Traction Between a Web and a Smooth Roller

2004 ◽  
Vol 126 (1) ◽  
pp. 177-184 ◽  
Author(s):  
Sinan Mu¨ftu¨ ◽  
John J. Jagodnik
Keyword(s):  
Air Entrainment ◽  
Air Bearing ◽  
Simultaneous Solution ◽  
Lubrication Equation ◽  
Out Of Plane ◽  
Plane Equilibrium ◽  
Range Of Values ◽  
Roller Radius ◽  
The Web ◽  
Smooth Roller

Web traction over rollers is known to deteriorate due to air entrainment at high web speeds. In this paper, a general model is presented to predict the traction capability of an impermeable web over a smooth roller. The model considers the effects of the web and roller speeds, roller radius, combined roughness of the two surfaces, web tension and thickness, friction coefficient, and compressible air bearing. The change of tension ΔN due to mechanical slip between the roller and the web is calculated by a simultaneous solution of the in-plane and out-of-plane equilibrium of the web and the compressible Reynolds lubrication equation. The problem is nondimensionalized and the effects of nine of the eleven nondimensional parameters on traction are investigated for a range of values. Formulas involving the nondimensional parameters for the traction capability are presented in two-variable polynomial forms.

scholarly journals Locally Corroded Stiffener Effect on Shear Buckling Behaviors of Web Panel in the Plate Girder

2015 ◽  
Vol 2015 ◽  
pp. 1-19 ◽  
Author(s):  
Jungwon Huh ◽  
In-Tae Kim ◽  
Jin-Hee Ahn
Keyword(s):  
Corrosion Damage ◽  
Element Analysis ◽  
Buckling Strength ◽  
Lower Shear ◽  
Out Of Plane ◽  
Shear Buckling ◽  
Buckling Failure ◽  
Plane Displacement ◽  
The Web ◽  
Plate Girder

The shear buckling failure and strength of a web panel stiffened by stiffeners with corrosion damage were examined according to the degree of corrosion of the stiffeners, using the finite element analysis method. For this purpose, a plate girder with a four-panel web girder stiffened by vertical and longitudinal stiffeners was selected, and its deformable behaviors and the principal stress distribution of the web panel at the shear buckling strength of the web were compared after their post-shear buckling behaviors, as well as their out-of-plane displacement, to evaluate the effect of the stiffener in the web panel on the shear buckling failure. Their critical shear buckling load and shear buckling strength were also examined. The FE analyses showed that their typical shear buckling failures were affected by the structural relationship between the web panel and each stiffener in the plate girder, to resist shear buckling of the web panel. Their critical shear buckling loads decreased from 82% to 59%, and their shear buckling strength decreased from 88% to 76%, due to the effect of corrosion of the stiffeners on their shear buckling behavior. Thus, especially in cases with over 40% corrosion damage of the vertical stiffener, they can have lower shear buckling strength than their design level.

scholarly journals A New Solution to Well-Known Hencky Problem: Improvement of In-Plane Equilibrium Equation

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 653
Author(s):  
Xue Li ◽  
Jun-Yi Sun ◽  
Zhi-Hang Zhao ◽  
Shou-Zhen Li ◽  
Xiao-Ting He
Keyword(s):  
Closed Form ◽  
Equilibrium Equation ◽  
Circumferential Stress ◽  
Closed Form Solution ◽  
Form Solution ◽  
Circular Membrane ◽  
Equilibrium Equations ◽  
Power Series Method ◽  
Out Of Plane ◽  
Plane Equilibrium

In this paper, the well-known Hencky problem—that is, the problem of axisymmetric deformation of a peripherally fixed and initially flat circular membrane subjected to transverse uniformly distributed loads—is re-solved by simultaneously considering the improvement of the out-of-plane and in-plane equilibrium equations. In which, the so-called small rotation angle assumption of the membrane is given up when establishing the out-of-plane equilibrium equation, and the in-plane equilibrium equation is, for the first time, improved by considering the effect of the deflection on the equilibrium between the radial and circumferential stress. Furthermore, the resulting nonlinear differential equation is successfully solved by using the power series method, and a new closed-form solution of the problem is finally presented. The conducted numerical example indicates that the closed-form solution presented here has a higher computational accuracy in comparison with the existing solutions of the well-known Hencky problem, especially when the deflection of the membrane is relatively large.

Longitudinal and Out-of-Plane Stiffness of a Web in an Air-Flotation Oven

1999 ◽  
Author(s):  
Young B. Chang ◽  
Ronald P. Swanson ◽  
Peter M. Moretti
Keyword(s):  
Analytical Model ◽  
Experimental Results ◽  
Photographic Film ◽  
Longitudinal Stiffness ◽  
Out Of Plane ◽  
Air Cushion ◽  
Air Flotation ◽  
Low Tension ◽  
The Web ◽  
Web Tension

Abstract Air-flotation ovens are used for non-contact drying of coated web materials such as photographic film, magnetic media, and paper. In a typical air-flotation oven, the air bars are arranged in such a way that the path of web is nearly sinusoidal. When web tension fluctuates, the distance between the web and the air bars also changes. This phenomenon affects the longitudinal dynamics and tension control of an air-floated web. In some cases, tension fluctuations can cause the web to touch the air bars, resulting in damage to the coating and the web. This paper discusses an analytical model of the extensional resiliency of an air-floated web. The analysis shows that at low tension the longitudinal stiffness of an air-floated web is small, being dominated by the air cushion effects. At higher web tension, however, the effects of material deformation become more important than the air cushion effects. The analysis is compared with the experimental results obtained in a pilot air-flotation oven. The analytical and experimental results show the same trends, though the analytical model tends to underpredict the longitudinal stiffness of air-supported webs.

scholarly journals Generalized Out-of-Plane Equilibrium Points in the Frame of Elliptic Restricted Three-Body Problem: Impact of Oblate Primary and Luminous-Triaxial Secondary

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Aminu Abubakar Hussain ◽  
Aishetu Umar
Keyword(s):  
Binary Systems ◽  
Equilibrium Points ◽  
Semimajor Axis ◽  
Three Body Problem ◽  
Out Of Plane ◽  
Elliptic Restricted Problem ◽  
The Stability ◽  
Zero Velocity Curves ◽  
Three Body ◽  
Plane Equilibrium

This paper studies the motion of a third body near the 1st family of the out-of-plane equilibrium points, L6,7, in the elliptic restricted problem of three bodies under an oblate primary and a radiating-triaxial secondary. It is seen that the pair of points (ξ0,0,±ζ0) which correspond to the positions of the 1st family of the out-of-plane equilibrium points, L6,7, are affected by the oblateness of the primary, radiation pressure and triaxiality of the secondary, semimajor axis, and eccentricity of the orbits of the principal bodies. But the point ±ζ0 is unaffected by the semimajor axis and eccentricity of the orbits of the principal bodies. The effects of the parameters involved in this problem are shown on the topologies of the zero-velocity curves for the binary systems PSR 1903+0327 and DP-Leonis. An investigation of the stability of the out-of-plane equilibrium points, L6,7 numerically, shows that they can be stable for 0.32≤μ≤0.5 and for very low eccentricity. L6,7 of PSR 1903+0327 and DP-Leonis are however linearly unstable.

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