Технические науки/2.
Механика
Postgraduate Yu. A. Pozhidaev, Student E.B. Blondinskaya.
Magnitogorsk State Technical University named after G.I. Nosov, Russia
Design of electromechanical damping systems
Abstract – The design of damping system on the basis of
electromechanical modules is proposed. Thisapproach is considered for dynamic
systems. Laboratory data are analyzed.
Comprehensive energy recuperation reduces powercosts. One possibility
here is to create a network ofautonomous consumers—for example, a network
ofconsumers for plant illumination or a network basedon a particular
residential complex.
The basic stages in the design of damping systemsare as follows:
1.
identification
of the oscillatory process;
2.
assessment
of how steady and ergodic the random oscillatory processes are;
3.
determination
of the level of the oscillatory process;
4.
identification
of the frequency composition ofthe oscillatory process;
5.
analysis
of the relation between the oscillatoryprocesses;
6.
investigation
of the oscillatory trajectories;
7.
determination
of the system’s dynamic pliability;
8.
construction
of intrinsic forms of oscillation;
9.
creation
of a mathematical model of thedynamic system;
10.
formulation
of boundary conditions and identification rational operating conditions for
thedynamic system;
11.
configuration
of the known design solutions sothat the operation of the damping system
ensures satisfactory functioning of the machine.
These design stages may be partially automated ifthe damping systems are
constructed from electromechanical modules – in other words, if there is a
kinematic relation between the mobile part of the dynamicsystem that is
involved in the oscillatory process andthe electrical machine (generator).
Theuse of electromechanical modules as damping systemssignificantly
simplifies this task. In fact, semiautomatic diagnostics is possible. Instead
of a sensor, wemay use an electrical generator, whose signals are deciphered
and analyzed. The results may be investigatedby means of statistical software
or algorithms implemented in the microprocessor control module of thedynamic
system.
The use of damping systems based on electromechanical modules simplifies
the determination of thelevel of the oscillatory process, the identification of
itsfrequency composition, and the analysis of the relations between the
oscillatory processes. At this stage ofthe design, the generator is regarded
not only as a sensor but as a damper.
Study of numerous dynamic systems in metallurgical production permits
the review of calculation methods adequately describing the scope of damper
systemsbased on electromechanical modules. Spectral theorywith the use of
Fourier transformation is applicablehere [3, 4].
Fig. 1. Experimental apparatus: (1) load; (2)
electrical generator; (3) spring; (4) cable; (5) pulley; ADC, analog- digital
converter; PC, personal computer.
If the dynamic system permits work that is
affected by its functional parameters, we need to identify the dependence of
the drag coefficient on those factors (the mass, speed, etc.). In most cases,
the oscillatory process of the dynamic system may be objectively described by a
regression formula for the drag coefficient [3].
If we regard the dynamic system as a set of
subsystems that are connected by feedback, then the damper subsystem equipped
with electromechanical modules is of most interest when some of the system’s
kinetic energy is recuperated by quenching of the oscillations. In order to
obtain energy of satisfactory quality from the electrical generator, we need
not only to create kinematically correct operating conditions but also to
carefully organize the feedback. It makes sense to use the generator at less
than the rated load, since the resonance is quenched by increasing the damping
factor. Several methods may be employed here.
The first is to increase the drag force or
torque of the electrical generator. This is simple to accomplish, the quality
of the energy will not comply with State Standard GOST 13109-97. This method is
effective for steady oscillatory processes without sharp changes or resonance.
The second method is to increase the drag
force by means of another mechanical shock absorber – for example, a hydraulic
shock absorber with a controllable choke. In that case, the electrical
generator serves as a damper, a recuperator, and a sensor. The coupling between
the mechanical and electrical components permits quenching of the oscillations,
and the high speed of this damper system permits active damping in
stabilization of the dynamic system.
On the experimental apparatus in Fig. 1, we
investigate a dynamic system in which an electromechanical module serves as
the damper system. We estimate the energy lost in the oscillatory process and
its recuperation (in percent).
When the system is shifted from equilibrium
by perturbing force Fpe in
the direction of action of gravitational force Fγ, the
torque is transmitted by the cable to pulley 5 of electrical generator 2.
The signal from the electrical generator is sent through an analog-digital
converter to a personal computer, where the recuperated energy E is
estimated.
The change in total energy of the mechanical
system in forced oscillations takes the form [7]
where
For simpler estimation of the oscillatory
energy, we consider the process in the absence of an external perturbation.
Experimentally, this situation arises each time that air is admitted to the
pneumatic cylinder’s chamber: the choke opens the valve to equalize the
pressure with the atmosphere. At that moment, the oscillation characteristics
are measured. Thus, the mechanical oscillatory system is considered with
damping oscillations. The change in mechanical energy may be expressed as
This suggests that the system’s potential
energy is completely scattered by dissipative forces. Then the accumulated
potential energy will be consumed in restoring the kinematic elements of the
dynamic system to the static state; some of the energy will be scattered by
the damper system. Since this dynamic system has elastic elements – that is,
the springs – we may assume that the energy W of the system is equal to
the potential energy Wpo
of the elastic elements. Then
where c is the quasi-elastic force
coefficient, N/m; x is the displacement
of the system from stable equilibrium, m; Wd
is the energy dissipation, J.
By comparing the energy dissipation Wd and the recuperated energy E
– that is, when using electromechanical modules in the damper system – we may
estimate the recuperated energy. The experiment shows that the recuperated
energy is 5 – 10% of the dynamic system’s energy W.
The proposed design method takes account of
the operational principles of the electromechanical modules in the creation of
damping systems. The introduction of damping systems based electromechanical
modules expands the potential of dynamic systems: the overall efficiency of the
machine is increased, since some of the dynamic system’s oscillatory energy is
recuperated, while the energy dissipation is reduced; the electrical machine
operates as a generator, while the mechanical component may contain any known
damping device or shock absorber; and the electrical generator acts
simultaneously as a damper, a sensor, and a recuperator, thereby permitting
control not only of the operating conditions in the damping system but also of
the dynamic system in the oscillatory process.
REFERENCES
1. Пожидаев Ю.А. Проектирование демпфирующих
систем для рекуперации энергии / Ю.А. Пожидаев, В.И. Кадошников, Л.В. Савочкина
// Вестник МГТУ им. Г.И. Носова / ФГБОУ ВПО «МГТУ». – Магнитогорск, 2011. – №3.
– С. 80-83.
2. Добрынин С. А. Методы автоматизированного исследования вибрации машин (Automated Analysis of Machine Vibrations), С. А. Добрынин, М. С. Фельдман, Г. И. Фирсов. – М.: Машиностроение, 1987 г.
3. Орлов А. Г. Методы расчёта в количественном спектральном анализе
(Computation Methods in Quantitative Spectral Analysis), Л.: Недра, 1977 г.
4. Силаев А. А. Спектральная теория
подрессоривания транспортных машин (Spectral Theory of Cushioning in Vehicles), М.: Машиностроение, – 1972 г.
5. Timoshenko,
S.P., Young, D.H., and Weaver, W., Vibration Problems in Engineering,
New York: Wiley, 1974.
6. Хитерер М. Я. Синхронные электрические
машины возвратно-поступательного движения (Synchronous Reciprocating Electrical Machines), М. Я. Хитерер, И. Е. Овчинников. – СПб.:
КОРОНА принт, – 2004 г.
7.
Яворский Б. М.
Справочник по физике для
инженеров и студентов вузов (Physics Handbooks for Engineers and University Students), Б. М. Яворский, А.А. Детлаф. – М.: Наука,
1965.