Two-body and three-body abrasion: A critical discussion

It is argued that the common classification of abrasive wear into 'two-body abrasion' and 'three-body abrasion' is seriously flawed. No definitions have been agreed upon for these terms, and indeed there are two quite different interpretations, the implications of which are mutually inconsistent. In the dominant interpretation, the primary thrust of the two-body/three-body concept is to describe whether the abrasive particles are constrained (two-body) or free to roll (three-body). In this view, two-body abrasion is generally much more severe than three-body. The alternative interpretation emphasises the presence (three-body) or absence (two-body) of a rigid counterface backing the abrasive. In this view, three-body abrasion is equated to high-stress (or grinding) abrasion and is generally more severe than two-body (low-stress) abrasion. This paper recommends that the 'two-body/three-body' terminology be abandoned, to be replaced by an alternative classification scheme based directly upon the manifest severity of wear. (C) 1998 Elsevier Science S.A.

Mild and severe wear of steels and cast irons in sliding abrasion

This paper presents the results obtained in pin-on-disk test apparatus using glass and alumina as abrasive materials, showing the rates and mechanisms of abrasive wear of 1070 and 52100 steels, and ductile and white cast irons. The test conditions were selected in order to obtain wear rates that correspond to mild and severe abrasion, using different metal hardness-to-abrasive hardness ratios(H/H(A)) and 0.2 or 0.06 mm abrasive grains. The use of bulk Vickers hardness, instead of microhardness, allows a better description of the different abrasion regions. Under severe abrasion, the microcutting mechanism of wear prevailed together with friction coefficients larger than 0.4. On the other hand, when relatively soft abrasives are tested, indentation of abrasive particles followed by its fragmentation, and a creation of a thin deformed layer were the main damage mechanisms, with the friction coefficient lying below 0.4. The abrasive particle size under mild regime is able to change the wear rates in an order of magnitude. (C) 2009 Elsevier B.V. All rights reserved.

Periodic orbits of the planar collision restricted 3-body problem

Using the continuation method we prove that the circular and the elliptic symmetric periodic orbits of the planar rotating Kepler problem can be continued into periodic orbits of the planar collision restricted 3–body problem. Additionally, we also continue to this restricted problem the so called “comets orbits”.

Periodic orbits near a heteroclinic loop formed by one dimensional orbit and a 2-dimensional manifold: application to the charged collinear 3-body problem

The paper is devoted to the study of a type of differential systems which appear usually in the study of some Hamiltonian systems with 2 degrees of freedom. We prove the existence of infinitely many periodic orbits on each negative energy level. All these periodic orbits pass near the total collision. Finally we apply these results to study the existence of periodic orbits in the charged collinear 3–body problem.

Families of periodic orbits for the spatial isosceles 3-body problem

We study the families of periodic orbits of the spatial isosceles 3-body problem (for small enough values of the mass lying on the symmetry axis) coming via the analytic continuation method from periodic orbits of the circular Sitnikov problem. Using the first integral of the angular momentum, we reduce the dimension of the phase space of the problem by two units. Since periodic orbits of the reduced isosceles problem generate invariant two-dimensional tori of the nonreduced problem, the analytic continuation of periodic orbits of the (reduced) circular Sitnikov problem at this level becomes the continuation of invariant two-dimensional tori from the circular Sitnikov problem to the nonreduced isosceles problem, each one filled with periodic or quasi-periodic orbits. These tori are not KAM tori but just isotropic, since we are dealing with a three-degrees-of-freedom system. The continuation of periodic orbits is done in two different ways, the first going directly from the reduced circular Sitnikov problem to the reduced isosceles problem, and the second one using two steps: first we continue the periodic orbits from the reduced circular Sitnikov problem to the reduced elliptic Sitnikov problem, and then we continue those periodic orbits of the reduced elliptic Sitnikov problem to the reduced isosceles problem. The continuation in one or two steps produces different results. This work is merely analytic and uses the variational equations in order to apply Poincar´e’s continuation method.

Equilibrium points and central configurations for the Lennard-Jones 2-and 3-body problems

Abstract. In this paper we study the relative equilibria and their stability for a system of three point particles moving under the action of a Lennard{Jones potential. A central con guration is a special position of the particles where the position and acceleration vectors of each particle are proportional, and the constant of proportionality is the same for all particles. Since the Lennard{Jones potential depends only on the mutual distances among the particles, it is invariant under rotations. In a rotating frame the orbits coming from central con gurations become equilibrium points, the relative equilibria. Due to the form of the potential, the relative equilibria depend on the size of the system, that is, depend strongly of the momentum of inertia I. In this work we characterize the relative equilibria, we nd the bifurcation values of I for which the number of relative equilibria is changing, we also analyze the stability of the relative equilibria.

Bifurcation of relative equilibria of the (1+3)-body problem

We study the relative equilibria of the limit case of the pla- nar Newtonian 4{body problem when three masses tend to zero, the so-called (1 + 3){body problem. Depending on the values of the in- nitesimal masses the number of relative equilibria varies from ten to fourteen. Always six of these relative equilibria are convex and the oth- ers are concave. Each convex relative equilibrium of the (1 + 3){body problem can be continued to a unique family of relative equilibria of the general 4{body problem when three of the masses are su ciently small and every convex relative equilibrium for these masses belongs to one of these six families.

