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74
CHAPTER 5
QUASI-STATIC TESTING OF LARGE-SCALE MR DAMPERS
To investigate the fundamental behavior of the 20-ton large-scale MR damper, a
series of quasi-static experiments were conducted at the Structural Dynamics and Control/
Earthquake Engineering Laboratory (SDC/EEL) at the University of Notre Dame. In this
chapter, following the description of the experimental setup, experimental results for the
variable input current tests, amplitude-dependent tests, frequency-dependent tests, con-
stant peak velocity tests, and temperature effect tests are presented. The experimental
results are then compared with theoretical results obtained using previously developed
quasi-static models. Excellent comparisons in force-displacement behavior are observed.
Although useful for MR damper design, quasi-static models are shown to be insufficient
to describe the MR damper nonlinear force-velocity behavior under dynamic loading,
thus, setting the stage for development of a more accurate dynamic model in Chapter 7.
Some phenomena observed during the experiment are also discussed, and possible expla-
nations are given.
5.1 Experimental Setup
The experimental setup constructed at the University of Notre Dame for MR damper
testing is shown in Fig. 5.1. The MR damper was attached to a 7.5 cm thick plate that was
grouted to a 2 m thick strong floor. The equipment used for testing consists of:
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• Hydraulic system: The damper was driven by an actuator configured with two 15-gpm
Moog servo valves with a bandwidth of 80 Hz. The actuator was built by Shore West-
ern Manufacturing. It is rated at 125 kips with a 12 inch stroke. The actuator was con-
trolled by a Schenck-Pegasus 5910 servo-hydraulic controller in displacement
feedback mode. The maximum speed under this configuration was 7.26 cm/sec.
• Sensors: A position sensor, manufactured by Houston Scientific International Inc., was
employed to measured the damper displacement. The position sensor has a full range of
10 inches and a sensitivity of 1 inch/V. A load cell made by Key Transducers Inc., rated
at 100 kLb with a sensitivity of 10 kLb/V, was used to measure the damper resisting
force. The input current going into the MR damper coils was measured by a Tektronix
current probe with a sensitivity of 100 mV/A. Additionally, a Fluke 80T-IR infrared
temperature probe with a sensitivity of 1 mv/°F was utilized to monitor the damper
temperature during the experiment.
Figure 5.1: Experimental setup of 20-ton large-scale MR fluid damper.
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• Spectrum analyzer: A 4-input/2-output PC-based spectrum analyzer manufactured by
DSP Technology was employed for data acquisition and analysis.
• Power supply: An HP 6271B DC power supply with a full capacity of 60 volts and 3
amps was employed to input current to the MR damper coils for quasi-static damper
testing.
5.2 Configurations of Tested MR Dampers
Four configurations of MR dampers, each utilizing different cylinder housing materi-
als, gap sizes and MR fluids, were tested. Parameters for each configuration are given in
Table 5.1. Damper configurations 1 and 2 each have a nominal gap size of 2 mm and a
nominal effective pole length of 8.4 cm. However, configurations 3 and 4 each have a
TABLE 5.1: PARAMETERS FOR 20-TON LARGE-SCALE MR DAMPERS.
MR Damper Configuration Damper 1 Damper 2 Damper 3 Damper 4
Stroke ±8 cm
Maximum Velocity ~10 cm/s
Maximum Input Power < 50 watts
Fluid Maximum Yield Stress ~70 kPa
Maximum Force (nominal) 200,000 N
Coils 3 x 930 turns 3 x 1050 turns
Inductance (L) ~6 henries ~6 henries
Coil Resistance (R) 3 × 6.03 ohms 3 × 7 ohms
Cylinder Bore (ID) 20.326 cm20.340 cm
(Low Carbon Steel)
20.317 cm20.343 cm
(Low Carbon Steel)
Gap 2.057 mm 2.127 mm 1.508 mm 1.641 mm
Effective Axial Pole Length 84.428 mm 84.708 mm 55.372 cm 55.904 mm
MR Fluids MRF-140ND
MRX-145-2BD
MRX-145-2BD
MRX-145-2BD
τ0
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nominal gap size of 1.5 mm and a nominal effective pole length of 5.5 cm. The cylinder
housings used in configurations 1 and 3 are made of normal steel, while configurations 2
and 4 use low carbon steel. Moreover, damper 1 utilizes the MR fluid MRF-140ND,
which contains 40% iron by volume; other damper configurations utilize the MR fluid
MRX-145-2BD, which has a 45% iron by volume. The higher iron content results in an
increased yield stress and saturation current.
5.3 Damper Testing under Triangular Displacement Excitations
Force-displacement tests under triangular displacement excitation were conducted to
investigate the fundamental behavior of the MR damper. In this experiment, 2.54-cm tri-
angular displacement excitations at frequencies of 0.025, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5 and
0.6 Hz were employed. The input current to the damper coil was constant at 0, 0.25, 0.5,
0.75, 1, 1.5 and 2 A, respectively. All tests were conducted at a temperature of 80±3 °F to
reduce temperature effects. Note that the triangular waveform does not introduce inertial
forces into the overall system except when the velocity changes direction. This allows for
an accurate measurement of the damping force.
5.3.1 MR damper force-displacement and force-velocity behavior
Figs. 5.2–5.5 show the measured force-displacement loops with different input cur-
rent levels for each damper configuration. The displacement excitation is a triangular
waveform with a velocity of 6 cm/s. Other experimental results with velocities of 0.25,
0.5, 1, 2, 3, 4, 5 cm/s can be found at “http://www.nd.edu/~quake/gyang2/appendix.pdf”
under Section A.1. As can be seen, the MR damper resisting force increases as the applied
current increases. Moreover, the area enclosed by the force-displacement loop also
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-4 -3 -2 -1 0 1 2 3 4
-200
-150
-100
-50
0
50
100
150
200
Displacement (cm)
For
ce (
kN)
0 A 0.25 A0.5 A 0.75 A1 A 1.5 A 2 A
Figure 5.2: Measured force-displacement relationships at velocity of 6 cm/sec for MR damper configuration 1.
-4 -3 -2 -1 0 1 2 3 4
-200
-150
-100
-50
0
50
100
150
200
Displacement (cm)
For
ce (
kN)
0 A 0.25 A0.5 A 0.75 A1 A 1.5 A 2 A
Figure 5.3: Measured force-displacement relationships at velocity of 6 cm/sec for MR damper configuration 2.
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-4 -3 -2 -1 0 1 2 3 4
-200
-150
-100
-50
0
50
100
150
200
Displacement (cm)
For
ce (
kN)
0 A 0.25 A0.5 A 0.75 A1 A 1.5 A 2 A
Figure 5.4: Measured force-displacement relationships at velocity of 6 cm/sec for MR damper configuration 3.
-4 -3 -2 -1 0 1 2 3 4
-200
-150
-100
-50
0
50
100
150
200
Displacement (cm)
For
ce (
kN)
0 A 0.25 A0.5 A 0.75 A1 A 1.5 A 2 A
Figure 5.5: Measured force-displacement relationships at velocity of 6 cm/sec for MR damper configuration 4.
