Circular Contact Research Articles

Three-dimensional static analysis of multilayered one-dimensional orthorhombic quasicrystal spherical shells with the piezoelectric effect

The static analysis of multilayered one-dimensional orthorhombic piezoelectric quasicrystals spherical shells is presented by using the state vector method. Based on two separated state equations, the solution of a homogenous spherical shell is derived, and the solution for the corresponding multilayered case is obtained via the propagator matrix method. Mechanical behaviors of spherical shells subjected to two kinds of symmetric loads are analyzed, respectively. Under uniformed loads, smaller phonon displacements are achieved in a quasicrystal-skin structure than those in crystal-skin one. Under the compression of rigid half-plane, the radius of the circular contact area increases with decreasing thickness of quasicrystal layers.

Effect of arbitrary entrainment angle in elastohydrodynamic lubrication elliptical and circular contacts

Conventional elastohydrodynamic lubrication models assume parallel surface velocities such as in cam-follower and ball bearing systems. However, many important machine elements like hypoid gear and spiral bevel, the sliding and entrainment velocities are along different directions that could possibly influence the elastohydrodynamic lubrication performance characteristics significantly. For such complex conditions, the existing film thickness formulae and shear-thinning correction factors available in the literature are not suitable. Therefore, this paper investigates the effect of arbitrarily oriented surface velocity vectors on elastohydrodynamic lubrication characteristics considering realistic rheological models and experimentally established viscosity–pressure and compressibility laws. The Reynolds equation employed herein includes the surface velocity components along both the reference axes in the plane of contact. The elastohydrodynamic lubrication film thickness is found to deviate up to a maximum of 61% with respect to its conventional value. This deviation in film thickness behavior is shown to be a function of ellipticity and shear-thinning parameters.

Optimum design of compressive residual stress field caused by ultrasonic surface rolling with a mathematical model

• An analytical study on residual stress field caused by ultrasonic surface rolling is presented. • An optimum fatigue resistance is obtained based on the study. • Analytical solutions of characteristic parameters in residual stress fields are presented. • Residual stresses in x and y directions of circular and elliptical contact areas are investigated. Compressive residual stress fields induced by ultrasonic surface rolling process play a key role in determining the fatigue performance of machine parts. The present work is an analytical approach to conducting optimum design of this field to obtain an optimum fatigue resistance. Thus, a mathematical model was presented to predict residual stresses based on circular and elliptical Hertz contact areas. Moreover, to validate the proposed analytical approach, experimental verification was carried out on 18CrNiMo7-6 steel. Analytic solutions were derived from the mathematical model and optimum characteristic parameters were obtained by investigating the characteristic parameters in this field, such as surface residual stress, maximum residual stress and its depths. Results showed that increasing the total force, Hertz contact area and ratio of the radius of tool tip to that of target body could significantly enhance the peak of compressive residual stress and its depth.

Investigation of the evaporation heat transfer mechanism of a non-axisymmetric droplet confined on a heated micropillar structure

