STUDY OF ROLLING FORCE DISTRIBUTION ALONG THE ROLLING OF PAIR CROSS MILL

The theory of three-dimensional deformation is used.Based on rigid plastic assumption, the theory of stick friction and the sheet crown curve at the entry and the exit are used. The mathematical analytical formula of the rolling force in lateral distribution is deriven.

Rolling Force and Rolling Moment in Spline Cold Rolling Using Slip-line Field Method

Rolling force and rolling moment are prime process parameter of external spline cold rolling. However, the precise theoretical formulae of rolling force and rolling moment are still very fewer, and the determination of them depends on experience. In the present study, the mathematical models of rolling force and rolling moment are established based on stress field theory of slip-line. And the isotropic hardening is used to improve the yield criterion. Based on MATLAB program language environment, calculation program is developed according to mathematical models established. The rolling force and rolling moment could be predicted quickly via the calculation program, and then the reliability of the models is validated by FEM. Within the range of module of spline m=0.5-1.5 mm, pressure angle of reference circle α=30.0°-45.0°, and number of spline teeth Z=19-54, the rolling force and rolling moment in rolling process （finishing rolling is excluded） are researched by means of virtualizing orthogonal experiment design. The results of the present study indicate that： the influences of module and number of spline teeth on the maximum rolling force and rolling moment in the process are remarkable; in the case of pressure angle of reference circle is little, module of spline is great, and number of spline teeth is little, the peak value of rolling force in rolling process may appear in the midst of the process; the peak value of rolling moment in rolling process appears in the midst of the process, and then oscillator weaken to a stable value. The results of the present study may provide guidelines for the determination of power of the motor and the design of hydraulic system of special machine, and provide basis for the farther researches on the precise forming process of external spline cold rolling.

Cast-rolling force model in solid-liquid cast-rolling bonding(SLCRB) process for fabricating bimetal clad strips

Based on twin-roll casting, a cast-rolling force model was proposed to predict the rolling force in the bimetal solid-liquid cast-rolling bonding(SLCRB) process. The solid-liquid bonding zone was assumed to be below the kiss point(KP). The deformation resistance of the liquid zone was ignored. Then, the calculation model was derived. A 2D thermal-flow coupled simulation was established to provide a basis for the parameters in the model, and then the rolling forces of the Cu/Al clad strip at different rolling speeds were calculated. Meanwhile, through measurement experiments, the accuracy of the model was verified. The influence of the rolling speed, the substrate strip thickness, and the material on the rolling force was obtained. The results indicate that the rolling force decreases with the increase of the rolling speed and increases with the increase of the thickness and thermal conductivity of the substrate strip. The rolling force is closely related to the KP height. Therefore, the formulation of reasonable process parameters to control the KP height is of great significance to the stability of cast-rolling forming.

MENDED GENETIC BP NETWORK AND APPLICATION TO ROLLING FORCE PREDICTION OF 4-STAND TANDEM COLD STRIP MILL

In order to make good use of the ability to approach any function of BP (backpropagation) network and overcome its local astringency, and also make good use of the overallsearch ability of GA (genetic algorithms), a proposal to regulate the network's weights using bothGA and BP algorithms is suggested. An integrated network system of MGA (mended genetic algorithms)and BP algorithms has been established. The MGA-BP network's functions consist of optimizing GAperformance parameters, the network's structural parameters, performance parameters, and regulatingthe network's weights using both GA and BP algorithms. Rolling forces of 4-stand tandem cold stripmill are predicted by the MGA-BP network, and good results are obtained.

Dynamic Correction Algorithm of Rolling Force in Plate Rolling

Based on the Shougang plat mill project, an on-line dynamic correction algorithm was analyzed. This algorithm can adjust model coefficients better because the reasonable correction is based on the measured and calculated rolling force. The results of application on site show that this on-line dynamic correction algorithm is effective.

