Page 232 - Servo Motors and Industrial Control Theory -

230 Appendix C

Note that the data presented in this and the following problems are typical of
ER fluids and for real applications you should obtain the exact values from the
manufacturers of these fluids. You should also note that ER fluid is the subject of
research to ensure that they are reliable and durable. Also researchers are trying
to develop ER fluid with a larger maximum shear stress. If you are interested
in these fluids you should follow and obtain up to date data from researchers in
these fields.
2. ER fluid may be used as flow control like valves. For this application consider
two coaxial cylinders as shown below. The length of cylinder is 60 mm and
its diameter is also 60 mm, the gap between two cylinders is 0.5 mm. When a
voltage of 2 kV is applied across the cylinders the ER fluid produces a maxi-
mum of shear stress of 2 KN/m . For the above dimensions determine the maxi-
2
mum pressure difference where the valve stops the fluid from flowing through
the valve. The above dimensions are considered because the author has been
involved on practical experimentations of such valves. Assume that the input
pressure is as determined above; hence calculate the flow rate through the valve
when the voltage is removed from the valve. Assume that the viscosity of the
−5
2
fluid is 5 × 10 (m /s).
0V

Inlet Outlet
ER Ruid

V+

Repeat the analysis if the length of the valve is increased to 120 mm.
3. One of the possible applications of ER fluid is in design of variable damper.
The figure below show a schematic diagram of the system in which two coax-
ial cylinders with gap of 0.5 mm are constructed and the gap is filled with ER
fluid. When approximately 2 kV is applied across the gap the maximum shear
stress of the fluid becomes 2 KN/M . When the voltage is removed the solidified
2
−5
fluid becomes like ordinary fluid with viscosity of approximately 5 × 10 (m /s).
2
Assume that the dimension of the inner piston is 40 mm in diameter and 60 mm
in length.
Determine the damping coefficient of the damper for two cases of when the volt-
age is applied and for the case when the voltage is removed. If you have difficul-
ties consult a fluid mechanics book.