Crease Formation in the Processing of Thin Web Material

A mathematical model is developed to describe the conditions for buckling of steel strip between transport rolls due to strip camber, together with conditions necessary for the subsequent “ironing-in” of the buckle as it passes over the downstream roll. For a permanent crease to form, the buckle must be sufficiently stable so that it is prohibited by friction to spread laterally, and the stresses from the buckle defect must be large enough for plastic deformation to occur as it travels over the downstream roll. Once the conditions to produce a permanent crease are known they can be avoided in plant operations

Lifting of Steel Coils in Bore-Vertical Orientation

Lifting of coils with the bore in the vertical orientation could give rise to safety issues if the coil integrity is compromised during the slitting and packing operation. Coil telescoping (whereby the inner wraps of the coil spiral out) is known to occur during lifting, which could pose as a serious threat to the safety of personnel involved. In this type of incident, the coil straps are also broken when their breaking strength is exceeded and the whole coil would unwrap itself at an elevated position. Back tension is applied to the strip while shearing wide strip into narrower slits; this allows sufficient radial pressure to be built up within the bulk of the narrow coils. Upon unloading, the radial pressures at the innermost and outermost wraps decrease to zero but the bulk of the inter-wrap pressure within the coil remains largely unchanged. The interwrap frictional forces developed within the coil enable the coil to retain its integrity under its own weight. It is found that the radial pressures developed within the slit coil play the most crucial role in providing sufficient frictional resistance to support the weight of the coil wraps during lifting with the bore in the vertical orientation. In addition, the inter-wrap pressures near the footprint of the mechanical lifting device, near the bore, have the most significant influence in preventing coil telescoping

On the Heat Transfer of a loving Composite Strip Compressed by Two Rotating Cylinders

Two influential parameters in rolling mil

A matched solution method for the prediction of residual stresses for flat rolling

Steel strip must meet tight dimensional tolerances as well as having good `flatness' such that the strip is planar when not subject to external forces. This latter attribute demands extremely small residual stresses. A computational model is developed to describe the lateral variations of the magnitude and direction of the plastic deformation of the strip during rolling, together with the corresponding strip stresses and the degree of elastic roll flattening. In addition the downstream lateral variation in longitudinal strains, and resultant stresses, are calculated. From these the strip flatness can be predicted. It was found that for thin, wide strip the procedure became numerically unstable. This was overcome by developing an analytical solution for the simpler rolling conditions, away from the strip edge, and iteratively matching this solution to the numerical solution found for the edge region. This provided a more stable solution procedure

Light atom quantum oscillations in UC and US

High energy vibrational scattering in the binary systems UC and US is measured using time-of-flight inelastic neutron scattering. A clear set of well-defined peaks equally separated in energy is observed in UC, corresponding to harmonic oscillations of the light C atoms in a cage of heavy U atoms. The scattering is much weaker in US and only a few oscillator peaks are visible. We show how the difference between the materials can be understood by considering the neutron scattering lengths and masses of the lighter atoms. Monte Carlo ray tracing is used to simulate the scattering, with near quantitative agreement with the data in UC, and some differences with US. The possibility of observing anharmonicity and anisotropy in the potentials of the light atoms is investigated in UC. Overall the observed data is well accounted for by considering each light atom as a single atom isotropic quantum harmonic oscillator.Comment: 10 pages, 8 figure

Nonlinear multidimensional scaling and visualization of earthquake clusters over space, time and feature space

International audienceWe present a novel technique based on a multi-resolutional clustering and nonlinear multi-dimensional scaling of earthquake patterns to investigate observed and synthetic seismic catalogs. The observed data represent seismic activities around the Japanese islands during 1997-2003. The synthetic data were generated by numerical simulations for various cases of a heterogeneous fault governed by 3-D elastic dislocation and power-law creep. At the highest resolution, we analyze the local cluster structures in the data space of seismic events for the two types of catalogs by using an agglomerative clustering algorithm. We demonstrate that small magnitude events produce local spatio-temporal patches delineating neighboring large events. Seismic events, quantized in space and time, generate the multi-dimensional feature space characterized by the earthquake parameters. Using a non-hierarchical clustering algorithm and nonlinear multi-dimensional scaling, we explore the multitudinous earthquakes by real-time 3-D visualization and inspection of the multivariate clusters. At the spatial resolutions characteristic of the earthquake parameters, all of the ongoing seismicity both before and after the largest events accumulates to a global structure consisting of a few separate clusters in the feature space. We show that by combining the results of clustering in both low and high resolution spaces, we can recognize precursory events more precisely and unravel vital information that cannot be discerned at a single resolution

