Prediction Model of Deformation Resistance and Rolling Force of ESP Production Line Based on the Temperature Gradient

The precision of traditional deformation resistance model is limited, which leads to the inaccuracy of the existing rolling force model. In this paper, the back propagation (BP) neural network model was established according to the industrial big data to accurately predict the deformation resistance. Then, a new rolling force model was established by using the BP neural network model. During the establishment of the neural network model, the data set of deformation resistance was established, which was calculated back from the actual rolling force data. Based on the data set after normalization, the BP neural network model of deformation resistance was established through the optimization of algorithm and network structure. It is shown that both the prediction accuracy of the neural network model on the training set and the test set are high, indicating that the generalization ability of the model is strong. The neural network model of the deformation resistance is compared with the theoretical one, and the maximum error is only 3.96%. Furthermore, by comparison with the traditional rolling force model, it is found that the prediction accuracy of the rolling force model imbedding with the present neural network model is improved obviously. The maximum error of the present rolling force model is just 3.86%. The research in this paper provides a new way to improve the prediction accuracy of rolling force model.

In the pursuit of intelligent manufacturing goals, industrial big data technology has emerged as a key enabler in advancing the steel industry. Traditional rolling force (RF) models typically rely on data from individual cold rolling production lines, leading to lower accuracy and limited interpretability. To overcome this, an industrial data platform has been developed, offering a complete and reliable dataset to enhance the performance of RF prediction models. A data-driven machine learning framework is proposed, employing an improved sparrow search algorithm to optimise the weighting parameters of the broad learning system. The Shapley additive explanations method is further applied to elucidate the contributions of multivariate features from hot and cold rolling, thereby enhancing the interpretability of RF predictions. The performance of the proposed framework was validated on the production line of a leading steel plant, demonstrating significant advantages over existing state-of-the-art models. Furthermore, this study demonstrates and extensively elaborates on the significant impact of hot rolling parameters in enhancing the predictive accuracy of cold RF models. Industrial application validation demonstrates that the proposed framework accurately predicts the RF at the head of cold-rolled strip, enabling feedforward compensation for bending force and effectively improving flatness defects, further confirming the method's efficacy.

Rolling force model is a basic model of cold rolling process control system, and the main influential factors on forecasting accuracy of rolling force are the material deformation resistance and friction coefficient. Bland-Ford-Hill model which is the classic rolling force model of cold rolling process is selected to calculate rolling force. Five methods of calculating friction coefficient are explained. Deformation resistance is calculated by the deformation resistance formula derived through Bland-Ford-Hill formula, and its model parameters are acquired through the least squares method. Then the friction coefficient and the deformation resistance are substituted into the rolling force model to calculate rolling force. By comparing with the actual rolling force, the method 4 can make the average error smaller. therefore, method 4 is selected to establish the model library of friction coefficient and deformation resistance of different kinds of steels. Finally, the model parameters adaptive learning method is proposed to improve the prediction precision of rolling force in this paper.

An off-line model was developed and used to improve an on-line model for a Finishing Mill (FM) operation set-up in a Hot Strip Mill (HSM). The off-line model estimated the temperature and roll force of the steel hot band which passed through the holding table and FM. The hot band temperature was estimated using the finite difference method. The steel specific heat and thermal conductivity were functions of not only temperature but also chemistry of steel. The heat transfer coefficient of water flowing on the hot strip surface in FM was expressed as a function of temperature. A semi-empirical equation was used to calculate temperature increase due to strip rolling deformation. Equations were also applied to calculate heat transfer coefficients by water jet descaling, bottom roller and strip contact, air velocity and radiation. The estimate for roll force was improved by modifying both the roll force modification equation (called Qp equation), and the deformation resistance equation. The new Qp equation included parameters such as reduction, aspect ratio of the deformation zone, inter-stand looper tensions, and steel deformation resistance. The deformation resistance equation was a function of strip temperature, chemical composition, strain, strain rate, and residual strain. The residual strain was found existing only for the Cb- and Ti-containing steels. The deformation resistance equation was derived using the strip temperature (estimated by the off-line model) and measured operation data (which included roll force and roll speed). A comparison was made between the off-line model estimation and mill measurements for temperature and roll force. The derived deformation resistance equation was tested in the plant on-line model. The roll force estimated by the on-line model, before and after modification of both the deformation resistance equation and the roll force Qp modification equation, was also compared with the measurements.

