scholarly journals The Central Strain Analytical Modeling and Analysis for the Plate Rolling Process

2021 ◽  
Author(s):  
Lian-Yun Jiang ◽  
Yaoyu Wei ◽  
Heng Li ◽  
Li-feng Ma
Keyword(s):  
Boundary Conditions ◽  
Function Method ◽  
Rolling Process ◽  
Equivalent Strain ◽  
Shear Strain Rate ◽  
Deformation Region ◽  
Rigid Zone ◽  
Plate Rolling ◽  
Geometric Boundary ◽  
Strain Model

Abstract The strain after rolling plays an important role in the prediction of the microstructure and properties and plate deformation permeability. So it is necessary to establish a more accurate theoretical strain model for the rolling process. This paper studies the modeling method of the equivalent strain based on the upper bound principle and stream function method. The rolling deformation region is divided into three zones (inlet rigid zone, plastic zone, and outlet rigid zone) according to the kinematics. The boundary conditions of adjacent deformation zones are modified according to the characteristics of each deformation zone. A near-real kinematics admissible velocity field is established by the stream function method on this basis. The geometric boundary conditions of the deformation region are obtained. The deformation power, friction power and velocity discontinuous power are calculated according to the redefined geometric boundary conditions. On this basis, the generalized shear strain rate intensity is calculated according to the minimum energy principle. Finally, the equivalent strain model after rolling is obtained by integrating the generalized shear strain rate in time. The plate rolling experiments of AA1060 and the numerical simulations are carried out with different rolling reductions to verify the analytic model precision of the equivalent strain. The results show that the minimum and maximum relative equivalent strain deviation between the analytic model and the experiment is 0.52% and 9.96%, respectively. The numerical calculation and experimental results show that the model can accurately calculate the strain along the plate thickness. This model can provide an important reference for the rolling process setup and the microstructure and properties prediction.

scholarly journals The Analysis of the Asymmetric Plate Rolling Process in the Finishing Stand 3600/ Analiza Asymetrycznego Procesu Walcowania Blach Grubych W Klatce Wykańczającej 3600

2014 ◽  
Vol 59 (4) ◽  
pp. 1533-1538
Author(s):  
A. Kawałek ◽  
H. Dyja ◽  
M. Knapinski ◽  
G. Banaszek ◽  
M. Kwapisz
Keyword(s):  
Process Parameters ◽  
Rotational Speed ◽  
Shape Factor ◽  
Rolling Process ◽  
Asymmetry Factor ◽  
Asymmetric Rolling ◽  
Rolling Mills ◽  
Plate Rolling ◽  
Strip Shape ◽  
Roll Gap

Abstract In order to enhance the quality of plates, various solutions are being implemented, including normalizing rolling, the process of rolling followed by accelerated cooling, as well as new roll gap control systems. The hydraulic positioning of rolls and the working roll bending system can be mentioned here. The implementation of those systems results in increased loads of the rolling stands and working tools, that is the rolls. Another solution aimed at enhancing the cross-sectional and longitudinal shape of rolled plate is the introduction of asymmetric rolling, which consists in the intentional change of the stress and strain state in the roll gap. Asymmetric rolling systems have been successfully implemented in strip cold rolling mills, as well as in sheet hot rolling mills. The paper present results of studies on the effect of roll rotational speed asymmetry and other rolling process parameters on the change in the shape of rolled strip and the change of rolls separating force for the conditions of normalizing rolling of plates in the finishing stand. The variable process parameters were: the roll rotational speed asymmetry factor, av; the strip shape factor, h0/D; and the relative rolling reduction, ε. Working rolls of the diameter equal to 1000 mm and a constant lower working roll rotational speed of n = 50 rpm were assumed for the tests. The asymmetric rolling process was run by varying the rotational speed of the upper roll, which was lower than that of the lower roll. The range of variation of the roll rotational speed factor, av =vd/vg, was 1.01÷1.15. A strip shape factor of h0/D = 0.05÷0.014 was assumed. The range of rolling reductions applied was ε = 0.08÷0.50. The material used for tests was steel of the S355J2G3 grade. For the simulation of the three-dimensional plastic flow of metal in the roll gap during the asymmetric hot rolling of plates, the mathematical model of the FORGE 2008 ® program was used. For the mathematical description of the effect of rolling parameters on the strip curvature and rolls separating force the special multivariable polynomial interpolation was used. This method of tensor interpolation in Borland Builder programming environment was implemented. On the basis of the carried out analysis can be state, that by using the appropriate relative rolling reduction and working roll peripheral speed asymmetry factor for a given feedstock thickness (strip shape ratio) it is possible to completely eliminate the unfavorable phenomenon of strip bending on exit from the roll gap, or to obtain the permissible strip curvature which does not obstructs the free feed of the strip to the next pass or transferring the plate to the accelerated plate cooling stations. Additionally by introducing the asymmetric plate rolling process through differentiating working roll peripheral speeds, depending on the asymmetry factor used, the magnitude of the total roll separating force can be reduced and, at the same time, a smaller elastic deflection of rolling stand elements can be achieved. As a result smaller elastic deflection of the working rolls, smaller dimensional deviations across its width and length finished plate can be obtained.

