Analysis of Core Buckling Defects in Sheet Metal Coil Processing

2003 ◽  
Vol 125 (4) ◽  
pp. 771-777 ◽  
Author(s):  
P. M. Lin ◽  
J. A. Wickert
Keyword(s):  
Sheet Metal ◽  
Numerical Technique ◽  
Elastic Stability ◽  
External Pressure ◽  
Internal Stresses ◽  
Geometric Imperfection ◽  
The Core ◽  
Nonlinear Stress ◽  
Core Thickness ◽  
The Stability

The elastic stability of a wound coil comprising a central core and many layers of sheet metal is modeled and analyzed. A common failure mode resulting from unfavorable internal stresses—called v-buckling—is characterized by a section of the core buckling inward, possibly with several nearby sheet metal layers. In the present study, the core is modeled as a thin cylinder that is subjected to (i) the uniform external pressure generated by the coil’s wound-in stresses and (ii) a nonuniform elastic foundation around its circumference that represents core-coil contact or loss thereof. The model and an iterative numerical technique are used to predict the critical winding pressure along the core-coil interface and the core’s ensuing buckled shape. The role of geometric imperfection in the core, and the sensitivity of the buckling pressure to such initial defects, are also examined. Critical imperfection wavenumbers that facilitate the onset of significant deformations are identified with a view toward applying the results to improve quality and core inspection procedures. The predicted buckling pressure and the maximum radial stress developed in the coil, as based on a nonlinear stress model, are together used to determine factors of safety against core buckling over a range of manufacturing process parameters. Three case studies evaluate sensitivity with respect to process tension, core radius, and core thickness. The results are intended to guide the development of solutions to control the stability and quality of coils in sheet metal manufacturing.

Elastic Stability of Cylindrical Shells under Axial and Lateral Loads

1964 ◽  
Vol 68 (647) ◽  
pp. 773-775 ◽  
Author(s):  
C. Lakshmikantham ◽  
George Gerard
Keyword(s):  
Axial Compression ◽  
Present Report ◽  
Compressive Loading ◽  
Elastic Stability ◽  
External Pressure ◽  
Point Of View ◽  
Combined Loading ◽  
External Loading ◽  
Lateral Loads ◽  
The Stability

In the stability analysis of cylinders under external loading, the axial compression and lateral pressure cases are relatively well established: see, for example, ref. 1. However, from a design point of view, a biaxial system of forces due to a combination of axial compression and external pressure is often encountered in launch vehicle structures. While many other combined loading cases have appeared in the literature, the case under present consideration has not; therefore, this note is devoted to a general treatment of this problem. It is to be noted that Radhakrishnan presented some specific results for this loading combination for elastic and plastic buckling.Using the Donnell equation for small deformations, the present report considers the effect of various compressive loading combinations on the stability problem of an un-stiffened circular cylinder.

Corrugation and Buckling Defects in Wound Rolls

2005 ◽  
Vol 128 (1) ◽  
pp. 56-64 ◽  
Author(s):  
P. M. Lin ◽  
J. A. Wickert
Keyword(s):  
Design Space ◽  
Elastic Stability ◽  
Internal Stresses ◽  
Core System ◽  
The Core ◽  
Acceptable Quality ◽  
Wound Rolls ◽  
Winding Tension ◽  
Elastic Shear ◽  
The Web

Sheet metal, paper, and polymer webs are often stored and processed as large rolls comprising thousands of layers. Depending on the elastic properties of the web material, the roll’s dimensions, the type of core, and the winding tension, the stresses that develop within the roll can be sufficiently high to cause local or gross buckling defects to form. For instance, the cylindrical core onto which the web is wound can collapse, a failure mode that is termed “v-buckling.” In other cases, while the core might remain intact, a group of layers interior to the roll can wrinkle into a near-sinusoidal corrugated pattern around the circumference. This paper examines such “starring” defects analytically and experimentally. Measurements on a laboratory-scale web transport system are used to validate the model, and to identify conditions where no defects occur and the roll has acceptable quality, where starring patterns develop, and where v-buckling occurs. For particular core and web materials, the tension and diameter are the primary variables that influence the roll’s stability, and demarcations between stable and buckled configurations are identified in the tension-diameter design space. A model for the elastic stability of the roll-core system is developed, in which the corrugated layers are treated as multiple rings subjected to the resultant pressure generated by the roll’s internal stresses, and to the elastic support provided by the core and neighboring web layers. At the onset of corrugation, adjacent web layers couple through surface contact which is incorporated in the model as an elastic shear layer.

