Improvement of Temperature Drop Model Parameters for 4200mm/3500mm Rolling of Baosteel Medium and Thick Plate

Based on the temperature situation during the rolling process of 4200 mm/3500 mm medium and thick plates at Baosteel,this article analyzes the influencing factors of temperature changes during the rolling process from the perspective of heat transfer theory and the temperature change law during the rolling process.The temperature loss during the four rolling processes is tracked on site,and the temperature drop model parameters during the rolling process of 4200mm/3500mm medium and thick plates at Baosteel are quantitatively provided.It is applied to actual rolling production and has achieved good results.

Dynamic Behaviors of Axially Moving Viscoelastic Plate with Varying Thickness

Structural components of varying thickness draw increasing attention these days due to economy and light-weight considerations. In view of the absence of research in vibration analysis of viscoelastic plate with varying thickness, this study devotes to investigate the dynamic behaviors of axially moving viscoelastic plate with varying thickness. Based on the thin plate theory and the two-dimensional viscoelastic differential constitutive relation, the differential equation of motion of the axially moving viscoelastic rectangular plate is derived, the plate constituted by Kelvin-Voigt model has linearly varying thickness in the y-direction. The dimensionless complex frequencies of axially moving viscoelastic plate with four edges simply supported are calculated by the differential quadrature method, curves of real parts and imaginary parts of the first three-order dimensionless complex frequencies versus dimensionless moving speed are obtained, the effects of the aspect ratio, thickness ratio, the dimensionless moving speed and delay time on the dynamic behaviors of the axially moving viscoelastic rectangular plate with varying thickness are analyzed. When other parameters keep constant, with the decrease of thickness ratio, the real parts of the first three-order natural frequencies decrease, and the critical divergence speeds of various modes decrease too, moreover, whether the delay time is large or small, the frequencies are all complex numbers.

NONLINEAR VIBRATION FOR MODERATE THICKNESS RECTANGULAR CRACKED PLATES INCLUDING COUPLED EFFECT OF ELASTIC FOUNDATION

Based on Reissner plate theory and Hamilton variational principle, the nonlinear equations of motion were derived for the moderate thickness rectangular plates with transverse surface penetrating crack on the two-parameter foundation. Under the condition of free boundary, a set of trial functions satisfying all boundary conditions and crack＇s continuous conditions were proposed. By employing the Galerkin method and the harmonic balance method, the nonlinear vibration equations were solved and the nonlinear vibration behaviors of the plate were analyzed. In numerical computation, the effects of the different location and depth of crack, the different structural parameters of plates and the different physical parameters of foundation on the nonlinear amplitude frequency response curves of the plate were discussed.

NON-LINEAR DYNAMIC BEHAVIOR OF THERMOELASTIC CIRCULAR PLATE WITH VARYING THICKNESS SUBJECTED TO NONCONSERVATIVE LOADING

The non-linear dynamic behaviors of thermoelastic circular plate with varying thickness subjected to radially uniformly distributed follower forces are considered. Two coupled non-linear differential equations of motion for this problem are derived in terms of the transverse deflection and radial displacement component of the mid-plane of the plate. Using the Kantorovich averaging method, the differential equation of mode shape of the plate is derived, and the eigenvalue problem is solved by using shooting method. The eigencurves for frequencies and critical loads of the circular plate with unmovable simply supported edge and clamped edge are obtained. The effects of the variation of thickness and temperature on the frequencies and critical loads of the thermoelastic circular plate subjected to radially uniformly distributed follower forces are then discussed.

BASIC EQUATIONS OF THE PROBLEM OF THE NONLINEAR UNSYMMETRICAL BENDING FOR ORTHOTROPIC RECTANGULAR THIN PLATE WITH VARIABLE THICKNESS

Under the case of ignoring the body forces and considering components caused by diversion of membrane in vertical direction (z-direction),the constitutive equations of the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with variable thickness are given;then introducing the dimensionless variables and three small parameters,the dimensionaless governing equations of the deflection function and stress function are given.

Distribution of Inherent Strains and Residual Stressesin Medium Thickness Plate Weldment

A fundamental theory for the analysis of residual welding stresses and deformation based on the inherent strain distribution along the welded joint is introduced. Distribution of inherent strains and longitudinal residual stresses in medium thickness plate weldment is calculated and analyzed. A new method of calculating inherent strains and longitudinal residual stresses is proposed.

