Self-oscillatory device for vibration tests
The present article suggests a method of controlling the resonance frequency of a mechanical oscillating system ensuring the diversity spacing of the resonance frequencies of the oscillator and of the tested structure, and it examines a self-oscillatory device which puts this method into practice.
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| Дата: | 1985 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут проблем міцності ім. Г.С. Писаренко НАН України
1985
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| Назва видання: | Проблемы прочности |
| Теми: | |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/182888 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Self-oscillatory device for vibration tests / A.E. Bozhko, O.F. Polishchuk // Проблемы прочности. — 1985. — № 8. — С. 1135-1137. — Бібліогр.: 3 назв. — англ. |
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irk-123456789-1828882022-01-24T01:27:05Z Self-oscillatory device for vibration tests Bozhko, A.E. Polishchuk, O.F. Scientific-technical section The present article suggests a method of controlling the resonance frequency of a mechanical oscillating system ensuring the diversity spacing of the resonance frequencies of the oscillator and of the tested structure, and it examines a self-oscillatory device which puts this method into practice. 1985 Article Self-oscillatory device for vibration tests / A.E. Bozhko, O.F. Polishchuk // Проблемы прочности. — 1985. — № 8. — С. 1135-1137. — Бібліогр.: 3 назв. — англ. 0556-171X http://dspace.nbuv.gov.ua/handle/123456789/182888 620.178.3.05--52 en Проблемы прочности Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
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Scientific-technical section Scientific-technical section |
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Scientific-technical section Scientific-technical section Bozhko, A.E. Polishchuk, O.F. Self-oscillatory device for vibration tests Проблемы прочности |
| description |
The present article suggests a method of controlling the resonance frequency of a mechanical oscillating system ensuring the diversity spacing of the resonance frequencies of the oscillator and of the tested structure, and it examines a self-oscillatory device which puts this method into practice. |
| format |
Article |
| author |
Bozhko, A.E. Polishchuk, O.F. |
| author_facet |
Bozhko, A.E. Polishchuk, O.F. |
| author_sort |
Bozhko, A.E. |
| title |
Self-oscillatory device for vibration tests |
| title_short |
Self-oscillatory device for vibration tests |
| title_full |
Self-oscillatory device for vibration tests |
| title_fullStr |
Self-oscillatory device for vibration tests |
| title_full_unstemmed |
Self-oscillatory device for vibration tests |
| title_sort |
self-oscillatory device for vibration tests |
| publisher |
Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| publishDate |
1985 |
| topic_facet |
Scientific-technical section |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/182888 |
| citation_txt |
Self-oscillatory device for vibration tests / A.E. Bozhko, O.F. Polishchuk // Проблемы прочности. — 1985. — № 8. — С. 1135-1137. — Бібліогр.: 3 назв. — англ. |
| series |
Проблемы прочности |
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AT bozhkoae selfoscillatorydeviceforvibrationtests AT polishchukof selfoscillatorydeviceforvibrationtests |
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2025-07-16T02:08:38Z |
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2025-07-16T02:08:38Z |
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1837767557614927872 |
| fulltext |
SELF-OSCILlATORY DEVICE FOR VIBRATION TESTS
A. E. Bozhko and O. F. Polishchuk UDC 620.178.3.05--52
In practical vibration tests of components and units of machines it is fairly often
necessary to test objects whose resonance frequencies lie in the range 20-30 Hz. In this
range also lie the resonance frequencies of the elastic suspensions of most industrially
produced oscillators, and these operate therefore in an unfavorable regime.
The present article suggests a method of controlling the resonance frequency of a
mechanical oscillating system ensuring the diversity spacing of the resonance frequencies
of the oscillator and of the tested structure, and it examines a self-oscillatory device
which puts this method into practice.
This method [i] consists in arranging, together with feedback for speed ensuring the
excitation of free vibrations, additional feedback for displacement and acceleration chang-
ing the dynamic parameters of the tested structure.
To devise the differential equations permitting investigations by the suggested method
to be put into practice, we will examine the principle of operation of a self-oscillatory
system [2] whose block diagram is shown in Fig. i. It consists of: the vibrator V with the
tested structure TS mounted on its platform; the chopper Ch; the matching amplifier MA; the
phase shifters FSI, FS2, FS3; the derivator D; the integrator I; the amplitude controls ACI,
AC3; the band-pass frequency filter F, the suTm, ator S; the power amplifier PA.
The self-oscillatory system can be subdivided into the principal self-oscillatory cir-
cuit containing the chopper Ch, the matching amplifier MA, the phase shifter FSI, the filter
F, the summator S, the power amplifier PA, the oscillator V with the tested structure TS;
the feedback circuit for displacement including the integrator I, the phase shifter FS3, the
amplitude control AC3; the feedback circuit for acceleration containing the derivator D,
the phase shifter FS2, and the amplitude control ACI.
When the conditions of phase and amplitude balance are fulfilled, free oscillations are
excited in the principal circuit, and their frequency is determined by the parameters of the
tested structure and by the amount of feedbacks for displacement and acceleration. When the
resonance frequency of the tested structure differs considerably from the resonance fre-
quency of the elastic suspension of the oscillator, then there is no need for diversity
spacing of the resonance frequencies, and the amplitudes of the feedback signals for dis-
placement and acceleration are set equal to zero.
