CHAPTER 5 QUASI-STATIC TESTING OF LARGE-SCALE MR DAMPERS To investigate the fundamental behavior of the 2-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, constant 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 explanations 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: 74
Hydraulic system: The damper was driven by an actuator configured with two 15-gpm Moog servo valves with a bandwidth of 8 Hz. The actuator was built by Shore Western Manufacturing. It is rated at 125 kips with a 12 inch stroke. The actuator was controlled by a Schenck-Pegasus 591 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 1 inches and a sensitivity of 1 inch/v. A load cell made by Key Transducers Inc., rated at 1 klb with a sensitivity of 1 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 1 mv/a. Additionally, a Fluke 8T-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 2-ton large-scale MR fluid damper. 75
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 6 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 materials, 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 2-TON LARGE-SCALE MR DAMPERS. MR Damper Configuration Damper 1 Damper 2 Damper 3 Damper 4 Stroke ±8 cm Maximum Velocity ~1 cm/s Maximum Input Power < 5 watts Fluid Maximum Yield Stress 76 ~7 kpa Maximum Force (nominal) 2, N Coils 3 x 93 turns 3 x 15 turns Inductance (L) ~6 henries ~6 henries Coil Resistance (R) 3 6.3 ohms 3 7 ohms Cylinder Bore (ID) 2.326 cm 2.34 cm (Low Carbon Steel) 2.317 cm 2.343 cm (Low Carbon Steel) Gap 2.57 mm 2.127 mm 1.58 mm 1.641 mm Effective Axial Pole Length 84.428 mm 84.78 mm 55.372 cm 55.94 mm MR Fluids τ MRF- 14ND MRX-145-2BD MRX-145-2BD MRX-145-2BD
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-14ND, which contains 4% 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 triangular displacement excitations at frequencies of.25,.5,.1,.2,.3,.4,.5 and.6 Hz were employed. The input current to the damper coil was constant at,.25,.5,.75, 1, 1.5 and 2 A, respectively. All tests were conducted at a temperature of 8±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 current 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.25,.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 77
2 15 1 A.25 A.5 A.75 A 1 A 1.5 A 2 A 5-5 -1-15 -2-4 -3-2 -1 1 2 3 4 Figure 5.2: Measured force-displacement relationships at velocity of 6 cm/sec for MR damper configuration 1. 2 15 1 A.25 A.5 A.75 A 1 A 1.5 A 2 A 5-5 -1-15 -2-4 -3-2 -1 1 2 3 4 Figure 5.3: Measured force-displacement relationships at velocity of 6 cm/sec for MR damper configuration 2. 78
2 15 1 A.25 A.5 A.75 A 1 A 1.5 A 2 A 5-5 -1-15 -2-4 -3-2 -1 1 2 3 4 Figure 5.4: Measured force-displacement relationships at velocity of 6 cm/sec for MR damper configuration 3. 2 15 1 A.25 A.5 A.75 A 1 A 1.5 A 2 A 5-5 -1-15 -2-4 -3-2 -1 1 2 3 4 Figure 5.5: Measured force-displacement relationships at velocity of 6 cm/sec for MR damper configuration 4. 79
enlarges, and more energy is dissipated. Figs. 5.6 5.9 provide the measured MR damper force-velocity behaviors and comparisons 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 K = 33 Pa-s and m = 1.6 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 experimental and theoretical results is achieved. One can easily see that the analytical and experimental results match well; a maximum error of less than 2.5% is obtained. Fig. 5.1 provides the relationship between the estimated yield stress and input current. Table 5.2 2 15 1 2. A 1.5 A 1. A.75 A.5 A 5-5.25 A A -1-15 -2-8 -6-4 -2 2 4 6 8 Velocity (cm/s) Experimental Results Axisymmetric Herschel-Bulkley Model Figure 5.6: Comparison between measured and predicted force-velocity behavior for MR damper configuration 1. 8
