Experimental study of an electromechanical system used to control the mechanical mobility
EXPERIMENTAL STUDY OF AN ELECTROMECHANICAL
SYSTEM USED TO CONTROL THE MECHANICAL MOBILITY
Drd. ing. Mihaela Andreea Mîţiu, Prof. dr. ing. Nicolae Alexandrescu, Conf.dr.ing. Daniel Comeagă,
As.dr.ing.Laurenţiu Cartal
Departamentul de Mecatronică şi Mecanică de Precizie
Facultatea de Inginerie Mecanică şi Mecatronică
Universitatea POLITEHNICA din Bucureşti, România
e-mail: mihaela.mitiu@yahoo.com
Abstract - Throughout this article are presented the main stages and results of experimental study carried
out on a electro-mechanical system used to control the mechanical mobility under the action of external
forces. The article presents the material used (apparatus, devices and instruments), how the experiments
were performed, the results and conclusions.
The article continues earlier research on control systems and active and/or passive control systems
performance of vibration isolation effects, research based on the simulation of the operation of such
systems.
Keywords: testing, adjusting mobility, mechanical mobility.
1. Introduction
This paper presents the continuation of previous
research in the field of control systems and active and/or
passive control systems performance of vibration
isolation effects.
If in the first part1 of research the focus has been placed
on modeling and the simulation of control systems
semiactive and active damper for the insulation, in the
present the focus has been placed on experimental study
of the electro-mechanical adjustment of mechanical
mobility.
The adjustment of the mechanical mobility for a system
can be made with or without the use of passive elements
using the semiactive control, which is a controlled
modification of passive system parameters, such as
stiffness, damping, etc.
In the case of active control system the parameters are
changed due to the existence of an actuator which
generates a ordered force based on information from a
sensor or transducer (accelerometer) integrated in the
system.
In all situations it is necessary to know the characteristics
of the materials and dynamic structures, on the basis of
which can be done both theoretical model to study the
dynamic behavior of the systems by simulating their
operation as well as the experimental study of systems.
This paper presents the experimental study carried out in
the case of a simple electro-mechanical system, used for
semiactive control of mechanical mobility.
The study aimed to determine the characteristics and the
values of technical parameters of the system by
experiments as well the analysis of electrical parameters
influence on the effectiveness control of the mechanical
mobility, on the way experimental.
The experimental study of the system allows the
refinement of its mathematical model.
2. The electromechanical
mechanical mobility
control
system
of
A. The main electro-mechanical system
The system studied can be defined synthetically as a
simple active control electromechanical system for
isolation against external influences to a body of mass m
using the adjusting of mechanical mobility.
The system integrates elements of passive isolation
(springs and shock absorbers), as well as an
electrodinamic actuator as an element in passiv,
semiactive or active control of the system.
In Fig.1 is shown a schematic diagram of the studied
electro-mechanical system.
1
Article "Modeling and simulation of semiactive and active
control systems for the isolation of vibrations " drd.ing
Mihaela Andreea Mîţiu, prof.dr.ing Nicolae Alexandrescu,
conf.dr.ing.Daniel Comeagă, sept. 2012
Fig. 1 The schematic diagram of the studied
electromechanical system.
The Romanian Review Precision Mechanics, Optics & Mechatronics, 2012, No. 42
7
Experimental study of an electromechanical system used to control the mechanical mobility
Operating principle of a control system of mechanical
transmissibility is simple: if the base of system is
moving at the speed vb the control system must ensure
an cancellation effects in such a way that the position of
the object to be a constant and its velocity vt to be zero
from the external coordinate system (XOY) (rel. 1).
vt  vr  vb
(1)
At the same time the system can be viewed by the effect
on mass m produced by an external applied force. In this
case the system is tuned to a specific response to
excitation conditions.
The parameter commonly used to describe the system
response is the mechanical mobility, defined as the ratio
between the speed of mass m and the force applied to it.
M 
v
F
The choice of this type of speaker was made because
it meets together, in one device, all the
electromechanical parts of the studied system: the object
to be isolated from the action of external forces is
represented by the speaker diaphragm, which has mass
m, the spring and the damper from the structure of the
studied system, with constants k and c, are equivalent
with the elastic damping system that supports the
speaker diaphragm and the electrodinamic actuator that
generates the force Fem is composed by the coil and his
electromagnetic circuit (magnet and metallic armature)
of the speaker.
