Abstract
The work concerns wire transducers, which use a system with a van der Pol oscillator, with the aim of maintaining non-decreasing natural vibrations in the wire. As opposed to classical solutions, in which the feedback signal of the oscillator contains the course of displacement and velocity of the vibrating mass, a simple solution based only on the course of velocity is used. Such a solution is more advantageous from a practical perspective as regards to physical systems, because in the case of velocity transducers it eliminates the need to integrate the signal and the problems connected with it.Particular places for this solution may be found in wire tensometer systems designated for the long-term constant measurement, as well as for the measurement of time-variable courses, including those of a chaotic character.In the work, analysis was conducted on a modified van der Pol equation adapted for the movement of a discrete mass for the determination conditions of the existence of a limit cycle, the vibration course as well as the definition of the capabilities of adapting the results in the case of a wire transducer.The results of theoretical analysis were confirmed by the results of the experimental tests conducted on a laboratory model constructed for this purpose.
Highlights
The van der Pol equation x − 1 − x2 x + x = 0, (1)presented in scientific literature, represents a great example for illustrating widely in nature occurring self-oscillation
Based on the theoretical analysis and experimental tests conducted in the work, it is possible to state that the application of the van der Pol oscillator with a velocity feedback with the objective of maintaining nondecreasing natural vibrations, no matter if there is a discrete mass or a wire, is possible
Vibrations created in this way are resistant to the loss of motion stability caused by external factors and obtain a set state with constant vibration amplitude and frequency, regardless of the initial conditions
Summary
Presented in scientific literature, represents a great example for illustrating widely in nature occurring self-oscillation. The idea of maintaining self-oscillating vibrations in a mechanical system with the application of the van der Pol oscillator was the inspiration for the author to conduct research into the wire transducer designated for the continuous measurement of displacement, including fast-changing displacement. The van der Pol oscillator was used for driving vibrations in wire transducer, a discrete system presented in Fig. 2 was analyzed. These changes are significant for the functioning of a wire transducer because the velocity signal directly obtained from the clamp of the electromagnet may be used, without the need for integrating, to generate the force realizing the van der Pol component. Taking damping into consideration provides the opportunity to research the influence of friction on the vibration amplitude or to check its influence on the existence of a limit cycle
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