Real-time controlled tuned mass damper based on MR technology
Contact: Dr. Felix Weber, felix.weber@empa.ch
Industrial partner: Maurer Söhne GmbH & Co. KG, Munich
MR-STMD Approach
The semi-active tuned mass damper with magnetorheological damper (MR-STMD) consists of its mass, its
passive springs and the real-time controlled magnetorheological damper (Figure 1). The control is as follows
(Weber and Maslanka, 2012):
1)
Design of the natural frequency of the passive mass spring system as for passive tuned mass
dampers according to Den Hartog (1934).
2)
The MR damper force is the sum of a controlled stiffness force and a controlled friction force. This
superposition is purely dissipative as long as the maximum stiffness is not greater than the friction
force and thereby can be fully realized with semi-active MR dampers. If the maximum stiffness force is
larger, the active forces are clipped to 0. Due to the clipping, the effective stiffness of the clipped force
displacement trajectory is smaller than the stiffness commanded by the controller. To compensate for
this, a stiffness correction method is adopted that generates correct effective stiffness also when
clipping is activated.
2a) The controlled stiffness force augments/diminishes the passive spring stiffness if the primary structure
vibrates at higher/lower frequencies than the frequency that was used to design the passive mass
spring system. Thus, the controlled stiffness force generates the frequency tuning of the MR-STMD to
the actual frequency of the primary structure.
2b) The controlled friction force generates the frequency dependent energy dissipation of the MR-STMD.
(a)
(situation as at Empa bridge)
modal mass of primary structure
mass
rack
(b)
rack
cantilever beam
displacement
sensor
MR damper
force
sensor
passive
spring
controlled
stiffness
force in
MR damper
controlled
friction
force in
MR damper
mass
4 passive springs
Figure 1. MR-STMD: sketch (a), prototype for Empa bridge (b).
Measured vibration reduction magnitudes
The prototype MR-STMD was experimentally validated in 2011 at the 19.2 m long Empa bridge for various
modal masses and disturbing frequencies (Figure 2, left). The benchmark damper was the tuned mass
damper (TMD) according to Den Hartog (1934) that was precisely realized with the MR-STMD by the
emulation of viscous damping in the MR damper. The measurements of the nominal bridge where the TMD
is precisely tuned show that the MR-STMD Approach is able to compensate for the frequency sensitivity of
the TMD (Figure 2, right) which is also the case for the tests where the bridge modal mass and resonance
frequency are changed (Figure 3). The measured improvements are 30% in case of the nominal bridge and
60% for frequency shifts of +/-12%.
measured, nominal bridge, eigendamping of bridge 0.4%
12
shaker
} TMD,
2 tests
non-dimensional bridge response (-)
11
additional masses
for frequency shifts
MR-STMD
10
} MR-STMD,
2 tests
9
8
7
6
5
f1
4
3
2
1
2.4
control hardware etc.
2.6
2.8
3
3.2
3.4
disturbing frequency (Hz)
3.6
Figure 2. Empa bridge (left); measured response of nominal bridge (right).
measured, TMD, max. frequency shift +/-12%
45
f1a =2.761Hz
40
f1b =2.876Hz
f1c =2.936Hz
f1d =2.997Hz
f1e =3.040Hz
35
30
f1=3.145Hz
(nominal)
f1f =3.258Hz
g
f1 =3.341Hz
h
f1 =3.473Hz
25
20
f1
15
10
5
0
(b)
non-dimensional bridge response (-)
non-dimensional bridge response (-)
(a)
measured, MR-STMD, max. frequency shift +/-12%
45
f1a =2.761Hz
40
35
30
f1b =2.876Hz
f1=3.145Hz
(nominal)
f1c =2.936Hz
f1f =3.258Hz
f1d =2.997Hz
f1e =3.040Hz
f1 =3.341Hz
f1h =3.473Hz
g
25
20
f1
15
10
5
2.4
2.6
2.8
3
3.2
3.4
disturbing frequency (Hz)
3.6
0
2.4
2.6
2.8
3
3.2
3.4
disturbing frequency (Hz)
3.6
Figure 3. Measured responses of all tested bridge versions.
MR-STMD for Volgograd Bridge
The Volgograd Bridge in Russia with 7.1 km length and bridge fields of up to 155 m is one of the longest
bridges in Europe. In 2010, severe wind-induced vibrations at 0.45 Hz, 0.57 Hz and 0.68 Hz with amplitudes
of up to 25 cm were observed (Figure 4). Videos of this vibration event are available on YouTube. In 2011,
Empa and Maurer designed the MR-STMD approach for this bridge, Empa programmed the control code in
PLC (Beckhoff® Automation Technology) and tested the force tracking with the MR damper by HIL
simulation for frequency shifts of 0% to a maximum of +/-20% (Figure 5, left), then Empa and Maurer tested
the frequency controllability of the real MR-STMD of 5.2 tonnes at the University of German Armed Forces in
Munich for frequency shifts between -18% and +20% successfully (Figure 5, right), after that all hard- and
software components of all 12 MR-STMDs were tested by Empa as quality assurance (Figure 6), and finally
Maurer installed all 12 MR-STMDs in the Volgograd Bridge in October 2011 (Figure 7).
References
Den Hartog JP 1934 Mechanical Vibrations McGraw-Hill Book Company, The Maple Press Company,
York, Pa.
Weber F and Maslanka M Frequency and damping adaptation of a TMD with controlled MR damper Smart
Mater. Struct. 21 (2012) 055011.
Figure 4. Volgograd Bridge, Russia.
MR-STMD for
Volgograd Bridge
(5.2 tonnes)
MR damper
MR damper
force
sensor
passive
compression
springs
hydraulic
cylinder for
MR damper
excitation
data
acquisition
displacement
sensor
Beckhoff®
controller
Figure 5. Programming code in PLC and testing force tracking by HIL simulation (left); testing frequency
controllability on real MR-STMD for Volgograd Bridge (right).
Figure 6. Quality assurance tests: Beckhoff® controller (top left), displacement and force sensors (top right),
rotational MR damper (bottom left), sensor wires (bottom right).
Figure 7. MR-STMDs installed in Volgograd Bridge.