In scaling computer performance, closely integrating heterogeneous components in a single system-in-package assembly provides faster signal communication and a tighter footprint – but also generates more heat: state-of-the-art microelectronic devices can produce more than 1 kW cm−2. The next generation high-powered electronics will need two-phase liquid cooling, such as droplet evaporation, which utilizes the latent heat of vaporization to remove excessive heat. Compared to traditional single-phase cooling techniques, two-phase cooling offers both high efficiency and an exceptionally high heat dissipation rate. Although droplet evaporation has been explored for over a hundred years, many fundamental transport mechanisms are still not well understood. For example, most droplet evaporation studies focused only on spherical droplets, which possess a uniform curvature, κ (for a low Bond Number), along the meniscus interface. Evaporation from a non-spherical droplet, due to the change in perimeter-to-area ratio and the meniscus curvature, exhibits very different interfacial mass transport features from a spherical droplet. In particular, a higher perimeter-to-solid-liquid-area ratio will yield a larger fraction of thin film region and therefore a smaller thermal resistance in an evaporating droplet, while a high local curvature will facilitate a stronger local vapor diffusion rate. In this study, we develop a numerical model to investigate the evaporation behavior of asymmetrical microdroplets suspended on heated porous micropillar structures. We explore the equilibrium profiles and mass transport characteristics of droplets with circular, triangular, and square contact shapes, using the Volume of Fluid (VOF) method, and we use a simplified Schrage model [1] to study the evaporative mass transport at the liquid-vapor interface. The results show that microdroplets evaporating on a triangular substrate possess 12.8% smaller effective film thickness compared to that on a circular substrate, due to a longer length of the contact line. During the evaporative heat transfer process, the triangular-based droplets also exhibit the smallest temperature difference between the droplets’ solid-liquid interface and ambient temperature, which leads to a higher heat transfer coefficient (21% larger than a spherical droplet at a supplied heat flux of 500 W/cm2). When the supplied heat increases to a higher value (e.g., 1000 W/cm2), the shape effect becomes less significant where the diffusion resistance is dominated by the liquid-vapor interfacial temperature instead of the meniscus curvature.

Fretting wear accumulation in partial-slip circular Hertzian contact

An axisymmetric Hertzian type elastic contact under a constant normal and oscillating tangential loading is considered in the framework of Archard’s law of wear. The dissipated energy approach is employed for modeling the volume wear rate, and a simple two-parameter regression model has been introduced, which accounts for the wear rate’s non-monotonicity. After fixing one of its parameters based on the numerical solution available in the literature, the developed model does not contain any free parameters, since the other one is determined by matching to the final (limiting) contact configuration, which evolves as a result of fretting wear.

Small signal analysis of MPCVD diamond Schottky diodes

Polycrystalline diamond (PCD) grown by chemical vapor deposition (CVD) is an intrinsic semiconductor particularly attractive for high power/high temperature devices. Nevertheless, the physical models for injection and transport of electrical carriers are remarkable complex and depend on the microstructure and composition of carbon species in the film. In this work, free-standing CVD PCD films were deposited by microwave plasma CVD (MPCVD) and were characterized by Raman spectroscopy. Gold and aluminum circular contacts were deposited on the growth surface in order to fabricate a planar diode. The current-voltage characteristics were measured at different temperatures. The application of a non-homogeneous barrier model to fit the current-voltage characteristics reveals the existence of two barriers related with the grain/electrode and grain boundary/electrode interfaces. Small signal analysis was performed at room temperature to understand the nature of electrical process involved in the injection and carrier transport. The existence of parallel channels through with charge flows was confirmed and the fittings suggest the existence of a nearly equipotential surface at the interface diamond/electrode. The physical origin of the inclusion of a constant phase element in the equivalent circuit model is discussed. The results obtained are of particular importance to further devices fabrication. Prime noveltyAn equivalent circuit model for the diamond Schottky diode is proposed; the physical origin of the constant phase element included in the model is discussed.

Modeling the elastic impact of a body with a special point at its surface

We have considered the elastic straight impact along a flat border of the stationary half-space of the body bounded in a zone of contact interaction by the surface of rotation, whose order is smaller than two. The feature of the problem is that for the selected case an infinite curvature of the boundary surface at a point of initial contact, from which the process of dynamic compression of bodies in time starts. In addition to basic assumptions from the quasi-static theory of elastic impact between solid bodies, we have used a known solution to the static axisymmetric contact problem from the theory of elasticity. The process of an impact at a small initial velocity is divided into two stages: the dynamic compression and the dynamic decompression. For each of them, we have built an analytic solution to the nonlinear differential equation of relative convergence of the centers of bodies' masses in time. A solution to the non-linear problem with initial conditions for the differential equation of second order at the first stage was expressed through the Ateb-sinus, and at the second stage ‒ through the Ateb-cosine. To simplify calculations, we have compiled separate tables for the specified special functions, as well as proposed their compact approximations using basic functions. It was established that an error of analytical approximations of both special functions is less than one percent. We have also derived closed expressions for computing the maximum values: compression of a body, impact strength, radius of the circular contact area, and pressure, which is limited in the center of this area. We have considered a numerical example related to the impact of a rigid elastic body against a rubber half-space. Problems of this type arise when modeling the dynamic action of pieces of a solid mineral on rubber, when they fall on the rolls of a vibratory classifier lined with rubber. Based on the results from comparing the calculated parameters of an impact, we have received good agreement between numerical results, obtained from the constructed analytical solutions, and the integration of a nonlinear equation at a computer. This confirms the reliability of the built analytical solutions to the problem on impact, which provide for the convolution of a brief process over time

