Jtam.dvi


JOURNAL OF THEORETICAL

AND APPLIED MECHANICS

49, 4, pp. 1169-1181, Warsaw 2011

LABORATORY STAND FOR TESTING SELF-POWERED

VIBRATION REDUCTION SYSTEMS

Bogdan Sapiński, Jacek Snamina, Łukasz Jastrzębski

University of Science and Technology, Department of Process Control, Kraków, Poland

e-mail: deep@agh.edu.pl; snamina@agh.edu.pl; lukasz.jastrzebski83@gmail.com

Antoni Staśkiewicz

Cracow University of Technology, Department of Mechanics, Kraków, Poland

e-mail: as@mech.pk.edu.pl

The study describes the laboratory stand for testing semi-active vibra-
tion reduction systems comprising a magnetorheological (MR) damper,
powered from an electromagnetic generator. The design objectives, me-
chanical structure and parameters of the test stand are discussed.Dyna-
mic parameters of the stand are estimated basing on numerical simula-
tiondata.Thekey elements of the test standarepresented: the vibration
reduction system, the vibration generation system and the data acquisi-
tion system. Selected results of functional tests are provided.

Key words:MRdamper, electromagnetic generator, vibration reduction

1. Introduction

Various types of vibration reduction systems are employed tomitigate for the
effects of structural damage of buildings and structuresdue tovibrations.The-
se vibration reduction systems utilize the dissipation of energy of excitations,
such that its remaining portion should be transmitted by the structure.

In the case of tall structures, such as high buildings, vibration reduction
systems might be categorized depending on the applied damping devices and
depending on themanner they aremounted in the building. According to the
first classification, we get passive, semi-active and active systems. The other
categorization gives us base-insulating and stiffness-control (bracing systems).
Semi-active systems use various types of damping devices providing for con-
trollable damping force.



1170 B. Sapiński et al.

The research on potential applications of MR dampers in semi-active se-
ismic protection systems began in the 1990s. The first results obtained for
base-insulating sensorswere reported in (Spencer et al., 1996; Dyke and Spen-
cer, 1996; Dyke et al., 1996), focusing onmodeling, simulation and laboratory
testing of semi-active seismic protection systems equipped withMR dampers
providing the damping force of the order of several kN. Further results, obta-
ined for vibration reduction systems equipped with MR dampers generating
considerably larger forces (of the order of tens of tons), were reported in the
work by Yang (2001). Similar tests were done for MR bracing systems (Hie-
menez and Werely, 1999; Hiemenez et al., 2000). Control algorithms in MR
damper systems were investigated in Yosioka et al. (2002). Control systems
explored in those studies were feedback systems comprising a sensor, a con-
troller, and an external source of energy to power theMR damper.

The work by Cho et al. (2005) gives the conceptual design of the base
insulating systemwhere themotion of the structure is associatedwith theMR
damper force. In this system, the sensor, controller and a current driver are
replaced by an electromagnetic generator wherein themotion of the structure
is “converted” into the voltage signal inducing the current flow in the MR
damper coil. The current activates the magnetic field that controls the MR
damper force. In this approach, some portion of energy of the vibrating plant
is utilized for control of the damping force. Experimental data for the system
comprising anMRdamper of the RD-1097-1 type (http://www.lord.com) are
summarized in the work by Cho et al. (2007).

This study briefly describes the laboratory stand for testing the self-
powered vibration reduction system at the Laboratory of Adaptronics of the
Department of ProcessControl inAGH-UST.The design objectives,mechani-
cal structure andparameters of the test stand are discussed.Dynamic parame-
ters of the stand are estimated basing on numerical simulation data. Results
of functional tests are provided, which seem to confirm the adequacy of the
system design.

