Spherical Contact Research Articles

An extended JKR model for adhesion of a rigid sphere on a supported compressible elastic thin layer

This study aimed to develop an explicit JKR-type model for adhesive contact of a rigid sphere (of radius R) on a compressible elastic thin layer (of thickness h, Young’s modulus E, and Poisson ratio $$\nu $$) bonded or sliding on a rigid substrate. Based on a simple Kerr model for a compressible elastic layer, an explicit expression for strain energy of the elastic layer is derived in terms of the two JKR-type variables $$\left( {\delta ,\;a} \right) $$, where a is the radius of contact zone and $$\delta $$ is the indentation depth of the rigid sphere. Thus the equilibrium values of $$\left( {\delta ,\;a} \right) $$ can be determined as the stationary point of the potential energy. The explicit model is justified by detailed comparison of the predicted results (for Poisson ratio $$\nu \le 0.45$$) with known data reported in recent literature. For example, the validity and accuracy of the present model are demonstrated for moderately soft elastic thin layers under the condition $${2\left( {1-v^{2}} \right) WR^{2}} \big /{\left( {Eh^{3}} \right) }\ge 100$$ (where W is adhesion energy per unit contact area, for instance, for typical materials with $$R=500\ \upmu \mathrm{m}$$ $$E=100\ \mathrm{KPa}$$ and $$W=100\ \mathrm{mJ}/\mathrm{m}^{{2}}$$, the condition requests $$\;h<20\ \upmu \mathrm{m}$$). As compared to existing methods that request more substantial numerical calculations, the present model achieves an explicit expression for strain energy of a compressible elastic layer and could offer a simpler analytical method for adhesion mechanics of a rigid sphere on a compressible thin elastic layer bonded or sliding on a rigid substrate.

Experimental study on different behaviors of spheres entering water and PEO solution

We conducted an experimental study on the formation of cavity and splash crown during the impact of superhydrophobic and hydrophilic spheres on water and polyethylene oxide solution (non-Newtonian liquid). We investigated the influences of falling speed of spheres on splash crown and cavity formation. In particular, we focused on the evolution time of splash and cavity when spheres with different contact angles fall into different liquids under various speeds and the different behavior of splash curtain. Results show that sphere contact angle and liquid viscosity have a great effect on cavity formation. The increase in contact angle and liquid viscosity induces cavity formation. However, viscosity has a certain inhibitory effect on crown evolution. The faster the falling speed is, the shorter the splash crown’s evolution time, but the greater the volume will be. A pinch-off model of cavity has a great impact on the formation of “Worthington jet.”

Occlusal load modelling significantly impacts the predicted tooth stress response during biting: a simulation study

Computational models of the masticatory system can provide estimates of occlusal loading during (static) biting or (dynamic) chewing and therefore can be used to evaluate and optimize functional performance of prosthodontic devices and guide dental surgery planning. The modelling assumptions, however, need to be chosen carefully in order to obtain meaningful predictions. The objectives of this study were two-fold: (i) develop a computational model to calculate the stress response of the first molar during biting of a rubber sample and (ii) evaluate the influence of different occlusal load models on the stress response of dental structures. A three-dimensional finite element model was developed comprising the mandible, first molar, associated dental structures, and the articular fossa and discs. Simulations of a maximum force bite on a rubber sample were performed by applying muscle forces as boundary conditions on the mandible and computing the contact between the rubber and molars (GS case). The molar occlusal force was then modelled as a single point force (CF1 case), four point forces (CF2 case), and as a sphere compressing against the occlusal surface (SL case). The peak enamel stress for the GS case was 110 MPa and 677 MPa, 270 MPa and 305 MPa for the CF1, CF2 and SL cases, respectively. Peak dentin stress for the GS case was 44 MPa and 46 MPa, 50 MPa and 63 MPa for the CF1, CF2 and SL cases, respectively. Furthermore, the enamel stress distribution was also strongly correlated to the occlusal load model. The way in which occlusal load is modelled has a substantial influence on the stress response of enamel during biting, but has relatively little impact on the behavior of dentin. The use of point forces or sphere contact to model occlusal loading during mastication overestimates enamel stress magnitude and also influences enamel stress distribution.