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enlarges, and more energy is dissipated.
Figs. 5.6–5.9 provide the measured MR damper force-velocity behaviors and compar-
isons with theoretical results. Due to the plastic viscous force, a larger damping force is
seen at high velocity. As discussed in Chapter 3, the differences between the axisymmetric
and parallel-plate models are small; therefore, the experimental results are compared only
with the axisymmetric Herschel-Bulkley model. For this model, the MR fluid parameters
and are chosen, and the friction force is chosen to be 3.9 kN. The
fluid yield stress is determined such that the minimum RMS error between the experimen-
tal and theoretical results is achieved. One can easily see that the analytical and experi-
mental results match well; a maximum error of less than 2.5% is obtained. Fig. 5.10
provides the relationship between the estimated yield stress and input current. Table 5.2
-8 -6 -4 -2 0 2 4 6 8
-200
-150
-100
-50
0
50
100
150
200
Velocity (cm/s)
For
ce (
kN)
Experimental ResultsAxisymmetric Herschel-Bulkley Model
0 A
0.25 A
0.5 A
0.75 A1.0 A
2.0 A1.5 A
Figure 5.6: Comparison between measured and predicted force-velocity behavior for MR damper configuration 1.
K 33 Pa-s= m 1.6=
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-8 -6 -4 -2 0 2 4 6 8
-200
-150
-100
-50
0
50
100
150
200
Velocity (cm/s)
For
ce (
kN)
Experimental ResultsAxisymmetric Herschel-Bulkley Model
0 A
0.25 A
0.5 A
0.75 A
1.0 A
2.0 A1.5 A
Figure 5.7: Comparison between measured and predicted force-velocity behavior for MR damper configuration 2.
Figure 5.8: Comparison between measured and predicted force-velocity behavior for MR damper configuration 3.
-8 -6 -4 -2 0 2 4 6 8
-200
-150
-100
-50
0
50
100
150
200
Velocity (cm/s)
For
ce (
kN)
Experimental ResultsAxisymmetric Herschel-Bulkley Model
0 A
0.25 A
0.5 A
0.75 A1.0 A
2.0 A1.5 A
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-8 -6 -4 -2 0 2 4 6 8
-200
-150
-100
-50
0
50
100
150
200
Velocity (cm/s)
For
ce (
kN)
Experimental ResultsAxisymmetric Herschel-Bulkley Model
0 A
0.25 A
0.5 A
0.75 A1.0 A
2.0 A1.5 A
Figure 5.9: Comparison between measured and predicted force-velocity behavior for MR damper configuration 4.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
10
20
30
40
50
60
70
80
Current (Amp)
MR
Flu
id Y
ield
Str
ess
(kP
a)
Damper Configuration 1 Damper Configuration 2 Damper Configuration 3 Damper Configuration 4
Figure 5.10: Estimated MR fluid yield stress v.s. input current.
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provides the measured maximum damping force, dynamic range and controllable force,
and their comparison with analytical results. Again, close agreement is observed, with
maximum errors of less than 4.05%.
5.3.2 Discussion
1) Referring to Table 5.2, MR damper configurations 1 and 2 have higher dynamic
ranges than damper configurations 3 and 4; this is due to their larger gap sizes, which
result in lower viscous force, consequently, lower off-state forces at zero input current.
2) Damper configuration 2 has a slightly larger gap size than that of damper configu-
ration 1. However, this damper uses MR fluid MRX-145-2BD; this fluid contains a higher
percentage of iron by volume than the fluid used in damper 1 (MRF-140ND). Due to the
higher iron content, this fluid exhibits an increased saturation point and yield stress. Addi-
tionally, damper 2 employs a low carbon steel housing which increases the magnetic field
in the gap; consequently, the yield stress is further increased. Therefore, a higher resisting
TABLE 5.2: MEASURED MAXIMUM FORCE, DYNAMIC RANGE AND CONTROLLABLE FORCE AND THEIR COMPARISON WITH
ANALYTICAL RESULTS.
Damper 1 Damper 2 Damper 3 Damper 4
Maximum Force (kN)
(at 6 cm/sec)
Measured 182.01 188.59 201.72 183.66
Predicted 182.48 190.00 202.52 185.33
Error (%) 0.26% 0.74% 0.40% 0.91%
Dynamic Range
Measured 9.26 10.26 6.92 7.98
Predicted 9.30 10.36 7.20 8.26
Error (%) 0.43% 0.98% 4.05% 3.51%
Controllable Force (kN)
Measured 164.32 171.85 176.24 162.33
Predicted 164.74 173.27 177.83 165.31
Error (%) 0.24% 0.83% 0.90% 1.84%
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force for damper 2 is observed.
3) As shown in Fig. 5.10, the magnetic field is almost saturated at the input current
level of 1.5 A for damper configuration 3; only a very small increase in yield stress is
observed when the input current increases to 2 A. However, the yield stress increase is
more noticeable in damper configuration 4 due to its large gap size and low carbon steel
cylinder housing.
4) The gap size for damper configuration 4 is 8% larger than that of damper 3. Usu-
ally, a large gap size reduces the magnetic field due its larger magnetic resistance. Conse-
quently, it reduces the yield stress of the MR fluid if one assumes that the materials used in
the magnetic loop are the same. However, damper configuration 4 has a higher MR fluid
yield stress than damper 3 at an input current of 2 A, as shown in Fig. 5.10. This implies
that the use of low carbon steel, which has a high conductive permeability, increases the
magnetic field in the gap at a high current level. This results in an increased yield stress.
Nevertheless, an 8% controllable force drop compared with damper 3 is still observed in
the experimental data due to its large gap size, as predicted in Section 3.5.
5) Comparing damper configurations 1 and 2 (nominal gap size of 2 mm) with
damper configurations 3 and 4 (nominal gap size of 1.5 mm), one can see that a larger gap
size has a higher saturation current and a lower yield stress because of its larger magnetic
resistance. Moreover, these configurations also exhibit reduced damping forces due to
their geometry, as discussed in Section 3.5.
6) From Figs. 5.2–5.5, force overshoots are clearly seen at the displacement
extremes, where the velocity changes its direction. These overshoots appear to be prima-
rily due to the stiction phenomenon found in MR fluids (Weiss et al. 1994). Because large
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acceleration occurs at these points due to the velocity discontinuity of the triangular dis-
placement excitation, other effects, such as fluid inertial force, may also contributed to
these overshoot. A detailed discussion of these effects is presented in Section 5.5.
5.4 Damper Testing under Sinusoidal Displacement Excitations
In this section, results of various experimental tests under sinusoidal displacement
excitations are presented. These tests include: variable input current tests, frequency-
dependent test, amplitude-dependent tests, and constant peak velocity tests.
5.4.1 Variable input current tests
Force-displacement tests under sinusoidal displacement excitation with different con-
stant current levels of 0, 0.25, 0.5, 1 and 2 A were also conducted. At each current level,
excitations with different amplitudes and frequencies were applied to the MR damper. The
tests conducted for each damper configuration are summarized in Table 5.3, and complete
experimental results are provided at “http://www.nd.edu/~quake/gyang2/appendix.pdf”
under Section A.2. Again, to reduce temperature effects, the tests were conducted at a tem-
perature of 80±3 °F.
