Dynamic Modeling of Twin-roll Steel Strip Casting

We consider the problem of dynamic coupling between the rapid thermal solidification and mechanical compression of steel in twin-roll steel strip casting. In traditional steel casting, molten steel is first solidified into thick slabs and then compressed via a series of rollers to create thin sheets of steel. In twin-roll casting, these two processes are combined, thereby making control of the overall system significantly more challenging. Therefore, a simple and accurate model that characterizes these coupled dynamics is needed for model-based control of the system. We model the solidification process with explicit consideration for the mushy (semi-solid) region of steel by using a lumped parameter moving boundary approach. The moving boundaries are also used to estimate the size and composition of the region of steel that must be compressed to maintain a uniform strip thickness. A novelty of the proposed model is the use of a stiffening spring to characterize the stiffness of the resultant strip as a function of the relative amount of mushy and solid steel inside the compression region. In turn this model is used to determine the force required to carry out the compression. Simulation results demonstrate key features of the overall model. INTRODUCTION Motivation and Problem Definition: Near-net-shape manufacturing processes are becoming a major contributor in the reduction of both environmental and economic costs in the industrial sector [1]. For the steel industry, twin-roll strip casting is one of the most prominent near-net-shape manufacturing processes. ∗Address all correspondence to this author. It requires just one-tenth of the facility space, and it reduces the energy consumption by a factor of nine, as compared to traditional steel casting [2]. In the latter, molten steel is first solidified into thick slabs and then compressed via a series of rollers to create thin sheets of steel. In contrast, in twin-roll casting, molten steel is poured directly onto the surface of two casting rolls which simultaneously cool and compress the steel into a strip with a thickness of 1−3 millimeters. Combining these two steps into a single continuous casting process introduces coupling between the rapid thermal solidification dynamics and the mechanical stiffness of the resulting steel strip. To compensate for this coupling from a controls perspective, we require a simple and accurate model that characterizes the system dynamics. Gaps in Literature: Many researchers have modeled the solidification process in twin-roll casting [3–7] but few have considered the coupling between the thermal and mechanical dynamics [5, 6]. In order to design a controller that achieves the desired performance objective of uniform strip thickness, we require a simple model that captures the relevant input-output dynamics of the process. Santos et al. [3] and Liu et al. [4] created high-resolution simulations of the solidification process, but these are too complex to be used for control design. For example, Santos et. al derived a model with over 400 states. Furthermore, these models were intended to only capture the solidification process, and they do not examine the coupling between the solidification dynamics and the mechanical stiffness of the steel strip. Other researchers have derived control-oriented models of the entire process [5–7]. However, their models assume an abrupt phase transition from liquid to solid steel when, in reality, this transition involves the storage of latent heat in a two1 Copyright c © 2016 by ASME