Tribology Analysis of Spherical-Surface Contact Sliding Pairs Under Fluctuating Loads

Background: Spherical contacting surfaces are often designed to increase the contact surface area and bearing ability, and frequently suffer fluctuating loading, which will play an important role in tribological properties. Objective: Effects of high-frequency fluctuating loading on friction and wear performance of spherical- surface contact sliding pairs should be experimentally investigated. Methods: Bench tests with the differential gear contacting pairs of heave trucks were conducted under fluctuating loading generated by the traction force of spring-connecting hanging weights. Results: High amplitude of fluctuating loads tends to result in different wear forms such as fatigue wear, plowing damages, material side flow and plastic deformation. The amplitude of the fluctuating loads has significant influence on the tribological performance of the spherical-surface contact sliding pairs and is apt to break the frictional stability of the friction pairs indicated by the variation of the signal components of friction force signals decomposed by discrete wavelet transform method. Conclusion: The high frequency and large amplitude are the main factors of fluctuating loading that plays very important role in the tribological characteristics of spherical-surface contact sliding pairs.

Recent Development in Modeling of Coated Spherical Contact.

Since a coated rough surface can be modeled as a collection of many spherical coated asperities, in order to understand the coated rough surface contact, it is required to first model a single coated spherical contact. This review paper presents a comprehensive summary of the coated spherical contact modeling and its experimental validation that was done mostly by the authors’ group at the Technion and published in the relevant literature. The coated spherical contact is considered under two loading modes, namely pure normal loading and combined normal and tangential loading. Based on the normally loaded spherical contact results, a coated rough surface contact modeling is presented. In addition, experimental results that show an interesting correlation with the coated spherical modeling are briefly discussed. Finally, some limited work on the bilayer/multilayer coated spherical contact is introduced.

A remark on the contactomorphism group of overtwisted contact spheres

We show the existence of elements of infinite order in some homotopy groups of the contactomorphism group of overtwisted spheres. It follows in particular that the contactomorphism group of some high dimensional overtwisted spheres is not homotopically equivalent to a finite dimensional Lie group.

Positive topological entropy of positive contactomorphisms

A positive contactomorphism of a contact manifold $M$ is the end point of a contact isotopy on $M$ that is always positively transverse to the contact structure. Assume that $M$ contains a Legendrian sphere $\Lambda$, and that $(M,\Lambda)$ is fillable by a Liouville domain $(W,\omega)$ with exact Lagrangian $L$ such that $\omega|_{\pi_2(W,L)}=0$. We show that if the exponential growth of the action filtered wrapped Floer homology of $(W,L)$ is positive, then every positive contactomorphism of $M$ has positive topological entropy. This result generalizes the result of Alves and Meiwes from Reeb flows to positive contactomorphisms, and it yields many examples of contact manifolds on which every positive contactomorphism has positive topological entropy, among them the exotic contact spheres found by Alves and Meiwes. A main step in the proof is to show that wrapped Floer homology is isomorphic to the positive part of Lagrangian Rabinowitz-Floer homology.

Krajobraz językowy polsko-czeskiego pogranicza jako przestrzeń dyskursu wielojęzyczności — analiza tablic informacyjnych z sektora publicznego

Celem artykułu jest analiza krajobrazu językowego polsko-czeskiego pogranicza jako przestrzeni wielojęzycznych praktyk dyskursywnych. Materiał badawczy stanowią tabliczki informacyjne z sektora publicznego pochodzące z kilku miejscowości: po stronie czeskiej — z Adršpach, Náchodu i Hronova, po stronie polskiej — z Kudowy-Zdroju, Karłowa oraz Dusznik-Zdroju. Pogranicze jest rozumiane w sensie geograficzno-terytorialnym jako strefa zetknięcia się i przenikania różnych narodów i grup etnicznych, kultur i języków na terenach przygranicznych. Zmienne konfiguracje i hierarchia języków występujących na tabliczkach informacyjnych świadczą zarówno o historycznych zaszłościach, jak i aktualnej społecznej dynamice na terenie polsko-czeskiego pogranicza.