Effect of Surface Curvature on Contact Resistance Between Cylinders

Due to the microscopic roughness of contacting materials, an additional thermal resistance arises from the constriction and spreading of heat near contact spots. Predictive models for contact resistance typically consider abutting semi-infinite cylinders subjected to an adiabatic boundary condition along their outer radius. At the nominal plane of contact, an isothermal and circular contact spot is surrounded by an adiabatic annulus and the far-field boundary condition is one of constant heat flux. However, cylinders with flat bases do not mimic the geometry of contacts. To remedy this, we perturb the geometry of the problem such that, in cross section, the circular contact is surrounded by an adiabatic arc. When the curvature of this arc is small, we employ a series solution for the leading-order (flat base) problem. Then, Green's second identity is used to compute the increase in spreading resistance in a single cylinder, and thus the contact resistance for abutting ones, without fully resolving the temperature field. Complementary numerical results for contact resistance span the full range of contact fraction and protrusion angle of the arc. The results suggest as much as a 10–15% increase in contact resistance for realistic contact fraction and asperity slopes. When the protrusion angle is negative, the decrease in spreading resistance for a single cylinder is also provided.

Design and manufacturing of a novel high contact ratio internal gear with a circular arc contact path

A new internal gear drive with a high contact ratio (HCR) is presented in this paper. In the new gear drive, the number of teeth working at the same time has reached 7, which is usually only less than 2 in the traditional involute gear drive. The bearing capacity of the new gear is improved significantly. To obtain a high contact ratio, the addendum tooth profiles of the pinion and internal gear are deduced by a given path of contact based on gear meshing theory and the dedendum tooth profile is designed as the envelope to the family of addendum tooth profile of the mating gear. The mathematical models, including the equation of the path of contact, the equations of addendum and dedendum tooth profiles and the equation of modification, are established. An example drive in the three-dimensional (3D) model is presented. The characteristics, such as contact ratio, sliding ratio, induced curvature, and the contact and bending stress are evaluated. The results confirm that the novel internal gear drive has a higher contact ratio and lower sliding coefficient, and the contact and bending stresses are reduced in comparison with the involute gear drive. Furthermore, a prototype is produced, which illustrate the feasibility of manufacturing.

