Rolling Force Model Research Articles

Study on vertical-torsional chatter under asymmetric conditions in tandem cold rolling

The vibrations generated by the rolling mills significantly impair the production quality and efficiency of cold tandem rolling. Considering that the main drive system constitutes one of the energy sources of vibration, this study integrates the vertical structure of the rolling mill with the torsional structure of the main drive system for a comprehensive analysis. This study establishes an asymmetric dynamic rolling force model that accounts for the structural asymmetry of the rolling mill, the asymmetric power transmission between the upper and lower connecting shafts of the main drive system, and the long-term wear and friction conditions of the mechanical equipment. Furthermore, this study accounts for the speed differential between the upper and lower work rolls induced by torsional vibrations. Based on these interdependent parameters, this study develops a rolling mill vibration coupling model to comprehensively assess stability. The validation of the model confirms its high accuracy. Variations in rolling torque under different roll speed ratios, friction coefficient ratios, and roll diameter ratios were analyzed, along with the impact of the cross-shear zone's proportion on system stability under key rolling parameters. Furthermore, changes in rolling torque, amplitude, and the cross-shear zone during unstable operating conditions were examined. Finally, the interaction between the vertical and torsional structures was studied, providing a theoretical foundation for optimizing process parameters and mitigating vibrations in the continuous cold rolling process.

Iterative Convergence for Solving the Exit Plastic Zone and Friction Coefficient Model of Ultra-thin Strip Rolling Force

Iterative Convergence for Solving the Exit Plastic Zone and Friction Coefficient Model of Ultra-thin Strip Rolling Force

Relationship between tension and vertical vibration of roll system of twenty-high rolling mill

Abnormal vibration of the roll system seriously affects the quality of the rolled product and even the occurrence of strip breakage. There are many reasons for roll system vibration, such as roll damage, roll bearing failure, and fluctuations in rolling parameters. Especially for 20-roll high-precision ultra-thin strip mills, a key condition for strip rolling is to apply substantial inlet and outlet tension, with the impact of tension fluctuation increasing as the strip becomes thinner. In this paper, firstly, a dynamic rolling force model that accounts for tension fluctuations and vertical vibrations is established. Subsequently, a vertical vibration dynamics equation for the roll system of the twenty-high rolling mill was established. Then the rolling force model was substituted into the dynamics equation to investigate the relationship between tension fluctuations and roll system vibrations. The results indicate that: (1) Tension fluctuations can cause vibrations in the roll system. With the same fluctuation amplitude, the amplitude of the roller system vibration caused by the inlet tension can reach 10 times the amplitude of the roller system vibration caused by the outlet tension; (2) The vibration amplitude is affected by both the tension magnitude and the fluctuations amplitude and it is mainly influenced by the tension fluctuation when the tension magnitude changes are not significant; (3) Fluctuations in inlet and outlet tension will reduce the damping term and stiffness term, respectively, which increases the main resonance amplitude. Finally, the effectiveness of the model is verified by the experiment. The average inaccuracy between the simulated and measured vibration amplitudes is 13 %.

Vertical vibration analysis of rolling interface based on dynamic rolling force with variable friction characteristics

This study investigates the impact of variable friction characteristics at the rolling interface on the vertical vibration of plate and strip rolling mills. Based on the optimized Karman equilibrium theory, a dynamic rolling force model considering the front and back tension, elastic stretching, and rolling speed was established. The amplitude-frequency response equation of rolling mill system is solved by multi-scale method, and the influence of main parameters on vertical vibration of rolling mill system is analyzed. The results show that the increase of the first stiffness coefficient of dynamic rolling force leads to the decrease of the principal common amplitude of the system. On the contrary, when the third stiffness coefficient increases, the system exhibits a jump phenomenon. When the third stiffness coefficient of dynamic rolling force is reduced within a certain range, a stable and unique solution is obtained without jumping phenomenon. Moreover, the smaller the damping coefficient of the upper and lower roller system is, the larger the vibration amplitude is and the jump phenomenon occurs. Decreasing the external disturbance force can effectively reduce the system’s vertical vibration amplitude and suppress the resonance. In addition, with the change of external disturbance force, the roll system of the rolling mill shows a variety of complex motion states, such as periodic motion, double-periodic motion, and chaotic motion. The research results provide an effective theoretical reference for the suppression of vertical vibration of rolling mill.