TABLE 5.3: FORCE-DISPLACEMENT TESTS UNDER SINUSOIDAL DISPLACEMENT EXCITATION.
Amplitude (cm) Frequencies (Hz)
0.254 0.05 0.1 0.2 0.5 1 2 5
1.27 0.05 0.1 0.2 0.5 1 – –
2.54 0.05 0.1 0.2 0.5 – – –
5.08 0.05 0.1 0.2 – – – –
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Figs. 5.11–5.14 show the MR damper force-displacement and force-velocity behav-
iors under a 2.54 cm, 0.5 Hz sinusoidal displacement excitation at various input current
levels. Note that the force-displacement loops progress along a clockwise path over time,
whereas the force-velocity loops progress along a counter-clockwise path over time.
While not obvious in the hysteresis plots, this time-behavior can be easily determined
from the experimental time history data. As shown in the figures, the force-displacement
and force-velocity behaviors for different damper configurations are quite consistent.
The effects of changing input current are readily observed. At an input current of 0 A,
the MR damper primarily exhibits the characteristics of a purely viscous device (i.e., the
force-displacement relationship is approximately elliptical, and the force-velocity rela-
tionship is nearly linear). As the input current increases, the force required to yield the MR
Figure 5.11: Force-displacement and force-velocity relationships under 2.54 cm, 0.5 Hz sinusoidal displacement excitation for damper configuration 1.
-4 -2 0 2 4
-200
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0
50
100
150
200
Displacement (cm)
For
ce (
kN)
-5 0 5
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-50
0
50
100
150
200
Velocity (cm/sec)
For
ce (
kN)
0 A 0.25 A0.5 A 1 A2 A
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Figure 5.12: Force-displacement and force-velocity relationships under 2.54 cm, 0.5 Hz sinusoidal displacement excitation for damper configuration 2.
-4 -2 0 2 4
-200
-150
-100
-50
0
50
100
150
200
Displacement (cm)
For
ce (
kN)
-5 0 5
-200
-150
-100
-50
0
50
100
150
200
Velocity (cm/sec)F
orce
(kN
)
0 A 0.25 A0.5 A 1 A 2 A
Figure 5.13: Force-displacement and force-velocity relationships under 2.54 cm, 0.5 Hz sinusoidal displacement excitation for damper configuration 3.
-4 -2 0 2 4
-200
-150
-100
-50
0
50
100
150
200
Displacement (cm)
For
ce (
kN)
-5 0 5
-200
-150
-100
-50
0
50
100
150
200
Velocity (cm/sec)
For
ce (
kN)
0 A 0.25 A0.5 A 1 A 2 A
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fluid in the damper also increases, and a plastic-like behavior is shown in the hysteresis
loops.
Fig. 5.15 compares the predicted and experimentally-obtained responses using the
axisymmetric Herschel-Bulkley model. The force-displacement behavior is shown to be
reasonably modeled. However, the Herschel-Bulkley and Bingham models have a one-to-
one mapping relationship between the force and velocity. Because the damper force-
velocity loops does not exhibit such a relationship, these quasi-static models are inade-
quate to capture the nonlinear force-velocity behavior of the MR damper as observed from
the experimental results. Therefore, a more accurate dynamic model is required and is pre-
sented in Chapter 7.
Figure 5.14: Force-displacement and force-velocity relationships under 2.54 cm, 0.5 Hz sinusoidal displacement excitation for damper configuration 4.
-4 -2 0 2 4
-200
-150
-100
-50
0
50
100
150
200
Displacement (cm)
For
ce (
kN)
-5 0 5
-200
-150
-100
-50
0
50
100
150
200
Velocity (cm/sec)F
orce
(kN
)
0 A 0.25 A0.5 A 1 A 2 A
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Figure 5.15: Comparison between the predicted and experimentally-obtained responses under 2.54 cm, 0.5 Hz sinusoidal displacement excitation using the
axisymmetric Herschel-Bulkley for damper configuration 1.
-4 -2 0 2 4
-200
-150
-100
-50
0
50
100
150
200
Displacement (cm)
For
ce (
kN)
-5 0 5
-200
-150
-100
-50
0
50
100
150
200
Velocity (cm/sec)
For
ce (
kN)
MeasuredPredicted
0 A
0.5 A
0.25 A
1.0 A
2.0 A
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-200
-150
-100
-50
0
50
100
150
200
Time (sec)
For
ce (
kN)
MeasuredPredicted
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It is worth noting that two additional clockwise loops are observed at velocity
extremes in the force-velocity plot. The stiction phenomenon of MR fluids (Weiss et al
1994) and possibly the fluid inertial force contribute to these loops, as well as to force
overshoots at displacement maximums. A detailed discussion of these effects is presented
in Section 5.5.
5.4.2 Frequency-dependent tests
This section investigates the behavior of the MR damper under different frequencies
of sinusoidal displacement excitations. In this experiment, sinusoidal displacement excita-
tions with amplitudes of 0.254, 1.27, 2.54 and 5.08 cm were chosen. For each amplitude,
the MR damper is subjected to the following input current levels: 0, 0.25, 0.5, 1 and 2 A.
The tests conducted for each damper configuration are summarized in Table 5.4, and com-
plete experimental results can be found at “http://www.nd.edu/~quake/gyang2/appen-
dix.pdf” under Section A.3.
Figs. 5.16–5.19 show the MR damper force-displacement and force-velocity
responses under a 2.54 cm sinusoidal displacement excitation at an input current of 2 A.
Obviously, the overall behavior for different damper configurations is very similar. One
TABLE 5.4: FREQUENCY-DEPENDENT TESTS.
Amplitude (cm) Frequencies (Hz)
0.254 0.05 0.1 0.2 0.5 1 2 5
1.27 0.05 0.1 0.2 0.5 1 – –
2.54 0.05 0.1 0.2 0.5 – – –
5.08 0.05 0.1 0.2 – – – –
91
Figure 5.16: Force-displacement and force-velocity relationships under 2.54 cm sinusoidal displacement excitation at input current of 2 A for damper
configuration 1.
-4 -2 0 2 4
-200
-150
-100
-50
0
50
100
150
200
Displacement (cm)
For
ce (
kN)
-5 0 5
-200
-150
-100
-50
0
50
100
150
200
Velocity (cm/sec)F
orce
(kN
)
0.05 Hz0.1 Hz 0.2 Hz 0.5 Hz
Figure 5.17: Force-displacement and force-velocity relationships under 2.54 cm sinusoidal displacement excitation at input current of 2 A for damper
configuration 2.
-4 -2 0 2 4
-200
-150
-100
-50
0
50
100
150
200
Displacement (cm)
For
ce (
kN)
-5 0 5
-200
-150
-100
-50
0
50
100
150
200
Velocity (cm/sec)
For
ce (
kN)
0.05 Hz0.1 Hz 0.2 Hz 0.5 Hz
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-4 -2 0 2 4
-200
-150
-100
-50
0
50
100
150
200
Displacement (cm)
For
ce (
kN)
-5 0 5
-200
-150
-100
-50
0
50
100
150
200
Velocity (cm/sec)F
orce
(kN
)
0.05 Hz0.1 Hz 0.2 Hz 0.5 Hz
Figure 5.18: Force-displacement and force-velocity relationships under 2.54 cm sinusoidal displacement excitation at input current of 2 A for damper
configuration 3.