The main structural elements of the speaker (Fig. 3),
and its functioning allows the experimental study of the
control system of the mechanical mobility.
(2)
In the structure of passive and semiactive control system
are placed the following components: a spring with
constant k, a dumper with constant c and an
electrodinamic actuator who will generate a force of
nature to cancel the effects of external disturbing forces
corresponding to the applied voltage U command.
The electrodinamic actuator represents the semiactive
item to control the characteristics of the system or can
be considered as an element of the same semiactive
system where it is used as a converter of mechanical
energy into electrical energy that can be subsequently
dissipated by external impedance (Ze).
The main parameters of the system, including the
electrodinamic actuator, both mechanical and electrical,
are the following:
- B – [N/A m] – magnetic induction;
- c – [N/m/s] - mechanical viscous amortization constant;
- i – [A] - the control current applied to the coil;
- k – [N/m] – the elastic constant of spring;
- l - [m] - the length of the coil wire;
- Lb – [H] – coil inductance;
- m – [kg] – the mass of the stabilized system;
- Rb – [] – the coil resistance;
- U – [V] - the control voltage of the coil;
- Uem – [V] – the electromotive force voltage induced
in the coil;
- vr – [m/s] – the speed of movement of the mass m
relative to the base;
Ze –[] -the external electrical impedance
To perform the experimental study has chosen a
system that integrates all the items and properties listed,
an electrodinamic speaker type PRO WEST WW 2020
(Fig.2).
Fig. 3 Constructive elements of the speaker and those
which are equivalent to the components of the
adjustment system of mechanical mobility. 1-speaker
casing; 2-spring; 3- system with mass m to be isolated;
4-command coil; 5-magnet; 6-metallic armature; 7conical membrane of the speaker; 8 – embossed area of
membrane (equivalent of an elastic element of spring).
The main technical parameters of speaker, considered as
an electrodinamic actuator are presented in table 1.
The electrodynamic actuator parameters (Table 1)
Nr.
crt
1
2
3
4
5
6
7
Parameter
UM
L
R
m
c
k
km
ke
H

kg
N/m/s
N/m
-
Value
0,00056
8,00
0,0434
2,2305
2452,5
4
4
B. The stand for the experimental study of the
control system of mechanical mobility
Fig. 2 The electrodynamic speaker type PRO WEST
WW 2020.
8
To carry out experiments in order to investigate the
adjustment system of mechanical mobility has been
made a stand consisting of equipment, devices and
selected accessories so that it can be obtained results
and data to characterize the system technical and
operational as a complete system.
The Romanian Review Precision Mechanics, Optics & Mechatronics, 2012, No. 42
Experimental study of an electromechanical system used to control the mechanical mobility
The stand allows for measurements with controlled
input parameters (vibrator with adjustable parameters,
adjustable sources of electrical power or electric
currents etc) and performance measuring equipment
(analyzer of signals on two channels, digital devices for
measuring electrical quantities, etc).
The stand of carrying out the experiments include:
 the subject studied, in this case the electrodynamic
actuator (the electodinamic speaker);
 an analyzer for low frequency signals, which
represents the primary element to control the stand
and for the registration/processing of the data
obtained as a result of the experimental work;
 one or two piezoelectric accelerometers to measure
the accelerations that occur or are applied to the
studied system;
 a force transducer for measuring the forces that
apply or appear in the studied system;
 one electrodynamic vibration exciter with
adjustable parameters, which is used to apply to the
studied system controlled vibration, necessary for
the determination of response to the operating
conditions;
 a electrical power source of adjustable voltage and
current, required for the application of continuous
or variable voltages;
 tools and clamping devices, for mounting or
handling the studied system, which help to set on
or positioning the system (speaker) and accessories
(transducers, sensors etc.).
In Figure 4 is shown the composition of the stand for
the experimental study and the connections between the
main apparatus and devices.
Fig. 4 The schematic diagram of the stand for
experimental study of the control system of mechanical
mobility. 1-speaker, 2 - accelerometer, 3 - force
transducer, 4 - electrodynamic vibration exciter; 5 power amplifier, 6 - signal analyzer; 7 - preamp signal,
8 - input signal power; 9 - input signal acceleration, 10
- control signal for vibrator parameters; 11 - signal
power for vibrator.