Rolling force model of V-shaped variable thickness rolling based on energy approach

V-shaped Variable Thickness Rolling (V-VTR) serves as a specialized cold rolling method for manufacturing rolled profiled strips, particularly useful for quickly preparing rolled profiled strips with large thickness ratios. In the process of variable thickness rolling, metal predominantly flows in the lateral direction. However, there is a scarcity of theoretical models for calculating the rolling force of variable thickness rolling, leading to a void in theoretical guidance for both device design and product thickness control. To fill this gap, we introduce a novel mathematical model specifically designed to calculate the rolling force, considering the lateral flow of the metal. Initially, the deformation pattern is investigated and subsequently modeled. Then, the models for kinematically permissible velocity and strain fields are developed, and their validity is confirmed through both experimental data and simulation analysis. Incorporating factors like strain energy and frictional work, a formula for rolling force of variable thickness rolling is derived based on the upper bound theory. The efficacy of this newly proposed rolling force model is confirmed through experimental testing, which indicates that the formula offers a high degree of accuracy.

Research on the analytical model of rolling force for TiAl alloy pack rolling

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.

An analytical model of hot rolling force for a thick plate by combining globally optimal approximation yield criterion and egg-circular velocity field

An analytical model of hot rolling force for a thick plate by combining globally optimal approximation yield criterion and egg-circular velocity field

Application of machine learning methods for the prediction of roll force and torque during plate rolling of micro-alloyed steel

Machine learning technique is extensively used to establish the relationship between non-linear data sets which cannot be described mathematically and thus an exact analytic model is either intractable or too time-consuming to develop. During hot rolling, the effect of process parameters that cannot be captured in mathematical models, such as roll dimensions and its wear, the inter-pass time between rolling passes, temperature variation has been incorporated using multivariate supervised machine learning technique for accurate prediction of roll force and torque during plate rolling of micro-alloyed steel. An ensemble method was used to combine various machine learning techniques and average them to develop one final predictive model. K-cross validation of the model was carried out to validate the results and ensure the model gets the correct pattern of data. Root mean square error of ensemble roll force model was compared with roll force calculation using Sims theory. It was found that the machine learning model can predict the roll force and torque accurately as it takes care of various non-linear process variables which cannot be accounted for mathematically. The R-value of the machine learning model was >98 %, whereas it was 92.2 % for roll force calculation using Sims theory.

A new model for thermal-mechanical coupled of gradient temperature rolling force based on geometrical unified yield criterion

In order to precisely describe the yield deformation behavior of various materials, a generalized yield criterion known as geometrical unified (GU) yield criterion is firstly established in this paper. Based on this yield criterion, an analytical rolling force model of gradient temperature rolling process was established, and the impact of the temperature field was taken into consideration. The GU yield criterion is a function of shear tension ratio, and the classical yield criteria can be obtained as its special cases. The gradient temperature rolling process of an ultra-heavy plate was analyzed depending on the GU yield criterion, and the corresponding energy functional was established. In the meanwhile, the temperature field expression was developed by taking temperature permeability into account. Finally, the analytical model of the force and energy parameters of the gradient temperature rolling process was constructed by fusing the temperature field with the energy functional. The model can very precisely estimate the rolling force and rolling torque when compared to the measured data. The errors of the rolling force and rolling torque are less than 3.27 %.

Establishment and Numerical Analysis of Rolling Force Model Based on Dynamic Roll Gap

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.

A new prediction model for disc cutter wear based on Cerchar Abrasivity Index

The wear evolution indicated that abrasive wear is the dominant wear mechanism for disc cutter wear. Considering the uneven rolling force distribution on the cutterhead, the relative installation radius is introduced to reflect the influence of installation radius on the rolling force, and the CSM rolling force model is corrected based on linear assumption. To accurately predict disc cutter wear, the relative sliding distance between disc cutters and rock is derived based on corrected rolling force and contact theory. The effect of installation radius, cutters radius and penetration on the relative sliding distance is investigated, the results illustrated that the relative sliding distance increase with the installation radius and penetration, conversely, the relative sliding distance increase with the disc cutter radius decrease. In addition, the relationship between wear coefficient and Cerchar Abrasivity Index (CAI) is analyzed by a series CAI test. According to CAI change trend as stylus sliding distance, the effect of stylus shear failure on the abrasivity property within initial test stage was excluded. Furthermore, A new model is proposed to predict disc cutter wear based on the relative sliding distance and wear coefficient. And the effect of installation radius, cutters radius, Uniaxial Compressive Strength (UCS), CAI et al. on the disc cutter wear is investigated, the results illustrate that the disc cutter wear increase with installation radius, penetration, UCS, CAI and spacing between adjacent cutter, conversely, the disc cutter wear increase with the cutter radius and thickness decrease. Finally, the accuracy of proposed model is verified by Yintao water conveyance tunnel project. The research of parameters provides a theoretical basis for optimizing excavation parameters and reducing cutters wear.

