The construction of the space-like surface of constant breadth

2019 ◽  
Vol 16 (04) ◽  
pp. 1950060
Author(s):  
Muradi̇ye Çi̇mdi̇ker ◽  
Yasi̇n Ünlütürk
Keyword(s):  
Radius Of Curvature ◽  
Closed Space ◽  
Principal Curvatures ◽  
Geometrical Properties ◽  
Constant Breadth

The objective of this study is to define an ovaloid surface on the convex closed space-like surfaces of constant breadth when principal curvatures of these surfaces are continuous, non-vanishing functions, and to obtain some special geometrical properties of this ovaloid surface by using the radius of curvature, diameter of the surface in [Formula: see text].

The Maximum Drawing Ratio in Hydroforming Processes

1990 ◽  
Vol 112 (1) ◽  
pp. 47-56 ◽  
Author(s):  
S. Yossifon ◽  
J. Tirosh
Keyword(s):  
Failure Modes ◽  
Fluid Pressure ◽  
Radius Of Curvature ◽  
Strain Hardening Exponent ◽  
Drawing Ratio ◽  
Limit Drawing Ratio ◽  
Normal Anisotropy ◽  
Geometrical Properties ◽  
Buckling Instability ◽  
Hydroforming Process

The concept of Maximum Drawing Ratio (MDR), supplementary to the well-known Limit Drawing Ratio (LDR), is defined, examined, and illustrated by experiments. In essence the MDR is reached when the two basic failure modes, namely: rupture (due to tensile instability) and wrinkling (due to buckling instability) are delayed till they occur simultaneously. Thus the process is beneficially utilized for higher drawing ratio by postponing earlier interception of either one of the above failures alone. The ability to suppress (up to a certain extent) the appearance of these failure modes depends heavily on the fluid-pressure path which controls the hydroforming process. The effect of the material properties, like the strain hardening exponent, the normal anisotropy of the blank, etc., as well as the geometrical properties (i.e., the thickness of the blank, the radius of curvature at the lip, etc.) on the MDR, are considered here in some detail. The nature of the solutions by which MDR is reached is discussed.

DESIGN AND ANALYSIS OF CONSTANT-BREADTH CAM MECHANISM WITH OSCILLATING FLAT-FACED FOLLOWER

2017 ◽  
Vol 41 (2) ◽  
pp. 211-225
Author(s):  
Jung-Fa Hsieh
Keyword(s):  
Design Methodology ◽  
Sliding Velocity ◽  
Principal Curvatures ◽  
Surface Theory ◽  
Cam Mechanism ◽  
Contact Points ◽  
Comprehensive Method ◽  
Cam Follower ◽  
Cam Profile ◽  
Constant Breadth

A simple yet comprehensive method is presented for the design and analysis of a constant-breadth cam mechanism with an oscillating flat-faced follower. In the proposed approach, the kinematic characteristics of the cam mechanism are first derived. The cam profile is then designed using homogenous coordinate transformation and conjugate surface theory. Moreover, the sliding velocity at the cam-follower contact points is determined. Finally, the pressure angle of the constant-breadth cam mechanism and the principal curvatures of the cam are analyzed. The validity of the proposed design methodology is verified by means of motion simulations performed using CAD software.

scholarly journals THREE DIMENSIONAL COMPLEX SHAPES ANALYSIS FROM 3D LOCAL CURVATURE MEASUREMENTS. APPLICATION TO INTERMETALLIC PARTICLES IN ALUMINIUM ALLOY 5XXX

2011 ◽  
Vol 26 (3) ◽  
pp. 157 ◽  
Author(s):  
Estelle Parra-Denis ◽  
Nicolas Moulin ◽  
Dominique Jeulin
Keyword(s):  
Aluminium Alloys ◽  
Three Dimensional ◽  
Bivariate Distribution ◽  
Factorial Correspondence Analysis ◽  
Principal Curvatures ◽  
Local Curvature ◽  
Car Industry ◽  
Geometrical Properties ◽  
Intermetallic Particles ◽  
Complex Shapes

