Environmental Engineering Reference
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C d
F
F dy
Fig. 13.10
Bingham model for MR dampers
measured force turned out to be approximately 2 kN when no current was given to
the damper and to achieve the values 12, 22, and 27 kN when the feeding currents
0.9, 1.8, and 2.7 A were provided, respectively.
The force-displacement loops look substantially like a superposition of a vis-
cous and friction-like behavior (Fig. 13.10 ), both depending on the magnitude of
the current intensity [ 15 ]. This behavior, based on the properties of Bingham solids
[ 16 ], can be analytically described as in Eq. 13.1 where x is the relative velocity
between the damper's ends, C d the viscous damping, F dy the plastic threshold, both
functions of the applied magnetic field and, in turn, of the intensity of current i:
F ¼ C d ðÞ x þ F dy ðÞ sgn
ðÞ:
ð 13 : 1 Þ
The relationships C d (i) and F dy (i) have been found by interpolating by a
second order polynomial function the experimental data (Eqs. 13.2 - 13.3 , where A,
kN, s, m are the adopted units of measure) and are graphically described in
Fig. 13.11 .
C d ðÞ¼ 1 : 870 i 2 þ 13 : 241 i þ 6 : 851
ð 13 : 2 Þ
F dy ðÞ¼ 1 : 952 i 2 þ 13 : 962 i þ 0 : 181 :
ð 13 : 3 Þ
The curves in Fig. 13.11 show an asymptotic trend of the MR effect associated
to magnetic saturation of the MR fluid.
A detailed report of the response time analysis of such prototype MR dampers
based on the above-mentioned experimental data is also presented in [ 17 ]. The
promptness turned out to be mainly related to the electric part of the control chain.
''Power source—power sink'' capabilities resulted to be crucial to make the device
able to operate in real time. Furthermore, current-driven operations rather than
voltage-driven resulted to be strongly recommended to dramatically shorten
control lead times. In voltage-driven operations, the power supply provides a fixed
voltage and the current slowly modifies until it reaches the desired value, corre-
sponding to the ratio voltage/resistance. In current-driven operations, the power
supply provides a fast changing voltage spike so as to quickly modify the current
inside the damper, causing in turn a fast change in the mechanical behavior of the
damper. If the current must be increased, the power supply provides for a short
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