Page 562 - Mechatronics with Experiments

JWST499-Cetinkunt
JWST499-c07
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A = output port cross-sectional area, (7.519)
4
V = the volume between the poppet housing and the poppet (7.520)
2
(approximately constant) (7.521)
V = the volume between the poppet housing and the poppet in the section 3 (7.522)
3
= bulk modulus of the fluid (7.523)
l = length of the overlap between the poppet and housing in area 3 (7.524)
3
d = diameter of the cross-section between the poppet and housing in area 3 (7.525)
3
= clearance between the poppet and housing along the back of (7.526)
3
the poppet (area 3) (7.527)
F shear = shear force function (7.528)
Q leak = leakage flow rate function (7.529)
K = current to force gain of the electric actuator (i.e., solenoid) (7.530)
fi
x = preload compression in spring (7.531)
preload
The initial conditions needed for a specific time domain simulation of the poppet
valve behavior are
x (t ) = initial position of the poppet (i.e., zero, closed valve condition) (7.532)
p 0
̇ x (t ) = initial speed of the poppet (i.e., zero, stationary valve condition) (7.533)
p 0
p (t ) = initial pressure inside the poppet chamber (7.534)
2 0
p (t ) = initial pressure inside the poppet chamber section 3. (7.535)
3 0
This pressure may be assumed to stay constant and equal (7.536)
to tank pressure, by setting initial condition (7.537)
to the tank pressure and defining the net flow rate (7.538)
into the area as zero by setting Q (t) = Q leak (t) (7.539)
3t
instead of using the orifice equation for Q (t) (7.540)
3t
Given input pressure p (t) = p (t) and load pressure p (t) conditions, and the control
1 s l
signal i (t), we can determine the motion of the poppet (x (t)), flow rate through the valve
sol p
(Q (t), Q (t)), pressure inside the valve p (t), as well as leakage flow rate and shear forces
2
2
4
Q leak (t), F shear (t) via numerical solution of the above equations.
In proportional control applications of poppet valves, the challenge is the high fre-
quency content of the flow forces acting on the valve and the resulting difficulty in control-
ling the position of the poppet accurately. The control challenge is two fold:
knowing (measuring and/or estimating) the flow force,
having a fast and large enough valve actuator to be able to compensate for the flow
force.

The benefits of poppet valves are that

they seal the flow well in closed position (practically zero leakage, hence excellent

position holding capability under load),
reliability of operation against dirt in the hydraulic fluid (poppet does not easily get

stuck due to dirt unlike the case in sliding spool valves), and
low manufacturing cost of the poppet valves.