Development of Complex Analytical Model for Optimizing Software of Wire Drawing Technology

Abstract

In the manufacture of products requiring multi-step wire drawing, it is helpful to use software that can aid in planning and that can calculate the values needed for optimum performance. The model described by analytical closed/explicit formulas provides the shortest calculation time. The aim of this study is to create a model described by analytical closed/explicit formulas approximating the measured data in the best way. An objective mathematical procedure are defined for model selection, and the selected model is proposed for the development of software with a short calculation time that optimizes the technological parameters of multi-step wire drawing and plans the drawing technology.

Examination of Complex Optimization Objective Functions of Parameters of Multi-Step Wire Drawing Technology

“…First of all, it is necessary to define the model describing exactly the parameters of multi-step wire-drawing technology in order to calculate the complex optimizing method. This model, described in [16], yields exactness identical with the exactness of FEM, but a much shorter time is necessary for its calculation. The model is as follows:…”

“…The absolute error-norm (10) introduced in [16] was used for digitizing the difference between the two objective functions; as input, it substitutes the values for power consumption obtained by the complex optimizations belonging to the identical technological adjustment to the place with identical index.…”

“…In [16] a complex model was chosen from among the published models described by explicit analytical formulas on the basis of measurement data. The best approximation of the measured data is given by this complex model, as well as the most important parameters of planning the technology (the wire drawing force, the maximum drawing stress arising in the wire, and the temperature of the wire) are included in this model.…”

“…In order to perform fast calculation of the optimization, it is necessary to choose a model to describe the technological parameters, which requires an exact and a short-time calculation. This requirement is met by the complex model described in [16], as it is very exact, and moreover the time necessary for calculating the analytical models is much shorter than that needed for FEM.…”

Development of a Complex Optimizing Model of Wire Drawing Technology

“…As a first step, it is necessary to find models describing the real technological parameters of multiple-step wire drawing loaded by back tension drawing force. Of the most exact models, it is necessary to choose the model requiring the shortest calculation process, as described in [1]. In our present research work, the results obtained from the model concerning the drawing force are compared with the measurement data as well as with the data obtained from the FEM investigations.…”