C. Equipment and devices used for the stand
The low frequency signal analyzer SR 785 is a
device that provides accurate analysis of the dynamics
of a signal and provide a complete characterization of
signal parameters. The SR785 analyzer is in fact a series
of integrated equipments and tools: a spectrum analyzer,
a network analyzer, a vibration analyzer, an octave
analyzer and an oscilloscope. The unique architecture of
the SR785 analyzer allows function as a typical signal
analyzer with two channels and measurements such as
frequency spectrum, frequency response, coherence, etc.
In the experiments the measuring mode used was the
frequency-sweep (Swept-sine mode). This is a best
systems analysis, involving high dynamic range and
high frequency limits.
Amplification or gain is optimized at each
measurement point, ensuring a dynamic range up to 145
dB. It is also possible to achieve a frequency resolution
of up to 2000 points.
The vibration test system TIRA Vib S 513
consists of a vibrator type S 513, an power amplifier,
type 2647B and accessories (accelerometers and special
cables). The system is equipped with control systems
for sinusoidal modes, random modes and shock modes.
The main technical specifications and operational
parameters for the vibrator (shaker) are presented in
table 2.
The main characteristics of vibrator type S 513.
(Table 2)
Nr.
Parameter or characteristic
Value
crt
1
Maximum force (N): sinus/aleator
100/70
2
Frequency range (Hz)
2 -7000
3
Maximum stroke (mm), peak to peak
13
Maximum speed (m/s):
4
1.5/1.5
sinus/random/shock
2
Maximum acceleration (m/s ):
5
440/310
sinus/random
6
Nominal current (A)
5,5
7
Nominal impedance (Ohm)
4
8
Moving mass (kg)
0,23
9
The main resonance frequency (Hz)
>6500
10 Weight with frame (kg)
12 kg
The force transducer Bruel&Kjaer Type 82032,
designed for use by lightweight or fragile items, is used
to measure the force applied to the center of the disc
membrane of speaker when performing experiments.
The piezoelectric force transducer is designed to
measure dynamic and impact forces.
The accelerometer Bruel&Kjaer Type 45173 is
an accelerometer which is based on generating an
electrical charge to the deformation due to acceleration
of the elements made of piezoelectric material, elements
integrated in its construction.
To perform the experiments that require the
application of a force with controlled parameters, from
the vibrator to the central disk of the vibrating
membrane of speaker, while measuring the acceleration
of the disk, it proceeded to achieve the assembling
presented in Fig. 5.
2
Force Transducer Type 8203, Product Data, 2008,
Bruel&Kjaer
3
Piezoelectric Accelerometer - Miniature Charge
Accelerometer Type 4517 C, Product Data, 2008,
Bruel&Kjaer
The Romanian Review Precision Mechanics, Optics & Mechatronics, 2012, No. 42
9
Experimental study of an electromechanical system used to control the mechanical mobility

coefficient.
it was introduced in the statement of experiment,
the response function diagram:
Fraspuns( f ) 
Fig. 5 Detail on how the force transducer (3) and
accelerometer (2) are caught on central disc of speaker
membrane (1) and the manner in which the force is
transmitted from the vibrator (5) the central disk
membrane through a thin rigid rods (4).