A Model to Predict Rolling Force of Finishing Stands with RBF Neural Networks

In view of intrinsic imperfection of traditional models of rolling force, in ord er to improve the prediction accuracy of rolling force, a new method combining radial basis function(RBF) neural networks with traditional models to predict rolling f orce was proposed. The off-line simulation indicates that the predicted results are much more accurate than that with traditional models.

Accuracy improvement of the traditional rolling force and torque model powered by an industrial data platform

The calculation results of the rolling force and torque model based on Orowan's differential equation numerical solution method do not fit with the industrial measurements very well.In particular,a quite large deviation on the torque model was found.On the basis of analyzing the shortcomings of the existing method,an improved rolling force and torque model algorithm aided by the Process Integrated Data Application System platform is proposed.Accordingly,the calculation accuracy of the rolling torque model is improved.The improved models are verified by 1711136 records of a data platform.The improved models are also based on Orowan's differential equation.Two coefficients,namely,friction factor and forward slip,are recognized as the crucial factors to be determined from industrial measurements to improve the accuracy.Therefore,the proposed method is a hybrid method that can be used to deeply understand the rolling process and improve the model's accuracy by combining traditional plastic mechanics and data-driving global optimization algorithms.This paper proposes a new approach to studying theoretical rolling deformation models powered by the industrial data platform.

Model of Aluminium Foil Rolling Force Based on Neural Networks

Based on the principle of BP neural networks, the rolling force model is established after thoroughly analyzing and reprocessing the data of 1 350 mm aluminium foil mill. It states that the difference between the output of artificial neural networks rolling force model and the real value is in the order of 3 percent. The model reflects the real feature of process.

Application of cluster analysis on optimization of rolling force learning

The rolling force learning function is an important part of the hot strip parameter calculation process, and the steel classification is the basis of the model parameter calculation,which has a direct impact on the model calculation precision,and the classification of steel quality will directly affect the accuracy of the model calculation.This paper is for the classification of a certain type of steel,in order to find the optimal classification of steel model to achieve greater precision of the rolling force set.Cluster analysis is a method for the study of affinities between samples or variables,in which Distance Coefficient method can be used to demonstrate the differences between the equivalent measured values of the steel deformation resistance in hot strip rolling.Based on the characteristics of the steel components the composition calculation formula CEQ is created by the trial and error method,so as to achieve the consistency between the CEQ and the equivalent deformation resistance by cluster analysis,that is the composition calculation formula CEQ can be used to characterize the equivalent deformation resistance of the steel in hot rolling.In the actual production process,through the composition formula CEQ,the classification of the steel is made,by which the steel rolling force learning calculation is classified and the rolling force setup deviation is reduced,the rolling stability is improved.

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

For the sake of solving the problem that it is difficult to be integrated for the Mises specific plastic power due to its nonlinearity,a new linear criterion,named the globally optimal approximation criterion,is constructed by the polygonal approximation to the Mises circle.The new criterion is proved to be the linear function of the principal stress componentsσ1,σ2 andσ3 and the trajectory of it on theπ-plane is a non-equiangular but equilateral dodecagon intersecting the Mises circle.The theoretical results of the current criterion described by the Lode stress parameters are in excellent accordance with the experimental results.Meanwhile,according to the trend that the metallic flow velocity between rollers aggrandizes gradually from the inlet to the outlet during the hot rolling of a thick plate,a biomimetic velocity field is proposed in which the horizontal velocity component fits the egg-circular curve distribution.The velocity field and its simulated results agree quite well.Subsequently,using the determined linear criterion,energy analysis of the constructed velocity field is utilized to obtain the interior deformation power,while the vector decomposition approach is utilized to obtain the frictional power and shear power.On this basis,the overall power is obtained and the analytical solutions are generated for the rolling torque,rolling force and the coefficient of the stress state under different egg curves by minimizing the neutral angle.Furthermore,the parameter optimization of the characteristic parameterρwhich affects the slope of the egg-circular curve is carried out and the best egg-circular curve which can minimize the energy consumption is determined.The best agreement between the theoretical and observed values of rolling force and rolling torque is under this curve,and the mean relative errors of the rolling torque and rolling force are no more than 2.93%,while the maximum error is no more than 8.35%.