THE PROBLEM OF THE NON-LINEAR UNSYMMETRICAL BENDING FOR CYLINDRICALLY ORTHOTROPIC CIRCULAR THIN PLATE WITH VARIABLE THICKNESS

To begin with, in this paper, the governing equations of the problem of the non-linear unsymmetrical bending for cylindrically orthotropic circular thin plate with variable thickness are derived. By using 'the method of two-variable' and introducing four small parameters, the problem of the non-linear unsymmetrical bending for cylindrically orthotropic circular thin plate with linear variable thickness are studied, and the uniformly valid asymptotic solution of Nth-order for epsilon(1) and Mth-order for epsilon(2) are obtained.

UNIFORMLY VALID ASYMPTOTIC SOLUTIONS OF THE NONLINEAR UNSYMMETRICAL BENDING FOR ORTHOTROPIC RECTANGULAR THIN PLATE OF FOUR CLAMPED EDGES WITH VARIABLE THICKNESS

By using “the method of modified two-variable”,“the method of mixing perturbation” and introducing four small parameters,the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with linear variable thickness is studied.And the uniformly valid asymptotic solution of Nth-order for ε_1 and Mth-order for ε_2 of the deflection functions and stress function are obtained.

LARGE DEFLECTION PROBLEM OF CIRCULAR PLATES WITH VARIABLE THICKNESS UNDER THE ACTION OF COMBINED LOADS

By using the modified iteration method of large deflection theory of plates with variable thichness[1], we solve the problem of circular plates with variable thickness subjected to combined loads under the boundary conditions of the clamped edges and get comparatively more accurate second-order approximate analytical solution. If the results of this paper are degraded into the special cases, the results coinciding with those of papers [1,2] can be obtained. In this paper, the characteristic curves are plotted and some comparisons are made. The results of this paper are satisfactory.

Nonlinear Vibration of Circular Plate with Variable Thickness

This paper is concerned with the nonlinear vibration problems of circular plates with variable thickness.The nonlinear equations of plates with variable thickness are extended to the dynamic case.The resulting equations can be solved by using an iterative method,a Galerkin's approach and a perturbation method.Detailed solutions and numerical results are given for two kinds of boundary conditions,the clamped edge and the supported edge.The results show that the solutions for the case of the plates with uniform thickness can be included in the solution herin as a special case.The effect of various thickness parameters is investigated in detail.Also,a Runge Kutta method is used to solve the free and forced vibrations of plates with variable thickness,and the results are obtained firstly.It has shown that the adoption of variable thickness plate would be useful in engineering design.

Analysis of the stress wave and rarefaction wave produced by hypervelocity impact of sphere onto thin plate

Shock wave is emitted into the plate and sphere when a sphere hypervelocity impacts onto a thin plate.The fragmentation and phase change of the material caused by the propagation and unloading of shock wave could result in the formation of debris cloud eventually.Propagation models are deduced based on one-dimensional shock wave theory and the geometry of sphere,which uses elliptic equations(corresponding to ellipsoid equations in physical space)to describe the propagation of shock wave and the rarefaction wave.The“Effective thickness”is defined as the critical plate thickness that ensures the rarefaction wave overtake the shock wave at the back of the sphere.The“Effective thickness”is directly related to the form of the debris cloud.The relation of the“Effective thickness”and the“Optimum thickness”is also discussed.The impacts of Al spheres onto Al plates are simulated within SPH to verify the propagation models and associated theories.The results show that the wave fronts predicted by the propagation models are closer to the simulation result at higher impact velocity.The curvatures of the wave fronts decrease with the increase of impact velocities.The predicted“Effective thickness”is consistent with the simulation results.The analysis about the shock wave propagation and unloading in this paper can provide a new sight and inspiration for the quantitative study of hypervelocity impact and space debris protection.

Inverse problem of pulsed eddy current field of ferromagnetic plates

To determine the wall thickness, conductivity and permeability of a ferromagnetic plate, an inverse problem is established with measured values and calculated values of time-domain induced voltage in pulsed eddy current testing on the plate. From time-domain analytical expressions of the partial derivatives of induced voltage with respect to parameters,it is deduced that the partial derivatives are approximately linearly dependent. Then the constraints of these parameters are obtained by solving a partial linear differential equation. It is indicated that only the product of conductivity and wall thickness, and the product of relative permeability and wall thickness can be determined accurately through the inverse problem with time-domain induced voltage. In the practical testing, supposing the conductivity of the ferromagnetic plate under test is a fixed value, and then the relative variation of wall thickness between two testing points can be calculated via the ratio of the corresponding inversion results of the product of conductivity and wall thickness. Finally, this method for wall thickness measurement is verified by the experiment results of a carbon steel plate.