-4 -2 0 2 4
-200
-150
-100
-50
0
50
100
150
200
Displacement (cm)
For
ce (
kN)
-5 0 5
-200
-150
-100
-50
0
50
100
150
200
Velocity (cm/sec)
For
ce (
kN)
0.05 Hz0.1 Hz 0.2 Hz 0.5 Hz
Figure 5.19: Force-displacement and force-velocity relationships under 2.54 cm sinusoidal displacement excitation at input current of 2 A for damper
configuration 4.
93
can also see that the maximum damping force increases when the frequency increases due
to the larger plastic viscous force at higher velocity.
Fig. 5.20 illustrates the comparison between the predicted and experimentally-
obtained MR damper responses. As might be expected, the axisymmetric Herschel-Bulk-
ley model predicts the force-displacement well, but fails to portray the nonlinear force-
velocity behavior.
Note that the damper may be subjected to a small input current and a displacement
excitation with a large amplitude. In this situation, the yield force level is low and damper
operates mainly in post-yield region. Therefore, as the frequency increases, the plastic vis-
cous force starts to dominate the damper response, especially at higher frequencies. The
plastic viscous effect is clearly shown in Fig. 5.21.
5.4.3 Amplitude-dependent tests
Tests were also conducted to investigate the effect of amplitude on MR damper
behavior. In this experiment, sinusoidal displacement excitations with frequencies of 0.05,
0.1, 0.2 and 0.5 Hz were chosen. For each frequency, excitations with different amplitudes
were applied to the MR damper at current levels of 0, 0.25, 0.5, 1 and 2 A. The tests con-
ducted for each damper configuration are summarized in Table 5.5, and complete experi-
mental results are provided at “http://www.nd.edu/~quake/gyang2/appendix.pdf” under
Section A.4. Much like the results of the frequency-dependent tests, the peak velocity in
the amplitude-dependent tests varies as the frequency of the displacment excitation
changes, even though the amplitude is fixed.
Figs. 5.22–5.25 show the damper force-displacement and force-velocity relationships
94
0 5 10 15 20-200
-100
0
100
200
Time (sec)
For
ce (
kN)
0.05 Hz
0 2 4 6 8 10-200
-100
0
100
200
Time (sec)
For
ce (
kN)
0.1 Hz
0 1 2 3 4 5-200
-100
0
100
200
Time (sec)
For
ce (
kN)
0.2 Hz
0 0.5 1 1.5 2-200
-100
0
100
200
Time (sec)
For
ce (
kN)
0.5 Hz
Figure 5.20: Comparison between the predicted and experimentally-obtained damper responses under 2.54 cm sinusoidal displacement excitations with 2 A
input current using the axisymmetric Herschel-Bulkley model for damper configuration 1: (a) time responses; (b) force-displacement relationships; and
(c) force-velocity relationships.
-4 -2 0 2 4-200
-100
0
100
200
Displacement (cm)
For
ce (
kN)
-4 -2 0 2 4-200
-100
0
100
200
Displacement (cm)
For
ce (
kN)
-4 -2 0 2 4-200
-100
0
100
200
Displacement (cm)
For
ce (
kN)
-4 -2 0 2 4-200
-100
0
100
200
Displacement (cm)
For
ce (
kN)
0.05 Hz 0.1 Hz
0.2 Hz 0.5 Hz
(a)
(b)
-1 -0.5 0 0. 5 1-200
-100
0
100
200
Velocity (cm/sec)
For
ce (
kN)
-2 -1 0 1 2-200
-100
0
100
200
Velocity (cm/sec)
For
ce (
kN)
-5 0 5-200
-100
0
100
200
Velocity (cm/sec)
For
ce (
kN)
-5 0 5-200
-100
0
100
200
Velocity (cm/sec)
For
ce (
kN)
PredictedMeasured
0.05 Hz 0.1 Hz
0.2 Hz 0.5 Hz
(c)
95
under a 0.2 Hz displacement excitation at an input current of 2 A. One might see that
resisting force increases at larger amplitudes due to higher velocity. Fig. 5.26 provides a
comparison between the experimentally-obtained damper responses and analytical results
using the axisymmetric Herschel-Bulkley model.
As shown in Fig. 5.26(c), when the displacement excitation is small, such as the dis-
TABLE 5.5: AMPLITUDE-DEPENDENT TESTS.
Frequency (Hz) Amplitudes (cm)
0.05 0.254 1.27 2.54 5.08
0.1 0.254 1.27 1.27 5.08
0.2 0.254 1.27 1.27 5.08
0.5 0.254 1.27 1.27 –
-4 -2 0 2 4
-80
-60
-40
-20
0
20
40
60
80
Displacement (cm)
For
ce (
kN)
-5 0 5
-80
-60
-40
-20
0
20
40
60
80
Velocity (cm/sec)F
orce
(kN
)
0.05 Hz0.1 Hz 0.2 Hz 0.5 Hz
Figure 5.21: MR damper responses with plastic viscous effect (sinusoidal displacement excitation with amplitude of 2.54 cm at input current of 0.25 A).
96
Figure 5.22: Force-displacement and force-velocity relationships under 0.2 Hz sinusoidal displacement excitation at input current of 2 A for
damper configuration 1.
-5 0 5
-200
150-
-100
-50
0
50
100
150
200
Displacement (cm)
For
ce (
kN)
-5 0 5
-200
-150
-100
-50
0
50
100
150
200
Velocity (cm/sec)F
orce
(kN
)
0.25 cm1.27 cm2.54 cm 5.08 cm
-5 0 5
-200
-150
-100
-50
0
50
100
150
200
Displacement (cm)
For
ce (
kN)
-5 0 5
-200
-150
-100
-50
0
50
100
150
200
Velocity (cm/sec)
For
ce (
kN)
0.25 cm1.27 cm2.54 cm 5.08 cm
Figure 5.23: Force-displacement and force-velocity relationships under 0.2 Hz sinusoidal displacement excitation with input current of 2 A for
damper configuration 2.
97
-5 0 5
-200
-150
-100
-50
0
50
100
150
200
Displacement (cm)
For
ce (
kN)
-5 0 5
-200
-150
-100
-50
0
50
100
150
200
Velocity (cm/sec)F
orce
(kN
)
0.25 cm1.27 cm2.54 cm 5.08 cm
Figure 5.24: Force-displacement and force-velocity relationships under 0.2 Hz sinusoidal displacement excitation with input current of 2 A for
damper configuration 3.
-5 0 5
-200
-150
-100
-50
0
50
100
150
200
Displacement (cm)
For
ce (
kN)
-5 0 5
-200
-150
-100
-50
0
50
100
150
200
Velocity (cm/sec)
For
ce (
kN)
0.25 cm1.27 cm2.54 cm 5.08 cm
Figure 5.25: Force-displacement and force-velocity relationships under 0.2 Hz sinusoidal displacement excitation with input current of 2 A for
damper configuration 4.