The Laser Thickness Measurement System Applied in Steel Rolling

2013 ◽  
Vol 718-720 ◽  
pp. 725-732
Author(s):  
Kuang I Chang ◽  
Weber Yi Yuan Lin ◽  
Bor Nian Chuang ◽  
Kuang Fu Huang
Keyword(s):  
Steel Plate ◽  
System Development ◽  
Plate Thickness ◽  
Measurement Data ◽  
Integrated Design ◽  
Rolling Process ◽  
Thickness Measurement ◽  
Thickness Gauge ◽  
Steel Rolling ◽  
Plate Rolling

This paper mainly describes application of non-contact laser thickness gauge in steel plate rolling process, including workstation site thickness measurement, data collection, information analysis and integration with ERP system, as well as problems may arise during applications and sustainable development in the future. Through the system development to realize traditional steel plate rolling industry information planning, paperless operations, increase work efficiency, enhance product quality and zero defective products. Integrated design of steel plate thickness measurement and tachometer, to understand the pros and cons of output products right after steel plate rolling, and do product level classification immediately to assist enterprises to save manpower, time and loss cost of export defective products to the market, and eventually increase products competition and profits.

scholarly journals Validation of the stream function method used for reconstruction of experimental ionospheric convection patterns

2000 ◽  
Vol 18 (4) ◽  
pp. 454-460
Author(s):  
P.L. Israelevich ◽  
V. O. Papitashvili ◽  
A. I. Ershkovich
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Stream Function ◽  
Electric Fields ◽  
Electric Potential ◽  
Potential Distribution ◽  
Function Method ◽  
Polar Cap ◽  
Ionospheric Convection ◽  
Convection Patterns

Abstract. In this study we test a stream function method suggested by Israelevich and Ershkovich for instantaneous reconstruction of global, high-latitude ionospheric convection patterns from a limited set of experimental observations, namely, from the electric field or ion drift velocity vector measurements taken along two polar satellite orbits only. These two satellite passes subdivide the polar cap into several adjacent areas. Measured electric fields or ion drifts can be considered as boundary conditions (together with the zero electric potential condition at the low-latitude boundary) for those areas, and the entire ionospheric convection pattern can be reconstructed as a solution of the boundary value problem for the stream function without any preliminary information on ionospheric conductivities. In order to validate the stream function method, we utilized the IZMIRAN electrodynamic model (IZMEM) recently calibrated by the DMSP ionospheric electrostatic potential observations. For the sake of simplicity, we took the modeled electric fields along the noon-midnight and dawn-dusk meridians as the boundary conditions. Then, the solution(s) of the boundary value problem (i.e., a reconstructed potential distribution over the entire polar region) is compared with the original IZMEM/DMSP electric potential distribution(s), as well as with the various cross cuts of the polar cap. It is found that reconstructed convection patterns are in good agreement with the original modelled patterns in both the northern and southern polar caps. The analysis is carried out for the winter and summer conditions, as well as for a number of configurations of the interplanetary magnetic field.Key words: Ionosphere (electric fields and currents; plasma convection; modelling and forecasting)

