Effect of Ellipsoidal Particle Shape on Tribological Properties of Lubricants Containing Nanoparticles

Adding nanoparticles can significantly improve the tribological properties of lubricants.However,there is a lack of understanding regarding the influence of nanoparticle shape on lubrication performance.In this work,the influence of diamond nanoparticles(DNPs)on the tribological properties of lubricants is investigated through friction experiments.Additionally,the friction characteristics of lubricants regarding ellipsoidal particle shape are investigated using molecular dynamics(MD)simulations.The results show that DNPs can drastically lower the lubricant's friction coefficientμfrom 0.21 to 0.117.The shearing process reveals that as the aspect ratio(α)of the nanoparticles approaches 1.0,the friction performance improves,and wear on the wall diminishes.At the same time,the shape of the nanoparticles tends to be spherical.When 0.85≤α≤1.0,rolling is ellipsoidal particles'main form of motion,and the friction force changes according to a periodic sinusoidal law.In the range of 0.80≤α<0.85,ellipsoidal particles primarily exhibit sliding as the dominant movement mode.Asαdecreases within this range,the friction force progressively increases.The friction coefficientμcalculated through MD simulation is 0.128,which is consistent with the experimental data.

Acoustic characteristics of pulse detonation engine with ellipsoidal reflector

Acoustic characteristics of a pulse detonation engine（PDE） with and without an ellipsoidal reflector are numerically and experimentally investigated. A two-dimensional（2 D） non-splitting unstructured triangular mesh Euler solver based on the space-time conservation element and solution element（CE/SE） method is employed to simulate the flow field of a PDE.The numerical results clearly demonstrate the external flow field of the PDE. The effect of an ellipsoidal reflector on the flow field characteristic near the PDE exit is investigated. The formation process of reflected shock wave and reflected jet shock are reported in detail. An acoustic measurement system is established for the PDE acoustic testing. The experimental results show that the ellipsoidal reflector changes the sound waveform and directivity of PDE sound. The reflected shock wave and reflected jet shock result in two more positive pressure peaks in the sound waveform. The ellipsoidal reflector changes the directivity of PDE sound from 20 to 0. It is found that the peak sound pressure level（PSPL） and overall sound pressure level（OASPL） each obtain an increment when the PDE is installed with a reflector. The maximum relative increase ratio of PSPL and OASPL are obtained at the focus point F2, whose values are 6.1% and 6.84% respectively. The results of the duration of the PDE sound indicate that the reflecting and focusing wave generated by the reflector result in the increment of A duration and B duration before and near focus point F2. Results show that the ellipsoidal reflector has a great influence on the acoustic characteristic of PDE sound. The research is helpful for understanding the influence of an ellipsoidal reflector on the formation and propagation process of PDE sound.

Research on Two-Step Hydro-Bulge Forming of Ellipsoidal Shell with Larger Axis Length Ratio

The two-step hydro-bulge forming technique was proposed to manufacture the ellipsoidal shell with the length ratio of the long axis to the short axis larger than 1.4. A central tube was introduced into the first step of the hydro-bulge forming process to constrain the over growth of the short axis during bulging,and then the central tube was replaced with two polar plates in the second step of the hydro-bulge forming process to manufacture an integral ellipsoidal shell. It is shown that the central tube restricts the growth of the short axis and simultaneously reduces the shrunk tendency of the long axis. The wrinkling occurs due to the latitudinal compressive stress at the equator at the early stage of hydro-bulge forming. However,with the increase of internal pressure,the compressive stress areas gradually decrease and finally the tensile latitudinal stress occupies approximately the whole shell,thus the wrinkles are eliminated. A sound ellipsoidal shell with the axis length ratio of 1.8 is obtained after two-step hydro bulging.

Comparison of Construction Method for DEM Simulation of Ellipsoidal Particles

Discrete element model was developed to simulate the ellipsoidal particles moving in the moving bed. Multi-element model was used to describe a ellipsoidal particle, the contact detection algorithm of ellipsoidal particle was developed, and both contact force and gravity force were considered in the models. The simulation results were validated by our experiment. Three algorithms for representing an ellipsoidal particle were compared in macro and micro aspects. The results show that there exists big difference in the microscopic parameters such as kinetic energy, rotational kinetic energy, deformation, contact force and collision number which leads to the difference of macroscopic parameters. The relative error in the discharge rate and tracer particle position is the largest between 3-tangent-element representation and experimental results. The flow pattern is similar for the 5-element and 3-intersection representations. The only difference is the discharge rate of 5-element representation is larger than the experimental value and that of the 3-intersection representation has the contrary result. Finally the 3-intersection- element reoresentation is chosen in the simulation due to less comouting time than that of the 5-element renresentation.

