Pressure and Traction Rippling in Elastohydrodynamic Contact of Rough Surfaces

1974 ◽  
Vol 96 (3) ◽  
pp. 398-406 ◽  
Author(s):  
T. E. Tallian
Keyword(s):  
High Pressure ◽  
Rough Surfaces ◽  
Mean Value ◽  
Surface Plastic ◽  
Two Dimensional ◽  
Plateau Region ◽  
Pressure Ripple ◽  
Ripple Amplitude ◽  
Roll Velocity ◽  
The Mean

Local variations in asperity dimensions (rippling) of elastohydrodynamic (EHD) pressure are calculated using Christensen’s stochastic model of the hydrodynamics of heavily loaded two-dimensional contacts between rough surfaces. Pressure ripple amplitudes of the order of the maximum Hertz pressure, i.e., well in excess of 105 psi (69.107 N/m2) are predicted at the inlet perimeter of the EHD contact plateau and at the upstream slope of the exit constriction for heavily loaded contacts, if the plateau film thickness to rms roughness ratio is h/σ = 2. Pressure ripple amplitudes in excess of 104 psi (69.106 N/m2) are probable even for the thick film condition h/σ = 10. Sliding traction rippling is calculated for small slide/roll velocity ratios in the same type of contact, and ripple amplitudes in excess of the mean value of the traction are predicted in the high pressure EHD plateau region of the contact for h/σ = 3. The predicted traction ripple amplitude exceeds 30 percent of the mean traction, even for h/σ = 6. Rippling increases the average traction over that for smooth surfaces. Both the pressure and traction rippling may contribute to surface plastic flow and fatigue.

Power Density Performance Improvements for High Pressure Ripple Energy Harvesting

2013 ◽  
Author(s):  
Nalin Verma ◽  
Kenneth A. Cunefare ◽  
Ellen Skow ◽  
Alper Erturk
Keyword(s):  
High Pressure ◽  
Root Mean Square ◽  
Power Output ◽  
Energy Harvester ◽  
Dynamic Pressure ◽  
Hydraulic Pressure ◽  
Pressure Amplitude ◽  
Mean Square ◽  
Pressure Ripple ◽  
Ripple Amplitude

A hydraulic pressure energy harvester (HPEH) device, which utilizes a housing to isolate a piezoelectric stack from the hydraulic fluid via a mechanical interface, generates power by converting the dynamic pressure within the system into electricity. Prior work developed an HPEH device capable of generating 2187 microWatts from an 85 kPa pressure ripple amplitude using a 1387 mm3 stack. A new generation of HPEH produced 157 microWatts at the test conditions of 18 MPa static pressure and 394 kPa root-mean-square pressure amplitude using a 50 mm3 stack, thus increasing the power produced per volume of piezoelectric stack principally due to the higher dynamic pressure input. The stack and housing design implemented on this new prototype device yield a compact, high-pressure hydraulic pressure energy harvester designed to withstand 35 MPa. The device, which is less than a 2.54 cm in length as compared to a 5.3 cm length of a previous HPEH, was statically tested up to 21.9 MPa and dynamically tested up to 19 MPa with 400 kPa root-mean-square dynamic pressure amplitude. An inductor was included in the load circuit in parallel with the stack and the load resistance to increase the power output of the device. A previously developed electromechanical power output model for this device that predicts the power output given the dynamic pressure ripple amplitude is compared to the power results. The power extracted from this device would be sufficient to meet the proposed applications of the device, which is to power sensor nodes in hydraulic systems.

On the envelope of a Gaussian random field

1978 ◽  
Vol 15 (3) ◽  
pp. 502-513 ◽  
Author(s):  
R. J. Adler
Keyword(s):  
Random Field ◽  
Spectral Theory ◽  
Gaussian Random Field ◽  
Sample Path ◽  
Mean Value ◽  
Two Dimensional ◽  
Qualitative Information ◽  
The Mean

For homogeneous, two-dimensional random field ξ(t), t ∈ R2 we develop the ‘half' spectral theory sufficient to rigorously define its envelope η (t). We then specialise to the case of ξ Gaussian, which implies η is Rayleigh, and consider the mean value of a certain characteristic of the sets {t:η(t) ≧ u} (u ≧ 0). From this we deduce some qualitative information about the sample path behaviour of the Rayleigh field η .

scholarly journals Asymptotics for multilinear averages of multiplicative functions

