Better annealing of brass with nonlinear models
The benefits of nonlinear modelling to brass production have been shown using processing data. An international team reports on a study conducted at the Zutphen plant in the Netherlands.
The microstructure of brass is highly sensitive to annealing conditions as well as its composition. Small variations in annealing temperatures or line speed result in significant variations in mechanical properties as well as grain sizes. A large number of variables influence the microstructure and mechanical properties. As a consequence, it is difficult for operators to decide how to anneal strips of different thicknesses and compositions to achieve a specified grain size and hardness.
Brasses are used for applications such as architecture, radiators, pipes, valves and musical instruments, and for decorative purposes. Brasses are alloys of copper and zinc, which may contain up to 40% zinc and sometimes other alloying elements in small amounts. Depending on the application, different material properties of brass are important. In many situations hardness and tensile strength are the most crucial, but in other cases electrical or thermal conductivities matter.
Hardness or microstructure specifications are often achieved by a continuous annealing process after cold rolling. The final hardness of the material depends on its composition and annealing process variables, as well as its thickness.
The production process starts with melting the metal in a furnace. The melt is shifted to a holding furnace, after which continuous casting of strips takes place. After cooling, these strips undergo flattening, milling of top and bottom surfaces, and then break-down rolling. Intermediate annealing is done in either a strand annealer or a batch annealer. After this, the strips are rolled to desired thickness in a four-high, five-stand rolling mill. These rolled strips are then continuously annealed in a vertical furnace.
The annealing furnace consists of a horizontal part where preheating takes place, followed by a long vertical part with four zones. Each zone has four fans with controllable speeds to improve convection. The strip passes through this furnace and arrives in a quench tank, where the temperature drops to around 30ºC. Temperatures in all four zones of the vertical part of the furnace are normally kept the same, but fan speeds are often different. After quenching, the strips are pickled, brushed and rinsed before coiling. The final operations consist of rolling to temper and then slitting, or just slitting (annealed to temper). The product is then tested for quality, including its microstructure. The annealed, coiled strips are then ready for shipping.
Different production processes have different objectives, variables and constraints, and different materials undergoing changes. Whatever type of process – batch, continuous or a fed-batch – there are a number of requirements a product must meet so that it falls within given upper and lower limits.
The consequences of a production process include: product properties, production rate, raw material consumption, energy consumption and emissions. The objective of process guidance is to determine the best values of process variables so the consequences of the production process fall within the desired limits. It is also important that a production economic variable (such as production rate, raw material consumption, energy efficiency, purity, number of defects, emissions or any other variable) is maximised or minimised. The problem looks similar for a wide variety of processes from the mathematical modelling point of view.
Nonlinear modelling has been in industrial use for about 15 years. In general, mathematical models represent knowledge of the quantitative effects of relevant variables in a concise and precise form. They can be used instead of experimentation if they are reliable enough. Mathematical models also permit the user to carry out various kinds of calculations, such as optimisation, which can be used to determine suitable values of process variables. Mathematical modelling can be performed in various ways, and these variations are applicable in different situations.
It is not possible to use physical modelling in many situations. Even if it is possible, physical models tend to compute the output more slowly than empirical or semi-empirical models. Development of physical models is time consuming. Nonlinear modelling tends to be expensive, but physical modelling is usually even more so. Physical models involve assumptions and simplifications, thus empirical modelling is often a better alternative when suitable data is available.
Conventional empirical modelling is based on linear statistical techniques. However, nature is not absolutely linear so it helps to take nonlinearities into account rather than ignore them. If the range of variables is small, linear techniques are sometimes sufficient. New techniques of nonlinear modelling based on feed-forward neural networks allow us to approximate without specifying in detail the nonlinearities to be accounted for. They allow for free-form nonlinearities, unlike linear and nonlinear regression methods.
Nonlinear modelling requires experimental or production data. In this case, a year’s worth of normal production data from the Zutphen plant in the Netherlands was used. The information contained over 50 different variables, which included the brass composition, annealing temperatures, and line and fan speeds, as well as the thickness of the strip, hardness and average grain size after annealing. The data was preprocessed, analysed and cleaned before the final nonlinear models were developed.
The resulting models were feed-forward neural networks with sigmoidal activation functions on the hidden layer. They were implemented in software suitable for use in metal industries. Testing of the nonlinear models at the Zutphen plant showed them to be sound and useful. It is now possible to predict the hardness of annealed strips before the process starts, and operators can make changes to the line speed, oven temperatures or fan speeds if the predicted hardness deviates from the desired value. Effects of the input variables on hardness can also be plotted.
The relationship between the composition of brass, and process variables of annealing and the resulting mechanical properties and microstructure, are complicated. It is not feasible to develop sufficiently accurate and reliable physical models for this process, partly because the phenomena taking place in the process are not well understood. Empirical or semi-empirical modelling, however, does not require full understanding. As shown by this work, it is sufficient to be able to measure the variables of interest. Due to the nonlinearity of nature, nonlinear modelling is often a better alternative to linear statistical techniques.