Adhesive contact of a diamond sphere with an iron substrate caused by interatomic interaction

By incorporating the adhesive force as a body force in the finite element method, the adhesive contact between a diamond sphere and the iron substrate is studied. The adhesive force is derived from Morse potential by integrating the pair potential function over the spherical domain. Based on the tensile behaviors of iron nanowires, the elastic and elastoplastic material parameters are obtained for the substrate. As the radius of the sphere is larger than 320 nm and the maximum depth of indentation is one-tenth of the radius of the sphere, the adhesion caused by interatomic interaction between diamond and iron is small enough to ignore. Then take the sphere whose radius is 20 nm as an example, the results of a single load–unload cycle and multiple load–unload cycles are discussed. In the contact process between the sphere and the surface, the phenomena jump-to-contact and jump-off-contact were observed. Further, the stress distributions inside the substrate and the pressure distribution are investigated. With the analysis of the results, the proposed method can be used to simulate the mechanical behaviors under micro-nano scale contact.

Geometric Error Identification and Analysis of Rotary Axes on Five-Axis Machine Tool Based on Precision Balls

This paper presents the design of a precise “ball-column” device to efficiently and accurately measure the geometric error terms of both rotary axes of the five-axis machine tool. A geometric error measurement method of spherical contact was proposed based on the influence of the geometric error term from a five-axis machine tool rotating axis on the integrated geometric error of the machine tool. A multiple degree of freedom, step-by-step contact method based on on-machine measure for measuring the spherical center point is proposed, and the solution formula of each geometric error term of the rotating axis is established, respectively. This method can identify 12 geometric errors based on the influence of one rotating axis on another rotating axis after long term operation. The spatial error field of the five-axis machine tool was constructed by analyzing the error law of the two rotating axes of machine tools based on various positions and postures. Finally, after the comparison of the experiment, the results showed that the accuracy of the developed error measurement device reached 91.8% and the detection time was as short as 30–40 min.

On Open Book Embedding of Contact Manifolds in the Standard Contact Sphere

AbstractWe prove some open book embedding results in the contact category with a constructive approach. As a consequence, we give an alternative proof of a theorem of Etnyre and Lekili that produces a large class of contact 3-manifolds admitting contact open book embeddings in the standard contact 5-sphere. We also show that all the Ustilovsky $(4m+1)$-spheres contact open book embed in the standard contact $(4m+3)$-sphere.

SpitzerSpace Telescope observations of bilobate comet 8P/Tuttle

Context.Comet 8P/Tuttle is a nearly isotropic comet whose physical properties are poorly known and might be different from those of ecliptic comets owing to their different origin. Two independent observations have shown that 8P/Tuttle has a bilobate nucleus.Aims.Our goal is to determine the physical properties of the nucleus (size, shape, thermal inertia, and albedo) and coma (water and dust) of 8P/Tuttle.Methods.We observed the inner coma of 8P/Tuttle with the infrared spectrograph and the infrared camera of theSpitzerSpace Telescope. We obtained one spectrum (5–40μm) on 2 November 2007 and a set of 19 images at 24μm on 22–23 June 2008 sampling the rotational period of the nucleus. The data were interpreted using thermal models for the nucleus and the dust coma, and we considered two possible shape models of the nucleus derived fromHubbleSpace Telescope visible and Arecibo radar observations.Results.We favor a model for the nucleus shape that is composed of two contact spheres with respective radii of 2.7 ± 0.1 km and 1.1 ± 0.1 km and a pole orientation with RA = 285 ± 12° and Dec = +20 ± 5°. The thermal inertia of the nucleus lies in the range 0–100 J K−1m−2s−1∕2and theR-band geometric albedo is 0.042 ± 0.008. The water production rate amounts to 1.1 ± 0.2 × 1028molecules s−1at 1.6 AU from the Sun pre-perihelion, which corresponds to an active fraction of ≈9%. At the same distance, theɛfρquantity amounts to 310 ± 34 cm, and it reaches 325 ± 36 cm at 2.2 AU post-perihelion. The dust grain temperature is estimated to be 258 ± 10 K, which is 37 K higher than the thermal equilibrium temperature at 1.6 AU. This indicates that the dust grains that contribute to the thermal infrared flux have a typical size of ≈10μm. The dust spectrum exhibits broad emission around 10μm (1.5σconfidence level) and 18μm (5σconfidence level) that we attribute to amorphous pyroxene.