We will examine the case when the resonance frequencies of the tested structure and of
the oscillator coincide, and for their diversity spacing the feedbacks for acceleration and
displacement are used. In constructing the differential equations describimg the dynamics
of the self-oscillatory system, we regard the oscillator and the tested structure as a system
with two degrees of freedom and with position correlation [3]. Since the self-oscillatory
system has crossed feedback, the system of differential equations describing the motion of
the tested structure and o F the oscillator has the following form:
m~ 7~ + h~k~ + c~x~ - - c~x~ = O; m.~ + h ~ + c,x~ - - c~x~ - - c~x~ = F~ ~ ) + F~ (kO x~ + F~ (xO, (1)
where mr, ha, ct, xt are the mass, the resistance coefficient, the rigidity, and the co-
ordinate of motion of the structure, respectively; m~, h2, c2, x2 are the same for the
elastic suspension of the oscillator; F,(~), F=(~), F3(x) are the forces corresponding to the
feedbacks for acceleration, speed, and displacement, respectively.
To determine the natural frequency of a system with two degrees of freedom and their
dependence on the parameters of the feedback, we use the method of Nyquist regeneration
diagrams. We assume that the excitation regime is gentle and that F~(x) = [s-F~(xt2)]k [4],
Institute of Engineering, Academy of Sciences of the Ukrainian SSR, Kharkov. Trans-
lated from Problemy Prochnosti, No. 8, pp. 86-88, August, 1985. Original article submitted
April 29, 1983.
0039-2316/85/1708-1135509.50 �9 1986 Plenum Publishing Corporation 1135
Ch
Ts
Fig. I. Block diagram of the self-oscilla-
tory device.
w/2n. Hz
201 i I I
a
I I r
o 0.5 ~.0 ~,5 ua,v
b
Fig. 2. Dependence of the natural frequency
of the tested structure (a) and of the amp-
litude of the free oscillations (b) on the
amount of feedback.
where k is the transmission coefficient of the feedback without matching amplifier (MA), a
nonlinear element. Imagining the principal self-oscillatory circuit to be open at the
place where the chopper is Joined to the tested structure, transmitting to the input the
external disturbance u = uoeJ ~t and representing x, and x2 in the complex form x, = xle j~t,
x2 = x2e j~t, we determine the complex transmission coefficient of the open system:
U '
( ,4~- ,o,) (,o~,-,o,)-4~,%o~,--~+,o~,_~ ~o, + j=,o [~, (~o& - ,o,) + ~, (,o~,_ o~,)1. (2)
We calculate the values of the possible self-oscillatory frequencies from the condition
of balance of the phases:
l~W (i~) = o;
Am
" - (~b. + % ~ + o% + 48~%~) co, x
x ct + Ac ( 3 )
m--T- + ~o~.% = o;
Am = Fl (x0 Ac = F , (xi) ,
"~l xi
_ cl ~z= ci+c, 61 hl . 62= h,
w h e r e ~ ! == m-T' m, ' ----- 2ml ' 2m,
1136
Equation (3) represents a parabola whose apex is shifted relative to the origin of co-
ordinates. The ordinate of the apex of the parabola determines the ratio between the natural
frequencies of the system, the abscissa determines their values.
The ordinate of the apex, which we denote Yo, is determined by the following expression:
2 2 2 2 ~
2 ci+Ac [~ol(•176176
~0 ~ ~0s ' m, 4 (4)
It follows from (4) that when the feedback for displacement is positive and the feed-
back for acceleration is negative, the difference between the natural frequencies of a system
with two degrees of freedom increases, and conversely, when the feedback for displacement is
negative and the feedback for acceleration is positive, the difference between the natural
frequencies becomes smaller.
In the self-oscillatory system under examination, the feedback signals are represented
by electric voltages which are sunnned in the summator. Let us examine the potential diagram
at the summator input. Here, u, corresponds to the feedback for acceleration, u2 to the feed-
back for speed, us to the feedback for displacement.
It follows from expression (4) that simultaneously using the feedbacks for displacement
and acceleration is inadvisable because the voltages proportional to displacement and ac-
celeration compensate each other. Therefore it is better if, basing ourselves on the tradi-
tional method of controlling the parameters of oscillatory effects in harmonic loading, we
regulate the natural frequencies of the tested objects in the range of low frequencies by us-
ing feedback for displacement, and in the range of high frequencies feedback for acceleration.
The results of the experimental verification of the method of regulating the natural
frequency are presented in Fig. 2 in the form of dependences of the natural frequency of the
tested structure and of the amplitude of the free oscillations on the amount of feedback for
acceleration. By changing the amount of feedback we succeeded in shifting the natural fre-
quency of the tested structure from 29 to 60 Hz, and with the resonance frequency of the
oscillator VEDS-4OOA, this ensured normal operation of the self-oscillatory system. We
found that the amplitude of the free oscillations decreased, but this can be avoided by
using automatic fine tuning of the phase shift in the feedback circuit and stabilization of
the amplitude of the free oscillations.
i.
2.
3.
LITERATURE CITED
A. E. Bozhko, O. F. Polishchuk, and I. D. Puz'ko, Inventor's Certificate 1001443,
"Method of controlling the resonance frequency of a mechanical oscillatory system,"
Byull. Izobret., No. 8 (1983).
A. E. Bozhko, V. I. Savchenko, and O. F. Pollshchuk, Inventor's Certificate No. 903724,
"Self-oscillatory device for vibration tests of products," Byull. Izobret., No. 5 (1982).
V. I. Litvak, "Investigation of self-oscillatory resonance installations for fatigue
and vibrostrength tests of real structures," Vestn. Mashlnostr., No. ii, 9-13 (1979).
1137
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