2. Design objectives, mechanical structure and basic parameters

of the stand

The test stand is designed to imitate a simple model of the first floor in the
structure, acting as the insulatingbaseprotecting the entire structure fromthe
effects of ground movements. This concept determines the series structure of
the test laboratory stand (Fig.1), and the vibration reduction system is placed



Laboratory stand for testing self-powered vibration... 1171

parallel to the spring representing the elastic capabilities of the insulatingbase.
The mass of the platform represents the mass of the building. The applied
shaker allows for reconstructing the ground motions in accordance with the
prescribedmotionprofiles.Themovements of theplatformemulate themotion
of the considered building or structure.

Fig. 1. Simplified mechanical structure of the stand

The selection of parameters of the laboratory stand consists in finding the
mass of theplatformand the springstiffness such that the engineeredvibration
reduction system should be effectively used. The following parameters of the
vibration reduction system are taken for calculations:
• amplitudeof relative velocity of thegenerator components atwhich it ge-
nerates the voltage required to endure the effective operation of theMR
damper; basing on the predicated and experimental data this amplitude
is taken as 0.2m/s;

• rms value of the damper force for the assumed amplitude 0.2m/s; the
rms force 460N is read off the experimental characteristics (Sapiński,
2010).

The stand should enable the testing of natural and excited vibration in the
frequency spectrum as broad as possible. The parameters of the stand were
chosen such that the dimensionless damping ratio should be 0.5. Then the
motionof theplatformbecomes oscillatory dampedmotion and theamplitude-
frequency characteristic will have a maximum.
Thus, the selected parameters can be treated as the baseline for further

testing.Additionally, taking into account the calculated forces andparameters
of the shaker, the amplitude of the excitation executed by the shaker is taken
as 0.004m. Other parameters of the stand are:
• natural vibration frequency underwhich the generator generates voltage
required to ensure the effective operation of theMRdamper (taking into
account the approximate displacement amplitude) – 5Hz;

• mass of the platform at which the dimensionless damping ratio reaches
the predetermined value, for the assumed damper force and calculated
natural frequency of vibration; mass of the platform – 100kg;



1172 B. Sapiński et al.

• stiffness ratio of the spring based on the calculatedmass of the platform
and natural frequency; stiffness ratio – 105N/m.

The assumed structure and parameters were used as the staring point for
the further stage of the research program.

3. Numerical simulation of the stand

Numerical simulations were performed to evaluate the dynamic parameters of
the stand. Schematic diagrams of the mechanical and electrical sub-systems
are shown in Figs,2 and 3 (Snamina and Sapiński, 2011). The diagram of
the mechanical sub-system (Fig.2) presents its main components as well as
the coordinate of the body position (platform) x, kinematic excitation z, the
generator force Fg, theMRdamper force F, the spring force Fs. Themodel of
the electric sub-system comprises the connected coils of the generator andMR
damper. Rg and Lg denote the resistance and inductance of the generator coil,
whilst Rg and Lg are the resistance and inductance of theMRdamper control
coil, e denotes electromotive force and i – current in the generator-damper
circuit.

Fig. 2. Schematic diagram of the mechanical sub-system

The force generated by the MR damper is given by the formula (Guo et
al., 2006; Kwok et al., 2006; Maślanka et al., 2007)

F =(c1|i|+ c2)tanh
[

β
((dz

dt
−
dx

dt

)

+p1(z−x)
)]

+(c3|i|+ c4)
((dz

dt
−
dx

dt

)

+p2(z−x)
)

(3.1)



Laboratory stand for testing self-powered vibration... 1173

Fig. 3. Schematic diagram of the electric sub-system

where: c1, c2, c3, c4 are constants in theMRdampermodel, and β, p1, p2 are
scaling parameters.
Admitting the state variables: x – body coordinate, w – velocity of the

body, i – current in the generator-MRdamper circuit, the state equations can
be written in the form (Snamina and Sapiński, 2011)

dx

dt
=w

dw

dt
=
1

m

{

c(z−x)+κi+(c1|i|+ c2)tanh
[

β
((dz

dt
−w
)

+p1(z−x)
)]

+(c3|i|+ c4)
((dz

dt
−w
)

