In this paper, the fractional order differential terms are introduced into a horizontal nonlinear dynamics model of a cold mill roller system. The resonance characteristics of the roller system under high-frequency and low-frequency excitation signals are investigated. Firstly, the dynamical equation of the roller system with a fractional order is established by replacing the normal damping term with a fractional damping term. Secondly, the fast-slow variable separation method is introduced to solve the dynamical equation. The amplitude frequency response characteristics of the system are analyzed. The study finds that there are three equilibrium points. The characteristics of the three equilibrium points and the critical forces causing the bifurcation are investigated. Due to the different orders of the fractional derivatives, various new resonant phenomena are found in the systems with single-well and double-well potentials. Additionally, the double resonance occurs while p = 0.3 or 1.0, and single resonance occurs while p = 1.8. Unlike integer order systems, the critical resonance amplitude of high-frequency signals in fractional order systems depends on the damping strength and is influenced by the fractional order damping. This study provides a broader picture of the vibration characteristics of the roll system for rolling mills.

Roll flattening is an important component in the roll stack elastic deformation, which has important influence on controlling of the strip crown and flatness. Foppl formula and semi-infinite body model are the most popular analytical models in the roll flattening calculation. However, the roll flattening calculated by traditional flattening models has a great deviation from actual situation, especially near the barrel edges. Therefore, in order to improve the accuracy of roll flattening, a new model is proposed based on the elastic half plane theory. The calculation formulas of roll flattening are deduced respectively under the assumptions of plane strain and plane stress. Then, the two assumptions are combined through the method of introducing an transition coefficient, and the distribution rules of roll flattening for different rolling force, flattening width, roll length and roll diameter are analyzed by using the FEM analysis software Marc. Regarding the ratio of the length to roll end and the roll diameter as variable to fit the transition coefficient, the new model of roll flattening is established based on the elastic half plane theory. Finally, the transition coefficient is fitted to establish the model. Compared with the traditional models, the new model can effectively improve the calculation deviation in the roll end, which has important significance for accurate simulation of plate shape, especially for the distribution of rolling force between rolls.

Aiming at the robotization of the grinding process in the steel bar finishing process, the steel bar grinding robot can achieve the goal of fast, efficient, and accurate online grinding operation, a multi-layer forward propagating deep neural network (DNN) method is proposed to efficiently predict the kinematic solution of grinding robot. The process and kinematics model of the grinding robot are introduced. Based on the proposed method, simulations of the end position and orientation, and joint angle of the grinding robot are given. Three different methods, including SGD + tanh, Nadam + tanh, Nadam + ELU, are used to test the DNN calculation process results show that the method combining Nadam with ELU function has the fastest solution speed and higher accuracy can be obtained with the increase in iteration times. Finally, the Nadam optimizer is used to optimize the calculation results of the example. The optimization results show that this method accelerates the convergence rate of trajectory prediction error and improves the accuracy of trajectory prediction. Thus, the proposed method in this paper is an effective method to predict the kinematic solution when the grinding robot works online.

An end face attitude detection system for special steel bars is designed to solve the problem of defect localization for steel bar grinding. A circle detection method based on improved Density-Based Spatial Clustering of Applications with Noise (DBSCAN) is proposed for calculating special steel bars’ end face attitude. Firstly, the images are subjected to edge detection, connected region marking, and improved DBSCAN in accordance with the image characteristics. After that, the arcs belonging to the same circle are clustered into the same category to create virtual connected regions. Then, circle parameters of a virtual connected region are clustered using an improved DBSCAN algorithm. The actual circle parameter is obtained by calculating the centroid of each category. Finally, the vector is generated under the set coordinate system, passing through the center of the circumcircle of the steel bar end and one endpoint of the two-dimensional code, and the angle of the vector is calculated to determine the attitude of the special steel bar’s end face. The experimental results demonstrate that the method can obtain an attitude angle resolution of 0.2 degrees with an error range of ±0.1 degrees. This will provide accurate defect localization support for the digitization and intelligence of the grinding platform on the special steel bar production line.