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the main ones consists in the development of stochastic nonlinear models, since, as
experimental studies have shown, the force of friction is a random process. The slope
of the friction to velocity dependence is not a constant, but changes unpredictably,
which is due to the irregularity of the surface profile, its contamination, inconsistency
of the sliding movement and other factors. One of the components of the stochastic
approach is the study of the probabilistic structure of friction-induced vibrations
based on experimental data. Knowledge of such a structure is necessary both for
building physical and mathematical models of vibration excitations and for analyzing
the state of contact surfaces. There are many examples of such analysis in the
literature, but the main drawback of most of them is the formal use of processing
methods, which are mainly reduced to the Fourier transformation of the obtained time
sequences. Since such sequences are stochastic and may contain hidden periodicities,
as shown in this work, the results of the analysis are inconsistent. So, data processing
methods should be justified based on a mathematical model that represents these
features of vibrations.
It was noted that analysis of the spectral composition of stochastic vibrations can
be carried out on the basis of the stationary approximation, the correlation function of
which is determined by time averaging. Such a function has all properties of the
correlation function of a stationary random process. Chapter gives a brief description
of this approach, and also describes the correlation-spectral properties of the
stationary narrow-band process, represented by the Rice model. The quadrature
components, which are extracting using the Hilbert transformation, as well as the
properties of a analytic signal, are analyzed.
The power spectrum of the stationary approximation of vibrations contains
information only about their spectral composition. The analysis of the time
repeatability of vibrations, both deterministic and stochastic parts, can be carried out
on the basis of their model in the form of periodically non-stationary random
processes (PNRP). The use of moment functions of the first and second orders of the
PNVP makes it possible completely characterizes the vibration properties.
the main ones consists in the development of stochastic nonlinear models, since, as
experimental studies have shown, the force of friction is a random process. The slope
of the friction to velocity dependence is not a constant, but changes unpredictably,
which is due to the irregularity of the surface profile, its contamination, inconsistency
of the sliding movement and other factors. One of the components of the stochastic
approach is the study of the probabilistic structure of friction-induced vibrations
based on experimental data. Knowledge of such a structure is necessary both for
building physical and mathematical models of vibration excitations and for analyzing
the state of contact surfaces. There are many examples of such analysis in the
literature, but the main drawback of most of them is the formal use of processing
methods, which are mainly reduced to the Fourier transformation of the obtained time
sequences. Since such sequences are stochastic and may contain hidden periodicities,
as shown in this work, the results of the analysis are inconsistent. So, data processing
methods should be justified based on a mathematical model that represents these
features of vibrations.
It was noted that analysis of the spectral composition of stochastic vibrations can
be carried out on the basis of the stationary approximation, the correlation function of
which is determined by time averaging. Such a function has all properties of the
correlation function of a stationary random process. Chapter gives a brief description
of this approach, and also describes the correlation-spectral properties of the
stationary narrow-band process, represented by the Rice model. The quadrature
components, which are extracting using the Hilbert transformation, as well as the
properties of a analytic signal, are analyzed.
The power spectrum of the stationary approximation of vibrations contains
information only about their spectral composition. The analysis of the time
repeatability of vibrations, both deterministic and stochastic parts, can be carried out
on the basis of their model in the form of periodically non-stationary random
processes (PNRP). The use of moment functions of the first and second orders of the
PNVP makes it possible completely characterizes the vibration properties.