Modeling and Software Development of the Interfacial Transition Zone of Ellipsoidal Aggregate in Cement-Based Composites

The interfacial transition zone (ITZ) between the aggregates and the bulk paste is the weakest zone of ordinary concrete, which largely determines its mechanical and transporting properties. However, a complete understanding and a quantitative modeling of ITZ are still lacking. Consequently, an integrated modeling and experimental study were conducted. First, the theoretical calculation model of the ITZ volume fraction about the rotary ellipsoidal aggregate particles was established based on the nearest surface function formula. Its calculation programs were written based on Visual Basic 6.0 language and achieved visualization and functionalization. Then, the influencing factors of ITZ volume fraction of the ellipsoidal aggregate particles and the overlapping degree between the ITZ were systematically analyzed. Finally, the calculation models of ITZ volume fraction on actual ellipsoidal aggregate were given, based on cobblestones or pebbles particles with naturally ellipsoidal shape. The results indicate that the calculation model proposed is highly reliable.

Route Height Connection Across the Sea by Using the Vertical Deflections and Ellipsoidal Height Data

Distance between the main land and island is so long that it is very difficult to precisely connect the height datum across the sea with the traditional method like the trigonometric leveling, or it is very expensive and takes long time to implement the height transfer with the geopotential technique. We combine the data of GPS surveying, astro-geodesy and EGM2008 to precisely connect the orthometric height across the sea with the improved astronomical leveling method in the paper. The Qiongzhou Strait is selected as the test area for the height connection over the sea. We precisely determine the geodetic latitudes, longitudes, heights and deflections of the vertical for four points on both sides across the strait. Modeled deflections of the vertical along the height connecting routes over the sea are determined with EGM2008 model based on the geodetic positions and heights of the sea segmentation points from DNSC08MSS model. Differences of the measured and modeled deflections of the vertical are calculated at four points on both sides and linearly change along the route. So the deflections of the vertical along the route over the sea can be improved by the linear interpolation model. The results are also in accord with those of trigonometirc levelings. The practical case shows that we can precisely connect the orthometric height across the Qiongzhou Strait to satisfy the requirement of order 3 leveling network of China. The method is very efficient to precisely connect the height datum across the sea along the route up to 80 km.

The ellipsoidal corrections for boundary value problems of deflection of the vertical with ellipsoid boundary

The boundary value problem of deflections of vertical with ellipsoid boundary is studied in the paper. Based on spherical harmonic series, the ellipsoidal corrections for the boundary value problem are derived so that it can be well solved. In addition, an imitation arithmetic is given for examining the accuracies of solutions for the boundary value problem as well as its spherical approximation problem, and the computational results illustrate that the boundary value problem has higher accuracy than its spherical approximation problem if deflection of the vertical are measured on geoid.

Numerical investigation on motion of an ellipsoidal particle inside confined microcavity flow

The behaviors of a neutrally buoyant ellipsoidal particle in vortical flow confined by a microcavity are numerically studied using the Lattice-Boltzmann method.For specific initial position,an isolated ellipsoid may develop a stable limit cycle orbit inside microcavity due to the interaction between particle and the carrier flow.It is observed that ellipsoidal particles of different shapes exhibit two different stable rotational modes depending on the initial orientation and lateral position.A prolate spheroid tends to enter a tumbling mode whereas an oblate spheroid is apt to achieve a rolling mode.The evolution of rotational velocities along the stable orbit is also analyzed for particles of different shapes.

A NOVEL ELLIPSOIDAL ACOUSTIC INFINITE ELEMENT

A novel ellipsoidal acoustic infinite element is proposed. It is based a new pressure representation, which can describe and solve the ellipsoidal acoustic field more exactly. The shape functions of this novel acoustic infinite element are similar to the (Burnett's) method, while the weight functions are defined as the product of the complex conjugates of the shaped functions and an additional weighting factor. The code of this method is cheap to generate as for 1-D element because only 1-D integral needs to be numerical. Coupling with the standard finite element, this method provides a capability for very efficiently modeling acoustic fields surrounding structures of virtually any practical shape. This novel method was deduced in brief and the conclusion was kept in detail. To test the feasibility of this novel method efficiently,in the examples the infinite elements were considered,excluding the finite elements relative. This novel ellipsoidal acoustic infinite element can deduce the analytic solution of an oscillating sphere. The example of a prolate spheroid shows that the novel infinite element is superior to the boundary element and other acoustic infinite elements. Analytical and numerical results of these examples show that this novel method is feasible.