3. Experimental study of the control system of
mechanical mobility
A. The working procedure during experiments
To perform experiments to study the mechanical
response function of an electrodynamic actuator was
prepared and used the following procedure:
 it was prepared and filed a statement of each
experiment, which includes key data and
information related to it, namely:
 technical parameters of electrodynamic actuator
(speaker);
 the parameters and settings for the signal
analyzer;
 the specific conditions or circumstances in
which the experiment is run;
 it was introduced in the statement of experiment the
mechanical mobility Bode diagram obtained using
Simulink software. It should be noted that for
running the Simulink software application have
been used the technical data of the system and the
conditions referred in the table at the beginning of
the statement of experiment;
 it was introduced in the statement, in tabular form,
immediately after the Bode diagram , the following
characteristic measures of the system, determined
by reading and processing specific values in the
diagram:
 ωr – the theoretical resonance pulsation for the
system (rad/s);
 fr – the theoretical resonance frecvency for the
system (Hz);
 Ym r – the theoretical maximal mechanical
mobility of the system (dB);
 ω1 – the theoretical pulsation 1 (left) - pulsation
equal to the theoretical maximum mobility
decreased with 3 dB (rad/s);
 ω2 – the theoretical pulsation 2 (right) - pulsation
equal to the theoretical maximum mobility
decreased with 3 dB (rad/s);
 ζ – the theoretical value of the damping
10
Acc
(f)
F
(3)
determined using data recorded by the signal
analyzer during the duration of the experiment;
 processing the data recorded by the signal analyser
during the experiment, using Excel software, was
determined and passed in to the statement of
experiment, all in tabular form, the following
specific values:
 ωr – the resonance pulsation for the system
(rad/s);
 fr – the resonance frecvency for the system (Hz);
 Ym r – the maximal mechanical mobility of the
system (dB);
 ω1 – the pulsation 1 (left) - pulsation equal to the
theoretical maximum mobility decreased with 3
dB (rad/s);
 ω2 – the pulsation 2 (right) - pulsation equal to
the theoretical maximum mobility decreased
with 3 dB (rad/s);
 ζ – the value of the damping coefficient.
 at the end of the statement of experiment was done,
in a distinct table, the comparison between the
theoretical values of specific parameters of system,
determined from simulation of system operation
and values of the same parameters, determined this
time based on data resulting from the experiment.
The last column of the table specifies the difference
ε, in percentage, between the value determined
theoretically and experimentally determined value.
If the values is represented in linear scales, the
difference ε was determined by the relation:
V V
  1 2  100 %
(4)
V1
and for the values represented in dB scales:

10

V1
10
 10
10

V1
10

V2
10
 100 %
(5)
B. Experimental results for the case of an external
electrical impedance type resistance Re
In the experiments with stand, an important step has
been the one in which the speaker terminals have been
connected to the electrical resistors of different values,
in order to observe the effect of the impedance of an
electrical exterior resistance R above the mechanical
mobility of the mobile speaker system.
In one case, the experiment objective was the
determination of mechanically response function of the
mobile part m of the speaker system under the
conditions of action on it of an exterior forces Fext , and
with the terminals of mobile coil connected to a external
resistor Re=2 .
The conditions of the experiment was:
The Romanian Review Precision Mechanics, Optics & Mechatronics, 2012, No. 42
Experimental study of an electromechanical system used to control the mechanical mobility
The parameters of the speaker (Table 3)
R
L
m
km
ke
k
c
Re

H
kg
Tm
Tm
m/N
N/m/s

8
0,00056
0,0434
4
4
2452,5
2,2305
2
The settings for signal analyzer (Table 4)
Mode measurement
Frequency Response
Measurement type
Swept Sine
No. of measuring points
1000
Starting frequency
10 Hz
Stop frequency
110 Hz
Sweep Type (sweep)
Linear
Amplitudine max
1000.0 mV
Sampling duration
7.8125 ms
No. of sampling cycles
5
Integration time
15.625 ms
No. of integration cycles
5
Acceleration scale 1
1000 m/s2/V
Acceleration scale 2
1000 m/s2/V
The theoretical values of the parameters of the
system, resulting from the Bode diagram reading and
processing values are presented in Table 5.
Table 5
Parameter
ωr – the resonance pulsation
fr 
r
2 
the
frecvency
resonance
Ym r - the max. mechanical mobility
ω1 – first pulsation for which obtain a
mobility Ym r –3 dB (left)
ω2 – the second pulsation for which
obtain a mobility Ym r –3 dB (right)
 
 2  1
2  r
the
coefficient
damping
Graph of function response4
UM
(rad/s)
Val
244,0
(Hz)
38,83
(dB)
-11,3
(rad/s)
201
(rad/s)
295,0
-
0,1926
Fraspuns f  
a
f 
F
Special conditions: the speaker’s mobile coil terminals
is linked to a external resistance: Re  2 
The Bode diagram – the theoretical variation of
mechanical response function of the system (result of
simulation experiment by using the Simulink software
application) is shown in Fig. 6.
Fig. 7 Graph of function response Fraspuns r dB,
obtained using signal analyzer, for the mobile part m of
the speaker system under the conditions of action on it
of a exterior forces Fext , and with the terminals of
mobile coil connected to a external resistor Re=2 .