98
0 1 2 3 4 5-200
-100
0
100
200
Time (sec)
For
ce (
kN)
0.1 inch
0 1 2 3 4 5-200
-100
0
100
200
Time (sec)
For
ce (
kN)
0.5 inch
0 1 2 3 4 5-200
-100
0
100
200
Time (sec)
For
ce (
kN)
1 inch
0 1 2 3 4 5-200
-100
0
100
200
Time (sec)
For
ce (
kN)
2 inch
-0.5 0 0.5200
100
0
100
200
Velocity (cm/sec)
For
ce (
kN)
-2 -1 0 1 2-200
-100
0
100
200
Velocity (cm/sec)
For
ce (
kN)
-5 0 5-200
-100
0
100
200
Velocity (cm/sec)
For
ce (
kN)
-5 0 5-200
-100
0
100
200
Velocity (cm/sec)
For
ce (
kN)
PredictedMeasured
0.1 inch 0.5 inch
1 inch 2 inch
-0.5 0 0.5-200
-100
0
100
200
Displacement (cm)
For
ce (
kN)
-2 -1 0 1 2-200
-100
0
100
200
Displacement (cm)
For
ce (
kN)
-4 -2 0 2 4-200
-100
0
100
200
Displacement (cm)
For
ce (
kN)
-5 0 5-200
-100
0
100
200
Displacement (cm)
For
ce (
kN)
0.1 inch 0.5 inch
1 inch 2 inch
Figure 5.26: Comparison between the predicted and experimentally-obtained damper responses under 0.2 Hz sinusoidal displacement excitations with input current of 2 A using the axisymmetric Herschel-Bulkley model for damper configuration 1: (a) time responses; (b) force-displacement relationships; and (c) force-velocity relationships.
(a)
(b)
(c)
99
placement amplitude of 0.254 cm, the MR damper operates mainly in the pre-yield region.
As the amplitude increases, the velocity increases accordingly. Thus more MR fluids
begin to yield, and a larger post-yield shear flow is developed. Consequently, the plastic
viscous force becomes significant, especially at large displacement amplitudes (e.g. dis-
placement amplitude of 6.28 cm).
5.4.4 Constant peak velocity tests
In the frequency-dependent tests, the displacement excitation amplitude was fixed,
and behavior of the MR damper was investigated under excitations at various frequencies.
Similarly, in the amplitude-dependent tests, excitations having constant frequencies and
variable amplitude were applied. Therefore, the peak velocities in those tests were differ-
ent. In this section, tests with different constant peak velocities are conducted at input cur-
rent levels of 0, 0.25, 0.5, 1 and 2 A. The tests conducted for each damper configuration
are summarized in Table 5.6, and complete experimental results are given at “http://
www.nd.edu/~quake/gyang2/appendix.pdf” under Section A.5.
Figs. 5.27–5.30 provide the damper force-displacement and force-velocity relation-
ships under a sinusoidal displacement excitation having a peak velocity of 8 cm/sec and
TABLE 5.6: CONSTANT PEAK VELOCITY TESTS.
Peak Velocity (cm/s) Amplitudes (cm)/ Frequency (Hz)
0.8 0.254/0.5 1.27/0.1 2.54/0.05 –
1.6 0.254/1 1.27/0.2 1.27/0.1 5.08/0.05
3.2 0.254/2 – 1.27/0.2 5.08/0.1
8.0 0.254/5 1.27/1 1.27/0.5 –
100
Figure 5.27: Force-displacement and force-velocity plots under sinusoidal displacement excitation at peak velocity of 8 cm/sec and input current of
2 A for damper configuration 1.
-5 0 5
-200
-150
-100
-50
0
50
100
150
200
Displacement (cm)
For
ce (
kN)
-5 0 5
-200
-150
-100
-50
0
50
100
150
200
Velocity (cm/sec)
For
ce (
kN)
0.25 cm, 5 Hz1.27 cm, 1 Hz2.54 cm, 0.5 Hz
-5 0 5
-200
-150
-100
-50
0
50
100
150
200
Displacement (cm)
For
ce (
kN)
-5 0 5
-200
-150
-100
-50
0
50
100
150
200
Velocity (cm/sec)
For
ce (
kN)
0.25 cm, 5 Hz1.27 cm, 1 Hz2.54 cm, 0.5 Hz
Figure 5.28: Force-displacement and force-velocity plots under sinusoidal displacement excitation at peak velocity of 8 cm/sec and input current of 2
A for damper configuration 2.
101
-5 0 5
-200
-150
-100
-50
0
50
100
150
200
Displacement (cm)
For
ce (
kN)
-5 0 5
-200
-150
-100
-50
0
50
100
150
200
Velocity (cm/sec)F
orce
(kN
)
0.25 cm, 5 Hz1.27 cm, 1 Hz2.54 cm, 0.5 Hz
Figure 5.29: Force-displacement and force-velocity plots under sinusoidal displacement excitation at peak velocity of 8 cm/sec and input current of 2
A for damper configuration 3.
-5 0 5
-200
-150
-100
-50
0
50
100
150
200
Displacement (cm)
For
ce (
kN)
-5 0 5
-200
-150
-100
-50
0
50
100
150
200
Velocity (cm/sec)
For
ce (
kN)
0.25 cm, 5 Hz1.27 cm, 1 Hz2.54 cm, 0.5 Hz
Figure 5.30: Force-displacement and force-velocity plots under sinusoidal displacement excitation at peak velocity of 8 cm/sec and input current of 2
A for damper configuration 4.
102
input current of 2 A. It can be seen that the peak resisting forces are almost identical if the
damper has the same peak velocity and input current, even though the amplitude and fre-
quency vary. It is worth noting that the damper force achieves its maximum when the
acceleration is zero (no inertial force). The experimental results are very promising, which
implies that the damping force depends only on the damper velocity and the input current
(or MR fluid yield stress) if the inertial force is ignored. Also, the amplitude and fre-
quency of the displacement excitations have almost no effect on the damping force. Fig.
5.31 shows a comparison between the experimentally-obtained damper responses and ana-
lytical results using the axisymmetric Herschel-Bulkley model. Note that the damper oper-
ates mainly in the pre-yield region under the 0.254 cm, 5 Hz displacement excitation.
5.5 MR Damper Force Response Analysis
As pointed out in the previous sections, the stiction phenomenon of MR fluids, and
possibly the fluid inertial force, play an important role in damper responses. This can be
clearly observed in the results of the sinusoidal response tests. Fig. 5.32 provides a typical
MR damper response.
