scholarly journals ANALYTICAL STUDY OF FRICTIONAL AUTO-VIBRATIONS IN SYSTEMS WITH TWO DEGREES OF FREEDOM

2021 ◽  
Author(s):  
E. Kalinin ◽  
◽  
S. Lebedev ◽  
Yu. Kozlov
Keyword(s):  
Degrees Of Freedom ◽  
System Analysis ◽  
Single Frequency ◽  
Uniform Rotation ◽  
Systems Methodology ◽  
Two Degrees Of Freedom ◽  
Resonance Modes ◽  
The Difference ◽  
Friction Function ◽  
The Masses

Abstract Purpose of the study is to study the properties of frictional self-oscillations in systems with two degrees of freedom. As a research method, the asymptotic method of N.N. Bogolyubov and Y.A. Metropolitan. Research methods. The methodological basis of the work is the generalization and analysis of the known scientific results of the dynamics of systems in resonance modes and the use of a systematic approach. The analytical method and comparative analysis were used to form a scientific problem, goal and formulation of research objectives. When developing empirical models, the main provisions of the theory of stability of systems, methodology of system analysis and research of functions were used. The results of the study. A system with two degrees of freedom is considered, assuming that the friction function is approximated by a cubic polynomial in the sliding velocity, and friction is applied only to one of the masses. The exclusion of uniform rotation, corresponding to the third degree of freedom, leads to consideration not of the frictional moment, but the difference between the frictional moment and the moment of the moving forces. From the analysis of the results of the solutions of the equation, we can conclude that, with an accuracy up to the first approximation, inclusive, self-oscillations occur with constant frequencies equal to the natural frequencies of the system. This is consistent with the conclusions of other authors obtained using other methods. Stationary values of the amplitudes are found. The following four cases are possible: trivial solution corresponding to uniform rotation of the system without oscillations; single frequency oscillations with the first frequency; single frequency oscillations with a second frequency; two-frequency oscillatory mode. Conclusions. G. Boyadzhiev's method can be applied to study multi-mass self-oscillating systems and gives their general solution in the form of asymptotic expansions to any degree of accuracy. The obtained conditions for the stability of stationary regimes confirm the experimental results that in multi-mass systems, self-oscillations are possible only in the falling sections of the friction characteristics. The nature of the developing vibrations - their frequency and the ratio of the amplitudes of the constituent harmonics - is completely determined by the structure of the system, its elastic and inertial properties.

scholarly journals STABILITY OF VIBRATIONS OF THE TRACTOR AS A TWO-MASS MODEL WITH TWO NONLINEARITIES OF THE TYPE OF DRY FRICTION IN RESONANCE MODES

2021 ◽  
Author(s):  
E. Kalinin ◽  
◽  
Y. Kolesnik ◽  
M. Myasushka
Keyword(s):  
Differential Equations ◽  
Dry Friction ◽  
System Analysis ◽  
Nonlinear Differential Equations ◽  
Support Surface ◽  
Systems Methodology ◽  
Friction Forces ◽  
Resonance Modes ◽  
At Resonance ◽  
Relative Friction

Purpose of the study is to assess the possibility of calculating the stability of tractor oscillations as a system with nonlinearities such as dry friction due to the inverse problem. Research methods. The methodological basis of the work is the generalization and analysis of known scientific results regarding the dynamics of two-mass systems in resonance modes and the use of a systematic approach. The analytical method and comparative analysis were used to form a scientific problem, determine the goal and formulate the research objectives. When creating empirical models, the main provisions of the theory of stability of systems, methodology of system analysis and research of operations were used. The results of the study. Oscillations of the system with harmonic excitation by its base are considered (for example, the movement of a tractor on an uneven supporting surface). Oscillations of this system are described by nonlinear differential equations. To solve this equation, instead of friction dampers with friction forces, linear dampers with corresponding drag coefficients are included in the system. By solving the obtained system of linear inhomogeneous differential equations for the steady-state mode of oscillation, the amplitudes of oscillations of masses and deformation of springs with certain stiffness are determined. To clarify the effect of friction forces on mass oscillations in resonance modes, the obtained expressions were analyzed. A diagram of stability of mass oscillations in resonance modes is obtained. Conclusions. It has been established that if the coefficients of relative friction have such values that the point that is determined by them lies within the region bounded by segments 1-2 and 2-3 and coordinate axes, then during oscillations in the low-frequency resonance mode, the friction forces do not limit the increase in amplitudes fluctuations of masses, but only reduce the rate of their growth. If the point, which is determined by the coefficients of relative friction, lies in the region 1-1'-2'-3 '3-2-1, then the springs have intermittent deformation, that is, during the period of oscillation, one mass of the system has stops relative to another mass, or the last has stops relative to the support surface, or both masses move part of the period as a whole with the support surface. At resonance with a high frequency, the friction forces limit the amplitudes of mass oscillations if the coefficients of relative friction have such values that the point that is determined by them does not lie in the region bounded by segments 4-5 and 5-6 and the coordinate axes. Sections 4-5 and 5-6 define the boundaries of vibration stability at resonance (lines of critical ratios of the coefficients of relative friction).

