Derivation of Tension Differential Equation for Tandem Rolling Process

The speed difference of strip between two stands is the origin of strip tension in tandem rolling process. The relation between elastic elongation and tension meets Hooke′s law, and the elastic elongation of strip produces speed difference. Based on these principles, the tension differential equations were derived for rolling strip with uniform and variant strip sections with one step or n-1 step disturbance points. The simplified forms of these equations are the same as reported in other references.

Influence of friction-lubrication characteristics varying with rolling speed on instability of chatter and slip in cold tandem rolling process

In the high-speed cold tandem rolling process of thin plate,chatter or slip instability gives rise to the deterioration of equipment and product quality.Macroscopic instability behavior is closely related to interfacial friction-lubrication con-dition which is generally characterized by the friction coefficient.However,with higher and higher speed requirements,the commonly used model of friction coefficient is no longer applicable and accurate.A novel approach is suggested to calculate the speed-dependent friction coefficient,in which the viscosity-pressure-temperature effects of the lubricant,surface roughness states of work rolls and rolled piece are comprehensively involved and the mixed flm lubrication theory is applied.Subsequently,the influences of friction coefficient on the instability of slip and chatter are investigated for a five-stand cold tandem rolling mill.On one side,the critical friction coefficient for each stand is determined by calculating the corresponding slip factor;on the other hand,the friction coefficient varying with rolling speed is combined with the model of theoretical critical rolling speed presented under constant friction coefficient,so that the speed threshold is determined.Furthermore,the stable and unstable regions corresponding to the rear three stands are individually discussed,and the technical strategies are proposed to suppress both slip and chatter frequently occurring in the actual rolling process.

Dynamics-based optimization of rolling schedule aiming at dual goals of chatter suppression and speed increase for a 5-stand cold tandem rolling mill

In the process of cold tandem rolling,chatter instability leads to serious impacts on enhancing rolling speed,improving product quality,reducing production cost and realizing intellectualization.Chatter occurs with the rolling speed up to a certain threshold value,but the critical speed is determined by both product specifications and rolling schedules.A 5-stand cold tandem rolling mill whose first three stands and subsequent two stands,respectively,have four and six rolls was investigated by formulating its dynamic equations with the corresponding structure-process coupling.By applying the stability-based calculation model about the critical rolling speed in each stand,the system dynamic responses around the critical rolling speed were simulated,and the system eigenvalues which represent instability and characteristic frequencies were figured out.Thereafter,via combining the critical rolling speeds with the system dynamic behavior,a dynamics-based optimization model of rolling schedule for the 5-stand cold tandem system was proposed for the purposes of both the chatter suppression and rolling speed increase.In the optimization model,eight rolling technique parameters(four strip thicknesses and four tensions between the upstream and downstream stands)were taken as design variables,and the constraint conditions were set as no chatter instability in all five stands,and the optimization goal was to maximize the outlet speed of the final stand.The pattern search method was introduced to solve the optimization model.By applying such a dynamics-based optimization model for the 5-stand cold tandem rolling process,the chatter instability was suppressed effectively and the rolling efficiency was improved considerably;therefore,such an optimization model is expected to be valuable for intelligent manufacturing of rolling process.

Analysis of Hot Tandem Rolling Force with Logarithmic Velocity Field and EA Yield Criterion

In order to analyze the hot tandem roiling force, a new logarithmic velocity field is proposed. Using the field and linear EA （equal area） yield criterion, the plastic deformation power for plate rolling is analyzed, and the friction power is obtained based on the co-line vector inner product method. Then analytical solution of plate rolling power functional is obtained. Finally, by minimizing the power functional, the rolling torce and torque are received. Compared with those measured ones in hot tandem rolling on-line, the calculated rolling forces are in good agreement with the actual measured ones since the maximum error is less than 12~. Moreover, the effects of various rolling conditions such as thickness reduction, friction factor and shape factor, upon separating force, location of neutral an- gle, and stress state coefficient are discussed systematically.