Contact integral geometry and the Heisenberg algebra

Generalizing Weyl's tube formula and building on Chern's work, Alesker reinterpreted the Lipschitz-Killing curvature integrals as a family of valuations (finitely-additive measures with good analytic properties), attached canonically to any Riemannian manifold, which is universal with respect to isometric embeddings. In this note, we uncover a similar structure for contact manifolds. Namely, we show that a contact manifold admits a canonical family of generalized valuations, which are universal under contact embeddings. Those valuations assign numerical invariants to even-dimensional submanifolds, which in a certain sense measure the curvature at points of tangency to the contact structure. Moreover, these valuations generalize to the class of manifolds equipped with the structure of a Heisenberg algebra on their cotangent bundle. Pursuing the analogy with Euclidean integral geometry, we construct symplectic-invariant distributions on Grassmannians to produce Crofton formulas on the contact sphere. Using closely related distributions, we obtain Crofton formulas also in the linear symplectic space.

The impact of soft contact lens surface and optics on symptoms associated with digital eye fatigue in symptomatic soft contact lens wearers

Purpose Near work, often on digital devices, now permeates the daily life of individuals of all ages at both work and play. Sustained near work on digital devices has been found to increase symptoms of eye strain. A contact lens which reduces the accommodative demand may help reduce symptoms. The current study compared subjectively reported eye strain, dryness, overall fatigue, and quality of vision of symptomatic subjects while binocularly wearing soft, daily disposable spherical and multifocal contact lenses.

Features of issues of ethics and morals of the leader

Entrepreneurship is considered as a driving force for the economic development of society. One of the tools of entrepreneurship is the choice of people of a certain type, with certain traits of character, those who will be able to create an innovative approach in the system “ethics – morality – collective – leader – entrepreneurship”. Since entrepreneurship is associated with a person with the process of personal professional growth, social adaptation and development through the formation of business ideas, the development of business projects and their implementation in real practice. The social co-operation of different types of human activity made the problem of leadership one of the most recent and, at the same time, constantly topical problems, the solutions of which were constantly changing both in content and form. Therefore, it becomes a task to consider different directions in the scientific study of leadership from the standpoint of modernity, the meaning of the word “ethics” and “morality”. The purpose of this research is to provide a holistic analysis of the leader's problems through the prism of ethics and morality in entrepreneurship. The ethical climate in the enterprise is described – the order of behavior in the sphere of business and business contacts is established. Etiquette, when understood as established behavior, helps to avoid mistakes or to look at them in accessible, generally accepted ways. Therefore, the basic function or meaning of the etiquette of a business person can be interpreted as the formation of such rules of conduct that promote understanding of people in the process of communication. The second meaning of the etiquette function is the convenience function, that is, expediency and practicality. Starting with the little things, up to the general rules – etiquette is approximate to the everyday system. A survey was conducted in which 156 respondents were interviewed, the purpose of the survey was to determine who is a leader, and on the basis of this research a model of a leader with ethical and moral leadership qualities was proposed. Therefore, to create moral subordinates of ethical care means to form high moral values, the mechanism of moral self-regulation, protection and interest, moral creativity and comfort, and also to accept the moral experience of the collective, to collection It was suggested that modern management covers moral socialization – self-assimilation of a person's life experience, self-acquisition of social qualities, its adaptation to the environment. The same group of activities includes providing a modern level of technical and technological equipment of the work process, rational organization, regulation and payment of prats, aesthetics of the working environment, active participation in social activity, spiritual environment moral and psychological climate of relationships.

Elastic and elastic-perfectly plastic analysis of an axisymmetric sinusoidal surface asperity contact

ABSTRACTClosed-form finite-element empirical models are available for elastic and elastic–plastic spherical and sinusoidal contact. However, some of these models do not consider the effect of interaction with adjacent asperities or require extensive numerical resources because they employ a full 3-D model. Therefore this work has analysed and quantified the behaviour of an elastic and elastic- perfectly plastic axisymmetric sinusoidal surface in contact with a rigid flat for a wide range of material properties and different values of the amplitude to wavelength ratio from initial to complete contact (high load). The numerical results agreed well with the Hertz model and the Jackson–Green elastic–plastic spherical contact model at low loads. Empirical equations for elastic and also elastic-perfectly plastic cases are formulated for the contact pressure, contact area and surface separation. From the current analysis, it is found that it is not any single parameter, but different combinations of material properties and surface roughness that govern the whole contact behaviour. The critical value of the amplitude of the sinusoidal asperity below which it will deform completely elastically from initial to complete contact is established. At low values of amplitude normalized by the critical amplitude, it was found that the contact behaved similar to a spherical contact, with the average pressure (hardness) always remaining lower than three times the yield strength. However, at higher values the average pressure increased toward a value as high as six times the yield strength at complete contact. All of these equations should be useful in rough surface contact modelling, lubrication analysis, electrical contact modelling and in many other applications.