The studied material is a 5xxx aluminium alloys containing 2 types of intermetallic particles : Alx(Fe;Mn) and Mg2Si. It is usually used in car industry as reinforcement pieces or in packaging industry, such as bottle liquid box lid. Scanning electronic microscope coupled with EDX analysis shows complex shapes of intermetallic particles. The particle shape is obtained during the solidification of alloys. Particles fill vacant spaces between aluminium grains. Therefore final sheet properties depend on intermetallic particles shapes and notably on the matrix-particle interface properties. The goal of the present study is to classify intermetallic particles versus their shapes using local curvature information. The aluminium alloys sample is observed by X ray micro tomography performed at the ESRF. Three dimensional images are segmented, and intermetallic particles are identified in a data base. Each particle is stored as a set of voxels. The surface of each particle is meshed by a marching cubes triangular meshing with the software Amira©. A simplification of the surface is performed by an algorithm contracting the edges. Finally, principal curvatures: kmin and kmax are estimated by Amira© on each facet centre of the mesh. From the full intermetallic population, the bivariate distribution of kmin and kmax is estimated. The obtained graph kmin ¡kmax shows geometrical properties of interface portions of the surface of particles. A factorial correspondence analysis is performed to summarize the information on all intermetallic particles. In the obtained subspace, particles are classified into five shape families, in relation with their interface geometrical properties.

CURVATURE ANALYSIS OF VARIABLE PITCH LEAD SCREWS WITH CYLINDRICAL MESHING ELEMENTS

1996 ◽  
Vol 20 (2) ◽  
pp. 139-157 ◽  
Author(s):  
Yaw-Hong Kang ◽  
Hong-Sen Yan
Keyword(s):  
Contact Point ◽  
Tangential Direction ◽  
Radius Of Curvature ◽  
Principal Curvatures ◽  
Surface Geometry ◽  
Variable Pitch ◽  
Transformation Matrices ◽  
Mathematical Expressions ◽  
Screw Surface ◽  
Principal Directions

Based on coordinate transformation matrices and theory of gearing, we derive the mathematical expressions of surface geometry and the location of contact point of variable pitch lead screws. According to curvature theory, we obtain the principal curvatures, the principal directions, and the orientation of the contacting line at any contact point. Furthermore, the condition of avoiding undercutting of the screw surface, the reduced radius of curvature along any tangential direction, and the angle between the normal of contact line and the relative velocity are also derived. The result of this work is necessary for the tasks of contact stress analysis and wear/lubrication analysis for variable pitch lead screws with cylindrical meshing elements.

Field ion microscopy

1988 ◽  
Vol 46 ◽  
pp. 434-435
Author(s):  
Gert Ehrlich
Keyword(s):  
Low Temperature ◽  
Sample Surface ◽  
Low Pressure ◽  
Radius Of Curvature ◽  
Field Ion Microscopy ◽  
Phosphor Screen ◽  
Ion Microscopy ◽  
Field Ion Microscope

The field ion microscope, devised by Erwin Muller in the 1950's, was the first instrument to depict the structure of surfaces in atomic detail. An FIM image of a (111) plane of tungsten (Fig.l) is typical of what can be done by this microscope: for this small plane, every atom, at a separation of 4.48Å from its neighbors in the plane, is revealed. The image of the plane is highly enlarged, as it is projected on a phosphor screen with a radius of curvature more than a million times that of the sample. Müller achieved the resolution necessary to reveal individual atoms by imaging with ions, accommodated to the object at a low temperature. The ions are created at the sample surface by ionization of an inert image gas (usually helium), present at a low pressure (< 1 mTorr). at fields on the order of 4V/Å.

Field-assisted ionization theory for microscopists

1994 ◽  
Vol 52 ◽  
pp. 820-821
Author(s):  
Patrick P. Camus
Keyword(s):  
Electric Field ◽  
Electron Tunneling ◽  
Ionization Probability ◽  
Critical Distance ◽  
Tunneling Probability ◽  
Field Ionization ◽  
Radius Of Curvature ◽  
Field Evaporation ◽  
A Value ◽  
Ion Emission

The theory of field ion emission is the study of electron tunneling probability enhanced by the application of a high electric field. At subnanometer distances and kilovolt potentials, the probability of tunneling of electrons increases markedly. Field ionization of gas atoms produce atomic resolution images of the surface of the specimen, while field evaporation of surface atoms sections the specimen. Details of emission theory may be found in monographs.Field ionization (FI) is the phenomena whereby an electric field assists in the ionization of gas atoms via tunneling. The tunneling probability is a maximum at a critical distance above the surface,xc, Fig. 1. Energy is required to ionize the gas atom at xc, I, but at a value reduced by the appliedelectric field, xcFe, while energy is recovered by placing the electron in the specimen, φ. The highest ionization probability occurs for those regions on the specimen that have the highest local electric field. Those atoms which protrude from the average surfacehave the smallest radius of curvature, the highest field and therefore produce the highest ionizationprobability and brightest spots on the imaging screen, Fig. 2. This technique is called field ion microscopy (FIM).