Control of Surface Thermal Scratch of Strip in Tandem Cold Rolling

The thermal scratch seriously affects the surface quality of the cold rolled stainless steel strip. Some researchers have carried out qualitative and theoretical studies in this field. However, there is currently a lack of research on effective forecast and control of thermal scratch defects in practical production, especially in tandem cold rolling. In order to establish precise mathematical model of oil film thickness in deformation zone, the lubrication in cold rolling process of SUS410L stainless steel strip is studied, and major factors affecting oil film thickness are also analyzed. According to the principle of statistics, mathematical model of critical oil film thickness in deformation zone for thermal scratch is built, with fitting and regression analytical method, and then based on temperature comparison method, the criterion for deciding thermal scratch defects is put forward. Storing and calling data through SQL Server 2010, a software on thermal scratch defects control is developed through Microsoft Visual Studio 2008 by MFC technique for stainless steel in tandem cold rolling, and then it is put into practical production. Statistics indicate that the hit rate of thermal scratch is as high as 92.38%, and the occurrence rate of thermal scratch is decreased by 89.13%. Owing to the application of the software, the rolling speed is increased by approximately 9.3%. The software developed provides an effective solution to the problem of thermal scratch defects in tandem cold rolling, and helps to promote products surface quality of stainless steel strips in practical production.

Backup roll contour of a SmartCrown tandem cold rolling mill

SmartCrown was a new system developed by VAI for improving the strip profile and flatness control first applied in 1700 mm tandem cold rolling mills at Wuhan Iron ＆ Steel （Group） Corporation （WISCO）. After tracing and testing, the application of the conventional crown backup roll matching the SmartCrown work roll of the production mill led to heavy and nonuniform wear, and the edge spalling of the backup roll often occurred. A 3-dimension finite element model of roll stacks was established, which was used to analyze the above-mentioned problems, and it was found that the main reason was the highly nonuniform contact pressure distribution between the work roll and the backup roll. A new FSR （flexible shape backup roll） was developed and applied in 1700 mm tandem cold rolling mills. A lot of good actual effects of FSR, such as evident improvement in profile and flatness of strips, non-occurring edge spalling, wear uniform, and remarkable decrease in roll consumption were validated by long-term industrial applications.

SENSITIVITY ANALYSIS FOR ROLLING PROCESS BASED ON SUPPORT VECTOR MACHINE

A method for the calculation of the sensitivity factors of the rollingprocess has been obtained by differentiating the roll force model based on support vector machine.It can eliminate the algebraic loop of the analytical model of the rolling process. The simulationsin the first stand of five stand cold tandem rolling mill indicate that the calculation forsensitivities by this proposed method can obtain a good accuracy, and an appropriate adjustment onthe control variables determined directly by the sensitivity has an excellent compensation accuracy.Moreover, the roll gap has larger effect on the exit thickness than both front tension and backtension, and it is more efficient to select the roll gap as the control variable of the thicknesscontrol system in the first stand.

Development of simulation system of strip flatness for hot tandem mill

Using three-dimensional rigid-plastic finite element method base on Lagrange multiplier to analyze the deformation of strip,influence function method to calculate the elastic deflection of rolls and three-dimensionalelastic FEM to analyze the flattening deformation between work roll and strip,a coupled model was established with a iteration way.The effect of various kinds flatness control method such as bending force,rolls shift and cross angle and also various kind of influence factors such as friction coefficient,strip crown,rolls wear and thermo-crown on strip flatness can be analyzed using this coupled model.A great deal of information for example outlet crown of the strip,front and back tension,rolling force distribution for per length,rolls elastic deformation and forward slip can be obtained.In order to improve computational efficiency,the average change of rolling force for per unit length was added into the criterion to determine if the coupled process is end,which can save 30 percent computing time for one pass but the changes of strip thickness is not large than 5μm.The exploration has certain conductive significance for improving efficiency of other type of mill.