On some developments and evaluation of an Eulerian-Lagrangian method for the transport equation

The modelling of typical engineering problems in industry, such as water-jet cooling of hot-rolled steel strip products, directly involves the solution of a transport (advection-diffusion) equation for the cooling characteristics of the strip. The non-linear nature of the heat conduction involved aggravates the difficulty of the problem. Traditional Finite Difference techniques for the solution of this advection dominated transport equation incur severe Courant number stability restrictions as well as instabilities in the presence of temperature discontinuities. Eulerian-Lagrangian Methods (ELM's) solve the transport equation in Lagrangian form `along' backward characteristics effectively decoupling the advection and diffusion terms but retaining the convenience of fixed computational grids. Typical interpolation methods used to obtain the values at the feet of characteristic lines lead to spurious oscillations, numerical diffusion, peak clipping and phase errors. Through the use of `peak tracking', by the forward-tracking of Eulerian nodal points, this paper attempts to alleviate these errors. A comparison of 1-D benchmark tests from the Convection-Diffusion Forum as well as appropriate error measures, are shown to produce appreciable improvements over the standard methods for a range of time steps, very large Peclet numbers and Courant numbers in excess of one

Web lateral dynamics with buckling in sheet metal rolling

The stability of web lateral motion is of importance in many engineering applications where the deviation of the web from the processing direction is highly undesirable and can cause various defects. This is especially true for sheet metal rolling, where sudden lateral deviations of the web from the rolling direction, known as strip track-off, is a serious operational problem that can lead to catastrophic consequences, such as mill crashes and damaged rolls.The early studies of strip track-off in metal rolling showed that neither the magnitude of lateral deviations nor the catastrophic track-off observed in practice can be explained by the model of strip deformation in the span based on beam theory, common in the web handling literature. It has been suggested that strip buckling may play an important role in strip track-off phenomenon. In addition, it has also been observed in web handling literature (1,2] that the model predictions based on conventional beam bending analysis do not agree with observed web lateral motion in the situations when buckling of the web is present.This paper presents a discussion of the recent studies of the effect of strip buckling on strip lateral dynamics in metal rolling. The analysis is based on the model of strip plastic deformation in the mill and a simplified physically based strip buckling model suggested by Benson [l]. Introduction of budding changes the nature of the strip lateral motion, which becomes unstable once a critical level of asymmetry in rolling conditions is exceeded.In metal rolling, the longitudinal residual stresses in the strip are usually present due to non-uniform plastic reduction. In this paper, an extension of the Benson's buckling model to include the effect of residual stress is proposed. The numerical analysis of the extended model suggests that the web with the tensile residual stress at the edges and compressive stress in the middle is less susceptible to instability compared to the web with compressive residual stresses at the edges and the case without residual stress

Relating Quantum Information to Charged Black Holes

Quantum non-cloning theorem and a thought experiment are discussed for charged black holes whose global structure exhibits an event and a Cauchy horizon. We take Reissner-Norstr\"{o}m black holes and two-dimensional dilaton black holes as concrete examples. The results show that the quantum non-cloning theorem and the black hole complementarity are far from consistent inside the inner horizon. The relevance of this work to non-local measurements is briefly discussed.Comment: 14 pages, 2 figure

Stokes Parameters as a Minkowskian Four-vector

It is noted that the Jones-matrix formalism for polarization optics is a six-parameter two-by-two representation of the Lorentz group. It is shown that the four independent Stokes parameters form a Minkowskian four-vector, just like the energy-momentum four-vector in special relativity. The optical filters are represented by four-by-four Lorentz-transformation matrices. This four-by-four formalism can deal with partial coherence described by the Stokes parameters. A four-by-four matrix formulation is given for decoherence effects on the Stokes parameters, and a possible experiment is proposed. It is shown also that this Lorentz-group formalism leads to optical filters with a symmetry property corresponding to that of two-dimensional Euclidean transformations.Comment: RevTeX, 22 pages, no figures, submitted to Phys. Rev.