Buckling of Circular Cylindrical Shells Using a Displacement Function

1974 ◽  
Vol 96 (4) ◽  
pp. 1322-1327
Author(s):  
Shun Cheng ◽  
C. K. Chang
Keyword(s):  
Boundary Conditions ◽  
Axial Compression ◽  
Cylindrical Shells ◽  
External Pressure ◽  
Displacement Function ◽  
Combined Loading ◽  
Trial Solution ◽  
Governing Differential Equation ◽  
Circular Cylindrical Shells ◽  
The Stability

The buckling problem of circular cylindrical shells under axial compression, external pressure, and torsion is investigated using a displacement function φ. A governing differential equation for the stability of thin cylindrical shells under combined loading of axial compression, external pressure, and torsion is derived. A method for the solutions of this equation is also presented. The advantage in using the present equation over the customary three differential equations for displacements is that only one trial solution is needed in solving the buckling problems as shown in the paper. Four possible combinations of boundary conditions for a simply supported edge are treated. The case of a cylinder under axial compression is carried out in detail. For two types of simple supported boundary conditions, SS1 and SS2, the minimum critical axial buckling stress is found to be 43.5 percent of the well-known classical value Eh/R3(1−ν2) against the 50 percent of the classical value presently known.

scholarly journals The elastic stability of an annular plate

1924 ◽  
Vol 106 (737) ◽  
pp. 268-284 ◽  
Keyword(s):  
Annular Plate ◽  
Practical Interest ◽  
Middle Surface ◽  
Elastic Stability ◽  
Thin Plates ◽  
Thin Shells ◽  
Stability Equation ◽  
Inner Radius ◽  
Plane Plate ◽  
The Stability

1. Introduction and Summary. —This paper deals with the elastic stability of a circular annular plate under uniform shearing forces applied at its edges. Investigations of the stability of plane plates are altogether simpler than those necessary in the case of curved plates or shells. In the first place, as shown by Mr. R. V. Southwell, two of the three equations of stability relate to a mode of instability that is not of practical interest, and are entirely independent of the third equation which gives the ordinary mode of instability resulting in the familiar bending of the middle surface of the plate. Consequently with a plane plate there is only one equation of stability to be solved, as contrasted with the case of a shell where the three equations are dependent, and must all be solved. In the second place the theory of thin shells can be used with confidence in a plane plate problem, though a more laborious procedure is necessary to deal adequately with a shell. The only stability equation required for the annular plate is therefore deduced without trouble from the theory of thin shells, and its solution presents no difficulty in the case of uniform shearing forces. A numerical discussion is given of the stability of the plate under such forces, the “favourite type of distortion” and the stess that will produce it being obtained for plates with clamped edges in wich the ratio of the outer to the inner radius exceeds 3·2. To some extent to results have been checked by experiment, in which part of the work the viter is indebted to Prof. G. I. Taylor for his valuable help and advice. Distrtion of the type predicted by the theory took place in the two thin plates of rober different ratio of radii, which were used. The disposition of the loci of points which undergo maximum normal displace nt gives some idea of the appearance of the plate after distortion has taken pce. The points have been calculated for a plate in which the ratio of radii 4·18, and the loci are shown on a diagram, which may be compared with a potograph of a distorted plate in which this ratio is 4·3. The ratio of normal dplacements of points of the plate can be seen from contours drawn on the ne diagram. (See pp. 280, 281.)