Tandem Strip Mill's Multi-parameter Coupling Dynamic Modeling Based on the Thickness Control

The rolling process is determined by the interaction of a number of different movements,during which the relative movement occurs between the vibrating roll system and the rolled piece,and the roll system＇s vibration interacts with the strip＇s deformation and rigid movement.So many parameters being involved leads to a complex mechanism of this coupling effect.Through testing and analyzing the vibration signals of the mill in the rolling process,the rolling mill＇s coupled model is established with comprehensive consideration of the coupling interaction between the mill＇s vertical vibration,its torsional vibration and the working roll＇s horizontal vibration,and vibration characteristics of different forms of rolling mill＇s vibration are analyzed under the coupling effect.With comprehensive attention to the relationship between the roll system,the moving strip and the rolling parameters＇dynamic properties,and also from the strip thickness control point of view,further research is done on the coupling mechanism between the roll system＇s movement and the moving strip＇s characteristics in the rolling process.As a result,the law of inertial coupling and the stiffness coupling effect caused by different forms of the roll system＇s vibration is determined and the existence of nonlinear characteristics caused by the elastic deformation of moving strip is also found.Furthermore,a multi-parameter coupling-dynamic model is established which takes the tandem strip mill as its research object by making a detailed kinematics analysis of the roll system and using the principle of virtual work.The coupling-dynamic model proposes the instruction to describe the roll system＇s movement,and analyzes its dynamic response and working stability,and provides a theoretical basis for the realization of the strip thickness＇dynamic control.

Mechanism of Gas Intrusion into Molten Metal during Horizontal Centrifugal Casting

Comprehensively considering the factors such as descaling cooling, air cooling, water cooling, frictional heat and deformation heat in gap of every stand, heat conduction between work roll and strip etc, a model of two-dimensional transient temperature field of finish rolling section in hot tandem rolling was built with finite difference method to calculate the temperature fields of strip and work roll. So two-dimensional accurate analysis and calculation of strip temperature were realized, and the theoretical basis for predicting and controlling strip temperature was provided. The simulated results show that the model is practical and reliable.

Prediction and Control of Thermal Scratch Defect on Surface of Strip in Tandem Cold Rolling

The thermal scratch significantly influences the surface quality of the cold rolled stainless steel strip. In or der to establish a precise mathematical model of oil film thickness in deformation zone, the lubrication in cold rolling process of B443NT stainless steel strip was studied in the laboratory. According to the principle of statistics, a math- ematical model of critical oil film thickness in deformation zone for thermal scratch was built, with fitting and regres- sion analytical method, and then based on temperature comparison method, the criterion for deciding thermal scratch defect was put forward. Storing and calling data through SQI. Server 2005, a software on thermal scratch control was developed in the Microsoft Visual Studio 2008 environment by MFC technique for stainless steel in tandem cold roll- ing, and then it was used into the practical production. Statistical results demonstrated that the hit rate of thermal scratch arrives at 91.47%, the occurrence rate of thermal scratch is decreased by 87.81%, and rolling speed is in- creased by 7.3%. The developed software is of significance to the control of products quality of stainless steel strips, and the analysis and solution to the problem of thermal scratch defects in tandem cold rolling.

Multi-Objective Optimization for Tandem Cold Rolling Schedule

Considering the multivariable, strong-coupled, and nonlinear features of tandem cold rolling mill, a mathematical model of multi-objective optimization was built to facilitate the design of new systems aiming at equating the relative load, preventing slip, and obtaining best shape. BP （back propagation） neural network based on Levenberg- Marquardt algorithm was used for predicting the rolling force. The multi-objective fuzzy theory and method were introduced during the optimization. With an example of 1 370 mm tandem cold rolling mill, the rolling schedule of the common rolling, the single-objective optimization design, and the multi-objective fuzzy optimization design were compared with each other. The results generated from the case study showed that the proposed approach could significantly decreased the values of three objective functions simultaneously and the performance of the optimal rolling schedule was satisfactory and promising. Moreover, the capability and usefulness of fuzzy application in tandem cold rolling schedule were clearly demonstrated.

Modeling and Analysis of Interstand Tension Control in 6-high Tandem Cold Rolling Mill

The interstand tension control is one of the most important ways to meet tight tolerances for strip product quality during tandem cold rolling process. Using coordinate analysis and parabolic approximation for the mass flow balance principle, the strip velocities eliminating the use of forward slips and backward slips were calculated. In order to reduce the effect of roll eccentricity on the tension measurement, a filter based on bilinear transformation was de- signed. Applying a first-order Taylor series approximation, the transfer function matrix model of interstand tension stress was derived. The actual measurements on-site and the final calculation results showed that the established model had high calculation accuracy and was beneficial for interstand tension control of random cold rolling process.