New classes of spatial central configurations for the n+3-body problem

In this paper, we show the existence of new families of spatial central configurations for the n + 3-body problem, n >= 3. We study spatial central configurations where n bodies are at the vertices of a regular n-gon T and the other three bodies are symmetrically located on the straight line that is perpendicular to the plane that contains T and passes through the center of T. The results have simple and analytic proofs. (c) 2010 Elsevier Ltd. All rights reserved.

3-BODY COLLAPSE FOR TABAKIN POTENTIALS AND THE THOMAS EFFECT

A system constituted of three bosons interacting via two-body separable potentials with fixed two-boson binding is known to lead to bound-state collapse in the case where the potential parameters allow two-boson S-matrix poles close to (resonance) and on (continuum bound state) the real momentum axis. The collapse is shown to be accompanied by an increase in the average kinetic energy of the two-body bound state, which signals a decrease in the range of the two-body interaction for fixed two-body binding. The collapse is claimed to be a manifestation of the well-known Thomas effect which leads to a collapse of the three-body system when the range of the two-body interaction goes to zero for a fixed two-body binding.

UNITARY POLE APPROXIMATION FOR THE COULOMB-PLUS-YAMAGUCHI POTENTIAL AND APPLICATION TO A 3-BODY BOUND-STATE CALCULATION

The unitary pole approximation is used to construct a separable representation for a potential U which consists of a Coulomb repulsion plus an attractive potential of the Yamaguchi type. The exact bound-state wave function is employed. U is chosen as the potential which binds the proton in the 1d5/2 single-particle orbit in F-17. Using the separable representation derived for U, and assuming a separable Yamaguchi potential to describe the 1d5/2 neutron in O-17, the energies and wave functions of the ground state (1+) and the lowest 0+ state of F-18 are calculated in the Gore-plus-two-nucleons model solving the Faddeev equations.

LATTICE-DYNAMICS OF ALKALI-METALS IN A 3-BODY INTERACTION

The original model of Das et al. is modified in extending the electron-ion interaction on a three-body forces and including the crystal equilibrium condition to reduce one independent parameter. We studied the phonon dispersion relations along the three principal symmetry directions i.e. [xi, 0, 0], [xi, xi, 0] and [xi, xi, xi] and theta-T curves of alkali metals, Na, K, Rb, Cs and Li. There is close agreement between the computed results and the experimental observations.

The Effect of low-grade aggregates on the abrasion resistance of concrete

Three types of crushed rock aggregate were appraised, these being Carboniferous Sandstone, Magnesian Limestone and Jurassic Limestone. A comprehensive aggregate testing programme assessed the properties of these materials. Two series of specimen slabs were cast and power finished using recognised site procedures to assess firstly the influence of these aggregates as the coarse fraction, and secondly as the fine fraction. Each specimen slab was tested at 28 days under three regimes to simulate 2-body abrasion, 3-body abrasion and the effect of water on the abrasion of concrete. The abrasion resistance was measured using a recognised accelerated abrasion testing apparatus employing rotating steel wheels. Relationships between the aggregate and concrete properties and the abrasion resistance have been developed with the following properties being particularly important - Los Angeles Abrasion and grading of the coarse aggregate, hardness of the fine aggregate and water-cement ratio of the concrete. The sole use of cube strength as a measure of abrasion resistance has been shown to be unreliable by this work. A graphical method for predicting the potential abrasion resistance of concrete using various aggregate and concrete properties has been proposed. The effect of varying the proportion of low-grade aggregate in the mix has also been investigated. Possible mechanisms involved during abrasion have been discussed, including localised crushing and failure of the aggregate/paste bond. Aggregates from each of the groups were found to satisfy current specifications for direct finished concrete floors. This work strengthens the case for the increased use of low-grade aggregates in the future.

3-body energy terms in a quartet state of H3

Calculations of the 3-body energy term in a quartet (4A2 ) state of H3 (equilateral triangle nuclear-configurations) show a minimum in the 3-body energy for a side length of about 1.3 bohrs.

Wear of rotary plows operating in a tropical clay loam soil

The wear resistance of rotary plows operating in a clay loam soil was studied. The degree of damage caused to the soil and the amount of mass lost by the tools were determined in order to establish correlations between the physical properties of the soil and the wear mechanisms acting on the tribosystem. Field tests were carried out in 12 plots and a randomized experimental design with 4 levels, 3 replicas per level and 2 passes per plot was applied. The levels relate to the tillage implements employed: rotary tiller, rotary power harrow, small motorized rotary tiller and control (unaltered soil). The highest mass losses were measured in rotary tiller and rotary power harrow's tools, while the small motorized rotary tiller's tools showed generally lower levels of damage. It was determined that the effective contact time between tool and soil, the rotating speed and the sudden impact forces are the most significant factors affecting the wear resistance in field operations. Thirty days after tillage operation the soil samples were taken from each plot at a mean depth of 100 mm in order to determine bulk density, gravimetric moisture content and percentage of aggregates smaller than 5 mm. No significant differences among the values of these properties were found in the experiments. The wear mechanisms acting on the tools' surface are complex and include 2-body and 3-body abrasion as well as the presence of sudden impact forces.