2016 ◽  
Vol 161 (1) ◽  
pp. 87-101 ◽  
Author(s):  
NIKOS FRANTZIKINAKIS ◽  
BERNARD HOST
Keyword(s):  
Unit Disc ◽  
Convergence Result ◽  
Mean Value ◽  
Arithmetic Mean ◽  
Mean Value Theorem ◽  
Two Dimensional ◽  
Multiplicative Functions ◽  
Structural Result ◽  
Convergence Results ◽  
The Mean

AbstractA celebrated result of Halász describes the asymptotic behavior of the arithmetic mean of an arbitrary multiplicative function with values on the unit disc. We extend this result to multilinear averages of multiplicative functions providing similar asymptotics, thus verifying a two dimensional variant of a conjecture of Elliott. As a consequence, we get several convergence results for such multilinear expressions, one of which generalises a well known convergence result of Wirsing. The key ingredients are a recent structural result for multiplicative functions with values on the unit disc proved by the authors and the mean value theorem of Halász.

On the envelope of a Gaussian random field

1978 ◽  
Vol 15 (03) ◽  
pp. 502-513 ◽  
Author(s):  
R. J. Adler
Keyword(s):  
Random Field ◽  
Spectral Theory ◽  
Gaussian Random Field ◽  
Sample Path ◽  
Mean Value ◽  
Two Dimensional ◽  
Qualitative Information ◽  
The Mean

For homogeneous, two-dimensional random field ξ(t), t ∈ R 2 we develop the ‘half' spectral theory sufficient to rigorously define its envelope η (t). We then specialise to the case of ξ Gaussian, which implies η is Rayleigh, and consider the mean value of a certain characteristic of the sets {t:η(t) ≧ u} (u ≧ 0). From this we deduce some qualitative information about the sample path behaviour of the Rayleigh field η .

The crystal and molecular structure of quaterrylene

1960 ◽  
Vol 257 (1291) ◽  
pp. 477-490 ◽  
Keyword(s):  
Molecular Structure ◽  
Crystal Structure ◽  
Crystal And Molecular Structure ◽  
Current Theory ◽  
Mean Value ◽  
Unit Cell ◽  
Two Dimensional ◽  
Monoclinic System ◽  
Space Group ◽  
The Mean

Quaterrylene (III) is isotypic with perylene (I); it crystallizes in the monoclinic system with a = 11·25, b = 10·66, c = 19·31 Å, β = 100·6°, and with four molecules per unit cell and the space group P 2 1 / a . The crystal structure has been determined by two-dimensional methods. In the b -axial projection a majority of the carbon atoms are resolved, and, since the molecule lies with its greatest length almost exactly perpendicular to this axis, the lengths of the peri -bonds connecting the naphthalenic residues have been determined with moderate accuracy. The mean value is assessed at 1·53 ± 0·01 Å, which is significantly larger than current theory predicts. Possible reasons for this difference are discussed.

scholarly journals ON BOUNDED-TYPE THIN LOCAL SETS OF THE TWO-DIMENSIONAL GAUSSIAN FREE FIELD

2017 ◽  
Vol 18 (3) ◽  
pp. 591-618 ◽  
Author(s):  
Juhan Aru ◽  
Avelio Sepúlveda ◽  
Wendelin Werner
Keyword(s):  
Harmonic Function ◽  
Connected Domain ◽  
Free Field ◽  
Mean Value ◽  
Two Dimensional ◽  
Gaussian Free Field ◽  
Simply Connected Domain ◽  
The Mean ◽  
Conformal Loop Ensemble ◽  
Simply Connected

We study certain classes of local sets of the two-dimensional Gaussian free field (GFF) in a simply connected domain, and their relation to the conformal loop ensemble$\text{CLE}_{4}$and its variants. More specifically, we consider bounded-type thin local sets (BTLS), where thin means that the local set is small in size, and bounded type means that the harmonic function describing the mean value of the field away from the local set is bounded by some deterministic constant. We show that a local set is a BTLS if and only if it is contained in some nested version of the$\text{CLE}_{4}$carpet, and prove that all BTLS are necessarily connected to the boundary of the domain. We also construct all possible BTLS for which the corresponding harmonic function takes only two prescribed values and show that all these sets (and this includes the case of$\text{CLE}_{4}$) are in fact measurable functions of the GFF.

scholarly journals Sur les processus arithmétiques liés aux diviseurs

2016 ◽  
Vol 48 (A) ◽  
pp. 63-76 ◽  
Author(s):  
R. de la Bretèche ◽  
G. Tenenbaum
Keyword(s):  
Distribution Function ◽  
Random Variable ◽  
Mean Value ◽  
Two Dimensional ◽  
Limit Laws ◽  
Uniform Probability ◽  
Dimensional Distribution ◽  
The Mean ◽  
Generalized Moments