Application of distributed model predictive control based on neighborhood optimization in gauge-looper integrated system of tandem hot rolling

To solve the coupling relationship between the strip automatic gauge control and the looper control in traditional control strategy of tandem hot rolling,a distributed model predictive control(DMPC)strategy for the tandem hot rolling was explored,and a series of simulation experiments were carried out.Firstly,based on the state space analysis method,the multivariable dynamic transition process of hot strip rolling was studied,and the state space model of a gauge-looper integrated system in tandem hot rolling was established.Secondly,DMPC strategy based on neighborhood optimization was proposed,which fully considered the coupling relationship in this integrated system.Finally,a series of experiments simulating disturbances and emergency situations were completed with actual rolling data.The experimental results showed that the proposed DMPC control strategy had better performance compared with the traditional proportional-integral control and centralized model predictive control,which is applicable for the gauge-looper integrated system.

Deformation resistance prediction of tandem cold rolling based on grey wolf optimization and support vector regression

In the traditional rolling force model of tandem cold rolling mills,the calculation of the deformation resistance of the strip head does not consider the actual size and mechanical properties of the incoming material,which results in a mismatch between the deformation resistance setting and the actual state of the incoming material and thus affects the accuracy of the rolling force during the low-speed rolling process of the strip head.The inverse calculation of deformation resistance was derived to obtain the actual deformation resistance of the strip head in the tandem cold rolling process,and the actual process parameters of the strip in the hot and cold rolling processes were integrated to create the cross-process dataset as the basis to establish the support vector regression(SVR)model.The grey wolf optimization(GWO)algorithm was used to optimize the hyperparameters in the SVR model,and a deformation resistance prediction model based on GWO–SVR was established.Compared with the traditional model,the GWO–SVR model shows different degrees of improvement in each stand,with significant improvement in stands S3–S5.The prediction results of the GWO–SVR model were applied to calculate the head rolling setting of a 1420 mm tandem rolling mill.The head rolling force had a similar degree of improvement in accuracy to the deformation resistance,and the phenomenon of low head rolling force setting from stands S3 to S5 was obviously improved.Meanwhile,the thickness quality and shape quality of the strip head were improved accordingly,and the application results were consistent with expectations.

Strip flatness prediction of cold rolling based on ensemble methods

Aiming at the problem of insufficient prediction accuracy of strip flatness at the outlet of cold tandem rolling,the prediction performance of strip flatness based on different ensemble methods was studied and a high-precision prediction ensemble model of strip flatness at the outlet was established.Firstly,based on linear regression(LR),K nearest neighbors(KNN),support vector regression,regression trees(RT),and backpropagation neural network(BPN),bagging,boosting,and stacking ensemble methods were used for ensemble experiments.Secondly,three existing ensemble models,i.e.,random forest,extreme random tree(ET)and extreme gradient boosting,were used to conduct experiments and compare the results.The research shows that bagging,boosting,and stacking three ensemble methods have the most significant improvement in the prediction accuracy of the regression trees model,which is increased by 5.28%,6.51%,and 5.32%,respectively.At the same time,the stacking ensemble method improves both the simple model and the complex model,and the improvement effect on the simple base model is the greatest,which is 4.69%higher than that of the base model KNN.Comparing all of the ensemble models,the stacking ensemble model of level-1(ET,AdaBoost-RT,LR,BPN)paired with level-2(LR)was discovered to be the best model(EALB-LR)and can be further studied for industrial applications.

Genetic Algorithm-Based Optimization Used in Rolling Schedule

A genetic algorithm-based optimization was used for 1 370 mm tandem cold rolling schedule,in which the press rates were coded and operated.The superiority individual is reserved in every generation.Analysis and comparison of optimized schedule with the existing schedule were offered.It is seen that the performance of the optimal rolling schedule is satisfactory and promising.