Computation of Coverage Probabilities in a Spherical Germ-Grain Model

We consider a spherical germ-grain model on $\mathbb {R}^{d}$ in which the centers of the spheres are driven by a possibly non-Poissonian point process. We show that various covering probabilities can be expressed using the cumulative distribution function of the random radii on one hand, and distances to certain subsets of $\mathbb {R}^{d}$ on the other hand. This result allows us to compute the spherical and linear contact distribution functions, and to derive expressions which are suitable for numerical computation. Determinantal point processes are an important class of examples for which the relevant quantities take the form of Fredholm determinants.

Digging for sanctuary: The garden as a contact sphere

The European ideal of connectivity across national borders is haunted by a dissolving of boundaries and categories. Public crises are carried into private spaces, generating an almost omnipresent anxiety exacerbated by various media. Almost omnipresent? Yes: for one space, the garden, tenaciously resists the maelstrom of late modernity, or appears to do so in reassuring ways. This article analyses how the multiple European crises are addressed in and by recent mediatisations of gardening. Drawing on selected Anglophone gardening programmes, I argue that the mediascape of gardening represents a relational ‘contact sphere’ where Otherness is negotiated. Focusing on regaining a sense of control and autarky, infotainment programmes on gardening have grown into interactive platforms which disseminate images and practices which contribute to a sustainable vision of Europe, while addressing seemingly uncontrollable problems of change, identity and emotion, threats to human health, and non-transparent food production.

The study of the formation of relations of educational cooperation of younger schoolchildren

Introduction: the need to study the current state of relations of educational cooperation of younger students is determined by the increasing role of communicative universal educational activities in the development of modern society. However, a number of studies it prove that often the life of a modern school does not provide any opportunities to use the potential resources of such an important component of the development of the student, as educational cooperation. Traditional school due to many restrictions does not always provide the possibility to build a student-centered relationship of educational cooperation in combination with a differentiated approach to younger students. Numerous studies often describe the interaction of students with adults and peers separately, that prevents making unified approaches to the child's socialization.The initial step towards solving this problem should be the complex study of the areas of interaction and diverse study of the formation of relations of educational cooperation of younger schoolchildrenMaterials and Methods: in article the diagnostic program-the complex made of the techniques giving the chance to get the idea of a modern state of development of the relations of educational cooperation in elementary school is declared. They were: a technique with the working title “ the Carpet”, allowing to establish levels of development of skills of group interaction of younger schoolchildren in the lessons; “Sociometric research”, intended for identification of the social status of the child in children's group; “Self-esteem ladder”, designed to determine the adequacy of children's self-esteem in the sphere of business contacts of the child with classmates.Results: the results of the study of the formation of relations of educational cooperation among younger schoolchildren with peers in a specially created innovative conditions in the context of a given procedure of learning and initiated by the child communication. The idea of teachers about the most important for younger schoolchildren’s psychological conditions of development of relations of educational cooperation is revealed.Discussion and Conclusions: the study suggests that for the effective development of relations of educational cooperation with children it is necessary to create a special innovative learning environment, which provides a high motivational basis for younger students to achieve their goals, initiatives, independence, strengthen their social status in the group of peers, increase self-esteem.

The electro-mechanics of a coating/substrate system under charged spherical contact

A general theory of the piezo-electric contact mechanics for a transversely isotropic piezo-electric elasticity coated system (TIPECS) under charged spherical contact is presented. Three-dimensional exact solutions for the stresses, displacements, electric displacements and electric potential are derived. The contact radius versus the total load relation is obtained to guide the indentation experiments. The relations of coating thickness versus voltage and coating thickness versus voltage are studied. The optimal thickness can be determined with an optimization procedure. The interfacial delamination area of the TIPECS can be predicted with the interfacial failure criterion. The theoretical results are helpful for the prediction of some transient electrical effects, which can be combined with experiments to estimate some elastic constants, dielectric constants and piezo-electric constants in the indentation process.