SHELL MATERIAL'S PERFORMANCE OF THE MICROCAPSULE FOR ELECTROLYTIC CO-DEPOSITION

2010 ◽  
Vol 24 (15n16) ◽  
pp. 3124-3130 ◽  
Author(s):  
HUI CONG LIU ◽  
XIU QING XU ◽  
WEI PING LI ◽  
YAN HONG GUO ◽  
LI-QUN ZHU
Keyword(s):  
Composite Coating ◽  
Methyl Cellulose ◽  
Water Vapor Permeability ◽  
Core Material ◽  
Vapor Permeability ◽  
Shell Material ◽  
The Core ◽  
Surface Performance ◽  
The Stability ◽  
Positive Effect

The shell material of microcapsules has an important effect on the electrolytic co-deposition behavior, the release of core material and the surface performance of composite coating. This paper discussed the tensile property and the stability of three shell materials including polyvinyl alcohol (PVA), gelatin and methyl cellulose (MC). It is found that these three shell materials have good mechanical strength and flexibility which are favorable to electrolytic co-deposition and stability of microcapsules in composite coating and that MC has well permeability and porosity which has a positive effect on the release of the core material in composite coating. Moreover, the study of the thermal properties and water vapor permeability of the three shell materials showed that their permeability improved with increase of temperature and humidity. In addition, the composite copper coating containing microcapsules with PVA, gelatin or MC as shell material was prepared respectively.

Mathematical Model Establishment and Analysis on the Pipe Deformation under External Pressure with the Ovality

2013 ◽  
Vol 760-762 ◽  
pp. 2263-2266
Author(s):  
Kang Yong ◽  
Wei Chen
Keyword(s):  
Mathematical Model ◽  
Theoretical Analysis ◽  
Yield Strength ◽  
Residual Stresses ◽  
Numerical Simulations ◽  
Significant Influence ◽  
External Pressure ◽  
Pipe Diameter ◽  
Axial Loads ◽  
The Stability

Beside the residual stresses and axial loads, other factors of pipe like ovality, moment could also bring a significant influence on pipe deformation under external pressure. The Standard of API-5C3 has discussed the influences of deformation caused by yield strength of pipe, pipe diameter and pipe thickness, but the factor of ovality degree is not included. Experiments and numerical simulations show that with the increasing of pipe ovality degree, the anti-deformation capability under external pressure will become lower, and ovality affecting the stability of pipe shape under external pressure is significant. So it could be a path to find out the mechanics relationship between ovality and pipe deformation under external pressure by the methods of numerical simulations and theoretical analysis.

Thermodynamic Studies of the Core Histones:  pH and Ionic Strength Effects on the Stability of the (H3−H4)/(H3−H4)2System†

Biochemistry ◽  
1996 ◽  
Vol 35 (6) ◽  
pp. 2037-2046 ◽  
Author(s):  
Vassiliki Karantza ◽  
Ernesto Freire ◽  
Evangelos N. Moudrianakis
Keyword(s):  
Ionic Strength ◽  
Thermodynamic Studies ◽  
The Core ◽  
Core Histones ◽  
The Stability

Release Profile of a Model Protein Drug Depending on the Stability of Microspheres Based on Polyelectrolyte Complex

2007 ◽  
Vol 342-343 ◽  
pp. 505-508
Author(s):  
Sung Won Kim ◽  
Yun Sik Nam ◽  
Yeon Jin Min ◽  
Jong Ho Kim ◽  
Kwang Meyong Kim ◽  
...  
Keyword(s):  
Polyelectrolyte Complex ◽  
Coating Layer ◽  
Great Influence ◽  
Release Profile ◽  
Core Material ◽  
Glycol Chitosan ◽  
The Core ◽  
Key Factor ◽  
Model Protein ◽  
The Stability

Stability and disintegration of natural polyelectrolyte complex microspheres for protein drugs delivery have been extensively investigated because of their great influence on the drug release patterns. In this study, we tested stability of microspheres with alginate (Alg) core layered by either chitosan (Chi) or glycol chitosan (GChi) by examining release profiles of fluorophorelabeled bovine serum albumin (BSA) and lysozyme (Lys) from the microspheres. While GChi shell was disintegrated quickly, Chi-shell microspheres showed good stability in PBS. Disintegration of the coated layer induced the core material instable. The results indicated that while the charges of the shell material provided additional diffusion barrier against the protein release, the key factor to hold the proteins inside the microspheres was the integrity of the outer coating layer.

