Identification and study of the characteristics of friction oscillations in the brake

Abstract

Purpose.The task of researching modes of established frictional oscillations of the braking mechanism is to find a solution to the initial dynamic problem with friction that satisfies the periodicity conditions. At the same time, the period of motion of the dynamic system is not known in advance. This dynamic system is described by a non-linear dissipative non-autonomous system of differential equations. The methods. The developed technique of spectral analysis of the braking mechanism's oscillations is based on the assumption that its movements are periodic. If deterministic chaos occurs in the analyzed dynamic system, then the autocorrelation function of the time series of movements must have a finite carrier, that is, vanish outside a finite time interval. Findings. In the paper, the method of computational experiment is used to identify and study the characteristics of oscillatory processes in brake mechanisms. At the first stage of the computational experiment, a numerical solution of the considered dynamic problem with friction is carried out using a computational algorithm. As a result, the time series of block movements are calculated. At the second stage of the computational experiment, the obtained time series are studied. The originality. The paper uses phase diagrams in the "displacement-velocity" variables to analyze the process of establishing the oscillations of the brake mechanism and visual detection of attractors. When studying the dependence of amplitudes of displacements, velocities and accelerations of the dynamic system under consideration on changes in its parameters, the method of continuation by parameter was used with a stepwise change in the parameters of the system. Practical implementation. The developed mathematical model of vibrations of the braking mechanism and the computational algorithm for its numerical study are implemented in the form of a computer program for personal computers in the FORTRAN algorithmic language. Almost all available commercial compilers can be used to compile the program, including Compaq Visual Fortran 6.6 and Intel Visual Fortran 10, as well as non-commercial compilers distributed under the GNU license.