For the purposes of this discussion, the damper response in Fig. 5.32 can be divided
into three regions. At the beginning of region I, the velocity changes in sign from negative
to positive, the velocity is quite small and flow direction reverses. At this stage, the MR
damper force is below the yield level, and the MR fluid operates mainly in the pre-yield
region, i.e., not flowing and having very small elastic deformation. After the damper force
exceeds the yield level, a damper force loss occurs during the transition from the pre-yield
to post-yield region due to the stiction phenomenon of MR fluids (Weiss et al. 1994;
103
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2-200
-100
0
100
200
Time (sec)
For
ce (
kN)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-200
-100
0
100
200
Time (sec)
For
ce (
kN)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-200
-100
0
100
200
Time (sec)
For
ce (
kN)
0.254 cm, 5 Hz
1.27 cm, 1 Hz
2.54 cm, 0.5 Hz
-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2-200
-100
0
100
200
Displacement (cm)
Fo
rce
(kN
)
-1.5 -1 -0.5 0 0.5 1 1.5
-200
-100
0
100
200
Displacement (cm)
Fo
rce
(kN
)
-3 -2 -1 0 1 2 3-200
-100
0
100
200
Displacement (cm)
Fo
rce
(kN
)
0.254 cm, 5 Hz
1.27 cm, 1 Hz
2.54 cm, 0.5 Hz
-8 -6 -4 -2 0 2 4 6 8-200
-100
0
100
200
Velocity (cm/sec)
Fo
rce
(kN
)
-8 -6 -4 -2 0 2 4 6 8-200
-100
0
100
200
Velocity (cm/sec)
Fo
rce
(kN
)
-8 -6 -4 -2 0 2 4 6 8-200
-100
0
100
200
Velocity (cm/sec)
Fo
rce
(kN
)
0.254 cm, 5 Hz
1.27 cm, 1 Hz
2.54 cm, 0.5 Hz
PredictedMeasured
Figure 5.31: Comparison between the predicted and experimentally-obtained damper responses with peak velocity of 8 cm/sec and input current of 2 A using the
axisymmetric Herschel-Bulkley model for damper configuration 1: (a) time responses; (b) force-displacement relationships; and (c) force-velocity relationships.
(a)
(c)(b)
104
Pignon et al. 1996; Powell 1995), resulting in an overshoot type of behavior in force. By
definition, stiction is a particle jamming or a mechanical restriction to flow that is highly
dependent upon both particle size and shape, as well as the prior electric field and flow
history of the material (Weiss et al. 1994). The illustration of stiction phenomenon is
shown in Fig. 5.33, which is similar to the Coulomb friction. As shown in the figure, the
MR fluid stress increases in the pre-yield region when strain increases. As the strain
exceeds the critical strain, the MR fluid changes from pre-yield to post-yield region and
begins to flow; consequently, the elastic stress is released, and stress loss is observed
(Weiss et al. 1994; Pignon et al. 1996). It is also worth noting that due to the stiction phe-
nomenon, the displacement measurement is behind the command signal during the force
Figure 5.32: MR damper responses under sinusoidal displacement excitation.
0
Time
I II IIIDisplacement lag
Displacement
Velocity
Force
Acceleration
DisplacementVelocityAccelerationDamper ForceCommand Signal
105
transition from pre-yield to post yield region, as shown in Fig. 5.32. Because the servo
controller uses displacement feedback, the controller tends to command a large valve
opening to facilitate the damper movement. Therefore, a substantial increase in accelera-
tion is observed (Fig. 5.32). After the damper force exceeds the yield level, the accelera-
tion quickly drops to its normal sinusoidal trajectory, as shown at the end of region I.
Because the fluid inertial force is related to the acceleration, an additional force overshoot
due to the dynamics of the experimental setup may be introduced, and may increase the
degree of force overshoot caused by the stiction phenomenon of MR fluids. However, the
magnitude of the fluid inertial force resulting by this acceleration surge is very difficult to
determine, and remains as an open research topic.
In region II, the velocity continues to increase while still remaining positive. There-
fore, the plastic-viscous force increases, and a damper force increase is observed.
Stress
Strain γ
γcritical
τ
τcritical
Pre-Yield Post-Yield
Figure 5.33: Illustration of stiction phenomenon of MR fluids (Weiss et al. 1994).
106
In region III, the velocity decreases. Note that the damper velocity approaches zero at
the end of this region, and the plastic viscous force drops more rapidly due to the fluid
shear thinning effect. Therefore, a force roll-off is observed. Note that the stiction phe-
nomenon or the damper force loss after yielding is irreversible (Powell 1995), the force
overshoot does not occur in this region; therefore, two clockwise loops are observed in the
force-velocity plot (see Fig. 5.19).
5.6 Inertial Effect of Damper Piston and Connection Parts
Figures 5.34–5.35 show the measured MR damper acceleration response under 2.54
cm, 0.2 Hz triangular and sinusoidal displacement excitations, respectively. The input cur-
rent levels are chosen to be 0, 0.5, 1 and 2 A. As shown in the figures, A response peak in
the acceleration can be readily observed, which corresponds to when the damper velocity
0 1 2 3 4 5 6 7 8-1.5
1
-0.5
0
0.5
1
1.5
Time (sec)
Acc
eler
atio
n (m
/s2 )
0A0.5A1A2A
Figure 5.34: MR damper acceleration response under a 2.54 cm, 0.2 Hz triangular displacement excitation with input current levels of 0, 0.5, 1 and 2 A.
107
changing in sign. As the input current increases, the magnitude of the acceleration has a
small increase and the duration of the acceleration peak response is slightly reduced. This
phenomenon is caused by a larger yield stress at higher input current, resulting in a larger
displacement lag.
By measuring the dimensions of the connecting parts between the damper and actua-
tor, a mass of about 260 kg was estimated. The masses of the load cell and damper piston
were also estimated to be 100 kg (25 kg and 75 kg, respectively). Therefore, the estimated
total mass is 360 kg. However, a more conservative mass of 500 kg is utilized in the fol-
lowing discussions.
For conciseness, only force responses under the 2.54 cm, 0.2 Hz triangular and sinu-
soidal displacement excitations are considered herein. For the triangular displacement
0 1 2 3 4 5 6 7 8-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
Time (sec)
Acc
eler
atio
n (m
/s2 )
0A0.5A1A2A
Figure 5.35: MR damper acceleration response under a 2.54 cm, 0.2 Hz sinusoidal displacement excitation with input current levels of 0, 0.5, 1 and 2 A.
108
excitation, the maximum acceleration is about 1 m/s2 (shown in Fig. 5.34); therefore, the
inertial force due to the connection parts and damper piston is less than 0.5 kN. However,
as shown in Fig. 5.36, the force overshoots are 8.21 kN when the force is positive and 4.56
kN when the force is negative. Similarly, under the sinusoidal displacement excitation, the
maximum acceleration is about 0.4 m/s2 (shown in Fig. 5.35); therefore, the inertial force
due to the solid masses is less than 0.2 kN. As shown in Fig. 5.37, the overshoots are 5.61
kN when the force is positive and 5.09 kN when the force is negative. Therefore, only a
very small portion of the force overshoot results from the inertial force due to the solid
masses, indicating that the stiction phenomenon dominates the force overshoot.
The pressure response is measured at different input current levels. Although the pres-
sure sensor only measures the pressure in one chamber of the MR damper, it does not
-4 -3 -2 -1 0 1 2 3 4
- 200
-150
-100
-50
0
50
100
150
200
Displacement (cm)
For
ce (
kN)
8.21 kN
4.56 kN
Figure 5.36: MR damper force-displacement response under a 2.54 cm, 0.2 Hz triangular displacement excitation with input current level of 2 A.