Simulation of x-ray transmission through an ellipsoidal capillary

This paper develops a simulation program for x-ray transmission in an ellipsoidal capillary based on a ray-tracing method. The influence of the parameters of ellipsoidal capillary and x-ray energy on transmission efficiency, full width at half maximum and power density gain of x-ray beams through an ellipsoidal capillary was analysed by this program. It shows that the particular rules of the ellipsoidai capillary x-ray lens are different from the polycapillary lens. Furthermore, this analysis method can be applied to the optimized design of ellipsoidal capillary.

Elastic deformation of ellipsoidal shell of different axis ratio under inner pressure

Discusses the elastic deformation of ellipsoidal shell of different axis ratio under inner pressure during hydraulic bulging forming with theoretical results in good agreement with actual result, thereby providing theoretical basis for hydraulic bulging forming of ellipsoidal shell.

Bounds on the overall properties of composites with ellipsoidal inclusions

A new model is put forward to bound the effective elastic moduli of composites with ellipsoidal inclusions. In the present paper, transition layer for each ellipsoidal inclusion is introduced to make the trial displacement field for the upper bound and the trial stress field for the lower bound satisfy the continuous interface conditions which are absolutely necessary for the application of variational principles. According to the principles of minimum potential energy and minimum complementary energy, the upper and lower bounds on the effective elastic moduli of composites with ellipsoidal inclusions are rigorously derived. The effects of the distribution and geometric parameters of ellipsoidal in- clusions on the bounds of the effective elastic moduli are an- alyzed in details. The present upper and lower bounds are still finite when the bulk and shear moduli of ellipsoidal inclusions tend to infinity and zero, respectively. It should be mentioned that the present method is simple and needs not calculate the complex integrals of multi-point correlation functions. Meanwhile, the present paper provides an entirely different way to bound the effective elastic moduli of composites with ellipsoidal inclusions, which can be developed to obtain a series of bounds by taking different trial displacement and stress fields.

Distribution characteristic of scattering field for an ellipsoidal target irradiated by an electromagnetic wave from an arbitrary direction

It is of great importance for engineering applications to obtain the expression of scattering field for an ellipsoidal target irradiated by an electromagnetic wave from an arbitrary direction. Literature relevant to this problem is seldom found. In this paper, the scattering field for an ellipsoidal target is presented by utilizing the scale transformation of electromagnetic field and the rotation of coordinate system, with an electromagnetic wave projecting on the target from an arbitrary direction. The obtained result is in good agreement with the solution available from the literature if we consider the scale factors to be unity. Taking a conducting ellipsoidal target for sample, we perform the partial simulations of the ellipsoidal model and a plant leaf model by choosing different scale factors. The obtained results show that the distribution characteristic of scattering field is sensitively affected by the polarization of the incident wave and varies not much with the incident wave angle but changes with the observation point. At some points the scattering energy arrives at its maximum.

Numerical evaluation of overestimation of the interface thickness around ellipsoidal particle

Abstract When interfacial layers are viewed as a separate phase, the interface thickness plays an essential role in assessing physico-mechanical properties of particulate materials. However, the interface thickness from sectional analysis is often overestimated, due to the irregularity of surface textures of grains in opaque materials that gives rise to the normal of a cross-sectional plane non-perpendicular to the surface of grains. Hence, the determination of the overestimation degree is very critical to precisely obtain the interface thickness. This article develops a numerical model for the overestimation degree of the interface thickness around an ellipsoidal grain with an arbitrary aspect ratio, by applying an accurate sectional analysis algorithm, and quantitative stereology and geometrical probability theories. Furthermore, on the basis of the developed numerical model, the influence of ellipsoidal particle shape on the overestimation degree is quantitatively charac-terized.

The Ellipsoidal Invariant Set of Fractional Order Systems Subject to Actuator Saturation:The Convex Combination Form

The domain of attraction of a class of fractional order systems subject to saturating actuators is investigated in this paper. We show the domain of attraction is the convex hull of a set of ellipsoids. In this paper, the Lyapunov direct approach and fractional order inequality are applied to estimating the domain of attraction for fractional order systems subject to actuator saturation. We demonstrate that the convex hull of ellipsoids can be made invariant for saturating actuators if each ellipsoid with a bounded control of the saturating actuators is invariant. The estimation on the contractively invariant ellipsoid and construction of the continuous feedback law are derived in terms of linear matrix inequalities (LMIs). Two numerical examples illustrate the effectiveness of the developed method. © 2014 Chinese Association of Automation.