Nonlinear Spline Method for Buckling Analysis of Steel Strip

2010 ◽  
Vol 145 ◽  
pp. 14-19
Author(s):  
Jian Qin ◽  
Qing Dong Zhang ◽  
Jie Tao Dai
Keyword(s):  
Function Method ◽  
Spline Function ◽  
Steel Strip ◽  
Rolling Process ◽  
Buckling Analysis ◽  
Spline Method ◽  
Residual Strains ◽  
Stress States ◽  
Rigid Plane ◽  
The Waves

The paper deals with numerical considerations of buckling phenomena in steel strip during rolling and leveling of sheet metal. The self-equilibrating stress states due to residual strains caused by the rolling process are calculated by the spline function method. The developed numerical model provides an estimation of buckling critical loads and wave configuration. It is shown how the waves observed on the strip sliding over or lying on a rigid plane, so one can provide information about the distribution of the differences in the plastic strains over the width of the strip which leads to the buckled configuration. The spline function method proposed in this paper is simpler and more convenient than traditional finite element method in the buckling analysis.

scholarly journals Exact Static Analysis of In-Plane Curved Timoshenko Beams with Strong Nonlinear Boundary Conditions

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Sen-Yung Lee ◽  
Qian-Zhi Yan
Keyword(s):  
Boundary Conditions ◽  
Function Method ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Strong Nonlinearity ◽  
Timoshenko Beams ◽  
Static Deflection ◽  
Boundary Problems ◽  
Beam System ◽  
Differential Characteristic

Analytical solutions have been developed for nonlinear boundary problems. In this paper, the shifting function method is applied to develop the static deflection of in-plane curved Timoshenko beams with nonlinear boundary conditions. Three coupled governing differential equations are derived via the Hamilton’s principle. The mathematical modeling of the curved beam system can be decomposed into a complete sixth-order ordinary differential characteristic equation and the associated boundary conditions. It is shown that the proposed method is valid and performs well for problems with strong nonlinearity.

Three-Dimensional Vibrations of Truncated Hollow Cones

1995 ◽  
Vol 1 (2) ◽  
pp. 145-158 ◽  
Author(s):  
Arthur W. Leissa ◽  
Jinyoung So
Keyword(s):  
Boundary Conditions ◽  
Cross Sections ◽  
Ritz Method ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Vibration Frequencies ◽  
Arbitrary Boundary ◽  
Conical Shells ◽  
Hole Radius ◽  
Geometric Boundary

This work presents a three-dimensional (3-D) method of analysis for determining the free vibration frequencies and corresponding mode shapes of truncated hollow cones of arbitrary thickness and having arbitrary boundary conditions. It also supplies the first known numerical results from 3-D analysis for such problems. The analysis is based upon the Ritz method. The vibration modes are separated into their Fourier components in terms of the circumferential coordinate. For each Fourier component, displacements are expressed as algebraic polynomials in the thickness and slant length coordinates. These polynomials satisfy the geometric boundary conditions exactly. Because the displacement functions are mathematically complete, upper bound values of the vibration frequencies are obtained that are as close to the exact values as desired. This convergence is demonstrated for a representative truncated hollow cone configuration where six-digit exactitude in the frequencies is achieved. The method is then used to obtain accurate and extensive frequencies for two sets of completely free, truncated hollow cones, one set consisting of thick conical shells and the other being tori having square-generating cross sections. Frequencies are presented for combinations of two values of apex angles and two values of inner hole radius ratios for each set of problems.

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