Analysis of force and deformation parameters in corrugated clad rolling

Corrugated clad rolling is an emerging and promising technology to produce composite plates with a three-dimensional corrugated interface and excellent performance. A new analytical model is proposed to predict and analyze force and deformation parameters in corrugated clad rolling using the slab method, which solves the problem that there is no suitable analytical model to improve the precision of automatic production control. The analytical model is proposed by selecting a differential element perpendicular to the rolling direction, analyzing the corresponding differential equilibrium equations and calculating the integral constants according to the yield and boundary conditions. Dynamic rolling forces under different contact states between the composite plate and rolls are presented creatively considering the special features of the new corrugated clad rolling that there are multiple complex shapes and stress states in the deformation zone and that there are various outlet conditions of the corrugated composite plate. The accuracy of the proposed analytical model is verified by the comparisons of the calculated values from the model, the FEM results, and the experimental measurements. The error of the proposed model is within 7.36%. The specific rolling pressure distributions along the projected contact arc, the specific horizontal stress distributions along the projected contact arc, the dynamic rolling forces, and the positions of the lower neutral point can be conveniently and accurately calculated by the proposed model, which can help to analyze the mechanism of the corrugated rolling with the variation of the rolling reduction rate, the shear yield stress ratio and the friction factor ratio. The proposed analytical model of dynamic rolling force and deformation parameters is especially suitable for the analysis of the new corrugated clad rolling and can provide technical support for the control precision of automatic production.

An analytical model for the prediction of rolling force of thin slab

ABSTRACTA rolling force model is established by using the unified yield criterion, in which both the changes of the slab temperature and the radius of the roller are considered. In order to solve the integral problem of the nonlinear specific plastic work rate, the unified yield criterion is used to analyse a simplified velocity field, and the internal deformation power is derived. Then, the shear power and friction power are also calculated based on the velocity field, and the total power is obtained by summarising these derived formulas. Finally, the analytic solution of rolling force in terms of the unified yield criterion is obtained by the variational method. Thereafter, the measured data from one domestic factory is used to check the analytical solution of rolling force, in which the temperature drop from the slab inlet to its outlet is considered. Meanwhile, the roller flattening is also considered. It is shown from the comparison and discussion that: the Mises yield criterion that is a special case of the unified yield criterion is more accurate in predicting the rolling force; the thinner the slab is, the more the temperature drop is; the calculation results by considering the roll flattening are improved.

Deduction of a quadratic velocity field and its application to rolling force of extra-thick plate

A quadratic velocity field that meets the kinematically admissible condition is constructed. To check the reliability of the proposed velocity field, the software ANSYS/LS-DYNA is used, and the change law of metal flow in the deformation zone is analyzed. Based on this velocity field, a three-dimensional rolling force model of extra-thick plate is established. During the analysis, the problem of integral difficulty due to the nonlinear Mises yield criterion is settled, and the internal power of deformation is deduced based on the method of inner product and accumulative summation of vector component. Meanwhile, the friction power and the shear power are also calculated by the method of co-line vector inner product and the variable upper bound integration method, respectively. The rolling force is acquired by the energy method and validated with the site measured value. The calculated deviations of the rolling forces between the model and the measured data are within 5.14%. Furthermore, the influences of the temperature difference of the workpiece, relative reduction, thickness-radius ratio, and friction factor on the rolling force model are analyzed. It is showing that the change law of the metal flow by simulation is consistent with the proposed velocity field, and the rolling force model accounting for the temperature difference of the workpiece is much closer to the actual situation.

An integrated model of rolling force for extra-thick plate by combining theoretical model and neural network model

To solve the problem of low precision of the existing theoretical model in predicting the rolling force of extra-thick plate, the genetic algorithm (GA) is used as an enhancing means to improve the global searching ability of the BP model, and a GA-BP model with high precision is firstly established. Furthermore, in order to solve the black box problem of the model, an integrated model is ultimately obtained by combining a theoretical model and the established neural network model. During the modeling, 1000 groups of production data of extra-thick plate rolling are selected and normalized as the data set. The optimal network structure of the GA-BP neural network is determined based on the method of trial and error, and the initial weight and threshold of the BP neural network is solved iteratively with the genetic algorithm. On this basis, an integrated model is ultimately obtained according to the principle of multiplication compensation of average error. It is shown that the maximum prediction error of the original BP model is 7.51%, while the value of the GA-BP model is down to 3.95%. This integrated model has not only inherited the rigorous mathematical structure of the theoretical model, but also occupies the high precision that comes from the GA-BP model. Therefore, the present integrated model is more suitable for the process optimization of extra-thick plate rolling.