2 15 1 2. A 1.5 A 1. A.75 A.5 A 5-5.25 A A -1-15 -2-8 -6-4 -2 2 4 6 8 Velocity (cm/s) Experimental Results Axisymmetric Herschel-Bulkley Model Figure 5.7: Comparison between measured and predicted force-velocity behavior for MR damper configuration 2. 2 15 2. A 1.5 A 1. A.75 A.5 A 1.25 A 5-5 A -1-15 -2 Experimental Results Axisymmetric Herschel-Bulkley Model -8-6 -4-2 2 4 6 8 Velocity (cm/s) Figure 5.8: Comparison between measured and predicted force-velocity behavior for MR damper configuration 3. 81
2 15 1 5-5 2. A 1.5 A 1. A.75 A.5 A.25 A A -1-15 -2-8 -6-4 -2 2 4 6 8 Velocity (cm/s) Experimental Results Axisymmetric Herschel-Bulkley Model Figure 5.9: Comparison between measured and predicted force-velocity behavior for MR damper configuration 4. 8 7 MR Fluid Yield Stress (kpa) 6 5 4 3 2 1 Damper Configuration 1 Damper Configuration 2 Damper Configuration 3 Damper Configuration 4.2.4.6.8 1 1.2 1.4 1.6 1.8 2 Current (Amp) Figure 5.1: Estimated MR fluid yield stress v.s. input current. 82
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 4.5%. TABLE 5.2: MEASURED MAXIMUM FORCE, DYNAMIC RANGE AND CONTROLLABLE FORCE AND THEIR COMPARISON WITH ANALYTICAL RESULTS. Maximum (at 6 cm/sec) Dynamic Range Controllable Damper 1 Damper 2 Damper 3 Damper 4 Measured 182.1 188.59 21.72 183.66 Predicted 182.48 19. 22.52 185.33 Error (%).26%.74%.4%.91% Measured 9.26 1.26 6.92 7.98 Predicted 9.3 1.36 7.2 8.26 Error (%).43%.98% 4.5% 3.51% Measured 164.32 171.85 176.24 162.33 Predicted 164.74 173.27 177.83 165.31 Error (%).24%.83%.9% 1.84% 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 configuration 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-14ND). Due to the higher iron content, this fluid exhibits an increased saturation point and yield stress. Additionally, 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 83
force for damper 2 is observed. 3) As shown in Fig. 5.1, 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. Usually, a large gap size reduces the magnetic field due its larger magnetic resistance. Consequently, 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. 5.1. 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 primarily due to the stiction phenomenon found in MR fluids (Weiss et al. 1994). Because large 84
acceleration occurs at these points due to the velocity discontinuity of the triangular displacement 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, frequencydependent 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 constant current levels of,.25,.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 temperature of 8±3 F. TABLE 5.3: FORCE-DISPLACEMENT TESTS UNDER SINUSOIDAL DISPLACEMENT EXCITATION. Amplitude (cm) Frequencies (Hz).254.5.1.2.5 1 2 5 1.27.5.1.2.5 1 2.54.5.1.2.5 5.8.5.1.2 85
Figs. 5.11 5.14 show the MR damper force-displacement and force-velocity behaviors under a 2.54 cm,.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 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 relationship is nearly linear). As the input current increases, the force required to yield the MR 2 2 15 15 1 1 5 5-5 -5-1 -1-15 -2-4 -2 2 4-15 -2-5 5 A.25 A.5 A 1 A 2 A Figure 5.11: Force-displacement and force-velocity relationships under 2.54 cm,.5 Hz sinusoidal displacement excitation for damper configuration 1. 86
2 2 15 15 1 1 5-5 5-5 -1-1 -15-2 -4-2 2 4-15 -2-5 5 A.25 A.5 A 1 A 2 A Figure 5.12: Force-displacement and force-velocity relationships under 2.54 cm,.5 Hz sinusoidal displacement excitation for damper configuration 2. 2 2 15 15 1 1 5-5 5-5 -1-1 -15-2 -4-2 2 4 Figure 5.13: Force-displacement and force-velocity relationships under 2.54 cm,.5 Hz sinusoidal displacement excitation for damper configuration 3. 87-15 -2-5 5 A.25 A.5 A 1 A 2 A
2 2 15 15 1 1 5-5 5-5 -1-1 -15-2 -4-2 2 4-5 5 Figure 5.14: Force-displacement and force-velocity relationships under 2.54 cm,.5 Hz sinusoidal displacement excitation for damper configuration 4. -15-2 A.25 A.5 A 1 A 2 A 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-toone mapping relationship between the force and velocity. Because the damper forcevelocity loops does not exhibit such a relationship, these quasi-static models are inadequate 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 presented in Chapter 7. 88