The value of the 1000 points in which have made
measurements, automatically stored by the signal
analyzer during the duration of the experiment, have
been transferred in EXCEL spreadsheet software
application for processing and interpretation.
In the following table are presented sequences and
especially the results the most important of this transfer.
Measurement results and the value of
mechanical mobility Ym dB
(Table 6)
Fig. 6 The Bode diagram – the theoretical variation of
mechanical response function of the mobile part m of
the speaker system under the conditions of action on it
of a exterior forces Fext , and with the terminals of
mobile coil connected to a external resistor Re=2 .
F
[Hz]
10,00
…
31,80
ω
[rad/s]
62,83
Fraspuns dB
[dBm/s2/N]
6,53
Ym dB
[dBm/s/N]
-29,43
199,80
31,50
-14,56
31,83
200
31,56
-14,53
Obs
Pulsation
for Ym r –3
dB (left)
4
File data recorded by signal analyzer SR785:
SRS002.78D din 02.08.2012
The Romanian Review Precision Mechanics, Optics & Mechatronics, 2012, No. 42
11
Experimental study of an electromechanical system used to control the mechanical mobility
F
[Hz]
31,90
…
40,10
ω
[rad/s]
200,43
Fraspuns dB
[dBm/s2/N]
31,60
Ym dB
[dBm/s/N]
-14,46
251,95
36,50
-11,56
40,20
252,58
36,50
-11,53
40,30
…
47,20
253,20
36,50
-11,59
296,56
35,00
-14,48
47,30
297,19
34,90
-14,53
47,40
…
110,00
297,81
35,00
-14,52
691,13
29,40
-27,43
Obs
Max. value
for Ym dB
Pulsation
for Ym r –3
dB (right)
Thus, the values have been calculated for pulsation
ω and for mechanical mobility Ym dB .
In the next step was identified in the table the value
of the maximum mechanical mobility and was
calculated the values of mechanical mobility for this is
less with 3 dB from maximum mechanical mobility (Ym
r -3 dB (left) and Ym r -3 dB (right)). Based on these
values were then calculated the pulsations ω1 and ω2,
values needed to determine the damping coefficient ζ.
Parameter values of the system, based on
measurements and processing results are as follows:
Table 7
Parameter
UM
Val
ωr – the resonance pulsation
(rad/s) 252,58
fr 
r
2 
- the resonance
frecvency
Ym r - the max. mechanical mobility
ω1 – first pulsation for which obtain a
mobility Ym r –3 dB (left)
ω2 – the second pulsation for which
obtain a mobility Ym r –3 dB (right)
 
 2  1
2  r
- the damping
coefficient
(Hz)
40,20
(dB)
-11,53
(rad/s)
200
Table summarizing the results of experiments
for different values of resistance Re
Table 8.
Nr.
crt
R
[ohm]
ω
[rad/s]
Ym max
[dB]
ζ
Obs
1
0
242
-11,44
0,1973
Coil
teminals in
short-circuit
2
2
252
-11,53
0,1924
3
10
253
-8,10
0,1359
4
40
246
-7,01
0,1168
5
100
246
-6,23
0,1097
6
∞
251
-5,41
0,1016
Coil
terminals
open
The graphic representation of the data in the table is
shown in the following figures.
(rad/s) 297,19
-
0,1924
The comparison between the theoretical and the
experimentally determined values for the parameters of
the system is shown in Table 7:
Comparison between theoretical values and the
experimentally determined values of the parameters
of the operation of the control system of mechanical
mobility
Table 7
Theoretical Measured
ε
Parameter
UM
value
value
(%)
(rad/s)
244,0
252,58
3,52
ωr
(Hz)
38,83
40,20
3,53
fr
(dB)
-11,3
-11,53
-5,16
Ym r
(rad/s)
201
200
-0,50
ω1
(rad/s)
295,0
297,19
0,74
ω2
0,1926
0,1924
-0,10
ζ
It can be seen that the differences between the
12
theoretical and the values that result from the
experiment are small, which indicates a good line of
mathematical model used to simulate real-world data
characterizing the studied system.
