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Identification parameters of the dynamic damper of vibrations with dry friction

DOI 10.18127/j19997493-201901-10

Keywords:

Yu.N. Pavlov – Dr.Sc.(Eng.), Professor, Bauman Moscow State Technical University
E-mail: pavlov@bmstu.ru
V.M. Nedashkovsky – Ph.D.(Eng.), Associate Professor, Bauman Moscow State Technical University
E-mail: vmniu3@bmstu.ru
V.I. Oganov – Associate Professor, Bauman Moscow State Technical University
E-mail: oganov@bmstu.ru
E.A. Tikhomirova – Associate Professor, Bauman Moscow State Technical University
E-mail: elizarti@mail.ru


The problem of identification of nonlinear dynamical systems based on experimental data obtained by feeding test signals to the system is considered in the article. The goal is to determine the unknown coefficients of the (frequency) transfer function of nonlinear dynamical systems from experimental frequency hodographs using the example of a dynamic vibration damper with dry friction consisting of two bodies: the main body, the forced oscillations of which must be extinguished, and the damper with dry friction itself. The energy introduced by the perturbing periodic force is dissipated a damper with dry friction by relative motion of the bodies. It is assumed that the form of the transfer function of the identified system is known. It is suggested to use the method of harmonic linearization and nonlinearity of the «dry friction» type to approximate the viscous (linear) friction with the corresponding harmonic linearization coefficient. It was assumed that in obtaining the frequency characteristics of a real system hindrances intervenes with the experiment, as a result of which the points of the experimentally obtained hodograph are randomly shifted.
The search for the solution of the identification problem was carried out in the class of hodographs given by the model of the system, the species of the transfer function of which is the same as the species of the transfer function of the system being identified. The search for unknown coefficients of the transfer function of the system model was carried out by minimizing the predetermined criterion (measure) of the proximity of the experimentally obtained hodograph of the system and the hodograph of the system model over the entire set of experimental points. The solution of the problem of identifying a linear dynamical system using a frequency hodograph is reduced to solving a system of equations that is linear with respect to unknown parameters of the transfer function of the model of system.
For a dynamic damper of vibrations with dry friction, a program has been developed for simulating the process of obtaining pseudo-experimental data containing random errors and determining the parameters of the dynamic damper of vibrations. A computational experiment was performed to evaluate the errors with which the proposed algorithm determines the values of the parameters of this system. An illustrative computational experiment has shown that the error in determining the values of the system parameters is comparable with the measurement error range of the experimental values (counts) of the hodograph of this system. The presented method of identification of nonlinear dynamical systems can find application in determining the parameters of not only the dynamic damper of vibrations with dry friction.

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