2 15 Measured Predicted 1 5-5 -1-15 -2.2.4.6.8 1 1.2 1.4 1.6 1.8 2 Time (sec) 2 2 2. A 15 15 1. A 1 1.5 A 5 5.25 A A -5-5 -1-1 -15-15 -2-4 -2 2 4 Figure 5.15: Comparison between the predicted and experimentally-obtained responses under 2.54 cm,.5 Hz sinusoidal displacement excitation using the axisymmetric Herschel-Bulkley for damper configuration 1. 89-2 -5 5 Measured Predicted
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 excitations with amplitudes of.254, 1.27, 2.54 and 5.8 cm were chosen. For each amplitude, the MR damper is subjected to the following input current levels:,.25,.5, 1 and 2 A. The tests conducted for each damper configuration are summarized in Table 5.4, and complete experimental results can be found at http://www.nd.edu/~quake/gyang2/appendix.pdf under Section A.3. TABLE 5.4: FREQUENCY-DEPENDENT TESTS. Amplitude (cm) Frequencies (Hz).254.5.1.2.5 1 2 5 1.27.5.1.2.5 1 2.54.5.1.2.5 5.8.5.1.2 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 9
2 2 15 15 1 1 5-5 5-5 -1-1 -15-2 -4-2 2 4.5 Hz.1 Hz.2 Hz.5 Hz -5 5 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. -15-2 2 2 15 15 1 1 5-5 5-5 -1-1 -15-2 -4-2 2 4 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. 91-15 -2.5 Hz.1 Hz.2 Hz.5 Hz -5 5
2 2 15 15 1 1 5-5 5-5 -1-1 -15-2 -4-2 2 4-15 -2.5 Hz.1 Hz.2 Hz.5 Hz -5 5 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. 2 2 15 15 1 1 5-5 5-5 -1-1 -15-2 -4-2 2 4 92-15 -2.5 Hz.1 Hz.2 Hz.5 Hz -5 5 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.
can also see that the maximum damping force increases when the frequency increases due to the larger plastic viscous force at higher velocity. Fig. 5.2 illustrates the comparison between the predicted and experimentallyobtained MR damper responses. As might be expected, the axisymmetric Herschel-Bulkley model predicts the force-displacement well, but fails to portray the nonlinear forcevelocity 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 viscous 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.5,.1,.2 and.5 Hz were chosen. For each frequency, excitations with different amplitudes were applied to the MR damper at current levels of,.25,.5, 1 and 2 A. The tests conducted for each damper configuration are summarized in Table 5.5, and complete experimental 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 93
(a) 2.5 Hz 2.1 Hz 1-1 1-1 -2 5 1 15 2 Time (sec) 2.2 Hz -2 2 4 6 8 1 Time (sec) 2.5 Hz 1-1 1-1 (b) -2 1 2 3 4 5 Time (sec) 2 1-1 -2-4 -2 2 4 2-2.5 1 1.5 2 Time (sec).5 Hz 2.1 Hz 1-1 -2-4 -2 2 4.2 Hz 2.5 Hz 1-1 1-1 (c) -2-4 -2 2 4 2-2 -4-2 2 4.5 Hz 2.1 Hz 1-1 1-1 -2-1 -.5. 5 1 2 1-1 -2-5 5 Figure 5.2: 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. 94-2 -2-1 1 2.2 Hz 2.5 Hz 1-1 -2 Predicted Measured -5 5
8 8 6 6 4 4 2-2 2-2 -4-4 -6-8 -4-2 2 4-6 -8.5 Hz.1 Hz.2 Hz.5 Hz -5 5 Figure 5.21: MR damper responses with plastic viscous effect (sinusoidal displacement excitation with amplitude of 2.54 cm at input current of.25 A). TABLE 5.5: AMPLITUDE-DEPENDENT TESTS. Frequency (Hz) Amplitudes (cm).5.254 1.27 2.54 5.8.1.254 1.27 1.27 5.8.2.254 1.27 1.27 5.8.5.254 1.27 1.27 under a.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- 95
2 2 15 15 1 1 5-5 5-5 -1-1 15- -2-5 5.25 cm 1.27 cm 2.54 cm 5.8 cm -5 5 Figure 5.22: Force-displacement and force-velocity relationships under.2 Hz sinusoidal displacement excitation at input current of 2 A for damper configuration 1. -15-2 2 2 15 15 1 1 5-5 5-5 -1-1 -15-2 -5 5 96-15 -2.25 cm 1.27 cm 2.54 cm 5.8 cm -5 5 Figure 5.23: Force-displacement and force-velocity relationships under.2 Hz sinusoidal displacement excitation with input current of 2 A for damper configuration 2.
