**1. Introduction**

Modern steel factories and enterprises of heavy industry, whose field of activity includes the production of long metallic articles, meet the issue of effective straightening of such products. Typical products that involve straightening during their production technology are billets [1,2], strips [3], railway rails [4], elevator guide rails [5], or more general long linear guideways that enable precise linear motion of machines [6]. For the mentioned commodities, there are only two straightening principles that mostly used in technical practice. The first option is continuous straightening [7,8], where the bar is straightened between two cross-rolling straighteners [9,10] or inside a multi-roller straightening machine [11]. This option, however, is very problematic for straightening bars with large cross-sections [12,13], mainly owing to the requirements of employing mighty bearings.

This article is devoted to the issue of billet straightening, where the second type of straightening is commonly used. The principle of this straightening type relies on threepoint bending [14,15], which is more accurate and admits higher dimension variability of straightened billets cross-sections [16]. In ironworks, three-point bending is a necessary operation performed before grinding billets. The straightening of billets is usually done manually by operators in a manual regime based on human vision and joystick control [1].

The straightening process can be automated in accordance with the Industry 4.0 strategy, but this is a challenging task [17,18]. An automatic straightening machine can achieve optimal effectivity only if the straightening algorithm is adopted to the various profile curvatures of the billet (e.g., single-arc shape, "S" shape, or shape with multiple vertices [19]). Each type of billet shape requires a unique approach to the straightening, which minimalizes the time of the process. This is the so-called multi-step straightening mechanism [6,19], for which functionality is necessary to correctly determine the velocity of the straightening force/stroke, the distance of supports, the number of straightening steps, and so on. Different parameter settings return differently straightened billets [5].

**Citation:** Halama, R.; Sikora, J.; Fusek, M.; Mec, J.; Bartecká, J.; Wagnerová, R. Billet Straightening by Three-Point Bending and Its Automation. *Materials* **2021**, *14*, 90. https://dx.doi.org/10.3390/ ma14010090

Received: 30 November 2020 Accepted: 22 December 2020 Published: 28 December 2020

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The crucial thing is to achieve accurate prediction of spring back [20,21] after releasing the straightening force. To achieve fast calculations, analytical and semianalytical approaches are currently used. The finite element method (FEM) is time-consuming and the solution is dependent on many parameters such as element type, and thus shape functions, geometry, and time discretization (according to the material model implementation), among others. For the purposes of the development of the straightening algorithm, the analytical approach could be inspired by other research works using an analytical solution for spring back prediction. During the last two decades, the strategy of multistep straightening was enhanced for deflected shafts with the circular cross-section by the fuzzy self-learning method [22], for steel wires using genetic programming [23] and for T-section beams using neural networks [24]. The latter approach required finite element simulations to develop the artificial neural network approach. The straightening history should be considered for the prediction of residual stresses, which play an important role in the service of the final products. Ling et al. [25] published an interesting study in this field including the prediction of residual stresses after grinding.

A significant benefit of analytical methods is also the accuracy of the solution, especially when a robust material model is considered in the analysis. Eggertsen and Mattiasson evaluated six cyclic plasticity models for spring back prediction [21]. They showed that the Yoshida–Uemori model [26,27] and its modification can correctly describe the Bauschinger effect, a transient behavior, a permanent softening, and a workhardening stagnation. Hajbarati and Zajkani [28] used the modified Yoshida–Uemori two-surface hardening model [21] to predict the spring back of an advanced high-strength steel. High-strength steels reveal significant spring back. FE analyses of three-point bending experiments were presented, for instance, by Zhao and Lee [29].

The following chapters of this article present the current results in the frame of a long-term project devoted to the development of an automatic billet straightening machine. The machine was designed, constructed, and manufactured by KOMA—Industry s.r.o. for TRINECK ˇ É ŽELEZÁRNY a.s. The camera system and visualisation of the straightening was developed by experts from ELCOM, a.s. The focus of the article is to show the basic ideas of the newly proposed algorithm and to explain the necessary optimisation procedure needed to obtain some process parameters. This is very important for achieving reliable and robust straightening.
