Karachun V.V, Mel’niсk V. N.

National Technical University of Ukraine «KPI»

tHE SPECTRUM OF MONOROTOR SIREN

Let’s define the range of monorotor siren, provided that on the stator evenly through π / 4 rad there are put 8 equal radial windows, which dimensions coincide with the smallest window of the rotor at the width and the largest – at height (fig.1). Number of places m on rotor chose equal, for example, 59.

Let’s break the circle of disk of rotor into 59 equal parts (the number of places m=59). In span of numbers 0...59 calculate squares of prime numbers, whereupon define their residual fission products by m. According to the residual quadratic chain code, it provides random nature of the distribution of windows on the disk of rotor. By these actions, it can be found that the windows on the disk of rotor lie at intervals - 1, 3, 4, 5, 7, 9, 12, 16, 17, 19, 20, 21, 22, 25, 26, 27, 28, 28, 35, 36, 41, 45, 46, 48, 49, 51, 53 and 57 (fig.2). Consequently, the number of windows on the rotor is 15.

Let’s put

and determine the spectral composition of generable with siren noise for the quantitative values of parameters: ω=300 sec-1 (n=3·103 revolutions per minute), φ1=0, (t0+t1)=1,77401·10-4 sec. Firstly let’s consider the simplest case where λ1 = λ2 =…= λр= 1, ie when the height of all the windows of rotor is the same.

Spectrum of siren, as the numerical analysis shows, in presence of the number of places m = 59 has uneven frequency response with multiple peaks (fig.3). Obviously, the average power of process is unevenly on the frequency distributed. Thus, two spectral bands - n = 25...35 and n = 50...55 have amplitudes twice bigger than the spectral components n = 35...50 and n = 55...65, for 3… 4 times more than other components of the spectrum. Rather it forms with numbers higher than 95, they are virtually absent in the spectrum of siren.

Thus, the use of the siren is limited in some cases because you can study the impact and explore products only at low (n≤70) forms of acoustic radiation.

Approved mechanical and mathematical models of homogeneous siren, apparently confirm the possibility of generating acoustic excitation by chosen design. These analytical relations allow conducting numerical analysis of amplitudes of frequency components of spectrum of siren, depending on the given value of constructions and serve for further qualitative and quantitative research opportunities for a siren to assess acoustic radiation of the desired composition.

It is a particular interest in studying the work of siren with modulation function in the form of a triangle. This form of modulation functions may occur, for example, by an absolute match the geometry of the rotor and stator windows. On the other hand, in the form of a triangle, or combinations windows of discs of rotor and stator can be made.

The total function of modulation in this case has the form –

. (1)

(2)

If to enter a notation

;

; , (3)

then, according to the Parseval equality, we get the formula for calculating the harmonic amplitudes of spectrum of siren:

. (4)