in modern manufacture, especially in mass manufacture. Manufacture of the leverarch mechanism is one such typical example (Fig. 1). Some of its parts have to be made very accurately from the functional and esthetical point of view. Since the manufacture rate is generally high, good dimensional stability is a prerequisite for successful and efficient manufacture [1].

In mass manufacture, availability of the machinery is one of the major problems. Improving it would yield more products in less time and at lower manufacture costs. Improvement in machinery availability is only possible through a stable process at a minimal number of the needed recalibrations. This means that manufacture should ensure a very narrow tolerance field. This fact being still a dream today shall have to become a reality in near future.

In the manufacturing process regard should be paid to many time-dependent input parameters. As it is not possible to control them, they play a crucial role in dimensional stability of products [2]. At the same time, many machinery parameters are adjustable. They affect the process performance and are on-line non-controllable. The problem to be solved is how to set all the parameters so that the most stable process area is found, at a certain number of non-controllable input parameters. The problem is quite trivial as long as there are only a few adjustable parameters. In most such cases it is possible to find a solution experimentally. In the case of wire straightening, the problem is more sophisticated, especially when a high geometrical accuracy is to be achieved [3].

Section snippets

Definition of the problem

Wire straightening is very sensitive to the input process parameters such as wire material properties. The reason for this can be found in the fact that material is submitted to a small reversed plastic deformation, which is not constant in the wire cross-section [4], [5]. Elastic deformations, which quite considerably affect the spring back, cannot be neglected in this case. Since the bound of plastic deformation is rather smeared in the wire cross-section, there is high sensibility to

Solution

Genetic programming is a very successful method provided several controllable parameters for the forming process are available. Wire straightening is one of them since the position of each forming roller can be changed and thus treated as a controllable process parameter. An experimental wire straightener and a schematic presentation of adjustable rollers are presented in Fig. 3. Parameters y1, y2 and y3 represent positions of the rollers (mm) in a horizontal straightening plane. z1, z2 and z3

Principles of genetic programming

Genetic programming is one of the methods of evolutionary calculating. Their common point is the principle of genetic combination and natural selection of the most adaptable subjects [10], [11]. They are powerful especially in describing large systems, where classic statistic methods fail. Genetic programming is a non-parametric method defining the connection between input (positions of the rollers) and output parameters (wire straightness). Its advantage is in combining the basic mathematical

Experiments

In our determination of the analytical connection, without having any knowledge about the yield stress of the material formed in a wire straightener, we used genetic programming. To take advantage of this approach, a considerable amount of data is required. This applies to cases with a lot of adjustable parameters, such as the roller position on the wire straightening equipment. The arch geometry very much depends on the initial curvature of the wire obtained after straightening. As clearly

Genetic programming

The experimental data presented in Table 1 were used for modeling the wire behavior by means of genetic programming. The major task was to define the hidden function connecting the input (y2, y3, z1, z2, z3) and output (u1, u2, u3) parameters. It can also be written in the form of Eq. (1) (defined by the genetic algorithm):(u1,u2,u3)=f(y1,y2,z1,z2,z3)The function obtained by the genetic algorithm can be used later in predicting the wire straightening process. The wire straightness can be

Conclusion

Though the numerical-based solution for the prediction of the wire forming behavior is rather complicated, it is rather easy, when the computer is used for reversing the function The related mathematical expression is presented in Fig. 8. It shows its hidden relations in a symbolic form. The reverse function can be used later for on-line control of the wire forming.

This paper describes application of genetic programming in predicting the wire forming behavior as well as the behavior of many

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