Similar experiments was performed, whith different
external electrical impedance, represented by external
resistance Re successively modified. The results are
summarised in table 8, which reflects the variation of
maximum pulsation ωr, of maximum mobility Ym max
and the dumping coefficient ζ, all as function of Re.
Fig. 8 The graph of variation of resonance pulsation in
function of resistence Re.
Fig. 9 The graph of variation of the maximum
mechanical mobility in function of resistence Re.
The Romanian Review Precision Mechanics, Optics & Mechatronics, 2012, No. 42
Experimental study of an electromechanical system used to control the mechanical mobility
Fig. 10 The graph of variation of dumping coefficient
in function of resistence Re.
C. Experimental results for the case of an external
electrical impedance type capacity Ce
At a later stage of experiments, at the speaker
terminals was connected capacitors of different values,
aiming to the effect that an external electrical
impedance of an electric capacity Ce aware mechanical
mobility of the mobile speaker system.
In one case, the experiment objective was the
determination of mechanically response function of the
mobile part m of the speaker system under the
conditions of action on it of a exterior forces Fext , and
with the terminals of mobile coil connected to a external
electical Ce=4400µF.
The conditions of the experiment was:
The parameters of the speaker (Table 9)
R
L
m
km
ke
k
c
Ce

H
kg
Tm
Tm
m/N
N/m/s
F
8
0,00056
0,0434
4
4
2452,5
2,2305
0,0044
The settings for signal analyzer (Table 10)
Mode measurement
Frequency Response
Measurement type
Swept Sine
No. of measuring points
1000
Starting frequency
10 Hz
Stop frequency
110 Hz
Sweep Type (sweep)
Linear
Amplitudine max
1000.0 mV
Sampling duration
7.8125 ms
No. of sampling cycles
5
Integration time
15.625 ms
No. of integration cycles
5
Acceleration scale 1
1000 m/s2/V
Acceleration scale 2
1000 m/s2/V
Special conditions: the speaker’s mobile coil terminals
is linked to a external electrical capacity: Ce=4400µF
The Bode diagram – the theoretical variation of
mechanical response function of the system (result of
simulation experiment by using the Simulink software
application) is shown in Fig.11.
Fig. 11 The Bode diagram – the theoretical variation of
mechanical response function of the mobile part m of
the speaker system under the conditions of action on it
of a exterior forces Fext , and with the terminals of
mobile coil connected to a external capacity
Ce=4400µF
The theoretical values of the parameters of the
system, resulting from the Bode diagram reading and
processing values are presented in Table 11.
Table 11
Parameter
UM
Val
ωr – the resonance pulsation
(rad/s) 245,0
- the resonance

(Hz)
38,99
fr  r
frecvency
2 
Ym r - the max. mechanical mobility (dB)
-12,7
ω1 – first pulsation for which obtain
(rad/s)
190
a mobility Ym r –3 dB (left)
ω2 – the second pulsation for which
(rad/s) 298,0
obtain a mobility Ym r –3 dB (right)
  1 - the damping
  2
0,2204
coefficient
2  r
Graph of function response5
Fraspuns f  
a
f 
F
Fig. 12 Graph of function response Fraspuns r dB,
obtained using signal analyzer, for the mobile part m of
the speaker system under the conditions of action on it
of a exterior forces Fext , and with the terminals of
mobile coil connected to a external capacity
Ce=4400µF.
5
File data recorded by signal analyzer SR785:
SRS006.78D din 02.08.2012
The Romanian Review Precision Mechanics, Optics & Mechatronics, 2012, No. 42
13
Experimental study of an electromechanical system used to control the mechanical mobility
The value of the 1000 points in which have made
measurements, automatically stored by the signal
analyzer during the duration of the experiment, have
been transferred in EXCEL spreadsheet software
application for processing and interpretation.
In the following table are presented sequences and
especially the results the most important of this transfer.