+p2(z−x)
)}

di

dt
=

1

Lg+Ld

[

κ
(dz

dt
−w
)

− (Rg+Rd)i
]

(3.2)

The calculations were performed for the following parameters of the sys-
tem: m = 100kg, c = 105N/m, Rg = 0.4Ω, Lg = 7.5mH, Rd = 5Ω,
Ld =100mH, κ=24N/A. For those parameters, the natural frequency of the
system is equal to 5Hz. The parameters of themodel used in the damperRD-
1005-3, estimated on the basis of former laboratory tests, are: c1 =800N/A,
c2 = 40N, c3 = 3745Ns/Am, c4 = 322Ns/m. A predicted and measured
damper force versus velocity is shown in Fig.4.
The simulation results for the applied kinematic excitations of frequency

4.5Hz and amplitude 3.5mmare shown in Figs.5 and 6. Figure 5 presents the
time histories of voltage and current in the generator-MRdamper circuit. The
phase shift of current with respect to voltage is about 35◦. This parameter is
of great significance to ensure the performance of the system.
Theplot of damper force (Fig.6b) reveals fast changes in those timeswhen

the relative velocity is close to zero (see Fig.5b). That is the consequence of
the adopted model of theMR damper.



1174 B. Sapiński et al.

Fig. 4. Damper force F versus relative velocity ż− ẋ

Fig. 5. Time histories of: (a) electromotive force e, (b) current i in the
generator-MRdamper circuit

4. Description of the stand

The design of the test stand (see Fig.1) should ensure the displacement of its
all mobile components in one direction. That requires precise guiding systems
tomove the platform and the vibration reduction system. The base is fixed to
the groundwith a rigid frame,made of steel C-profiles C50. The plates bolted
to theupper section of the frameuphold the linear guiding systems.Theguides



Laboratory stand for testing self-powered vibration... 1175

Fig. 6. Time histories of: (a) relative velocity v= ẋ− ż, (b) damper force F

and linear bearings allow the displacement of the vibration reduction system
and of the platform. Mobile elements of the structure are connected in series
with joints, so as to alleviate for irregularities of the guides position. The test
stand is shown in Fig.7.

Fig. 7. View of the stand

The stand incorporates an electromagnetic shaker equipped with a con-
troller, amplifier and a compressor, vibration reduction system and a spring
mounted parallel to it, platform, data acquisition and the control system. On



1176 B. Sapiński et al.

one end the vibration reduction system is attached to the shaker, on the other-
to themobile platform.Themain function of the shaker is to generate the line-
ar displacement so as to inducemotion of the vibration reduction system and
of the platform. The platform comprises three boards arranged horizontally
to which trolleys are attached that slide along the guides, thus enabling the
platformmovement along the horizontal axis.

Thevibration reduction system incorporatesaMRdamperof theRD-1005-
3 type manufactured by Lord Corporation and an electromagnetic generator
(Sapiński, 2010) whose ends are fixed between two base boards, and a spring
is provided between the two boards.

The schematic diagram of the measuring and control system is shown in
Fig.8. Actually, it comprises two systems, one for generating mechanical vi-
bration, the other used for acquisition of measurement data.

Fig. 8. Schematic diagram of the measurement and control system of the stand

The vibration generation system incorporates a shaker V780 of LDS, a
power amplifier and a controller connected to a computer via a USB port.
The shaker is controlled using the feedback signal from the piezoelectric acce-
lerometer 357B33 of PCBPiezotronics. TheDactron Shaker Control software
allows the displacement pattern to be preset, to imitate the seismicmovement
profile.

The data acquisition system comprises the hardware (laser and piezoelec-
tric sensors with conditioners, a computer with an I/OboardNational Instru-
mentsDAQPad-6052E connectedvia theFireWireport) and software elements
(DASYLab version 10.0).



