COMPUTER MODELING AND ANALYSIS OF VIBRATIONS IN ANNULAR CONCENTRATOR OF ULTRASONIC SYSTEM

The paper provides substantiation on application of elastic annular concentrators of ultrasonic systems which allows to increase an intensity of tool vibrations. It has been shown that elastic elements are used as resonators and tools in a number of ultrasonic technological systems. However an application of the elastic elements as concentrators of ultrasonic vibrations has been insufficiently studied and requires research and development of recommendations for usage. For this purpose theoretical studies have been carried out and they have helped to perform modal and harmonic analysis of several variants for a computer model of a ring with outer diameter D = 50 mm. Models of rings with various hole sizes from 20 to 40 mm have been analyzed while changing hole axis position relative to ring axis. The paper shows modes of ring flexural vibrations which can be either flat or three-dimensional depending on frequency of forced oscillations. It has been pointed out that an increase in a ring internal diameter is accompanied by higher amplitude of bending oscillations in the thinnest ring section. The same effect is achieved by increasing eccentricity of a hole axis. The paper contains recommendations for determination of rational geometric parameters which allows to increase an oscillation amplitude gain ratio and it is determined as ratio of ring section thickness. It has been established that decrease in section thickness is accompanied by higher number of frequencies for ring resonance oscillations. So, if a concentric ring and a ring with small hole diameter have only one resonance frequency, then thin-walled rings with a variable cross-section have not less than three natural resonance frequencies of oscillations that makes it possible to increase a range of vibration frequencies and technological capabilities of the ultrasonic system. It has been also found that an intensity in fluctuations of the ultrasonic system is increased even more if at the same time a cross-section of a ring with variable stiffness is decreased as along thickness so across the width.

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