Parameter
UM
Theoretical
value
Measured
value
ε
(%)
Measurement results and the value of
mechanical mobility Ym dB
(Table 12)
ωr
fr
(rad/s)
(Hz)
245,00
38,99
251,00
39,90
Ym r
(dB)
-12,70
-12,44
3,52
3,53
5,16
0,50
0,74
0,10
Comparison between theoretical values and the
experimentally determined values of the parameters
of the operation of the control system of mechanical
mobility
Table 14
F
[Hz]
ω
[rad/s]
Fraspuns dB
[dBm/s2/N]
Ym dB
[dBm/s/N]
10,00
…
30,30
62,80
7,26
-28,70
ω1
(rad/s)
190,00
190,00
190,00
30,10
-15,45
ω2
(rad/s)
298,00
302,50
30,30
190
30,12
-15,44
ζ
-
0,2204
0,2241
30,40
…
39,80
191,00
30,20
-15,40
250,00
35,50
-12,45
39,90
251,00
35,50
-12,44
40,00
…
48,10
251,00
35,50
-12,46
302,00
34,20
-15,42
48,15
302,50
34,20
-15,44
48,20
…
110,00
303,00
34,20
-15,47
691,00
29,20
-27,57
Obs
Pulsation
for Ym r –3
dB (left)
Max. value
for Ym dB
Similar experiments was performed, whith different
external electrical impedance, represented by external
capacity Ce successively modified.
The results are summarised in table 15, which
reflects the variation of maximum pulsation ωr, of
maximum mobility Ym max and the dumping coefficient
ζ, all as function of external capacity Ce.
Table summarizing the results of experiments
for different values of capacity Ce
Table 15.
Pulsation
for Ym r –3
dB (right)
Thus, the values have been calculated for pulsation
ω and for mechanical mobility Ym dB .
In the next step was identified in the table the value
of the maximum mechanical mobility and was
calculated the values of mechanical mobility for this is
less with 3 dB from maximum mechanical mobility (Ym
r -3 dB (left) and Ym r -3 dB (right)). Based on these
values were then calculated the pulsations ω1 and ω2,
values needed to determine the damping coefficient ζ.
Parameter values of the system, based on
measurements and processing results are as follows:
Nr.
crt
Ce
[µF]
ω
[rad/s]
Ym max
[dB]
ζ
1
890
237
-11,86
0,2067
2
1100
250
-12,18
0,2120
3
2200
239,6
-12,40
0,2257
4
4400
251
-12,44
0,2241
Obs
The graphic representation of the data in the table is
shown in the following figures.
Table 13
Parameter
ωr – the resonance pulsation
fr - the resonance frecvency
Ym r - the max. mechanical mobility
ω1 – pulsation for Ym r –3 dB (left)
ω2 – pulsation for Ym r –3 dB (right)
ζ - the damping coefficient
UM
(rad/s)
(Hz)
(dB)
(rad/s)
(rad/s)
-
Val
251,00
39,90
-12,44
190,00
302,50
0,2241
The comparison between the theoretical and the
experimentally determined values for the parameters of
the system is shown in Table 14:
14
Fig. 13 The graph of variation of resonance pulsation
in function of capacity Ce.
The Romanian Review Precision Mechanics, Optics & Mechatronics, 2012, No. 42
Experimental study of an electromechanical system used to control the mechanical mobility
Fig. 14 The graph of variation of the maximum
mechanical mobility in function of capacity Ce.
4. Conclusions
The paper presents an experimental study regarding
the possibility to modify the mechanical mobility of 1DOF system using electrical components.
The previous studies have proven the possibility to
adapt the mechanical properties of a system with
concentrated parameters not only by modifying the
mechanical components, expensive and difficult
techniques, but also using a converter of mechanical
energy to electrical energy and an impedance connected
intro the electrical circuit.
The experimental studies presented herein have
shown the possibility to modify significantly the
dynamical parameters (resonance frequencies and
damping) by simply adding resistors, capacitors and
inductance in the electrical circuit. The work will be
continued for establishing the optimum electrical
impedance for a desired modification of mechanical
characteristics.
5. References
Fig. 15 The graph of variation of dumping coefficient
in function of capacity Ce.
[1] www.cedrattechnologies.com/en/publications/categories/device
-systems/active-control-of-vibration.html.
[2] http://www.onera.fr/dads-en/active-controlprinciples.php
[3] S. J. Dyke, B. F. Spencer, M. K. Sain, and J. D.
Carlson, “Experimental verification of semi-active
structural control strategies using acceleration
feedback”, Proceedings of the 3rd International
Conference on Motion and Vibration Control,
Japan, vol. III, pp. 291-296, 1996.
The Romanian Review Precision Mechanics, Optics & Mechatronics, 2012, No. 42
15