2 2 15 15 1 1 5-5 5-5 -1-1 -15-15 -2-5 5-2 -5 5.25 cm 1.27 cm 2.54 cm 5.8 cm Figure 5.24: Force-displacement and force-velocity relationships under.2 Hz sinusoidal displacement excitation with input current of 2 A for damper configuration 3. 2 2 15 15 1 1 5-5 5-5 -1-1 -15-2 -5 5 97-15 -2.25 cm 1.27 cm 2.54 cm 5.8 cm -5 5 Figure 5.25: Force-displacement and force-velocity relationships under.2 Hz sinusoidal displacement excitation with input current of 2 A for damper configuration 4.
(a) 2 2 1-1 1-1.1 inch -2 1 2 3 4 5 Time (sec).5 inch -2 1 2 3 4 5 Time (sec) 2 2 1-1 1-1 (b) 1 inch -2 1 2 3 4 5 Time (sec) 2 2 inch -2 1 2 3 4 5 Time (sec) 2 1-1 1-1 -2.1 inch -2.5 inch -.5.5-2 -1 1 2 2 2 (c) 1-1 1 inch 2 inch -2-2 -4-2 2 4-5 5 2 1 1 2.1 inch.5 inch 1 1-1 -1 2 -.5.5 2 1-1 -2-5 5-2 -2-1 1 2 2 1 inch 2 inch 1-1 -2 Predicted Measured -5 5 Figure 5.26: Comparison between the predicted and experimentally-obtained damper responses under.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. 98
placement amplitude of.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. displacement 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 different. In this section, tests with different constant peak velocities are conducted at input current levels of,.25,.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. TABLE 5.6: CONSTANT PEAK VELOCITY TESTS. Peak Velocity (cm/s) Amplitudes (cm)/ Frequency (Hz).8.254/.5 1.27/.1 2.54/.5 1.6.254/1 1.27/.2 1.27/.1 5.8/.5 3.2.254/2 1.27/.2 5.8/.1 8..254/5 1.27/1 1.27/.5 Figs. 5.27 5.3 provide the damper force-displacement and force-velocity relationships under a sinusoidal displacement excitation having a peak velocity of 8 cm/sec and 99
2 2 15 15 1 1 5 5-5 -5-1 -1-15 -15-2 -5 5-2.25 cm, 5 Hz 1.27 cm, 1 Hz 2.54 cm,.5 Hz -5 5 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. 2 2 15 15 1 1 5-5 5-5 -1-1 -15-15 -2-5 5-2.25 cm, 5 Hz 1.27 cm, 1 Hz 2.54 cm,.5 Hz -5 5 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. 1
2 2 15 15 1 1 5-5 5-5 -1-1 -15-15 -2-5 5-2.25 cm, 5 Hz 1.27 cm, 1 Hz 2.54 cm,.5 Hz -5 5 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. 2 2 15 15 1 1 5-5 5-5 -1-1 -15-15 -2-5 5-2.25 cm, 5 Hz 1.27 cm, 1 Hz 2.54 cm,.5 Hz -5 5 Figure 5.3: 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. 11
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 frequency 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 frequency 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 analytical results using the axisymmetric Herschel-Bulkley model. Note that the damper operates mainly in the pre-yield region under the.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; 12
(a) 2 1-1.254 cm, 5 Hz -2.2.4.6.8.1.12.14.16.18.2 Time (sec) 2 1-1 1.27 cm, 1 Hz -2.1.2.3.4.5.6.7.8.9 1 Time (sec) 2 (b) 1-1 2.54 cm,.5 Hz -2.2.4.6.8 1 1.2 1.4 1.6 1.8 2 Time (sec) 2.254 cm, 5 Hz 1-1 (c) 2 1.254 cm, 5 Hz -1-2 -.2 -.15 -.1 -.5.5.1.15.2-2 -8-6 -4-2 2 4 6 8 2 2 1-1 1.27 cm, 1 Hz 1-1 1.27 cm, 1 Hz -2 2 1-1 -1.5-1 -.5.5 1 1.5 2.54 cm,.5 Hz -2-3 -2-1 1 2 3-2 2 1-1 -2-8 -6-4 -2 2 4 6 8 2.54 cm,.5 Hz Predicted Measured -8-6 -4-2 2 4 6 8 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. 13
Displacement Velocity Acceleration Damper Force Command Signal Force Velocity Displacement Acceleration Displacement lag I II III Time Figure 5.32: MR damper responses under sinusoidal displacement excitation. 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 phenomenon, the displacement measurement is behind the command signal during the force 14
Stress τ τ critical Pre-Yield Post-Yield Strain γ γ critical Figure 5.33: Illustration of stiction phenomenon of MR fluids (Weiss et al. 1994). 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 acceleration is observed (Fig. 5.32). After the damper force exceeds the yield level, the acceleration 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. Therefore, the plastic-viscous force increases, and a damper force increase is observed. 15
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 phenomenon 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,.2 Hz triangular and sinusoidal displacement excitations, respectively. The input current levels are chosen to be,.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 1.5 1 A.5A 1A 2A Acceleration (m/s 2 ).5 -.5 1-1.5 1 2 3 4 5 6 7 8 Time (sec) Figure 5.34: MR damper acceleration response under a 2.54 cm,.2 Hz triangular displacement excitation with input current levels of,.5, 1 and 2 A. 16