Analytical solution of the elastic impact problem for a cone over a half-space

Using the main provisions of the theory of H. Hertz on the mechanical impact of solids, the dynamic interaction of an elastic cone with an elastic half-space bounded by a flat surface is considered. The case is investigated when the axis of the cone of rotation is perpendicular to the boundary of the half-space, and the initial point of contact of the bodies is the vertex of the cone. To describe the local deformations of bodies in the zone of their interaction, the well-known solution of the axisymmetric static contact problem of the theory of elasticity, constructed by I. Ya. Shtaermann, is used. The problem of the collision of bodies is reduced to a second-order differential equation with quadratic nonlinearity. Two forms of analytical solution of this nonlinear Cauchy problem are obtained. The first uses the Ateb-sine, and the second uses the elliptical cosine. The equivalence of the obtained forms of solutions is established, that is, the possibility of replacing one form with another. To calculate the values of the Ateb-sine using the linear interpolation method, a special table is presented, and an analytical approximation by its elementary functions is proposed. The consistency of the results to which these two methods of approximate calculation of the Ateb-sine values are shown is shown. An approximate formula for calculating the values of the elliptic cosine is also derived and its reliability is confirmed. As a result of solving the impact problem, formulas were obtained that describe the change over time: the convergence of the centers of mass of the bodies, the forces of impact interaction, the radius of the circular contact area and the contact pressure. It is noted that the pressure is infinite in the center of the site, where the top of the cone is in contact with the half-space. The results are compared, to which two analytical forms of the solution result and numerical computer integration of the differential equation of compression of bodies subjected to impact. Established a good agreement of numerical results obtained in different ways. The effect of the taper angle on the main parameters of the dynamic interaction of bodies is investigated. It is shown that an increase in the angle of a solution of a conical body, which strikes, leads to a decrease in the maximum dynamic compression of bodies and the duration of their interaction, as well as to an increase in the maximum impact force, with a constant value of its momentum. A numerical example of calculation is given, where steel is taken as the material of a conical body, and rubber is used as the material of a fixed half-space. Problems of this type arise when calculating the parameters of impact of a piece of mineral raw materials on rubber-lined rolls of the vibration classifier.

The effect of multiple contacts between crack faces on crack contribution to the effective elastic properties

The compliance contribution of a penny-shaped crack having multiple contacts between crack faces is analyzed. In order to reduce the number of parameters involved, regular lattices of circular contacts are considered. It is found, in particular, that, at the same total area of contacts, a large number of small contacts produces stronger stiffening effect than a small number of large contacts; hence the total contact area is not the parameter controlling the crack compliance contribution. The effects of contacts on both the normal and the shear crack compliances are found to be very close. In the case of moderately non-regular contact lattices, the results were found to be only marginally different from the results for regular ones. Results are conveniently expressed in terms of “Holm's radius”—the radius of a single contact that would have produced the same effect. Being applied to multiple cracks with contacts, our results yield the “adjusted”, for the presence of contacts, value of crack density.

Nanodroplets at Membranes Create Tight-Lipped Membrane Necks via Negative Line Tension.

The response of biomembranes to aqueous-phase separation and to the resulting water-in-water droplets has been recently studied on the micrometer scale using optical microscopy and elasticity theory. When such a droplet adheres to the membrane, it forms a contact area that is bounded by a contact line. For a micrometer-sized droplet, the line tension associated with this contact line can usually be ignored compared with the surface tensions. However, for a small nanoscopic droplet, this line tension is expected to affect the membrane-droplet morphology. Here, we use molecular simulations to study nanodroplets at membranes and to gain insight into these line tension effects. The latter effects are shown to depend strongly on another key parameter, the mechanical tension experienced by the membrane. For a large membrane tension, a droplet adhering to the membrane is only partially engulfed by the membrane, and the membrane-droplet system exhibits an axisymmetric morphology. A reduction of the membrane tension leads to an increase in the contact area and a decrease in the interfacial area of the droplet, initially retaining its axisymmetric shape, which implies a circular contact line and a circular membrane neck. However, when the tension falls below a certain threshold value, the system undergoes a morphological transition toward a non-axisymmetric morphology with a non-circular membrane neck. This morphology persists until the nanodroplet is completely engulfed by the membrane and the membrane neck has closed into a tight-lipped shape. The latter morphology is caused by a negative line tension, which is shown to be a robust feature of membrane-droplet systems. A closed membrane neck with a tight-lipped shape suppresses both thermally activated and protein-induced scission of the neck, implying a reduction in the cellular uptake of nanodroplets by pinocytosis and fluid-phase endocytosis. Furthermore, based on our results, we can also draw important conclusions about the time-dependent processes corresponding to the surface nucleation and growth of nanodroplets at membranes.