Research on rolling force model in hot-rolling process of aluminum alloys

Applying mathematical models and numerical methods is crucial for describing and simulating the metal cold-rolling process, wherein the accurate prediction of rolling force is an effective way to improve the quality of rolled sheets. This paper considers key influencing parameters such as friction lubrication, stress, tension, and roll-flattening radius during the rolling process and establishes a calculation model for the friction coefficient and roll-flattening radius. By considering the coupling effect of the dynamic roll gap on rolling force, a rolling force model for non-steady-state friction lubrication during the rolling process is obtained. The correctness of the proposed model is verified by comparing it with industrial measurement results. The influences of the friction coefficient, stress, tension before and after rolling, and roll-flattening radius on rolling force are quantitatively studied. The results show that the rolling force increases with an increase in the friction coefficient. When the friction coefficient exceeds 0.2, the rate of increase slows down, approaching dry friction conditions. The rolling force increases linearly with stress but decreases with increasing tension before and after rolling. The rolling force model, considering the roll-flattening radius, provides numerical calculation results that are closer to an industrial measured rolling force. This work contributes to a better understanding of the mechanism behind the improvement of the cold rolling process.

For cold rolling process, the theoretical Bland-Ford-Hill model and Hitchcock model are used for the rolling force and roll flatten radius calculation. Friction coefficient and deformation resistance are calculated with empirical regression models. From rolling force model, the recalculation model for the friction coefficient and deformation resistance can be derived. After rolling, with actual measured data, friction coefficient and deformation resistance can be recalculated, and model parameter can be got by regression method. The practical application verifies that the accuracy of rolling force calculation model is good.

Modeling of rolling force of ultra-heavy plate considering the influence of deformation penetration coefficient

A primary factor in manufacturing high-quality cold-rolled sheet is the ability to accurately predict the required rolling force. The rolling force directly influences roll-stack deflections, which correlate to the resulting flatness quality of the rolled sheet. Increasingly high demand for thin and ultra-thin gauge for cold-rolled sheet metals, along with the correspondingly larger sensitivity of flatness defects when rolling thin gauges, makes it more important to accurately and rapidly predict the rolling force before the rolling operation begins. Accurate rolling force predictions enable assignment of appropriate pass schedules and flatness mechanism set-points early in the rolling process, thereby reducing rolling time, improving quality, and reducing scrap. Traditionally, force predictions in cold rolling have employed two-dimensional analytical models such as those proposed by Roberts and by Bland & Ford. These simplified methods are prone to inaccuracy, however, because of several uncertain, yet influential, model parameters that are difficult to establish deterministically for wide-ranging products. These parameters include, for example, the average compressive yield strength of the rolled strip, frictional characteristics relating to low and high mill speeds, and the strain rate dependency of yield strength. Conventionally, these unknown parameters have been evaluated deterministically by comparing force predictions with actual rolling force data and using a best-fit regression approach. In this work, Bayesian updating using a probability mass function (PMF) is applied to identify joint posterior probability distributions of the uncertain parameters in rolling force models. It is shown that the non-deterministic Bayesian updating approach is particularly useful as new evidence becomes available in the form of additional rolling force data. The aim of the work is to incorporate Bayesian inference into rolling force prediction for cold rolling mills to create a probabilistic modeling approach which can also “learn” as new production data is added. The goal is a model that can better predict necessary mill parameters based on accurate probability estimates of the actual rolling force. The rolling force data used in this work for applying Bayesian updating is actual production data of grades 301 and 304L (low carbon) stainless steels, rolled on a 10-inch wide 4-high cold rolling mill. This force data was collected by observing and averaging load cell measurements at steady rolling speeds.

A mathematical model of friction coefficient was established to calculate the roll force during hot strip rolling process. Firstly, a linear regression model with four input variables was proposed to describe friction behavior, namely rolling speed, strip temperature, reduction rate, and the number of rolled strips since roll change. Then, the method of principal component regression, which can eliminate the effect of multi-collinearity among the input variables, is used to build the friction model. The obtained model was tested by statistical functions, and the results indicated that the model was valid and showed as well that the cumulative contribution rate of the first two principal components of the regression model was as high as 98% and the first two principal components contained almost all the information of original input variables. The industrial experiment confirmed that the roll force model with the proposed friction model had the higher prediction accuracy than the Sims model, and the proposed model could be used in online calculation for hot-rolled roll force.