.4.3 A.5A 1A 2A.2 Acceleration (m/s 2 ).1 -.1 -.2 -.3 -.4 1 2 3 4 5 6 7 8 Time (sec) Figure 5.35: MR damper acceleration response under a 2.54 cm,.2 Hz sinusoidal displacement excitation with input current levels of,.5, 1 and 2 A. 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 actuator, a mass of about 26 kg was estimated. The masses of the load cell and damper piston were also estimated to be 1 kg (25 kg and 75 kg, respectively). Therefore, the estimated total mass is 36 kg. However, a more conservative mass of 5 kg is utilized in the following discussions. For conciseness, only force responses under the 2.54 cm,.2 Hz triangular and sinusoidal displacement excitations are considered herein. For the triangular displacement 17
excitation, the maximum acceleration is about 1 m/s 2 (shown in Fig. 5.34); therefore, the inertial force due to the connection parts and damper piston is less than.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.4 m/s 2 (shown in Fig. 5.35); therefore, the inertial force due to the solid masses is less than.2 kn. As shown in Fig. 5.37, the overshoots are 5.61 kn when the force is positive and 5.9 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 pressure sensor only measures the pressure in one chamber of the MR damper, it does not 2 8.21 kn 15 1 5-5 -1-15 - 2 4.56 kn -4-3 -2-1 1 2 3 4 Figure 5.36: MR damper force-displacement response under a 2.54 cm,.2 Hz triangular displacement excitation with input current level of 2 A. 18
2 5.61 kn 15 1 5-5 -1-15 -2 5.9 kn -4-3 -2-1 1 2 3 4 Figure 5.37: MR damper force-displacement response under a 2.54 cm,.2 Hz sinusoidal displacement excitation with input current level of 2 A. introduce an inertial force due to solid masses into the measurement. Figs. 5.38 5.39 provide the pressure-displacement relationship under 2.54 cm,.2 Hz triangular and sinusoidal displacement excitations, respectively. Note that the accumulator pressure was charged at 154 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. 5.4 5.41 provide the damper forces estimated using the pressure measurement and their comparison with force measurements 19
3 25 2 Pressure (psi) 15 1 5 A.5 A 1 A 2 A -4-3 -2-1 1 2 3 4 Figure 5.38: MR damper pressure-displacement response under a 2.54 cm,.2 Hz triangular displacement excitation with input current levels of,.5, 1 and 2 A. 3 25 A.5A 1A 2A 2 Pressure (psi) 15 1 5-4 -3-2 -1 1 2 3 4 Figure 5.39: MR damper pressure-displacement response under a 2.54 cm,.2 Hz sinusoidal displacement excitation with input current levels of,.5, 1 and 2 A. 11
2 2 15 15 1 1 5 5-5 -5-1 -1-15 -15-2 -2 Force estimated by pressure measurement Force measurement -4-2 2 4 Displacement(cm) -4-2 2 4 Figure 5.4: Damper force estimated using pressure measurement and its comparison with force measurements under 2.54 cm,.2 Hz triangular displacement excitations 2 2 15 15 1 1 5 5-5 -5-1 -1-15 -15-2 -4-2 2 4-2 Force estimated by pressure measurement Force measurement -4-2 2 4 Figure 5.41: Damper force estimated using pressure measurement and its comparison with force measurements under 2.54 cm,.2 Hz sinusoidal displacement excitations 111
under 2.54 cm,.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 system 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 performance. 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.1,.2 and.5 Hz. The constant input current was set at 2 A. The damper temperature was measured by a Fluke 8T-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 dissipation rate. At.1 Hz (Fig. 5.42), at least 8 seconds are required for the damper temperature to increase from room temperature to equilibrium; however, at.5 Hz (Fig. 5.44), less than 17 seconds are needed. Moreover, a 2 35 kn or 15 25% force drop 112
(a) 16 15 14 13 Temperature ( F) 12 11 1 9 8 Damper Configuration 1 Damper Configuration 2 Damper Configuration 3 Damper Configuration 4 7 1 2 3 4 5 6 7 8 9 1 Time (sec) (b) 18 175 Damper Configuration 1 Damper Configuration 2 Damper Configuration 3 Damper Configuration 4 17 165 16 155 15 145 14 135 13 8 9 1 11 12 13 14 15 16 Temperature ( F) Figure 5.42: Temperature effect test results under 2.54 cm,.1 Hz triangular displacement excitation at an input current of 2 A: (a) temperature vs. time; and (b) force vs. temperature. 113