General expression of double ellipsoidal heat source model and its error analysis

In order to analyze the maximum power density error with different heat flux distribution parameter values for double ellipsoidal heat source model, a general expression of double ellipsoidal heat source model was derived .front Goldak double ellipsoidal heat source model, and the error of maximum power density was analyzed under this foundation. The calculation error of thermal cycling parameters caused by the maximum power density error was compared quantitatively by numerical simulation. The results show that for guarantee the accuracy of welding numerical simulation, it is better to introduce an error correction coefficient into the Goldak double ellipsoidal heat source model expression. And, heat flux distribution parameter should get higher value for the higher power density welding methods.

Modelling Orthometric Heights from a Combination of Ellipsoidal Heights and Gravimetric Geoid Model in Rivers State, Nigeria

Many applications in geodesy, hydrography and engineering require geoid-related heights. Spirit leveling which is the traditional means of obtaining geoid- or mean sea level-related heights is slow, time-consuming and costly. Global Navigation Satellite Systems (GNSS) offer faster and relatively cheaper way of obtaining geoid-related heights when geoidal undulation is applied to ellipsoidal heights. However, difficulties involved in determining acceptable geoid height have seriously hampered the application of GNSS for leveling in Rivers State, thus necessitating the need to develop an acceptable geoid model which will serve as a means of conversion of GNSS-delivered ellipsoidal heights to their orthometric heights equivalent. In pursuance of this objective, a detailed gravimetric geoid has been evaluated for Rivers State, Nigeria. The computation of the geoid was carried out by the traditional remove-restore procedure. The Earth Geopotential Model 2008 (EGM08) was applied as the reference field for both the remove and restore parts of the procedures;spherical Fast Fourier Transform (FFT) was employed for the evaluation of the Molodenskii’s integral formula for the height anomaly, (ζ) to yield the quasi-geoid;while the Residual Terrain Modelling (RTM) was done by prism integration. The classical gravimetric geoid over Rivers State was obtained from the rigorously evaluated quasi-geoid by adding the quasi-geoid to geoid (N?- ζ) correction it. The minimum and maximum geoid height values are 18.599 m and 20.114 m respectively with standard deviation of 0.345 m across the study area. Comparison of the gravimetric geoidal heights with the GPS/Leveling-derived geoidal heights of 13 stations across Rivers State, Nigeria showed that the absolute agreement with respect to the GPS/leveling datum is generally better than 7 cm root mean squares (r.m.s) error. Results also showed that combining both GPS heights and the computed Rivers State geoid model can give orthometric heights accurate to 3 cm post-fit using a 4-parameter empirical model. The geoid model can thus serve as a good alternative to traditional leveling when used with GPS leveling, particularly for third order leveling in the study area.

A Theoretical Approach to Study J/Ψ Suppression in Relativistic Heavy Ion Collisions with Ellipsoidal Evolution

With a view to understanding J/Ψ suppression in relativistic heavy ion collisions, we compute the suppression rate within the framework of hy-drodynamical evolution model. For this, we consider an ellipsoidal flow and use an ansatz for temperature profile function which accounts for time and the three dimensional space evolution of the quark-gluon plas-ma. We have calculated the survival probability separately as the func-tion of transverse and longitudinal momentum. We have shown that previous calculations are special cases of this model.

STUDY ON A NOVEL ELLIPSOIDAL HELICAL ANTENNA

A novel ellipsoidal helical antenna is proposed and studied in this letter. As a special in-stance,the hemispherical helical antennas are analyzed firstly,which indicates that the characteristics of a two-arm unit are better than that of a single-arm unit. Based on this,the ellipsoidal helical antenna,formed by changing the axial direction’s dimension of the two-arm hemispherical helical antenna,is analyzed by the moment method with curved basic and testing function. The effects to VSWR (Voltage Standing Wave Ratio),gain,polarization and patterns by the axial direction’s dimensions are inves-tigated. The study results provide dependable gist to the choice of antenna format according to the practical requirements.

Stress Analysis of Ellipsoidal Shell with Inner Guide Structure

In order to overcome stress concentration and increase fatigue life of ellipsoidal shells with inner guide structure,the stress analysis for strength check is very important. Owing to the main sectional profile with ellipsoidal shape,the stress distribution for perfect ellipsoidal shell is firstly conducted based on the theoretical calculation and strain gauges measurement. The experiment results show that the stresses increase gradually from pole region to equatorial plane,but still within elastic range. Secondly,strain gauge measurement for ellipsoidal shells with inner guide structure is conducted. The results show that stresses are concentrated at the vicinity of bottom plate and beyond elastic range,so the structural redesign is needed. Finally based on the analysis mentioned above,a redesigned structure with local thickening is proposed. Experimental research shows that the stress varies more even after structural redesign and within allowable range. Numerical simulation shows that both the deformation and fatigue life after redesign are acceptable.