CHAPTER 5 QUASI-STATIC TESTING OF LARGE …sstl.cee.illinois.edu/papers/gyang2/Ch5.pdf74 CHAPTER 5 QUASI-STATIC TESTING OF LARGE-SCALE MR DAMPERS To investigate the fundamental behavior

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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.

76

• 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

77

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

78

-4 -3 -2 -1 0 1 2 3 4

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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

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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


79

-4 -3 -2 -1 0 1 2 3 4

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-150

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-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


-4 -3 -2 -1 0 1 2 3 4

-200

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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


80

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

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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=

81

-8 -6 -4 -2 0 2 4 6 8

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0

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200

Velocity (cm/s)

For

ce (

kN)


0 A

0.25 A

0.5 A

0.75 A

1.0 A

2.0 A1.5 A



-8 -6 -4 -2 0 2 4 6 8

-200

-150

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0

50

100

150

200

Velocity (cm/s)

For

ce (

kN)


0 A

0.25 A

0.5 A

0.75 A1.0 A

2.0 A1.5 A

82

-8 -6 -4 -2 0 2 4 6 8

-200

-150

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-50

0

50

100

150

200

Velocity (cm/s)

For

ce (

kN)


0 A

0.25 A

0.5 A

0.75 A1.0 A

2.0 A1.5 A


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.

83

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%

84

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

85

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 – – – –

86

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

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Displacement (cm)

For

ce (

kN)

-5 0 5

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0

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Velocity (cm/sec)

For

ce (

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0 A 0.25 A0.5 A 1 A2 A

87


-4 -2 0 2 4

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0

50

100

150

200

Displacement (cm)

For

ce (

kN)

-5 0 5

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0

50

100

150

200

Velocity (cm/sec)F

orce

(kN

)

0 A 0.25 A0.5 A 1 A 2 A


-4 -2 0 2 4

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0

50

100

150

200

Displacement (cm)

For

ce (

kN)

-5 0 5

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0

50

100

150

200

Velocity (cm/sec)

For

ce (

kN)

0 A 0.25 A0.5 A 1 A 2 A

88

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.


-4 -2 0 2 4

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0

50

100

150

200

Displacement (cm)

For

ce (

kN)

-5 0 5

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0

50

100

150

200

Velocity (cm/sec)F

orce

(kN

)

0 A 0.25 A0.5 A 1 A 2 A

89

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

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0

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Displacement (cm)

For

ce (

kN)

-5 0 5

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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

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0

50

100

150

200

Time (sec)

For

ce (

kN)

MeasuredPredicted

90

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

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0

50

100

150

200

Displacement (cm)

For

ce (

kN)

-5 0 5

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0

50

100

150

200

Velocity (cm/sec)F

orce

(kN

)

0.05 Hz0.1 Hz 0.2 Hz 0.5 Hz


configuration 2.

-4 -2 0 2 4

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0

50

100

150

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Displacement (cm)

For

ce (

kN)

-5 0 5

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0

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Velocity (cm/sec)

For

ce (

kN)

0.05 Hz0.1 Hz 0.2 Hz 0.5 Hz

92

-4 -2 0 2 4

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0

50

100

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200

Displacement (cm)

For

ce (

kN)

-5 0 5

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0

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Velocity (cm/sec)F

orce

(kN

)

0.05 Hz0.1 Hz 0.2 Hz 0.5 Hz


configuration 3.

-4 -2 0 2 4

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Displacement (cm)

For

ce (

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-5 0 5

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Velocity (cm/sec)

For

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0.05 Hz0.1 Hz 0.2 Hz 0.5 Hz


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

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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

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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-

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0

50

100

150

200

Displacement (cm)

For

ce (

kN)

-5 0 5

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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

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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


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



-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



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



-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



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

)


80 90 100 110 120 130 140 150 160130

135

140

145

150

155

160

165

170

175

180

Temperature (˚F)

For

ce (

kN)


(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;


0 100 200 300 400 500 600 700 800

80

100

120

140

160

180

200

Time (sec)

Tem

pera

ture

(˚F

)


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;


0 20 40 60 80 100 120 140 160 180

80

100

120

140

160

180

200

Time (sec)

Tem

pera

ture

(˚F

)


80 100 120 140 160 180 200130

140

150

160

170

180

190

200

Temperature (˚F)

For

ce (

kN)


(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,

118

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.

Documents

CHAPTER 5 QUASI-STATIC TESTING OF LARGE …sstl.cee.illinois.edu/papers/gyang2/Ch5.pdf74 CHAPTER 5 QUASI-STATIC TESTING OF LARGE-SCALE MR DAMPERS To investigate the fundamental behavior