Research progress and intelligent trend of accurate modeling of rolling force in metal sheet

The rolling force model is the basis for reasonable selection of rolling equipment and optimization of rolling process,and the establishment of an accurate mathematical model as well as doing the corresponding parameter analysis has been the focus of research in this field for many years.Different modeling methods of the rolling force and their research progress were introduced,the main methods of which are the theoretical analysis,the finite element simulation,the artificial neural network modeling,the hybrid modeling of theory and neural network,as well as the hybrid modeling of finite element and neural network.Meanwhile,the application examples of rolling force models in thickness control,strip crown control,and schedule optimization were presented,and an outlook on the new directions of future development was made,including establishing new type of hybrid models,solving the black box problem,and realizing the multi-objective optimization accounting for some special requirements.

High Precision Prediction of Rolling Force Based on Fuzzy and Nerve Method for Cold Tandem Mill

The rolling force model for cold tandem mill was put forward by using the Elman dynamic recursive network method,based on the actual measured data.Furthermore,a good assumption is put forward,which brings a full universe of discourse self-adjusting factor fuzzy control,closed-loop adjusting,based on error feedback and expertise into a rolling force prediction model,to modify prediction outputs and improve prediction precision and robustness.The simulated results indicate that the method is highly effective and the prediction precision is better than that of the traditional method.Predicted relative error is less than ±4%,so the prediction is high precise for the cold tandem mill.

Theoretical and Experimental Research on Rolling Force for Rail Hot Rolling by Universal Mill

For rail rolling by universal mill, a simplified three-dimensional theoretical model was built firstly. The kinematically admissible velocity field of the web, head, and base of rail was determined respectively; moreover, the corresponding strain rate field and the strength of shear strain rate were obtained. Then, the plastic deformation power of corresponding deformation zone, the power consumed on the velocity discontinuity surface, and the power generated by backward slip and forward slip were proposed. According to the upper-bound method, the roiling force of horizontal roll and two vertical rolls could be obtained. For verifying the theoretical model, the universal rolling experiments of 18 kg/m light rail was accomplished in Yanshan University Rolling Laboratory, and the experimental data of 60 kg/m heavy rail universal rolling were obtained from the Anshan Iron and Steel Group Corporation. Compared with the experimental data, the theoretical results of rolling force for 18 kg/m light rail and 60 kg/m heavy rail universal rolling were somewhat greater than experimental data, but in general did not exceed them by 15%. Thus, the simplified model was reliable and feasible for presetting and optimizing the parameters of rolling technology according to the upper-bound method.

Long-and Short-Term Self-Learning Models of Rolling Force in Rolling Process Without Gaugemeter of Plate

Owing to a lack of gaugemeter and the variety of steel grades and standards in some plate mills, the longand short-term self-learning models of rolling force based on gauge soft-measuring with high precision were brought up. The soft-measuring method and target value locked method were used in these models to confirm the actual exit gauge of passes, and thick layer division and exponential smoothing method were used to dispose the deformation resistance parameter, which could be calculated from the actual data of the rolling process. The correlative mathematical methods can also be adapted to self-learning with gaugemeter. The models were applied to the process control system of AGC （automatic gauge control） reconstruction on 2800 mm finishing mill of Anyang steel and favorable effect was obtained.

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.

A 3-D Differential Method for Solving Rolling Force of PC Hot Strip Mill

The character of the deformation zone on pair cross rolls is different from that of the regular 4-high mill. Considering comprehensive influences of normal stress and shear stress in rolling direction, width direction and thickness direction, the rolling force calculation model of the PC （pair crossed） hot strip mill is built. Taking the entry stress and the exit stress of strip as the boundary conditions, the longitudinal and transverse distribution of rolling force is worked out by the differential method. Then the total rolling force is calculated, and calculated results are verified by experimental data.

