Absence Of Friction Forces Research Articles

КАРУСЕЛЬНАЯ УСТАНОВКА ДЛЯ РЕСУРСНЫХ ИСПЫТАНИЙ НА АБРАЗИВНЫЙ ИЗНОС

When developing new methods to make hardening coatings on the cutting tool surfaces of tilling machines, the main characteristic parameter determining the ability to serve for a long time, resisting external environmental influences and mechanical wear, is wear resistance. At the same time, this parameter should be determined before life tests in the field. Various stands and installations are available for this purpose. Each of them is characterized by their own advantages and disadvantages. Therefore, based on the specific production conditions, new devices are being developed. In this paper, a rotary-table installation of a specific design is developed for life tests of abrasive wear of various parts. A patent is obtained for it. The differences of this installation from existing analogues are the following: 1 – the pressure of the abrasive material layer on the test sample is regulated by deepening the sample into the abrasive medium; 2 - the test sample is under constant influence of the abrasive material by filling it with the required amount of abrasive materials; 3 – higher efficiency of the installation. This is achieved due to lower power consumption in the absence of friction forces between the sample bracket and the abrasive material. Comparative life tests were carried out for two harrow teeth, the original tooth and the hardened one. The harrow teeth were tested on a simplified model of a developed installation. An experimental inverter vibration control unit of Kazan Federal University was used for treatment. Hardening was performed with a multi-rod electrode at an arc current of 60A. The frequency of the electrode vibration is 100 Hz. Tests show that the service life of hardened harrow teeth when treated by a vibrating arc with a multi-rod electrode is about 5-6 times higher than the service life of factory harrow teeth.

Mathematical model of fluid flow along a straight through filled with a distributed flow from above

In a one-dimensional approximation and in the absence of friction forces, a mathematical model has been developed for the steady flow of an incompressible fluid along a straight line, for example, a drainage gutter, into which a distributed flow flows from above. The boundary condition missing for solving the system of equations of momentum and continuity is determined using the principle of minimum potential energy. For a rectangular chute, equations are obtained that allow one to calculate the distributions of the layer thickness and fluid velocity along the length of the chute with a plug at one end and without a plug, slope and without slope to the horizon, depending on the intensity of the incoming flow, the size of the chute, and the density of the liquid. This model, by means of a simple recalculation, can also be extended to the flow in a trough of a different cross-sectional profile. The results of the study can be applied to the calculation of external drainage systems.

Analytical and Numerical Solution of the Problem on Brachistochrones in some General Cases

In this paper, we discuss J. Bernoulli’s brachistochrone problem and find its analytical and numerical solutions in the cases where viscous or dry friction are taken into account. We predict the existence of a point of “geometrical phase transition” u0 = ln(1/2k2b); it corresponds to the transition from one class of trajectories to another that qualitatively differs from the initial class. Numerical simulation of the motion in a neighborhood of points of geometric phase transitions is performed. We prove that in the absence of friction forces, the minimization problem for the motion time for any motion along a curvilinear trough under the action of the gravity force can always be reduced to the brachistochrone problem and can be solved without involving methods of calculus of variation, only by general dynamical laws. We find a solution to the classical Bernoulli problem under the condition that the length of the trajectory is fixed. We show that under this isoperimetric condition, the class of trajectories differs from the classical brachistochrone. We also observe the transformation of these trajectories to the cycloid by numerical and analytical analysis.

Contact Problems of Motion of Elastic Bodies Along Hard Surfaces

We propose a mathematical model of motion of an elastic body along a hard surface in the absence of friction forces. The formulations of the problem in the form of a variational inequality and in the form of the extremum variational problem are obtained. For the discretization of the extremum variational problem, we use the finite-element method. As an example, we consider the motion of a body with rectangular cross section under the conditions of plane deformation. We investigate strains and stresses formed in the case of motion along the surfaces in the horizontal and vertical directions.

Geometric aspects of the theory of fiber tension, storage, and transport mechanisms in the absence of friction forces

The mechanisms that perform drawing, storage, or transport of chemical fibres significantly affect their final properties. The possibility of using the small parameter method is examined for calculating the parameters of this effect: if an accurate solution of the problem is known for some initial values of the basic parameters, then its solutions for other values which differ comparatively little from the initial values can be obtained. The method allows gradually increasing the adequacy of the solution by using new or altered values of the basic parameters in the calculation. An accurate solution corresponding to negligibly small friction forces was obtained for the case where the mechanism consists of two rotating elongated cylinders which the fibre is repeatedly wound around.