Laboratory stand for testing self-powered vibration... 1177

The parameters that can be registered include: displacement z (applied
excitation), displacement of the platform x, velocity of the platform ẋ, dam-
per force F, terminal voltage u and current i in the generator-MR damper
circuit. Displacements aremeasuredwith laser sensors FT50RLAof SENSO-
PART; velocity measurements are taken with the laser vibrometer OFV-505
of Polytec with a PFV 5000 controller. The damper force is measured using
the piezoelectric sensor 208-C03 of PCBPiezotronics connected with a signal
conditioner 480B21. Current in the control coil is measured with a current-
voltage converter, incorporating a reference resistor (0.1Ω) andanoperational
amplifier. Thus, the measured quantities are converted into voltage signals in
the range (−10,+10)V and fed to the I/O board.

5. Testing of the stand

The purpose of the testing programwas to check the performance of the test
stand and capabilities. Selected results of functional tests are given in terms
of the transmissibility coefficient (Txz(f) = X(f)/Z(f)) (Fig.9) and time
patterns of themeasured quantities: z(t), x(t), e(t), u(t), i(t),F(t) under the
applied excitation z with the amplitude 3.5mm and frequency 4.5Hz (Figs.
10-12).

Fig. 9. Transmissibility coefficient T
xz

Theplots of the transmissibility coefficient of a passive vibration reduction
system UP (for the current level in the control coil: 0, 0.1, 0.15, 0.2, 0.3A)
and of a self-powered systemUS reveal that:



1178 B. Sapiński et al.

Fig. 10. Time histories of the electromotive force e, displacement of the platform x
and relative velocity v under a sine excitation z with the amplitude 3.5mm and

frequency 4.5Hz

Fig. 11. Time histories of the voltage u and current i in the generator-MRdamper
electric circuit under a sine excitation z with the amplitude 3.5mm and

frequency 4.5Hz

Fig. 12. Time histories of the damper force F under a sine excitation z with the
amplitude 3.5mm and frequency 4.5Hz



Laboratory stand for testing self-powered vibration... 1179

• the resonance frequency for the UP 0A system equals 4.5Hz,

• an increase in the current level in the control coil in the passive system
leads to an increase of the resonance frequency and to reduction of the
resonance gain,

• the resonance frequency for the self-powered system US is 5Hz,

• the transmissibility coefficient in the US system for the resonance fre-
quency is comparable to its value obtained for the passive system
UP 0.15A.

Figure10 showstimehistories of the electromotive force e registered for the
systemUP 0A. Itwas observed that theelectromotive force ewasproportional
to the relative velocity v = ẋ− ż and remained in phase with it. Figure 11
presents time histories of the voltage u and current i in the generator-MR
damperelectric circuit for the self-powered systemUS.Thephase shiftbetween
these two quantities was dependent on the frequency of excitation. Similarly,
Fig.12 shows time histories of the damper force F in the US system. It was
observed that the increase in the excitation frequency led to an increase of the
current in the control coil, bringing forth the increase of the damper force.

6. Summary

The study briefly describes the laboratory stand for testing the semi-active
vibration reduction systems. The design objectives, mechanical structure and
parameters of the test rig are discussed. Dynamic parameters of the stand are
estimated basing on numerical simulation data. The key elements of the stand
arepresented: vibration reduction system, thevibrationgeneration systemand
the data acquisition system. Selected results of functional testing are provided.

Functional tests evidenced good performance of all sub-assemblies, confir-
med the adequacy predictions of the variability range of key mechanical and
electric parameters. The measurement data are in agreement with the calcu-
lation results obtained at the stage of design. Simulated time patterns of the
generator terminal voltage u and current i in the generator-MR damper elec-
tric circuit (Fig.5) are in line with the registeredmeasurement data (Fig.11).
The shape of the simulated time histories of the damper force (Fig.6) agrees
well with those obtained during the functional testing (Fig.12) but the va-
lue of the damper force obtained from calculations is larger. It is probably
associated with the friction force present in the linear guiding systems.



