Search

The article describes the possibility of determining the damping coefficient of a support with an elastic ring based on dry friction forces using a special test bench. The forced excitation force is set by the oscillations of a compact speaker installed on top of the oscillating mass through a U-shaped crossbar. The object of the study is a damper with an elastic ring, that is a thin-walled ring with evenly distributed bulges inside and outside, arranged in a checkerboard pattern. The damping coefficient is estimated using a device for simulating a rotor support, an acceleration sensor, an exciter speaker, a controller and a processing station. The amount of damping is estimated according to the width of the peak at the resonant frequency. A comparison is given of the magnitude of the damping coefficient obtained from the analysis of the resonance peak and from the decay rate during the impact experiment.

Background. The study proposes a new variational approach to solving the problem of the brachistochrone the purpose of which is to mathematically rigorously substantiate all the basic equations of the dynamic motion of a body in a mobile basis. The relevance of the research topic is dictated primarily by the novelty of the task and the methodology of its solution. Materials and methods. The solution method is based on the use of a moving basis and a variational approach. Results. A general fundamental solution of the twodimensional Laplace equation for a function dependent on three independent coordinates is obtained. Conclusions. A system of differential equations strictly substantiated with the help of the variational approach describing the optimal trajectory of the body's motion in a mobile basis has been obtained.

In this paper, problems of asymptotic behavior of non-autonomous controlled systems with a matrix of derivatives and the feedbacks of relay type are considered. The research is based on the method of limiting equations in combination with the direct method of Lyapunov functions with semidefinite derivatives. The method of the limiting equations has arisen in works G.R. Sell (1967) and Z. Artstein (1977, 1978) on topological dynamics of nonautonomous systems. Now this method is advanced for a wide class of systems, including the systems with delay. Nevertheless the method of the limiting equations till now has not received development with reference to nonautonomous differential inclusions and discontinuous systems for which it has fragmentary character. The main results are bound up with development of this method for discontinuous systems represented in the form of differential inclusions. In this case, specific methods of multivalued analysis and development of new methods for constructing limiting differential inclusions were required. The structure of the systems under scrutiny makes it possible, in particular, to study mechanical systems controlled on the decomposition principle of E.S. Pyatnitsky, and systems with dry friction submitted by equations Lagrange of 2-nd kind.

The effect of anhydrous nitriding in a glow discharge on microhardness, phase composition, and wear resistance of long holes in steels C45, 37Cr4, and 41CrAlMo7 with direct current supply and in cyclically switched discharge (CSD) was studied. Nitriding was carried out on a UATR-1 anhydrous nitriding unit with a discharge chamber diameter of 400 mm and a working height of 700 mm. Anhydrous nitriding in a glowing discharge was carried out at a temperature of 560 °С, a voltage of 730 V, a pressure in the chamber of 120 MPa, and the nitriding duration was 6 h. It was established that using holes with a relatively small diameter of glow discharge in a cyclically switched discharge for nitriding creates conditions for obtaining modified layers with higher physical, mechanical, and tribological characteristics. The results of microhardness measurement and their comparison with X-ray phase analysis data confirm the formation of ε, γ, and α phases during nitriding along the entire height of the samples placed in the experimental model. The tests carried out in the dry friction mode showed an increase in the wear resistance of samples made of steel C45, 37Cr4, and 41CrAlMo7 during nitriding in a cyclically switched discharge. To achieve 100 μm wear of 41CrAlMo7 steel during nitriding in CSD, 1400 m of friction path and 1000 m – during nitriding with direct current is required. It was established that using long holes of a glow discharge with different types of power for nitriding creates conditions for obtaining modified layers with variable characteristics. Nitriding of holes with a relatively small diameter of a glow discharge with a different power supply creates conditions for obtaining modified layers with different physicomechanical and tribological characteristics.

An exact solution of the problem of contact interaction of an absolutely rigid stamp with a flat base with an elastic half-plane is constructed, when the shear stresses acting in the contact zone are related to the normal pressure by dry friction law. It is assumed that the coefficient of friction depends on the coordinates of the contacting points of the contacting bodies and is directly proportional to them. A numerical calculation was carried out, the results of which were compared with the results obtained for a similar contact problem solved using Galin’s contact model. [ABSTRACT FROM AUTHOR]

The problem of reflection of longitudinal and transverse waves from the boundary of a half-plane is considered. It is assumed that boundary conditions are a generalization the sliding contact and assume that the tangential stresses do not vanish, but obey the law of dry friction. Analytical expressions are obtained for the ratios of the amplitudes of reflected waves to the amplitude of an incident longitudinal or transverse wave. A numerical analysis of the dependence of these ratios on the wave incidence angle, friction coefficient, and Poisson's ratio is carried out. It is shown that when the direction of the boundary shear stresses and the direction of propagation of the incident both longitudinal and transverse waves coincide, there are critical angles of incidence at which the amplitudes of the reflected waves become infinite. [ABSTRACT FROM AUTHOR]

This paper considers the stress state for a piecewise homogeneous plane, containing an absolutely rigid thin interfacial inclusion, one of the long sides of which is completely coupled to the plane, and the other side is in contact with it under dry friction conditions. On the basis of discontinuous solutions of the theory of elasticity for a piecewise homogeneous plane, a closed solution of the mixed boundary value problem is constructed. The regularities for the behavior of contact stresses near the end points of the inclusion are clarified, and simple formulas are obtained for determining both normal and tangential contact stresses acting on the long sides of the inclusion. [ABSTRACT FROM AUTHOR]

