Nauka i Tehnika (May 2016)
SHAPE EFFECT OF ANNULAR CONCENTRATOR IN ULTRASONIC SYSTEM ON AMPLIFICATION FACTOR OF VIBRATIONS AMPLITUDE
Abstract
The paper contains a theoretical underpinning on creation of ultrasonic vibration concentrators based on annular elastic elements with non-circular (ellipse-like) eccentric shape of internal contour. Shape of internal contour in polar coordinates is described by Fourier series relative to angular coordinate that consists of a constant term and first and second harmonics. An effect of geometric parameters of the concentrator on amplification factor and natural vibration frequencies has been investigated with the help of a finite element method. The paper reveals the possibility to control an amplification factor of annular concentrators while varying eccentricity of internal contour and mean value of cross-section thickness. The amplification factor satisfies a condition K < N, where N is thickness ratio of amplifier input and output sections, and it is decreasing with increase of vibration mode order. The similar condition has been satisfied for conical bar concentrator with the difference that in the case of bar concentrators an amplification is ensured due to variation of diameter and N will represent ratio of diameters. It has been proved that modification of internal contour shape makes it possible to carry out a wide-band tuning of natural frequencies of concentrator vibrations without alteration of its overall dimensions and substantial change of amplification factor, which is important for frequency matching of the concentrator and ultrasonic vibratory system. Advantages of the proposed concentrators include simplicity of design and manufacturing, small overall dimensions, possibility for natural frequency tuning by means of static load variation. The developed concentrators can find their application in ultrasonic devices and instruments for technological and medical purposes.
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