1180 B. Sapiński et al.

Acknowledgement

The study is a part of the research project No N501 366934.

References

1. Cho S.W., Jung H.J., Lee I.W., 2005, Smart passive system based on a
magnetorheological dampers, Smart Materials and Structures, 1, 707-714

2. ChoS.W., JungH.J., Lee I.W., 2007,Feasibility studyof smartpassive con-
trol system equipped with electromagnetic induction device, Smart Materials
and Structures, 16, 2323-2329

3. Dyke S.J., Spencer B.F. Jr., 1996, An experimental study ofMR dampers
for seismic protection, Smart Materials and Structures (special issue on large
civil structures)

4. Dyke S.J., Spencer B.F., Sain M.K., Carlson J.D., 1996,Modeling and
control of magnetorheological dampers for seismic response reduction, Smart
Materials and Structures, 5, 565-575

5. Guo S., Yang S., Pan C., 2006, Dynamic modeling of magnetorheological
damper behaviours, Journal of Intelligent Materials Systems and Structures,
17, 1, 3-14

6. Hiemenez G.J., Choi Y., Werely N.M., 2000, Seismic control of civil engi-
neering structures utilizing semi-activeMR bracing systems, Smart Structures
and Materials: Smart Systems for Bridges, 217-228

7. HiemenezG.J.,WerelyN.M., 1999, Seismic response of civil structures uti-
lizing semi-activeMR andERbracing systems,Proceedings of the 7th Interna-
tional Conference Electrorhelogical Fluids and Magnetorheological Suspensions

8. Kwok N.M., Ha Q.P., Nguyen T.H., Samali B., 2006, A novel hystere-
tic model for magnetorheological fluid dampers and parameter identification
Rusing particie swarm optimization, Sensors and Actuators A, 132, 441-451

9. Maślanka M., Sapiński B., Snamina J., 2007, Experimental study of vi-
bration control of a cable with an attacheMR damper, Journal of Theoretical
and Applied Mechanics, 45, 893-917

10. Sapiński B., 2010, Vibration power generator for a linearMR damper, Smart
Materials and Structures, 19, 1050-1062

11. Snamina J., Sapiński B., 2011, Energy balance In self-poweredMRdamper-
based vibration reduction system, Bulletin of the Polish Academy of Science.
Technical Sciences, 59, 1, 75-80



Laboratory stand for testing self-powered vibration... 1181

12. Spencer B.F. Jr., Dyke S.J., Sain M.K., Carlson J.D., 1996, Phenome-
nologicalmodel of amagnetorheologicaldamper,ASCEJournal of Engineering
Mechanics, USA

13. Yang G., 2001, Large-scalemagnetorheological dampers for vibrationmitiga-
tion: modeling, testing and control, Doctoral Dissertation, The University of
Notre Dame

14. Yoshioka H., Ramallo J.C. Spencer B.F. Jr., 2002, Smart base isola-
tion strategies employingmagnetorheological dampers, Journal of Engineering
Mechanics, 128, 5, 540-551

15. http://www.lord.com

Stanowisko laboratoryjne do badań samozasilającego się układu

redukcji drgań

Streszczenie

W artykule przedstawiono stanowisko badawcze układu redukcji drgań z tłumi-
kiemmagnetoreologicznym (MR), który jest zasilany z generatora elektromagnetycz-
nego. Omówiono założenia projektowe i przyjęto strukturę mechaniczną stanowiska
oraz wykonano obliczenia jego podstawowych parametrów. Opisano budowę wcho-
dzących w skład stanowiska układów: redukcji drgań, wytwarzania drgań i akwizycji
danychpomiarowych.Wykonanoobliczenia symulacyjneukładupozwalającena osza-
cowanie istotnych dla działania stanowiska wielkości mechanicznych i elektrycznych.
Przedstawiono wybrane wyniki testów funkcjonalnych stanowiska.

Manuscript received December 15, 2010; accepted for print February 17, 2011