scholarly journals Interface Based on Electrooculography for Velocity Control of a Robot Arm

2010 ◽  
Vol 7 (3) ◽  
pp. 199-207 ◽  
Author(s):  
Eduardo Iáñez ◽  
José M. Azorín ◽  
Eduardo Fernández ◽  
Andrés Úbeda
Keyword(s):  
Degrees Of Freedom ◽  
Experimental Results ◽  
Processing Algorithm ◽  
Robot Arm ◽  
Velocity Control ◽  
Two Degrees Of Freedom ◽  
Real Robot ◽  
The Difference

This paper describes a technique based on electrooculography to control a robot arm. This technique detects the movement of the eyes, measuring the difference of potential between the cornea and the retina by placing electrodes around the ocular area. The processing algorithm developed to obtain the position of the eye at the blink of the user is explained. The output of the processing algorithm offers, apart from the direction, four different values (zero to three) to control the velocity of the robot arm according to how much the user is looking in one direction. This allows controlling two degrees of freedom of a robot arm with the eyes movement. The blink has been used to mark some targets in tests. In this paper, the experimental results obtained with a real robot arm are shown.

scholarly journals Periodic Motions With Overshooting Phases of a Two-Mass Stick–Slip Oscillator

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
Madeleine Pascal
Keyword(s):  
Periodic Orbits ◽  
Dry Friction ◽  
Constant Velocity ◽  
Degrees Of Freedom ◽  
Contact Forces ◽  
Periodic Motions ◽  
Stick Slip ◽  
Two Degrees Of Freedom ◽  
The Masses

We investigate the dynamics of a two degrees-of-freedom oscillator excited by dry friction. The system consists of two masses connected by linear springs and in contact with a belt moving at a constant velocity. The contact forces between the masses and the belt are given by Coulomb's laws. Several periodic orbits including slip and stick phases are obtained. In particular, the existence of periodic orbits involving a part where one of the masses moves at a higher speed than the belt is proved.

The scientific bases of autocontrol with vibration phase for a resonance beating-vibration system with two degrees of freedom driven by debalances

1996 ◽  
Vol 18 (2) ◽  
pp. 43-48
Author(s):  
Tran Van Tuan ◽  
Do Sanh ◽  
Luu Duc Thach
Keyword(s):  
Degrees Of Freedom ◽  
Regulation System ◽  
Vibration System ◽  
Two Degrees Of Freedom ◽  
System Operating

In the paper it is introduced a method for studying dynamics of beating-vibrators by means of digital calculation with the help of the machine in accordance with the needs by the helps of an available auto regulation system operating with high reability.

On the Use of Quantum Thermal Bath in Unimolecular Fragmentation Simulations

2019 ◽  
Author(s):  
Riccardo Spezia ◽  
Hichem Dammak
Keyword(s):  
Degrees Of Freedom ◽  
Molecular Simulations ◽  
Zero Point ◽  
Thermal Bath ◽  
Unimolecular Dissociation ◽  
Point Energy ◽  
Rotational Degrees Of Freedom ◽  
The Difference ◽  
Nuclear Effects

<div> <div> <div> <p>In the present work we have investigated the possibility of using the Quantum Thermal Bath (QTB) method in molecular simulations of unimolecular dissociation processes. Notably, QTB is aimed in introducing quantum nuclear effects with a com- putational time which is basically the same as in newtonian simulations. At this end we have considered the model fragmentation of CH4 for which an analytical function is present in the literature. Moreover, based on the same model a microcanonical algorithm which monitor zero-point energy of products, and eventually modifies tra- jectories, was recently proposed. We have thus compared classical and quantum rate constant with these different models. QTB seems to correctly reproduce some quantum features, in particular the difference between classical and quantum activation energies, making it a promising method to study unimolecular fragmentation of much complex systems with molecular simulations. The role of QTB thermostat on rotational degrees of freedom is also analyzed and discussed. </p> </div> </div> </div>

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