# Improved Billet Shape Modeling in Optimization of the Hot Rod and Wire Rolling Process

University essay from Linköpings universitet/Institutionen för systemteknik

Abstract:

The hot rod and wire rolling process is widely used to produce rolled iron alloys in different shapes and dimensions. This industry has been under a constant development during the last decades. Today, complex geometries are produced at a high speed since it is possible to use several stands in each mill at the same time. A reason for the development is rising demands from customers. The most important demands are to save energy, to get better material properties and higher dimension accuracy. To meet these demands on speed and accuracy, a better control of how the material behaves in the process is needed. There is also a need to be able to quickly find a new setup of the mill in order to be able to produce other geometries.

The purpose with this Master Thesis is to model and simulate the hot rod and wire rolling process with the modeling language Modelica. The model is given the known inputs and the desired final result in order to compute the unknown inputs to the mill. To meet these goals, a model that depends on for example the gap between the rolls, the roll speeds and the tensions between different stands is needed. It should be possible to make simulations to find roll speeds or to calculate the tensions caused by known roll speeds.

With the help of models of the steps in the process, a model has been developed in Modelica. The model can be expanded to a mill with an arbitrary number of stands. In the search for the best way of modeling a hot rod and wire rolling mill, several algorithms have been simulated and analyzed in Modelica. The results from all simulations show that the billet and the groove should be described by different functions for the upper and the lower half. Furthermore, it is not a good solution to use only polynomials to describe the shapes in the process. A function with infinite derivative in the endpoints is needed to describe the billet in an acceptable way. The problem has also been solved using Matlab. In this work it is shown that the Modelica solution is preferred, compared to solving the optimization problems in Matlab. An advantage with the Modelica solution is that the model can be split into several easily connected sub models. Unfortunately it was even hard for Modelica to solve general problems. The describing functions made it hard to find the intersections and to keep the area constant during the rotation. The least square method could lead to bad approximations of the shapes.