A criterion for flow mechanisms through vertical sharp-edged orifice and model for the orifice discharge coefficient

According to the experimental data of the orifice discharge coefficient for the flow through a vertical sharp-edged orifice obtained in the previous study of this work,a theoretical criterion for flow mechanisms of small orifice（viz.thick-walled orifice and nozzle） and large orifice（viz.thin-walled orifice） was proposed based on the ratio of orifice diameter to plate thickness.It can help explain the dissipation of the mechanical energy loss in the flow process for the two flow mechanisms under different operating regimes.The main parameters such as orifice diameter,plate thickness and liquid head were correlated,and a semi-empirical model for orifice coefficient and an empirical model with high precision at the stable region were developed.

非均匀加筋板格极限受压强度计算建模研究

The aim of this paper is to develop computational models for the ultimate compressive strength analysis of stiffened plate panels with nonuniform thickness.Modeling welding-induced initial deformations and residual stresses was presented with the measured data.Three methods,i.e.,ANSYS finite element method,ALPS/SPINE incremental Galerkin method,and ALPS/ULSAP analytical method,were employed together with existing test database obtained from a full-scale collapse testing of steel-stiffened plate structures.Sensitivity study was conducted with varying the difference in plate thickness to define a representative(equivalent)thickness for plate panels with nonuniform thickness.Guidelines are provided for structural modeling to compute the ultimate compressive strength of plate panels with variable thickness.

Stress concentration coefficients of optimized cope-hole welded detail

The fatigue performance of optimized welded detail has been investigated by fatigue experiments of three welded specimens under different loadings.In addition,local finite element models of this welded detail were established using finite element software ANSYS.The influences of different factors such as plate thickness,plate gap and initial geometric imperfections on the stress concentration coefficient(SCC) were discussed.The experimental results indicate that the fatigue life of three specimens for this welded detail is 736,000,1,044,200 and 1,920,300 times,respectively.The web thickness,the filler plate thickness and the initial geometric imperfection have relatively less effect on the SCCs of this welded detail.However,cope-hole radius is influential on the SCCs of the web and the weld.The SCC of weld is significantly affected by the weld size and plate gap,but the SCCs of other parts of the welded detail are hardly affected by the plate gap.

Design and Engineering Application of Direct Mixing Lubrication System for Emulsion Pipeline in Secondary Cold Rolling Mill

With the benefit fierce competition in the steel industry market in recent years,double cold reduction products have been developed towards strength improvement and thickness reduction.The traditional cold-rolling lubrication process with a fixed flow rate and concentration cannot solve the problems,which are uncontrollable plate shape and the excessive consumption of lubricating oil.Moreover,based on the analysis of the traditional direct aplication lubrication system of double cold reduction mill,a set of design scheme suitable for the emulsion pipeline direct mixing lubrication system of double cold reduction mill unit was proposed.The design completed the selection of key components,which included the static mixer and atomization nozzle selection,pump and oil pump design selection,pipeline design selection,flow type selection,pressure gauge selection,electronic control cabinet design selection and other eight aspects.Equipment of the emulsion pipeline direct mixing lubrication system of double cold reduction has been developed.Comparing with characteristics of the traditional direct aplication lubrication system,the emulsion pipeline direct mixing lubrication system was better applied to the production practice of a 1220 double cold reduction mill.The consumption of ton of steel was reduced by 9.6%.The rolling energy consumption and fuel consumption comprehensive costs decreased by 10.7%,and the strip steel section thickness difference was reduced by 19.3%.In addition,the plate shape quality defect rate decreased by 25.6%,otherwise creating a large economic benefit for the unit and promoting the application value.

A spectroscopic method for determining thickness of quartz wave plate

A spectroscopic method to determine thickness on chromatic polarization interferometry. With of quartz wave plate is presented. The method is based the polarization-resolved transmission spectrum （PRTS） curve, the phase retardation of quartz wave plate can be determined at a wide spectral range from 200 to 2000 nm obviously. Through accurate judgment of extreme points of PRTS curve at long-wave band, the physical thickness of quartz wave plates can be obtained exactly. We give a measuring example and the error analysis. It is found that the measuring precision of thickness is mainly determined by the spectral resolution of spectrometer.

INVESTIGATION OF THE THICKNESS VARIABILITY AND MATERIAL HETEROGENEITY EFFECTS ON FREE VIBRATION OF THE VISCOELASTIC CIRCULAR PLATES

The present study deals with free vibration analysis of variable thickness viscoelastic circular plates made of heterogeneous materials and resting on two-parameter elastic foundations in addition to their edge conditions. It is assumed that the viscoelastic material properties vary in the transverse and radial directions simultaneously. The complex modulus approach is employed in conjunction with the elastic-viscoelastic correspondence principle to obtain the solution. The governing equations are solved by means of a power series solution. Finally, a sensitivity analysis including evaluation of effects of various edge conditions, thickness variations, coefficients of the elastic foundation, and material loss factor and heterogeneity on the natural frequencies and modal loss factors is accomplished.