# Robust Algorithm for Calculating the Alignment of Guide Rolls in Slab Continuous Casting Machines
###### Abstract  
To ensure the product quality of a steel slab continuous casting machine, the mechanical alignment of the guide rolls must be monitored and corrected regularly. Misaligned guide rolls cause stress and strain in the partially solidified steel strand, leading to internal cracks and other quality issues. Current methods of alignment measurement are either not suited for regular maintenance or provide only indirect alignment information in the form of angle measurements. This paper presents three new algorithms that convert the available angle measurements into the absolute position of each guide roll, which is equivalent to the mechanical alignment. The algorithms are based on geometry and trigonometry or the gradient descent optimization algorithm. Under near ideal conditions, all algorithms yield very accurate position results. However, when tested and evaluated under various conditions, their susceptibility to real-world disturbances is revealed. Here, only the optimization-based algorithm reaches the desired accuracy. Under the influence of randomly distributed angle measurement errors with an amplitude of 0.01\({}^{\circ}\), it is able to determine 90% of roll positions within 0.1 mm of their actual position. continuous casting; guide roll alignment; strand condition monitoring; optimization algorithm; gradient descent  
27 May 202530 June 202  
strand is in a very delicate state. Misaligned rolls exert excessive force on the strand, deforming it and causing mechanical strain within the material [11]. The solidification front within the strand is vulnerable to strains, ultimately leading to internal cracks [12; 13; 14; 15; 16; 17; 12]. Maintaining the best possible alignment of the guide rolls at all times is, therefore, a high priority for continuous casting machine (CCM) operators. During casting, extreme forces and temperatures act on each roll, degrading their positional accuracies over time [2; 14; 19; 20; 21]. To maintain high-quality production at all times, the alignment must be checked and corrected regularly. However, measuring the alignment of a CCM within the desired accuracy is not a trivial task. The rough machine environment (dirt, cooling water, electromagnetic contamination, vibrations, etc.) and tight production schedules make measuring the positions of the guide rolls with the required precision very challenging. Given the tolerated position deviations, the measuring accuracy should be at least 0.1 mm. Devices like high precision total stations or laser trackers are often used to determine the alignment of CCM [8; 10; 20; 22; 23]. They are able to achieve the desired accuracy, which is why they are the standard in factory workshops where segments of the CCM are maintained, realigned and repaired. For regular in situ alignment measurements, however, these devices are unsuitable. They require long production pauses as well as trained and experienced personnel. In situ measurements are of crucial importance to CCM operators, since they provide information about which segments need to be replaced and how to realign the machine without time-intensive removal of segments. The most common tool to measure the alignment in situ is a Strand Condition Monitoring System (SCM). SCMs are measuring systems that are integrated into the dummy bar of a CCM, which allows them to be pulled through the machine and physically touch and measure every roll. An SCM is fitted with spring-loaded rulers that push against and glide over the outer rolls, while the SCM travels through the casting machine. Each time a ruler has contact with two consecutive outer rolls, its angle is uniquely defined by the positions of the two rolls (see Figure 1). The rulers edge forms a tangent with the circumferences of the two rolls. This tangential angle is stored for each consecutive roll pair. The result of one measurement is, therefore, a set of \(n-1\) angles, where \(n\) is the number of outer rolls. In this paper, a CCM with \(n=102\) outer rolls is used as an example.