Karachun V.V, Mel’niсk V. N.

National Technical University of Ukraine «KPI»

REPRODUCTION OF EXPECTED FREQUENCY

SPECTRUM BANDS

If the number of pleces is m = 18 (fig. 1) in the spectrum of siren it can be observed clearly outlined three frequency bands – 0...20, 35…55, 75…95, and in areas 25...35, 55...75 і 95...100 – dip. In fact, these forms are missing in the spectrum. Thus, the rotor of siren with the number of places m = 18 is convenient to use for reproduction of expected frequency spectrum bands. Values m = 59, spectrum is similar to the spectrum of siren, in which the modulation function is quasi-trapezoid form. They, apparently, almost coincide.

Provided that the number of places m = 276, or higher, for example, m = 1528, spectrum of siren tends to increase amplitudes of harmonics with increasing of their numbers (fig.2). This feature, along with white noise is a significant interest for the practice, because allows to evaluate the acoustic compliance of construction and on-board equipment, which frequencies are very large. In this case, the siren with the number of places m = 59, for example, quite unsuitable because the amplitude of harmonics with numbers higher than 120, almost equal to zero, and all the energy of acoustic emission is concentrated at low frequencies.

With increasing number of places m in the rotor the characteristics of the spectrum is more steeply against the axis of frequencies (fig. 3 dotted line).

As already noted, the most dangerous, in terms of occurrence of the phenomenon of sonic fatique in material is a broadband sound load. Generating a lot of fluctuations in the details and components of products, acoustic radiation may cause irreversible deformities due to spatial or spatial-frequency resonance. So, it is undoubted interest to studying the issue of creation of broadband acoustic radiation using monorotor siren to reproduce conditions close to operational.

For definition, let’s outline the bandwidth of frequency with number of forms equal to 100, ie, let’s take

n = 100.

Spectrum optimization problem for these conditions can be reduced to analyze the expression:

. (1)

Let’s analyze, in which the values of m, λ_k and φ_i amplitude of spectral components of generable noise will be constant.

The solution of the assigned task will be illustrated as a modulation in a form of rectangular pulses, analytically shown by the expression:

(2)

whence it easily may be defined the amplitude of components of the spectrum:

. (3)

Replacement of quazi-trapezoid form of modulation functions into rectangular, as shown further calculation, do not make substantial differences in the assessment of structure of spectrum. At the same time achieve significant simplification of mathematical apparatus of problem witch is being solved. On the other hand, to determine the power of acoustic radiation it is not so only important the form of modulation function but also the maximum expenditure of air. In consideration of expressions (2) (3), formula (1) has a form:

. (4)

Here m – the number of equal parts in which the circle of rotor is broken into; f(t) = λ_kf₀ (0≤ λ_k ≤1, k – number of area) - modulation function on those areas where windows are put; f₀ – amplitude; φ_і - angle of displacement of windows relatively to the basis radial line equidistant from the center of the stator disc, the sum means that the value of parameter k is not used in succession, but only for areas with pulses; p – number of individual pulses per unit time T, therefore 1 <p ≤ m.