Three-dimensional exact solutions of transversely isotropic coated structures under tilted circular flat punch contact

Because of the large stress gradient in the coated structure and the more and more thin thickness of coating, it is too hard to guarantee the calculation accuracy by the commercial software in the design of the coated structure. In this case, a research work for an accurate and efficient calculation method for the coated structure is necessary and will contribute to the accurate design and quality promotion of the coated structure. In this paper, the three-dimensional solutions of transversely isotropic coated structure under tilted circular flat punch contact are derived based on the three-dimensional general solutions of the transversely isotropic material. The solutions are obtained in two cases including the smooth contact and the frictional contact. The numerical results show that this method has the good convergence, high accuracy, high efficiency and high stability. Based on this method, the optimal thickness of the coating and the interfacial stress between the coating and the substrate can be obtained accurately. The corresponding analysis will contribute to the strengthening design of the coated structure.

Droplet dynamics on chemically heterogeneous substrates

Slow droplet motion on chemically heterogeneous substrates is considered analytically and numerically. We adopt the long-wave approximation which yields a single partial differential equation for the droplet height in time and space. A matched asymptotic analysis in the limit of nearly circular contact lines and vanishingly small slip lengths yields a reduced model consisting of a set of ordinary differential equations for the evolution of the Fourier harmonics of the contact line. The analytical predictions are found, within the domain of their validity, to be in good agreement with the solutions to the governing partial differential equation. The limitations of the reduced model when the contact line undergoes stronger deformations are partially lifted by proposing a hybrid scheme which couples the results of the asymptotic analysis with the boundary integral method. This approach improves the agreement with the governing partial differential equation, but at a computational cost which is significantly lower compared to that required for the full problem.

A 2D and 3D study of the texture of wear scars for soybean oil additivated with nano graphite

Based on studies on characterization of surface topography, the following conclusions can be drawn: surface texture analyses are statistical. There is no agreed methodology for characterizing both the texture of worn surfaces and those of new ones (unworn). The methodology depends on many factors: the shape and size of triboelements, the available equipment and software, the set of selected parameters, the user experience and ingenuity. Worn scars were obtained after tests on four ball machine (European conditions [30], at LubriTest laboratory of “Dunarea de Jos” University). The test parameters for each tested lubricant were: force at main shaft of the four ball machine -100 N, 200 N and 300 N (± 5%). sliding speeds of 0.383 m/s, 0.537 m/s and 0.691 m/s, test time - 60 minutes (± 1%), the concentration of the additive is 0.25%, 0.50% and 1% (wt), respectively. Analysing the data from this study, it can be seen that for all measurements, St is higher than Rt, which means that the maximum values were not found on the axis of the ellipse perpendicular to the sliding direction. This is logical because in a circular or almost circular contact, the maximum contact pressure is towards the front of the contact. Thus, a 3D study will also include the area of maximum contact pressure that will most likely affect the surface texture quality to a greater extent. For some test regimes, i.e. (F=100 N, v=0.38 m/s), lower values were obtained than those obtained on the initial surfaces of the balls, which implies that the test regime acts as a running-in process, improving the surface quality Amplitude parameters and three functional parameters will be analysed in this paper.

An Isothermal Elastohydrodynamic lubrication of elliptical contact with Multigrid method

ABSTRACT The paper presents steady isothermal elastohydrodynamic lubrication (EHL) of elliptical contact with Roelands pressure–viscosity model over varying rotational speed. The governing Reynolds and film-thickness equation for elliptical contact in roller bearings are analysed by using multigrid method with full approximation scheme. The non-dimensional pressure distribution and film-thickness for elliptical contacts are obtained. The distinct friction models appropriate to lubricants in contact regions are predicted. The result shows that rolling contact weariness does not occur on the surfaces with longitudinal roughness and wear or scraping exists in circular EHL contacts with entrainment along major axis to that of minor axis. The computation predicts that minimum film thickness, central film thickness and elastic deformation increase as the rotational speed increases. The computed results are compared with earlier finding which are in good agreement.