Simplified Weighted Velocity Field for Prediction of Hot Strip Rolling Force by Taking into Account Flattening of Rolls

The weighted velocity field was simplified for analysis of hot strip rolling. Using the field and GM （geometric midline） yield criterion, the deformation power, friction power and shear power were obtained respectively. Summing the partial power contributions, the total deformation power for strip rolling was presented. Then, by minimizing the power function, the rolling force was obtained; meanwhile, considering the effect of roll elastic flattening, iterative calculation of the roll radius was carried out until the radius was convergent. On line data were corn pared with the calculated results to verify the model accuracy. It was indicated that the calculated rolling forces were basically in agreement with the measured ones since the maximum error was less than 10.0%. Moreover, the effects of various rolling conditions such as thickness reduction, friction factor and shape factor, upon separating force, location of neutral angle, and stress state coefficient were discussed systematically.

Prediction and Analysis of the Force and Shape Parameters in Variable Gauge Rolling

Variable gauge rolling is a new process to obtain a plate for which the thickness changes continuously by continuously and dynamically adjusting the roll gap upward and downward in the rolling process.This technology is an efective method for producing lightweight,low-cost,and economical plates.However,variable gauge rolling is an unsteady process,and the changes in the force and deformation parameters are complex.In this research,based on the minimum energy theory of the variational principle and considering the characteristics of the roll movement and workpiece deformation comprehensively,the internal plastic deformation,friction,shear and tension powers,and the minimum result of the total power functional in upward and downward rolling are obtained with the frst integral and then with a variation of adopting the specifc plastic power and strain rate vector inner product.The analytical results of the deformation and force parameters are also established using the variational method.Then the precision of this model is certifed using the measured values in a medium plate hot rolling plant and the experimental data for Tailor Rolled Blank rolling.Good agreement is found.Additionally,the variation rule of bite angle,neutral angle,and location neutral points are shown,and the change mechanism of the friction parameter on the stress state efect coefcient is given in variable gauge rolling.This research proposes a new mathematical model for rolling process control that provides a scientifc basis and technical support for obtaining an accurate section shape in variable gauge rolling production.

Flow stress equation in range of intermediate strain rates and high temperatures to predict roll force in four-pass continuous rod rolling

A flow stress equation was proposed to compute the roll force in the finishing stands of an actual rod mill where the strain rate and the temperature of the material range from 100 to 400 s-1 and from 900 to 1050 ℃,respectively.The underlying idea is to modify the Shida model and Misaka model,which provide flow stress equations（constitutive equations） frequently used to depict deformation behavior of high temperature material at different strain rates.The modified model was coupled with finite element method to compute the roll force during four-pass continuous rod rolling,where strain rates are in the range of 100-400 s-1 at high temperatures（900-1050 ℃）.The roll forces and the surface temperatures of the material at each stand were measured,and the measured data were compared with the computed values.Results reveal that the Misaka model is better than the Shida model for high temperatures and intermediate strain rates.The roll force error was-5.7 % when the Misaka model was used at 900 ℃.However,the error increased by-15.2% at 1050 ℃.When the modified Misaka model was used,the error was reduced to 1.8% on average.It can consequently be deduced that the modified Misaka model can be used to depict the deformation resistance behavior in intermediate ranges of strain rate and high temperature ranges in continuous rod rolling process.

Modeling and finite element analysis of rod and wire steel rolling process

Two thermomechanical coupled elastic-plastic finite element （FE） models were developed for predicting the 12-pass continuous rolling process of GCrl 5 rod and wire steel. The distances between stands in the proposed models were set according to the actual values, and the billets were shortened in the models to reduce the calculation time. To keep the continuity of simulation, a technique was developed to transfer temperature data between the meshes of different models in terms of nodal parameters by interpolation functions. The different process variables related to the rolling process, such as temperature, total equivalent plastic strain, equivalent plastic strain rate, and contact friction force, were analyzed. Also, the proposed models were applied to analyze the reason for the occurrence of an excessive spread in width. Meanwhile, it was also utilized to assess the influence of the roll diameter change on the simulated results such as temperature and rolling force. The simulated results of temperature are found to agree well with the measured results.