AbstractFor natural integer n, let Dn denote the random variable taking the values log d for d dividing n with uniform probability 1/τ(n). Then t↦ℙ(Dn≤nt) (0≤t≤1) is an arithmetic process with respect to the uniform probability over the first N integers. It is known from previous works that this process converges to a limit law and that the same holds for various extensions. We investigate the generalized moments of arbitrary orders for the limit laws. We also evaluate the mean value of the two-dimensional distribution function ℙ(Dn≤nu, D{n/Dn}≤nv).

scholarly journals Fluctuations of anisotropic flow from the finite number of rescatterings in a two-dimensional massless transport model

2021 ◽  
Vol 81 (5) ◽  
Author(s):  
Hendrik Roch ◽  
Nicolas Borghini
Keyword(s):  
Finite Number ◽  
Transport Model ◽  
Mean Value ◽  
Glauber Model ◽  
Dimensional System ◽  
Two Dimensional ◽  
Anisotropic Flow ◽  
The Mean ◽  
Participant Plane ◽  
Initial Geometry

AbstractWe investigate the fluctuations of anisotropic transverse flow due to the finite number of scatterings in a two-dimensional system of massless particles. Using a set of initial geometries from a Monte Carlo Glauber model, we study how flow coefficients fluctuate about their mean value at the corresponding eccentricity, for several values of the scattering cross section. We also show how the distributions of the second and third event planes of anisotropic flow about the corresponding participant plane in the initial geometry evolve as a function of the mean number of scatterings in the system.

scholarly journals The Mean Value Theorem for Integrals Method for Estimating Two-Dimensional Renewal Functions

2020 ◽  
Vol 4 (1) ◽  
pp. 49
Author(s):  
Leopoldus Ricky Sasongko ◽  
Bambang Susanto
Keyword(s):  
Weibull Model ◽  
Mean Value ◽  
The Other ◽  
Mean Value Theorem ◽  
Two Dimensional ◽  
Failure Model ◽  
Expected Number ◽  
Warranty Period ◽  
Bivariate Data ◽  
The Mean

An important aspect in the provision of a two-dimensional warranty is the expected number of failures of a component during the two-dimensional warranty period. The purpose of this paper is to present a new method to obtain the expected number of failures of a nonrepairable compo­nent from the two-dimensional renewal functions as the so­lution of two-dimensional renewal integral equations through the Mean Value Theorem for Integrals (MeVTI) method. The two-dimensional renewal integral equation involves Lu-Bhattacharyya’s bivariate Weibull model as a two-dimensional failure model. It turns out that the estimation of the expected number of failures using the MeVTI method is close to that of the other method, Riemann-Stieljies method. The bivariate data behaviour of the failures of an automobile component is also studied in this paper.

scholarly journals Free Vibration Analysis of Composite Plates via Refined Theories Accounting for Uncertainties

2011 ◽  
Vol 18 (4) ◽  
pp. 537-554 ◽  
Author(s):  
G. Giunta ◽  
E. Carrera ◽  
S. Belouettar
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Mean Value ◽  
Cumulative Distribution ◽  
Geometrical Parameters ◽  
Two Dimensional ◽  
Thick Plates ◽  
The Mean

The free vibration analysis of composite thin and relatively thick plates accounting for uncertainty is addressed in this work. Classical and refined two-dimensional models derived via Carrera's Unified Formulation (CUF) are considered. Material properties and geometrical parameters are supposed to be random. The fundamental frequency related to the first bending eigenmode is stochastically described in terms of the mean value, the standard deviation, the related confidence intervals and the cumulative distribution function. The Monte Carlo Method is employed to account for uncertainty. Cross-ply, simply supported, orthotropic plates are accounted for. Symmetric and anti-symmetric lay-ups are investigated. Displacements based and mixed two-dimensional theories are adopted. Equivalent single layer and layer wise approaches are considered. A Navier type solution is assumed. The conducted analyses have shown that for the considered cases, the fundamental natural frequency is not very sensitive to the uncertainty in the material parameters, while uncertainty in the geometrical parameters should be accounted for. In the case of thin plates, all the considered models yield statistically matching results. For relatively thick plates, the difference in the mean value of the natural frequency is due to the different number of degrees of freedom in the model.

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