Page 589 - Mechatronics with Experiments

Printer: Yet to Come
October 9, 2014 8:41 254mm×178mm
JWST499-c07
JWST499-Cetinkunt
ELECTROHYDRAULIC MOTION CONTROL SYSTEMS 575
Unlike in open-center hydraulic systems, in closed-center systems the operator cannot
modulate the tool force.
For a moving load, Case 2, again we can trace the orifice openings as a function of the
spool position. Let us neglect the inertia force needed to accelerate or decelerate the load.
Then, the cylinder will start to move only after the developed pressure at the output of the
pump is larger than the load pressure (load force/area). In the large load force case versus
small load force case, the spool has to move more, restricting the P–T orifice area, making
it smaller, hence increasing the pressure drop across P–T in order to support the flow rate.
In other words, as the spool position x increases, A PT decreases and P increases. At the
s
P
same time, since the same pressure acts on the cylinder head-end side, it takes a larger
spool displacement in order to initiate the motion against a larger load. Although not shown
in the figure, we assume that there is a check valve between the pump and cylinder ports
so that the flow can only move in one direction: from pump to cylinder when the pump
pressure is larger than the cylinder port pressure. When the cylinder port pressure is larger
than the pump pressure, the check valve blocks the flow from cylinder to pump direction.
By analyzing the same relationship for different spool displacements, we can calculate data
points to plot the speed modulation curves under different loads. The start of motion of
the actuator at different spool displacements against different loads shows up as a variable
deadband in the speed modulation curve. The effective deadband is a function of the load.
Neglecting the force needed to accelerate the load and assuming the only load to overcome
is the gravity load, the load will not move as long as the P–T orifice opening is such that
the pump pressure developed, p , is smaller than F ∕A
P l Cyl,HE
Q = ⋅ D ⋅ w (7.704)
s v p pump
√
Q PT = Q = C ⋅ A (x ) ⋅ p − p T (7.705)
s
s
P
D
PT
F = A ⋅ p < F (7.706)
s Cyl,HE P l
As the P–T orifice continues to close, p will increase in order support the flow Q PT = Q s
P
through a smaller orifice until A Cyl,HE ⋅ p is equal or larger than F , at which point the load
P
l
starts to move. Since we neglected the inertial forces, the pressure developed at the pump
output will be limited to p = F ∕A Cyl,HE +Δp , where Δp PC is the pressure drop across
P
PC
l
the valve between pump and cylinder port, which is at most 100–200 psi range by design.
As P–T closes and less orifice is available, more and more of the flow will go through the
P–C port, hence the speed of the cylinder will increase as spool displacement increases
HE
and P–T closes. For larger loads (F large), in order to develop larger p , the P–T port
L P
must get smaller compared to the lower loads. Hence, for larger loads, the first motion is
achieved after larger spool displacement. In other words, the effective deadband (the start
of motion as a function of spool displacement) is dependent on the load force, not just the
geometric deadband of the spool. When the spool position is such that it fully closes the
P–T port, all of the flow must go through the P–C HE port, while p < p relief , which means
p
while the relief valve is closed. For large spool displacements, as long as p < p relief and
P
A PT = 0.0, the maximum speed of the cylinder for the low and high load condition would
be the same.
Remarks Hydraulic systems which drive mechanisms such as those in construction
equipment, have a linkage mechanism between the hydraulic cylinder and tool (e.g., bucket).
Operator command signals are effectively translated to the speed of the cylinder. The linkage
is simply a power conversion mechanism. If we assume it operates with 100% efficiency,
the hydraulic power in the cylinder is converted to the tool’s mechanical power. That is,
power is converted from flow-rate times pressure to speed (angular or translational) times
force (or torque if translational motion). The control “modulation” of the hydraulic cylinder