In view of the influence of the fluctuation of incoming material composition, finishing temperature and coiling temperature on the deformation resistance in the cold rolling process during the hot rolling process, the optimization objective function is established by combining the analytic method and big data regression. Further, the relevant characteristic coefficients are calculated through a large number of on-site actual data, and the deformation resistance model of hot-rolled finished strip and the rolling pressure prediction model of cold rolling process are obtained. Through the field test, the deviation between the predicted rolling force and the actual rolling force is less than 2%, and the accuracy of the model can meet the engineering requirements. More importantly, after using the research results described in this paper, the quality of cold rolled strip shape has been significantly improved, which can greatly improve the economic efficiency and market competitiveness of enterprises.

Pack rolling is a hot rolling process for metals with poor plastic forming. The rolling force model is an important model for pack rolling process. Based on the E. Orowan differential equation and the characteristics of pack rolling process, the analytical model of rolling force for pack rolling process was established. Based on the established rolling force model, the influence of roll diameter, reduction rate, metal layer thickness ratio and shear yield stress ratio on the distribution of rolling stress, neutral angle and connection angle was studied. The results indicate that as the increase of reduction rate and shear yield stress ratio, and the reduction of metal layer thickness ratio, the middle layer metal is more prone to plastic deformation. The basic assumptions of the analytical model were verified through a three-dimensional finite element model. The outer layer metal and the middle layer metal were selected as 304 stainless steel and Ti-Al-2Cr-2Nb alloy for pack rolling experiments, respectively. The error between the calculated results of the analytical model and the experimental results is within 15%. The analytical model of rolling force can accurately predict the rolling force and provide theoretical guidance for the formulation of the pack rolling process.

Rolling force model is very important during the rolling process. The accuracy of the model not only affect the formulation of rolling process, the equipment designing, but also involve with the thickness precision of the product. SIMS formula is adopted to establish the rolling force model. The parameters of the model are obtained by using the fitting method[l]. After that, the factors of the formula affected the rolling force are analyzed, the result shows that the steel rolling temperature is the key influence factors of rolling force, and it indicates that the key factor of the stability of rolling process is temperature.

Due to the development of thin slab hot rolling technology, hot rolling thin strip at a higher speed is inevitable. As a result of high-speed rolling, thin slab is deformed at a wide range of strain rate inside the rolling zone. Because the flow stress of steel is strongly dependent on strain rate at elevated temperature, it is imperative to consider its variation when calculating roll force and roll pressure. By substituting time with speed and length, strain rate variation is obtained. A strain rate–dependent flow stress curve for non-oriented silicon steel is implemented into Karman equation to calculate rolling pressure distribution. It is revealed that the rolling force can be effectively reduced by decreasing the radius of work roll. It is further revealed that the appearance of strip/roll surface sticking is more likely at the exit of rolling zone than the neutral point, because strain rate reaches zero and the flow stress drops at the exit. Combined with Influence Function Method for elastic deformation of roll surface, the proposed model can predict roll force with a good accuracy compared with industrial data.

As significant theory evidence in thick plate or heavy gauge plate hot rolling, the deformation behavior at the thickness direction was investigated. In the present work, multi and single pass rolling processes were studied by 2D explicit dynamic finite element method (FEM) simulation and verified by laboratory hot rolling experiment. The value of stress and strain could be obtained in any passes and time in the hot rolling process accurately. The verified FEM model could be used as an important reference factor for other hot rolling processes. Strain and stress distribution data was obtained from four portions at the thickness direction. A cooper rod was knocked into the hot rolling specimen, as a reference substance to observe the deformation after the hot rolling experiment. In the multi-pass simulation with nearly 10% per-pass reduction, the core metal yield when the total reduction was 40%. The same performance could be achieved when the first pass reduction larger than 20%. However, extremely first pass reduction would cause an instability deformation result in a confusion of microstructure. Finally, the relation between the reduction and the number of rolling passes was discussed.