(a) 2 18 16 Temperature ( F) 14 12 1 Damper Configuration 1 8 Damper Configuration 2 Damper Configuration 3 Damper Configuration 4 1 2 3 4 5 6 7 8 Time (sec) (b) 19 18 Damper Configuration 1 Damper Configuration 2 Damper Configuration 3 Damper Configuration 4 17 16 15 14 13 12 8 9 1 11 12 13 14 15 16 17 18 19 Temperature ( F) Figure 5.43: Temperature effect test result under 2.54 cm,.2 Hz triangular displacement excitation at an input current of 2 A: (a) temperature vs. time; and (b) force vs. temperature. 114
(a) 2 18 Temperature ( F) 16 14 12 1 Damper Configuration 1 8 Damper Configuration 2 Damper Configuration 3 Damper Configuration 4 2 4 6 8 1 12 14 16 18 Time (sec) (b) 2 19 Damper Configuration 1 Damper Configuration 2 Damper Configuration 3 Damper Configuration 4 18 17 16 15 14 13 8 1 12 14 16 18 2 Temperature ( F) Figure 5.44: Temperature effect test result under 2.54 cm,.5 Hz triangular displacement excitation at an input current of 2 A: (a) temperature vs. time; and (b) force vs. temperature. 115
is observed when the damper temperature increases from room temperature to 18 F. This phenomenon is not confined to the large-scale MR damper tested in this dissertation. In a recent test on a LORD small-scale RD-15-3 MR damper, a 15% force drop in compression and a 25% force drop in tension were also observed when the temperature rose from room temperature to 15 F. As we know, the plastic viscosity-temperature dependence is found experimentally as an exponential function of the reciprocal of temperature (Constantinescu 1995). Therefore, as temperature increases, the plastic viscosity decreases, thereby reducing the damping force at high temperatures. However, theoretical 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 2 and 3 F. To see whether the off-centered piston caused the problem, the damper piston in configuration 3 was turned 9. The temperature test was then repeated. One might have 116
expected that the right side of the cylinder would be hotter than the top; in fact, the temperature 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 causing the surface temperature variations. To test this possibility, the swivel bolts were loosened, 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 expansion 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 11 psi. Note that the accumulator pressure can only compensate for a limited volume of air trapped in the damper. If there is too much air present, 117
18 9-9 -18 1 2 3 4 5 6 7 8 9 1 Time (sec) 4 2-2 -4 1 2 3 4 5 6 7 8 9 1 Time (sec) 18 18 9-9 9-9 -18-2.54 2.54-18 -8 8 Figure 5.45: Typical response with force lag due to trapped air in the MR damper. 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 13 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: 118
2 15 1 5-5 -1-15 psi 5 psi 8 psi 11 psi -2-4 -3-2 -1 1 2 3 4 Figure 5.46: Accumulator pressure effect tests under a 2.54 cm,.1 Hz triangular displacement excitation at an input current of 1 A. 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 pressurized 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 119
vacuum Air Cylinder MR Fluid Valve 1 Valve 2 vacuum MR Damper Figure 5.47: Schematic of MR fluid filling setup. between the piston rod and seals and, consequently, the off-state force of the MR damper. Fig. 5.48 displays damper off-state forces ( 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 2-ton large-scale MR damper in various configurations are provided; these include force-displacement tests, amplitudedependent 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 12
2 15 1 5-5 -1-15 psi 5 psi 8 psi 11 psi -2-4 -3-2 -1 1 2 3 4 Figure 5.48: Accumulator pressure effect tests under a 2.54 cm,.1 Hz triangular displacement excitation with an input current of A. 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, quasistatic models are not shown to be sufficient to describe the MR damper nonlinear forcevelocity 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. 121
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 displacement 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 velocity 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 behaviors 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. 122