Analytical Formula for the Ratio of Central to Minimum Film Thickness in a Circular EHL Contact

Prediction of minimum film thickness is often used in practice for calculation of film parameter to design machine operation in full film regime. It was reported several times that majority of prediction formulas cannot match experimental data in terms of minimum film thickness. These standard prediction formulas give almost constant ratio between central and minimum film thickness while numerical calculations show ratio which spans from 1 to more than 3 depending on M and L parameters. In this paper, an analytical formula of this ratio is presented for lubricants with various pressure–viscosity coefficients. The analytical formula is compared with optical interferometry measurements and differences are discussed. It allows better prediction, compared to standard formulas, of minimum film thickness for wide range of M and L parameters.

Friction of Poroelastic Contacts with Thin Hydrogel Films.

We report on the frictional behavior of thin poly(dimethylacrylamide) hydrogel films grafted on glass substrates in sliding contact with a glass spherical probe. Friction experiments are carried out at various velocities and normal loads applied with the contact fully immersed in water. In addition to friction force measurements, a novel optical setup is designed to image the shape of the contact under steady-state sliding. The velocity dependence of both friction force Ft and contact shape is found to be controlled by a Péclet number, Pe, defined as the ratio of the time τ needed to drain the water out of the contact region to a contact time a/ v, where v is the sliding velocity and a is the contact radius. When Pe < 1, the equilibrium circular contact achieved under static normal indentation remains unchanged during sliding. Conversely, for Pe > 1, a decrease in the contact area is observed together with the development of a contact asymmetry when the sliding velocity is increased. A maximum in Ft is also observed at Pe ≈1. These experimental observations are discussed in the light of a poroelastic contact model based on a thin-film approximation. This model indicates that the observed changes in contact geometry are due to the development of a pore pressure imbalance when Pe > 1. An order-of-magnitude estimate of the friction force and its dependence on normal load and velocity are also provided under the assumption that most of the frictional energy is dissipated by poroelastic flow at the leading and trailing edges of the sliding contact.

Response to Dr Greenwood\u2019s Comments on \u201cExtending the Double-Hertz Model to Allow Modeling of an Adhesive Elliptical Contact\u201d

© 2018, The Author(s). An adhesive elliptical contact is normally found in microscale applications that involve cylindrical solids, crossing at an angle between 0° and 90°. Currently, only one model is available to describe the elliptical contact’s surface interaction: the approximate Johnson–Kendall–Roberts (JKR) model which is limited to soft materials. In this paper, a new adhesive elliptical model is developed for a wide range of adhesive contacts by extending the double-Hertz theory, where adhesion is modeled by the difference between two Hertzian pressure distributions. Both Hertzian pressures are assumed to have an equivalent shape of contact areas, the only difference being in size. Assuming that the annular adhesive region is obtained by the area difference between the two Hertzian contact areas, the pull-off force curves can be calculated. In the limiting case of an adhesive circular contact, the results are very close to results from the existing models. However, for an adhesive elliptical contact in the JKR domain, lower pull-off forces are predicted when compared to the JKR values. Unlike the developed model, the shape of the JKR contact area varies throughout contact. Results show, particularly for conditions close to the JKR domain, that it is important to take into account that the adhesive region is the result of the two Hertzian contact areas having a non-equivalent shape.

A surface topography analysis of the curling stone curl mechanism

The curling motion of the curling stone on ice is well-known: if a small clockwise rotational velocity is imposed to the stone when it is released, in addition to the linear propagation velocity, the stone will curl to the right. A similar curl to the left is obtained by counter-clockwise rotation. This effect is widely used in the game to reach spots behind the already thrown stones, and the rotation also causes the stone to propagate in a more predictable fashion. Here, we report on novel experimental results which support one of the proposed theories to account for the curling motion of the stone, known as the “scratch-guiding theory”. By directly scanning the ice surface with a white light interferometer before and after each slide, we observed cross-scratches caused by the leading and trailing parts of the circular contact band of the linearly moving and rotating stone. By analyzing these scratches and a typical curling stone trajectory, we show that during most of the slide, the transverse force responsible for the sideways displacement of the stone is linearly proportional to the angle between these cross-scratches.