Bifurcation analysis of steady natural convection in a tilted cubical cavity with adiabatic sidewalls

2014 ◽  
Vol 756 ◽  
pp. 650-688 ◽  
Author(s):  
J. F. Torres ◽  
D. Henry ◽  
A. Komiya ◽  
S. Maruyama
Keyword(s):  
Natural Convection ◽  
Rotation Axis ◽  
Numerical Technique ◽  
Continuation Method ◽  
Rotation Vector ◽  
Saddle Node Bifurcation ◽  
Saddle Node ◽  
Stable Solutions ◽  
The Stability ◽  
Cubical Cavity

AbstractNatural convection in an inclined cubical cavity heated from two opposite walls maintained at different temperatures and with adiabatic sidewalls is investigated numerically. The cavity is inclined by an angle $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\theta $ around a lower horizontal edge and the isothermal wall set at the higher temperature is the lower wall in the horizontal situation ($\theta = 0^\circ $). A continuation method developed from a three-dimensional spectral finite-element code is applied to determine the bifurcation diagrams for steady flow solutions. The numerical technique is used to study the influence of ${\theta }$ on the stability of the flow for moderate Rayleigh numbers in the range $\mathit{Ra} \leq 150\, 000$, focusing on the Prandtl number $\mathit{Pr} = 5.9$. The results show that the inclination breaks the degeneracy of the stable solutions obtained at the first bifurcation point in the horizontal cubic cavity: (i) the transverse stable rolls, whose rotation vector is in the same direction as the inclination vector ${\boldsymbol{\Theta}}$, start from $\mathit{Ra} \to 0$ forming a leading branch and becoming more predominant with increasing $\theta $; (ii) a disconnected branch consisting of transverse rolls, whose rotation vector is opposite to ${\boldsymbol{\Theta}}$, develops from a saddle-node bifurcation, is stabilized at a pitchfork bifurcation, but globally disappears at a critical inclination angle; (iii) the semi-transverse stable rolls, whose rotation axis is perpendicular to ${\boldsymbol{\Theta}}$ at $\theta \to 0^\circ $, develop from another saddle-node bifurcation, but the branch also disappears at a critical angle. We also found the stability thresholds for the stable diagonal-roll and four-roll solutions, which increase with $\theta $ until they disappear at other critical angles. Finally, the families of stable solutions are presented in the $\mathit{Ra}-\theta $ parameter space by determining the locus of the primary, secondary, saddle-node, and Hopf bifurcation points as a function of $\mathit{Ra}$ and $\theta $.

Modeling of External Pressure Gradient Influence on the Stability of Disturbances in the Boundary Layers of Compressed Gas

2013 ◽  
Vol 8 (4) ◽  
pp. 64-75
Author(s):  
Sergey Gaponov ◽  
Natalya Terekhova
Keyword(s):  
Mach Number ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Leading Edge ◽  
External Pressure ◽  
Transition To Turbulence ◽  
Compressed Gas ◽  
High Mach ◽  
The Stability ◽  
Very High

This work continues the research on modeling of passive methods of management of flow regimes in the boundary layers of compressed gas. Authors consider the influence of pressure gradient on the evolution of perturbations of different nature. For low Mach number M = 2 increase in pressure contributes to an earlier transition of laminar to turbulent flow, and, on the contrary, drop in the pressure leads to a prolongation of the transition to turbulence. For high Mach number M = 5.35 found that the acoustic disturbances exhibit a very high dependence on the sign and magnitude of the external gradient, with a favorable gradient of the critical Reynolds number becomes smaller than the vortex disturbances, and at worst – boundary layer is destabilized directly on the leading edge

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