The Minimum Gauge Problem in Thin Strip Rolling

1971 ◽  
Vol 93 (3) ◽  
pp. 331-340 ◽  
Author(s):  
H. A. Kuhn ◽  
A. S. Weinstein
Keyword(s):  
Sliding Friction ◽  
Contact Region ◽  
Three Dimensional ◽  
Thin Strip ◽  
Theoretical Treatment ◽  
Plastic Yielding ◽  
Strip Rolling ◽  
Basic Assumptions ◽  
Traction Distribution

All previous analyses of the minimum gauge problem either fail to arrive at a criterion for determination of the minimum gauge or result in predictions which are grossly in error. The basic assumptions utilized in these analyses are investigated in the present work with a view toward improving the existing theories. Those assumptions whose validity appears questionable are considered in detail through appropriate analysis. In particular, these assumptions are: (i) the strip and rolls deform uniformly across the width of the strip; (ii) Coulomb (sliding) friction occurs between the rolls and strip. Theoretical treatment of the complex three-dimensional behavior of the rolls and strip is made tenable through simplifications to suitable two-dimensional problems. The primary result of the investigation indicates that the assumption of sliding friction is completely without justification in rolling at the limiting conditions. A new shear traction distribution is postulated which is consistent with the fundamental laws of friction and results in sticking friction (zero slip) over most of the contact region. Incorporating this shear distribution, limiting rolling conditions can be shown to exist theoretically and the minimum gauge can be predicted. It is also found that the Poisson’s ratio must be one-half in the regions of incipient plastic yielding in the strip if a minimum gauge is to be predicted.

Lateral Distribution of Pressure in Thin Strip Rolling

1970 ◽  
Vol 92 (2) ◽  
pp. 453-459 ◽  
Author(s):  
H. A. Kuhn ◽  
A. S. Weinstein
Keyword(s):  
Rolling Force ◽  
Contact Region ◽  
Three Dimensional ◽  
Work Roll ◽  
Lateral Distribution ◽  
Thin Strip ◽  
Strip Rolling ◽  
Edge Contact ◽  
Strip Shape

A method is presented for the determination of the lateral distribution of pressure in thin strip rolling. A simplified three-dimensional analysis of elastic deformation of the rolls is developed for use in the method. Pressure in the roll edge contact regions (in underface rolling), as well as in the roll-strip contact region, is considered. In the case of four-high, planetary, and Sendzimir-type mills, the lateral distribution of pressure between the work roll and backup rolls is also found. Calculated results indicate lateral pressure distributions which have peak values at each edge of the strip with a minimum at the center. The degree of this nonuniformity depends on roll geometry and configuration. Partition of the total rolling force between roll-strip contact and roll edge contact in underface rolling is also determined. Since interroll heat transfer is dependent on contact area, and hence, pressure, the results can also aid the determination of lateral temperature distributions in the rolls. In addition, the method is potentially useful for a study of the influence of roll geometry and configuration on strip shape.

A variational–Green's function approach to theoretical treatment and applications of the capacitance of three-dimensional geometries

1982 ◽  
Vol 60 (2) ◽  
pp. 179-195 ◽  
Author(s):  
Andreas Mandelis
Keyword(s):  
Thin Film ◽  
Spatial Distribution ◽  
Green’S Function ◽  
Green's Function ◽  
Finite Thickness ◽  
Three Dimensional ◽  
Function Approach ◽  
Theoretical Treatment ◽  
One Dimensional

A combined variational–Green's function approach to the determination of the capacitance of various useful three-dimensional geometries is developed. This formalism leads to general, exact expressions for the capacitance, which can be used with all geometries provided the spatial distribution of the charge can be determined. In particular, the theory takes into account the finite thickness and unequal areas of the capacitor plates. Specific applications of the theory include circular capacitors with disc and ring-shaped charged plate geometries. Such geometries are commonly encountered in experimental set-ups for capacitive measurements of thin film thicknesses in the field of microelectronics. Numerical results indicate that the values of thin film thicknesses calculated via simplified one-dimensional formulae for the capacitance may be incorrect by more than 10%

Prediction of Three-Dimensional Strip Profile for 6-High Mill in Thin-Strip Rolling

2011 ◽  
Vol 35 (8) ◽  
pp. 855-861 ◽  
Author(s):  
Sang-Ho Lee ◽  
Gil-Ho Song ◽  
Sung-Jin Lee ◽  
Byung-Min Kim
Keyword(s):  
Three Dimensional ◽  
Thin Strip ◽  
Strip Rolling ◽  
Strip Profile

Conformation of Ribosomes from Escherichia Coli

1974 ◽  
Vol 32 ◽  
pp. 210-211
Author(s):  
M. Boublik ◽  
W. Hellmann ◽  
F. Jenkins
Keyword(s):  
Binding Sites ◽  
Ribosomal Proteins ◽  
Fluorescent Dyes ◽  
Protein Biosynthesis ◽  
Three Dimensional ◽  
Spatial Arrangement ◽  
Dimensional Structure ◽  
Complete Understanding ◽  
And Function

The present knowledge of the three-dimensional structure of ribosomes is far too limited to enable a complete understanding of the various roles which ribosomes play in protein biosynthesis. The spatial arrangement of proteins and ribonuclec acids in ribosomes can be analysed in many ways. Determination of binding sites for individual proteins on ribonuclec acid and locations of the mutual positions of proteins on the ribosome using labeling with fluorescent dyes, cross-linking reagents, neutron-diffraction or antibodies against ribosomal proteins seem to be most successful approaches. Structure and function of ribosomes can be correlated be depleting the complete ribosomes of some proteins to the functionally inactive core and by subsequent partial reconstitution in order to regain active ribosomal particles.

scholarly journals Meso-Scale Transmission Electron Microscope Tomography Applied for Wax Distribution in Toner Particles

2013 ◽  
Vol 19 (S5) ◽  
pp. 58-61 ◽  
Author(s):  
Mino Yang ◽  
Jun-Ho Lee ◽  
Hee-Goo Kim ◽  
Euna Kim ◽  
Young-Nam Kwon ◽  
...  
Keyword(s):  
Electron Microscope ◽  
Transmission Electron Microscope ◽  
Three Dimensional ◽  
Chromatic Aberration ◽  
Laser Printer ◽  
Medium Voltage ◽  
Transmission Electron ◽  
Z Contrast ◽  
Contrast Image

AbstractDistribution of wax in laser printer toner was observed using an ultra-high-voltage (UHV) and a medium-voltage transmission electron microscope (TEM). As the radius of the wax spans a hundred to greater than a thousand nanometers, its three-dimensional recognition via TEM requires large depth of focus (DOF) for a volumetric specimen. A tomogram with a series of the captured images would allow the determination of their spatial distribution. In this study, bright-field (BF) images acquired with UHV-TEM at a high tilt angle prevented the construction of the tomogram. Conversely, the Z-contrast images acquired by the medium-voltage TEM produced a successful tomogram. The spatial resolution for both is discussed, illustrating that the image degradation was primarily caused by beam divergence of the Z-contrast image and the combination of DOF and chromatic aberration of the BF image from the UHV-TEM.

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