An approximate method for a three-dimensional analysis of rolling

doi:10.1016/0020-7403(75)90010-7

International Journal of Mechanical Sciences

Volume 17, Issue 4, April 1975, Pages 293-305

https://doi.org/10.1016/0020-7403(75)90010-7 Get rights and content

Abstract

A theory, based on the extremum principle for rigid perfectly plastic materials, is given for the analysis of three-dimensional deformation in rolling. Theoretical solutions are obtained for single-pass rolling in terms of sideways spread, roll torque and the location of neutral points. The results on spread and roll torque showed excellent agreement with those found by experiments in the literature.

References (20)

R. Hill
J. Mech. Phys. Solids
(1963)
G.D. Lahoti et al.
Int. J. mech. Sci.
(1974)
N. Loizou et al.
J. Mech. Phys. Solids
(1953)
E. Orowan
J.M. Alexander
D.R. Bland et al.
D.R. Bland et al.
J. Iron Steel Inst.
(1952)
D.R. Bland et al.
S. Rudistill et al.
C.W. MacGregor et al.
Trans. ASME, J. appl. Mech.
(1943)

There are more references available in the full text version of this article.

Cited by (140)

Dynamic compensation of the threading speed drop in rolling processes
2024, Journal of Process Control
This paper presents an approach for the dynamic speed drop compensation during threading in rolling processes. The feedforward control design exploits the differential flatness of the mechanical model and accelerates both the rolls and the drive train in a manner such that the acceleration torque is equal to the rolling torque during threading, while simultaneously maintaining the roll at the desired target speed. Ideally, this prevents the speed drop and enhances the quality and stability of the rolling process. The flatness-based feedforward trajectories are optimized in an online fashion to determine the optimal initial roll speed and duration of the acceleration process. An extensive experimental validation on a hot strip finishing mill shows superior performance in terms of various key performance indicators in comparison with a standard overspeed approach.
Mechanics and modeling of cold rolling of polymeric films at large strains — A rate-independent approach
2023, Mechanics of Materials
Recently a new phenomenon of bonding polymeric films in solid-state, via symmetric rolling, at ambient temperatures ( $\approx$ 20 $°$ C) well below the glass transition temperature ( $T_{g}$ $\approx 78 °$ C) of the polymer has been reported. In this new type of bonding, polymer films are subject to plane strain active bulk plastic compression between the rollers during deformation. Here, we analyze these plane strain cold rolling processes, at large strains but slow strain rates, by finite element modeling. We find that at low temperatures, slow strain rates, and moderate thickness reductions during rolling (at which the Bauschinger effect can be neglected for the particular class of polymeric films studied here), the task of material modeling is greatly simplified and enables us to deploy a computationally efficient, yet accurate, finite deformation rate-independent elastic–plastic material behavior (with the inclusion of isotropic-hardening). The finite deformation elastic–plastic material behavior based on (i) the additive decomposition of stretching tensor ( ${D = D}^{e} + D^{p}$ , i.e., a hypoelastic formulation) with incrementally objective time integration and, (ii) multiplicative decomposition of deformation gradient ( $F = F^{e} F^{p}$ ) into elastic and plastic parts, are programmed and carried out for cold rolling within Abaqus Explicit. Frictional interactions are modeled using a consistent rate-independent Coulombic law. Predictions from both formulations, i.e., hypoelastic and multiplicative decomposition, closely match the experimentally observed rolling loads. No specialized hyperelastic/visco-plastic material model is required to describe the behavior of the particular blend of polymeric films under the conditions described here, thereby significantly speeding up the computation for steady-state rolling simulations. It is revealed that under the deformation conditions when principal axes show negligible rotation, hypoelastic formulation can be valid at large elastic stretches. Moreover, the use of classical rigid-plastic modeling (often applicable to metals) is found to greatly underestimate the rolling loads for polymers due to large elastic stretches in the polymer films at large strains. Deformation aspects of solid-state polymeric sheets presented here are expected to facilitate the development of new processes involving (or related to) cold roll-bonding of polymers.
Prediction and analysis of key parameters of head deformation of hot-rolled plates based on artificial neural networks
2022, Journal of Manufacturing Processes
In plate hot rolling, the prediction of head deformation of steel plates is crucial to improve the yield. In this paper, a novel prediction model based on neural networks for head deformation of medium-thick plates is proposed. The dataset of parameters of head deformation of medium-thick plates was established based on machine vision, and the artificial neural networks optimized by improved sparrow search algorithm (ISSA-ANN) was proposed to predict the irregular length and area of the head of finished medium-thick plates. During model parameters setting, mean error (MAE), root mean square error (RMSE), mean absolute percentage error (MAPE), and correlation coefficient (R) are used as the evaluation indexes. Results show that ISSA-ANN performs better than other models in this paper in predicting the head deformation of medium-thick plates. Meanwhile, the effect of key variables on head deformation is investigated and suggestions for improving the head shape of medium-thick plates are given according to the influence of key variables of the model.
Deduction of a quadratic velocity field and its application to rolling force of extra-thick plate
2022, Computers and Mathematics with Applications
Citation Excerpt :
The most common method of establishing a rolling force model is the energy method in terms of a velocity field. The research of velocity field in the three-dimensional rolling can be traced back to the one by Oh and Kobayashi (1975) [5]. They proposed the stream function velocity field and acquired the numerical solution of the rolling force.
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
2022, Journal of Manufacturing Processes
Citation Excerpt :
They simplified the strip rolling process to be the plain deformation, and derived the approximated expressions of rolling torque and force. After then, Kabayashi and Oh [4,5] analyzed three-dimensional rolling process, and constructed the integral framework of rolling energy rate. But, due to the integral difficulty, they can't solve out the analytical solution of rolling force, and just obtained the numerical solution of rolling force by the method of Runge-Kutta.
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.
Dynamic rolling model based on uniform deformation
2020, Journal of Manufacturing Processes
Citation Excerpt :
Simultaneously, the energy method has been extensively studied in the solution of rolling forces. Oh et al. [5] used a kinematically admissible three-dimensional velocity field and considered the influence of shear deformation, and assumed that the friction force was constant, established a three-dimensional deformation model for analyzing the rolling process, then the theoretical solutions of rolling torque, sideways spread and the location of neutral positions are obtained. However, the model does not give a theoretical solution for the rolling force.
Accurate prediction of rolling force is a core point during the hot-rolled strip production. In-depth research on static rolling processes has been carried out in the past. Most models, however, can only be used under static conditions. Therefore, it is challenging to research the dynamic rolling process. This paper presents a dynamic rolling model for hot rolling. Firstly, the strip dynamic velocity model and the dynamic boundary condition model are established, and then the total power equation of the dynamic rolling process is solved based on the energy method. Furthermore, by minimizing the total power function, the dynamic rolling force equation can be obtained. Finally, the effectiveness of the proposed dynamic model is verified by hot strip rolling plant experiments and finite element simulations. The results show that the dynamic model of this paper has higher prediction accuracy and can be applied to the research on the dynamic hot rolling process. Besides, the influence of the vertical velocity of the rolls on the dynamic rolling force and influencing factors of dynamic rolling force are discussed.

View all citing articles on Scopus

View full text

An approximate method for a three-dimensional analysis of rolling

Abstract

J. Mech. Phys. Solids

Int. J. mech. Sci.

J. Mech. Phys. Solids

J. Iron Steel Inst.

Trans. ASME, J. appl. Mech.