The buckling of thin EM specimens

1990 ◽  
Vol 48 (4) ◽  
pp. 850-851
Author(s):  
A.R. Thölén
Keyword(s):  
Electron Microscope ◽  
Elastic Properties ◽  
Crystal Surface ◽  
Specimen Surface ◽  
Radius Of Curvature ◽  
Thin Foils ◽  
Thin Electron ◽  
Regular Patterns

Thin electron microscope specimens often contain irregular bend contours (Figs. 1-3). Very regular bend patterns have, however, been observed around holes in some ion-milled specimens. The purpose of this investigation is twofold. Firstly, to find the geometry of bent specimens and the elastic properties of extremely thin foils and secondly, to obtain more information about the background to the observed regular patterns.The specimen surface is described by z = f(x,y,p), where p is a parameter, eg. the radius of curvature of a sphere. The beam is entering along the z—direction, which coincides with the foil normal, FN, of the undisturbed crystal surface (z = 0). We have here used FN = [001]. Furthermore some low indexed reflections are chosen around the pole FN and in our fcc crystal the following g-vectors are selected:

Point-Cathode Electron Gun Using Electron-Beam Bombardment for Cathode Tip Heating

1990 ◽  
Vol 48 (1) ◽  
pp. 198-199
Author(s):  
Ryo Iiyoshi ◽  
Susumu Maruse ◽  
Hideo Takematsu
Keyword(s):  
Electron Beam ◽  
Tungsten Wire ◽  
Local Heating ◽  
Electron Gun ◽  
Original Position ◽  
Beam Power ◽  
Radius Of Curvature ◽  
High Brightness ◽  
Beam Focusing ◽  
Time Operation

Point cathode electron gun with high brightness and long cathode life has been developed. In this gun, a straightened tungsten wire is used as the point cathode, and the tip is locally heated to higher temperatures by electron beam bombardment. The high brightness operation and some findings on the local heating are presented.Gun construction is shown in Fig.l. Small heater assembly (annular electron gun: 5 keV, 1 mA) is set inside the Wehnelt electrode. The heater provides a disk-shaped bombarding electron beam focusing onto the cathode tip. The cathode is the tungsten wire of 0.1 mm in diameter. The tip temperature is raised to the melting point (3,650 K) at the beam power of 5 W, without any serious problem of secondary electrons for the gun operation. Figure 2 shows the cathode after a long time operation at high temperatures, or high brightnesses. Evaporation occurs at the tip, and the tip part retains a conical shape. The cathode can be used for a long period of time. The tip apex keeps the radius of curvature of 0.4 μm at 3,000 K and 0.3 μm at 3,200 K. The gun provides the stable beam up to the brightness of 6.4×106 A/cm2sr (3,150 K) at the accelerating voltage of 50 kV. At 3.4×l06 A/cm2sr (3,040 K), the tip recedes at a slow rate (26 μm/h), so that the effect can be offset by adjusting the Wehnelt bias voltage. The tip temperature is decreased as the tip moves out from the original position, but it can be kept at constant by increasing the bombarding beam power. This way of operation is possible for 10 h. A stepwise movement of the cathode is enough for the subsequent operation. Higher brightness operations with the rapid receding rates of the tip may be improved by a continuous movement of the wire cathode during the operations. Figure 3 shows the relation between the beam brightness, the tip receding rate by evaporation (αis the half-angle of the tip cone), and the cathode life per unit length, as a function of the cathode temperature. The working life of the point cathode is greatly improved by the local heating.

Comparison of Cross-sectional Geometrical Properties and Bone Density between Saint-Bernard and other Giant Breed Dogs

2019 ◽  
Author(s):  
S. Mejia ◽  
A. Iodence ◽  
L. Griffin ◽  
S.J. Withrow ◽  
M. Salman ◽  
...  
Keyword(s):  
Bone Density ◽  
Cross Sectional ◽  
Geometrical Properties ◽  
Saint Bernard
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