Parametric Mid-Spatial Frequency Surface Error Synthesis

Standard mid-spatial frequency tooling mark errors were parameterized into a series of characteristic features and systematically investigated. Diffraction encircled and ensquared energy radii at the 90% levels from an unpowered optical surface were determined as a function of the root-mean-square surface irregularity, characteristic tooling mark parameters, fold mirror rotation angle, and incident beam f-number. Tooling mark frequencies on the order of 20 cycles per aperture or less were considered. This subset encompasses small footprints on single-point diamond turned optics or large footprints on sub-aperture tool polished optics. Of the characteristic features, off-axis fabrication distance held the highest impact to encircled and ensquared energy radii. The transverse oscillation of a tooling path was found to be the second highest contributor. Both impacts increased with radial tooling mark frequency.

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On the Nature of O-Rings in Contact With Rough Surfaces

Journal of Tribology ◽

10.1115/1.3261705 ◽

1988 ◽

Vol 110 (4) ◽

pp. 632-637 ◽

Cited By ~ 5

Author(s):

W. E. Warren ◽

J. G. Curro ◽

D. E. Amos

Keyword(s):

Theoretical Analysis ◽

Root Mean Square ◽

Contact Pressure ◽

Contact Force ◽

Rough Surfaces ◽

Fundamental Importance ◽

Elastic Behavior ◽

Surface Irregularity ◽

Mean Square ◽

Irregular Surfaces

This work provides a theoretical analysis of the elastic behavior of an O-ring compressed between two rigid plates with irregular surfaces. Relations between deflection, contact force and contact pressure are obtained. The contact pressure, which is of fundamental importance in establishing criteria for effective sealing, is dependent upon both the amplitude and wavelength of the surface irregularity. This analysis suggests that surfaces in contact with O-ring seals should be characterized by the root mean square slope Δq in addition to the usual Ra which depends on amplitude only.

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A statistical model of turbulence in two-dimensional mixing layers

Journal of Fluid Mechanics ◽

10.1017/s002211207900063x ◽

1979 ◽

Vol 92 (2) ◽

pp. 303-326 ◽

Cited By ~ 82

Author(s):

Christopher K. W. Tam ◽

K. C. Chen

Keyword(s):

Statistical Model ◽

Root Mean Square ◽

Flow Direction ◽

Single Point ◽

Mixing Layer ◽

Normal Wave ◽

Quasi Equilibrium ◽

Mean Square ◽

Two Dimensional ◽

Large Structures

A statistical model based on the proposition that the turbulence of a fully developed two-dimensional incompressible mixing layer is in a state of quasi-equilibrium is developed. In this model the large structures observed by Brown & Roshko (1974) which will be assumed to persist into the fully developed turbulent region are represented by a superposition of the normal wave modes of the flow with arbitrary random amplitudes. The turbulence at a point in the flow is assumed to be dominated by the fluctuations associated with these large structures. These structures grow and amalgamate as they are convected in the flow direction. Because of the lack of intrinsic length and time scales the turbulence in question can, therefore, be regarded as created or initiated at an upstream point, the virtual origin of the mixing layer, by turbulence with a white noise spectrum and are subsequently convected downstream. The model is used to predict the second-order turbulence statistics of the flow including single point turbulent Reynolds stress distribution, intensity of turbulent velocity components, root-mean-square turbulent pressure fluctuations, power spectra and two-point space-time correlation functions. Numerical results based on the proposed model compare favourably with available experimental measurements. Predictions of physical quantities not yet measured by experiments, e.g. the root-mean-square pressure distribution across the mixing layer, are also made. This permits the present model to be further tested experimentally.

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Submicron Roughness Determination at the Si-SiO2 Interface and Correlations to Prccessing Steps and Electronic Properties

MRS Proceedings ◽

10.1557/proc-105-247 ◽

1987 ◽

Vol 105 ◽

Cited By ~ 6

Author(s):

Peter O. Hahn ◽

I. Lampert ◽

A. Schnegg

Keyword(s):

Electronic Properties ◽

Root Mean Square ◽

Surface Characterization ◽

Scattered Light ◽

Laser Beams ◽

Root Mean Square Roughness ◽

Mean Square ◽

Optical Surface ◽

Correlation Lengths ◽

Characterization Technique

AbstractA newly developed optical surface characterization technique using the diffuse scattered light of two laser beams will be presented. The method determines root-mean-square roughness values (RMS) of surfaces down to 1 Å and corresponding correlation lengths in the submicron area.

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Numerical Simulation of Unsaturated Soil Water Flow from a Trickle Point System, Considering Evaporation and Root Water Uptake

Al-Khwarizmi Engineering Journal ◽

10.22153/kej.2018.05.005 ◽

2018 ◽

Vol 14 (4) ◽

pp. 103-114

Author(s):

Lina Ali Khalil ◽

Maysoon Basheer Abid

Keyword(s):

Soil Moisture ◽

Root Mean Square Error ◽

Mean Square Error ◽

Root Mean Square ◽

Water Flow ◽

Single Point ◽

Maximum Error ◽

Soil Types ◽

Point System ◽

Mean Square

This research was carried out to study the effect of plants on the wetted area for two soil types in Iraq and predict an equation to determine the wetted radius and depth for two different soil types cultivated with different types of plants, the wetting patterns for the soils were predicted at every thirty minute for a total irrigation time equal to 3 hr. Five defferent discharges of emitter and five initial volumetric soil moisture contents were used ranged between field capacity and wilting point were utilized to simulate the wetting patterns. The simulation of the water flow from a single point emitter was completed by utilized HYDRUS-2D/3D software, version 2.05. Two methods were used in developing equations to predict the domains of the wetting pattern. The principal strategy manages each soil independently and includes plotting, fitting, and communicating relevant connections for wetted zone and profundity, maximum error did not exceed 31.2%, modeling efficiency did not less 0.95, and root mean square error did not surpass 1.43 cm. The second strategy additionally treated each soil independently yet used electronic programming that uses different relapse methods for wetted territory and profundity, the maximum error did not exceed 15.64 %, modeling efficiency did not less 0.98, and root mean square error did not surpass 1.18 cm. a field test was directed to quantify the wetted radius to check the outcome acquired by the software HYDRUS-2D, contrast the estimation and the reproduced by the software. The after effects of the conditions to express the wetted radius and depth regarding the time of water system, producer release, and initial soil moisture content were general and can be utilized with great precision.

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