109
introduce an inertial force due to solid masses into the measurement. Figs. 5.38–5.39 pro-
vide the pressure-displacement relationship under 2.54 cm, 0.2 Hz triangular and sinusoi-
dal displacement excitations, respectively. Note that the accumulator pressure was charged
at 1540 psi during the experiment. As shown in the figures, the pressure overshoot can be
readily seen when the velocity changes in sign.
To further confirm that the inertial force due to solid masses is very small, the damper
force is estimated by using the pressure measurement. As we know, the damper force can
be calculated by taking the product of the pressure difference between two chambers of
MR damper and the piston cross-section area. Figs. 5.40–5.41 provide the damper forces
estimated using the pressure measurement and their comparison with force measurements
-4 -3 -2 -1 0 1 2 3 4
-200
-150
-100
-50
0
50
100
150
200
Displacement (cm)
For
ce (
kN)
5.61 kN
5.09 kN
Figure 5.37: MR damper force-displacement response under a 2.54 cm, 0.2 Hz sinusoidal displacement excitation with input current level of 2 A.
110
-4 -3 -2 -1 0 1 2 3 40
500
1000
1500
2000
2500
3000
Displacement (cm)
Pre
ssur
e (p
si)
0.5 A1 A2 A
0 A
Figure 5.38: MR damper pressure-displacement response under a 2.54 cm, 0.2 Hz triangular displacement excitation with input current levels of 0, 0.5, 1 and 2 A.
-4 -3 -2 -1 0 1 2 3 40
500
1000
1500
2000
2500
3000
Displacement (cm)
Pre
ssur
e (p
si)
0A0.5A1A2A
Figure 5.39: MR damper pressure-displacement response under a 2.54 cm, 0.2 Hz sinusoidal displacement excitation with input current levels of 0, 0.5, 1 and 2 A.
111
-4 -2 0 2 4
-200
-150
-100
-50
0
50
100
150
200
Displacement(cm)
For
ce (
kN)
-4 -2 0 2 4
-200
-150
-100
-50
0
50
100
150
200
Velocity (cm/sec)F
orce
(kN
)
Force estimated by pressure measurement
Force measurement
Figure 5.40: Damper force estimated using pressure measurement and its comparison with force measurements under 2.54 cm, 0.2 Hz triangular displacement excitations
-4 -2 0 2 4
-200
-150
-100
-50
0
50
100
150
200
Displacement (cm)
For
ce (
kN)
-4 -2 0 2 4
-200
-150
-100
-50
0
50
100
150
200
Velocity (cm/sec)
For
ce (
kN)
Force estimated by pressure measurementForce measurement
Figure 5.41: Damper force estimated using pressure measurement and its comparison with force measurements under 2.54 cm, 0.2 Hz sinusoidal displacement excitations
112
under 2.54 cm, 0.2 Hz triangular and sinusoidal displacement excitations, respectively.
Note that in comparison with measured force, the pressure of the chamber connected to
the accumulator is assumed to be a constant, and the inertia due to solid masses in the sys-
tem is ignored. As can be seen, the pressure measurement estimates the damper force well,
especially in the negative velocity region. This result is because the damper moves toward
the pressure sensor when the velocity is negative; in this case, the pressure of the chamber
connected to the accumulator is almost constant. However, when the damper piston moves
toward the accumulator side, the chamber pressure of the accumulator side may have
some small variations.
5.7 Temperature Effect
Tests were conducted to investigate the influence of temperature on MR damper per-
formance. As we know, the damper temperature increases when it is under operation due
to energy absorption, and a higher temperature reduces the maximum damping force. In
this test, the MR damper was subjected to a 1-inch triangular displacement excitation at
frequencies of 0.1, 0.2 and 0.5 Hz. The constant input current was set at 2 A. The damper
temperature was measured by a Fluke 80T-IR infrared temperature probe with a sensitivity
of 1 mv/°F during the experiment.
Figs. 5.42–5.44 provide the temperature-time and force-temperature relationships
under 1-inch displacement excitations at various frequencies. It can been seen that the
temperature rises much faster at higher frequencies due to its higher energy dissipa-
tion rate. At 0.1 Hz (Fig. 5.42), at least 800 seconds are required for the damper tem-
perature to increase from room temperature to equilibrium; however, at 0.5 Hz (Fig.
5.44), less than 170 seconds are needed. Moreover, a 20–35 kN or 15–25% force drop
113
Figure 5.42: Temperature effect test results under 2.54 cm, 0.1 Hz triangular displacement excitation at an input current of 2 A: (a) temperature vs. time;
and (b) force vs. temperature.
0 100 200 300 400 500 600 700 800 900 100070
80
90
100
110
120
130
140
150
160
Time (sec)
Tem
pera
ture
(˚F
)
Damper Configuration 1 Damper Configuration 2 Damper Configuration 3 Damper Configuration 4
80 90 100 110 120 130 140 150 160130
135
140
145
150
155
160
165
170
175
180
Temperature (˚F)
For
ce (
kN)
Damper Configuration 1 Damper Configuration 2 Damper Configuration 3 Damper Configuration 4
(a)
(b)
114
Figure 5.43: Temperature effect test result under 2.54 cm, 0.2 Hz triangular displacement excitation at an input current of 2 A: (a) temperature vs. time;
and (b) force vs. temperature.
0 100 200 300 400 500 600 700 800
80
100
120
140
160
180
200
Time (sec)
Tem
pera
ture
(˚F
)
Damper Configuration 1 Damper Configuration 2 Damper Configuration 3 Damper Configuration 4
80 90 100 110 120 130 140 150 160 170 180 190120
130
140
150
160
170
180
190
Temperature (˚F)
For
ce (
kN)
Damper Configuration 1Damper Configuration 2Damper Configuration 3Damper Configuration 4
(a)
(b)
115
Figure 5.44: Temperature effect test result under 2.54 cm, 0.5 Hz triangular displacement excitation at an input current of 2 A: (a) temperature vs. time;
and (b) force vs. temperature.
0 20 40 60 80 100 120 140 160 180
80
100
120
140
160
180
200
Time (sec)
Tem
pera
ture
(˚F
)
Damper Configuration 1Damper Configuration 2Damper Configuration 3Damper Configuration 4
80 100 120 140 160 180 200130
140
150
160
170
180
190
200
Temperature (˚F)
For
ce (
kN)
Damper Configuration 1Damper Configuration 2Damper Configuration 3Damper Configuration 4
(a)
(b)
116
is observed when the damper temperature increases from room temperature to 180°F.
This phenomenon is not confined to the large-scale MR damper tested in this disserta-
tion. In a recent test on a LORD small-scale RD-1005-3 MR damper, a 15% force drop
in compression and a 25% force drop in tension were also observed when the temper-
ature rose from room temperature to 150°F. As we know, the plastic viscosity-tempera-
ture dependence is found experimentally as an exponential function of the reciprocal of
temperature (Constantinescu 1995). Therefore, as temperature increases, the plastic vis-
cosity decreases, thereby reducing the damping force at high temperatures. However, the-
oretical calculation demonstrates that the decrease of plastic viscosity is not sufficient to
account for the 15–25% force drop observed in the experiment. Furthermore, the yield
stress varies only slightly with temperature (Carlson and Weiss 1994); therefore, the
explanation for the force drop remains unresolved.