Modelling of Deformation Resistance with Big Data and Its Application in the Prediction of Rolling Force of Thick Plate

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.

Optimization solution of vertical rolling force using unified yield criterion

Vertical rolling is an important technique used to control the width of continuous casting slabs in the hot-rolling field. Accurate prediction of vertical rolling force is a core point maintaining rolling-mill equipment. Owing to the limitation of the algorithm in use, the prediction accuracy of most vertical rolling force models based on the energy method can only reach more than 10%. Therefore, it is challenging to optimize the rolling-force model to improve prediction accuracy. An innovative approach for optimizing the calculation of vertical rolling force with a unified yield criterion is presented in this paper. First, the maximal width of a dog-bone region is determined by the slip-line method, and the dog-bone shape is described using a sine-function model. Second, the velocity and corresponding strain-rate fields satisfying kinematically admissible conditions are proposed to calculate the total power of the vertical rolling process. Finally, the analytical solution of the rolling force and the dog-bone-shape model is obtained by repeatedly optimizing the weighted coefficient b of intermediate principal shear stress on the yield criterion. Moreover, the effectiveness of the proposed mechanical model is verified by measured data in the strip hot-rolling field and other models’ results. Results show that the prediction accuracy of the vertical rolling force model can be improved by optimizing the value of b. Then, the impacts of reduction rate, initial thickness, and friction factor on dog-bone shape size and vertical rolling force are discussed.

Development of an Integrated Flow Stress and Roll Force Models for Plate Rolling of Microalloyed Steel

The hot deformation behavior of Nb–V–Ti containing high‐strength steel is studied using compression test. Based on the data generated during hot compression tests, a deep neural network (DNN) flow stress model is developed for the experimental microalloyed steel. The predicted flow stress by the DNN model is compared with flow stress predicted by conventional strain‐compensated Arrhenius constitutive equation. Results using the DNN model are found to be superior to the constitutive equation with overall correlation coefficient (R) greater than 99.8%. The accuracy of the developed DNN flow stress model finds to be significantly higher even at higher strain rates. A DNN roll force model is also developed for the plate rolling of the experimental steel. The predicted flow stress from the DNN flow stress model for the given rolling condition is also used as an input to the roll force model. It is found that DNN model is able to predict the roll force accurately by >98.4% as it takes care of various nonlinear process variable which cannot be accounted mathematically. It also validates the accuracy of DNN flow stress model.

Modeling of Rolling Force for Thick Plate of Multicomponent Alloys and Its Application on Thickness Prediction

During the rolling process of thick plate, the nonlinear specific plastic power that derived from the non-linear Mises yield criterion is difficult to be integrated, which has restricted the establishment of a rolling force model. To solve this problem, a new yield criterion is firstly established, and then used to derive a linear specific plastic power. Meanwhile, a kinematically admissible velocity field whose horizontal velocity component obeys the Logistic function is proposed to describe the metal flow of the deformed plate. On these bases, the rolling energy items including the internal deformation power of the deformed body, friction power on the contact surface, and shear power on the entry and exit sections are integrated successively, and the rolling force model is established. It is proved that the model can predict the rolling force well when compared with the actual data of multicomponent alloys. Besides, the formula for predicting the outlet thickness is ultimately given upon this derived model, and a good agreement is also found between the predicted values and the actual ones, since the absolute errors between them are within 0.50 mm.

Modeling of rolling force of ultra-heavy plate accounting for gradient temperature

In this paper, the nonlinear specific plastic power of the Mises criterion is integrated analytically to establish the rolling force model of gradient temperature rolling for an ultra-heavy plate by a new method called the root vector decomposition method. Firstly, the sinusoidal velocity field is proposed in terms of the characteristics of metal flow during ultra-heavy plate rolling, which satisfies the kinematically admissible condition. Meanwhile, the characteristics of the temperature distribution along the thickness direction of the plate during the gradient temperature rolling is described mathematically. Based on the velocity field and the temperature distribution expression, the rolling energy functional is obtained by using the root vector decomposition method, and the analytical solution of rolling force is derived according to the variational principle. Through comparison and verification, the rolling force model solved by the root vector decomposition method in this paper is in good agreement with the measured one, and the maximum error of the rolling force is just 10.21%.