Copyright of Problems of Friction & Wear is the property of National Aviation University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Problems of Friction & Wear is the property of National Aviation University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Problems of Friction & Wear is the property of National Aviation University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Introduction. A three-dimensional dry friction model in the interaction of a rectangular body and a horizontal rough surface is considered. It is assumed that there is no separation of the body from the horizontal surface. The body motion occurs under the conditions of combined dynamics when, in addition to the longitudinal movement, the body participates in twisting.Materials and Methods. Linear fractional Pade approximations are proposed, which replaced the cumbersome analytical expressions that most accurately describe the motion of bodies on rough surfaces. New mathematical models describing sliding and twisting of bodies with a rectangular base are proposed.Results. Analytical expressions of the principal vector and moment of friction for rectangular contact areas are developed and scientifically established. A friction model that takes into account the relationship between sliding and twisting speeds, which provides finding solutions for Pade dependences, is developed. After numerical solution to the equations of motion, the dependences of the sliding speed and angular velocity on time were obtained and constructed. Graphs of the dependences of the friction forces and their moment on two parameters (angular velocity and slip velocity) were constructed, which enabled to compare the integral and normalized models of friction. The comparison results showed good agreement of the integral model and the model based on Pade approximations.Discussion and Conclusions. The results obtained provide considering the dynamic coupling of components, which determines the force interaction of a rectangular body and a horizontal surface. These results can be used in mobile robotics. The analyzed motion of the body occurs through the motion control of a material point inside the body. Such mobile robots can be used when solving a wide class of problems: when creating autonomous robots for the exploration of outer space and planets; in the diagnosis and treatment in case of passing through complex structures of veins and arteries; in research under water, in places of large differential temperature; in underground operations.

Copyright of Problems of Friction & Wear is the property of National Aviation University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Problems of Friction & Wear is the property of National Aviation University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Problems of Friction & Wear is the property of National Aviation University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Problems of Friction & Wear is the property of National Aviation University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Problems of Friction & Wear is the property of National Aviation University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Problems of Friction & Wear is the property of National Aviation University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Introduction. The article is devoted to the search for a method of reducing the effect of friction links mobility industrial robot PR (production mechanism PM) with frequency-controlled electric drive (FCED) on the static error (accuracy) positioning of the working body (WB) when moving in a low speed zone. The random character of friction forces changes in the implementation process start-braking modes of induction motor (IM) operation create difficulties in performance specified technological process parameters. The formation of pulsating moments on the IM shaft, due to the stator IM current harmonics, combined with the friction torque of the moving parts in the IR (IM) guide, accompanied by a deterioration of the WB (IM output link) movement dynamics.Materials and Methods. To correction the motion of the WB (PM output link) in the IM start-brake modes, the authors proposed to use dual-mode control of the Autonomous voltage inverter (AVI), providing software control of the IM stator current harmonics amplitudes and the corresponding regulation of the pulsating moments on the IM shaft by introducing a multiple "m — submodulation" of the AVI carrier frequency (CF). Results. The simplified representation of the FCED block diagram with local and global negative feedbacks (GNF) allowed to reveal the features of specific parameters influence on the static error δ and the FCED dynamic stability with the limiting gain of the corrective amplifier K1. Discussion and Conclusions. The introduction of rotor "microvibration", allows the IM "conditionally reduce" the moving link friction force in the guides, reduce the drive power to overcome the friction forces. The use of dual-mode control AVI expands the scope of use of scalar control in process equipment, multi-link mechanisms of automated production, operating in the zone of "low and creeping speeds".

In the work, by methods of discontinuous solutions of the equations of elasticity theory and of the singular integral equations, a governing system of singular integral equations of the problem of the plane stress state of a homogeneous elastic plane with a finite crack, onto one of the sides of which an absolutely rigid stamp with dry friction is pressed, and constructed exact solution. Simple formulas are obtained both for determining the contact stresses under the stamp and for the intensity stress factors of the breaking stresses of normal separation and transverse shear. [ABSTRACT FROM AUTHOR]

The paradoxical domain of nonexistence or double solution for the problem on definition of the motion of elliptical pendulum with registration the empirical dry Coulomb friction law is being investigated in this paper. It has been revealed that the parametric condition this domain definition has the mechanical meaning, which does agree with static friction low for the slider of pendulum.

Equations of plane-parallel sliding of a rigid body with the ring support under dry friction are derived. For the time of braking of a nonhomogeneous ring, we obtain a two-sided estimate which coincides with the "unimproved" estimate in the limit case of the narrow ring. As an example, the problem of braking of a system of two nearly situated narrow rings is considered.

Despite the large number of discussions about the systems of shock- and vibroprotection, little attention has been paid to vibroprotection with dry friction. The single-axis system of vibro- and shock protection with dry friction, which at the given level limits the maximum acceleration of the isolated body at the single high-level shocks and at vibrations with the absent static zone of stagnation near the equilibrium, is first considered in the paper. The system is designed for providing the operational protection of the navigation device, installed on the aircraft, against shock overloads of large amplitude. The system design, principle of operation, the method for obtaining the mathematical model are given in the paper, components of this model are shown. The obtained results prove the prospective of the new system of shock- and vibroprotection in use in navigation complexes of aircrafts, operating in extreme conditions. [ABSTRACT FROM AUTHOR]