Several interesting MR damper temperature behaviors were also observed in the
experimental results.
1) For different damper configurations, temperature-time and force-temperature
behaviors are quite different, which is clearly shown in Figs. 5.42–5.44.
2) The temperature of the cylinder housing does not increase uniformly. For example,
in damper configuration 1, the temperature on the top of the cylinder increases much faster
than on the sides; however, in damper configuration 3, the temperature on the left side is
higher. The temperature difference between the top and side is usually between 20 and
30°F.
To see whether the off-centered piston caused the problem, the damper piston in con-
figuration 3 was turned 90°. The temperature test was then repeated. One might have
117
expected that the right side of the cylinder would be hotter than the top; in fact, the tem-
perature on the top was still higher, but the temperature difference was smaller than
before. Therefore, the test did not confirm that the off-centered piston was responsible for
the cylinder housing temperature variations. Another possibility was that the side load due
to improper alignment between the actuator swivel and damper mounting plate was caus-
ing the surface temperature variations. To test this possibility, the swivel bolts were loos-
ened, the swivel and mounting plate were realigned, and the bolts were retightened. The
temperature test was then repeated, and the same phenomenon was observed. To date, the
explanation of MR damper temperature effects is still an open research topic.
5.8 Effect of Accumulator Pressure
Due to the relatively high viscosity of the MR fluid, eliminating air pockets in the
damper and air dissolved in the fluid is very difficult, even though special care is taken to
do so. The trapped air results in a force lag (compliance) in the MR damper responses, as
shown in Fig. 5.45.
To reduce the effect of trapped air on damper performance, a pressurized accumulator
is utilized. Moreover, the accumulator can also be used to accommodate thermal expan-
sion of the MR fluid. Tests were performed to determine the effect of varying accumulator
pressure, and the experimental results are shown in Fig. 5.46. As can be seen, the force lag
decreases as accumulator pressure increases. The more air the damper has, the higher the
pressure needs to be to remove the force lag. In this experiment, the force lag disappeared
when the pressure was above 1100 psi. Note that the accumulator pressure can only com-
pensate for a limited volume of air trapped in the damper. If there is too much air present,
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an increase in the accumulator pressure may reduce, but not eliminate, the force lag. In the
results shown in this dissertation, the accumulator was charged at a pressure of 1300 psi.
To minimize the trapped air in the damper, special care is taken during the fluid filling
process. The MR fluid filling setup is shown in Fig. 5.47; this apparatus was designed by
Dr. J.D. Carlson at the LORD Cooperation. The following steps outline the filling process:
0 2 4 6 8 10-180
-90
0
90
180
Time (sec)
For
ce (
kN)
-2.54 0 2.54-180
-90
0
90
180
Displacement (cm)
Forc
e (k
N)
-8 0 8-180
-90
0
90
180
Velocity (cm/sec)
-4
-2
0
2
4
Time (sec)
Dis
plac
emen
t (cm
)
1 3 5 7 9
0 2 4 6 8 101 3 5 7 9
Figure 5.45: Typical response with force lag due to trapped air in the MR damper.
119
1) Close valve 1, and fill the PVC tube with MR fluid.
2) Use a vacuum pump to pull a vacuum on the PVC tube for 15 minutes to eliminate
the absorbed gas and moisture in the MR fluid.
3) Leaving valve 1 closed, open valve 2. Pull a vacuum on the damper housing for 15
minutes.
4) Close valve 2 and open valve 1. The MR fluid in the PVC tube will be drawn in by
the vacuum in the damper.
5) Stroke the MR damper using the air cylinder to ensure a complete fill.
Even when following this procedure, some air will remain in the damper. A pressur-
ized accumulator must then be used to eliminate the force lag. One might guess that the
pressure induced by the presence of an accumulator may increase the friction force
-4 -3 -2 -1 0 1 2 3 4-200
-150
-100
-50
0
50
100
150
200
Displacement (cm)
For
ce (
kN)
0 psi500 psi800 psi1100 psi
Figure 5.46: Accumulator pressure effect tests under a 2.54 cm, 0.1 Hz triangular displacement excitation at an input current of 1 A.
120
between the piston rod and seals and, consequently, the off-state force of the MR damper.
Fig. 5.48 displays damper off-state forces (0 A input current) at various pressure levels. As
can be seen, the accumulator pressure does increase the off-state force slightly. However,
the off-state force remains at a constant above a certain pressure level. Further increasing
the accumulator pressure will not result in a continued increase of the off-state force.
5.9 Summary
In this chapter, quasi-static experimental results of the 20-ton large-scale MR damper
in various configurations are provided; these include force-displacement tests, amplitude-
dependent tests, frequency-dependent tests, constant peak velocity tests and temperature
effect tests. The overall performance of the MR damper is very promising, and the damper
MR Fluid
vacuum
vacuum
Valve 2
Valve 1
Air Cylinder
MR Damper
Figure 5.47: Schematic of MR fluid filling setup.
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behaviors under various configurations are quite consistent.
The quasi-static experimental data is compared with quasi-static models developed in
Chapter 3, and an error of less than 3.5% is observed in MR damper resisting force,
dynamic range and controllable force. Although useful for MR damper design, quasi-
static models are not shown to be sufficient to describe the MR damper nonlinear force-
velocity behavior under dynamic loading. A more accurate dynamic model is presented in
Chapter 7 to accommodate this nonlinear force-velocity behavior.
MR dampers with different cylinder housing materials are investigated. Experimental
results have shown that the low carbon steel, which has a high permeability, increases the
magnetic field in the gap and the saturation current resulting in an increased damping
force.
-4 -3 -2 -1 0 1 2 3 4-20
-15
-10
-5
0
5
10
15
20
Displacement (cm)
For
ce (
kN)
0 psi500 psi800 psi1100 psi
Figure 5.48: Accumulator pressure effect tests under a 2.54 cm, 0.1 Hz triangular displacement excitation with an input current of 0 A.
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MR damper response analysis is also performed, and MR fluid stiction phenomenon,
as well as inertial and shear thinning effects on MR damper response, are discussed. The
stiction phenomenon and possibly the fluid inertial effect result in force overshoots at dis-
placement maximums and two additional loops at velocity extremes. In addition, the shear
thinning effect can be used to explain the force roll-off when the displacement and veloc-
ity have the same sign and the magnitude of the velocity is small.
In the MR damper temperature test, a force drop of between 15% and 25% is
observed. However, the explanation of several interesting MR damper temperature behav-
iors discovered in the temperature effect tests remains unresolved, i.e., the temperature of
the cylinder housing does not increase uniformly, etc.
Furthermore, the effect of accumulator pressure on MR damper response is discussed.
A pressurized accumulator is shown to be effective in reducing the force lag due to the
residual air trapped in the damper. Moreover, an approach for minimizing the air in the
damper during the filling process is provided.