Stressed state of a transversally isotropic half-space in the case of a nonplane elliptical die under forces and bending moments

UDC 539.3 An exact solution is constructed for the problem of the stressed state of an elastic tramversally isotropic half-space affected by a nonplane elliptical die when the die is subjected to compressive forces and bending moments. The problem is solved in the absence of frictional forces. Expressions are given for determining the compressive load, the transition of points in the die bottom, projections of the rotation vector, the semimajor axis, and the eccentricity of the contact area. A large number of studies of contact problems for elliptical dies were maae by Lur'e [2], Galin [1, 4], and Mossakovskii [3]. Those studies, however, dealt mainly with the stresses in an isotropic solid. Such problems for a transversally isotropic half-space were studied little. In this work we construct an exact solution for problems of the stressed state of an elastic transversally isotropic halfspace under the action of a nonplane elliptical die. The bottom of the die is assumed to be absolutely smooth. The die is considered as an absolutely hard solid subjected to compressive forces and bending moments. The surface of the die bottom in the region of contact with the bourdary of the half-space is approximated by an elliptical paraboioid. The equation of the surface is represented by a power series expansion. The plane bounding the half-space is taken to be the xy plane. Suppose that the z axis is directed on the outside of the solid normal to the plane of isotropy and the x and y axes are oriented arbitrarily in that plane. For a nonplane elliptical die the contact area S is an elliptical region in the plane Z = 0,

Analysis of free surface forms of flow with its bilateral symmetric division in parabolic channels

1. It follows from the investigations indicated above that in the case of bilateral division of the flow (in the absence of frictional forces) in parabolic channels, the surface curve of the flow is similar to the surface curve in the case of the division of a flow in rectangular channels. 2. The equations (2), (4), (5), (6), (7), and (8) obtained make it possible to calculate water dividers on canals.

Contact problems for thin-walled structures

Contact problems for thin-walled structures are ordinarily solved on the basis of the equations of applied elasticity theory (the binding theory of beams, plates, shells, etc.). However, a number of substantial difficulties occur here [2, 4]: The contact stresses determined directly from the bending equations do not satisfy the equilibrium conditions of the structure (stamp) in the large; the contour concentrated forces introduced a priori are not determined by the solution of incorrectly posed problems of mathematical physics; the different kind of mathematical method for regularizing these problems results in solutions whose physical interpretation is difficult. The fundamental propositions on overcoming the difficulties mentioned are the following: The applied bending equations for thln-walled structures are nonuniform in the bilateral contact zone; for instance, shells with stiff support; an asymptotic analysis of the equations elasticity theory in a study of the deformation of thin layer show [I, 3] that the fundamental state in its zone of contact with a stiffer foundation is determined by compression in the transverse direction with full defined compression stiffness parameters (Winkler model); the differential nature of the equations governing the contact stressesin given displacements that have continuous first derivatives when crossingthe boundary contour of the contact zone requires the introduction of concentrated contour forces and moments whose magnitude is determined by jumps in the second and third derivatives of the displacements with respect to the normal; there are no contour moments for unilateral contact between the shell and the support, which assumes shell stand-off from the support; determination of the contact domain~in this case becomes fundamental in the solution of the contact problem during the solution. The assertions formulated are illustrated by solving a number of contact problems for beams, plates, and rings (shells). We consider the contact problem for a beam supported partially by a stiff support under a constant load q (Fig. i). Then, in the absence of friction forces in the contact zone and beam stand-off from the support, we can obtain

Behavior of Simple Screw Dislocation Arrays under an Applied Stress

A detailed numerical analysis has been made of the behavior of passing screw dislocation arrays on parallel slip planes as a first step in the development of a computer model of workhardening. It is found that in the absence of frictional forces, dislocations cannot pass one another since they form dipoles and become unstable. The introduction of frictional forces shows that for each dislocation there is a range of positions within which it is stable, and the actual position of the dislocation depends on its initial position as well as its direction of motion. The frictional-force concept is extended to determine the equilibrium separation of superlattice dislocations and to determine the relaxation of a pile-up in the absence of an applied stress. In order to determine unique positions for passing dislocations under an applied stress and a frictional stress, a model has been postulated in which the dislocations are generated from distant sources. Equilibrium configurations are determined as a function of the applied stress for a single source, as well as for two opposite sources on parallel slip planes. The stress-strain curves are developed for both cases, and the results are discussed in detail.