Assessment of flat rolling theories for the use in a model-based controller for high-precision rolling applications

Abstract

In the electrical and medical industries the trend towards further miniaturization of devices is accompanied by the demand for smaller manufacturing tolerances. Such industries use a plentitude of small and narrow cold rolled metal strips with high thickness accuracy. Conventional rolling mills can hardly achieve further improvement of these tolerances. However, a model-based controller in combination with an additional piezoelectric actuator for high dynamic roll adjustment is expected to enable the production of the required metal strips with a thickness tolerance of +/-1 µm. The model-based controller has to be based on a rolling theory which can describe the rolling process very accurately. Additionally, the required computing time has to be low in order to predict the rolling process in real-time. In this work, four rolling theories from literature with different levels of complexity are tested for their suitability for the predictive controller. Rolling theories of von Karman, Siebel, Bland & Ford and Alexander are implemented in Matlab and afterwards transferred to the real-time computer used for the controller. The prediction accuracy of these theories is validated using rolling trials with different thickness reduction and a comparison to the calculated results. Furthermore, the required computing time on the real-time computer is measured. Adequate results according the prediction accuracy can be achieved with the rolling theories developed by Bland & Ford and Alexander. A comparison of the computing time of those two theories reveals that Alexander’s theory exceeds the sample rate of 1 kHz of the real-time computer.