Page 587 - Mechatronics with Experiments

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JWST499-c07
JWST499-Cetinkunt
ELECTROHYDRAULIC MOTION CONTROL SYSTEMS 573
A = 0 (7.692)
PC RE
A C HE T = 0 (7.693)
Notice that the valve has a large deadband. As the spool moves for up to about 25% of
its total travel range, none of the orifices to either side of the cylinder open. In many
cases, this deadband is built on purpose into the valve design in order to reduce leakage
and unintended motion, at the expense of dynamic response. When the spool moves in
the opposite direction, the orifice opening values change, establishing different hydraulic
connection between ports P, T, C HE , C RE . Let us consider the case that spool moves to the
left side in the following increments of its total displacement: 0, −25, −50, −100%. As that
happens, the orifice openings between ports, pump, tank, cylinder head-end, and cylinder
rod-end vary as follows,

A ≠ 0 (7.694)
PT
A = 0 (7.695)
PC HE
A = 0 (7.696)
C RE T
A ≠ 0 (7.697)
PC RE
A C HE T ≠ 0 (7.698)
resulting in cylinder motion in the opposite direction.
Flow rate across each orifice is defined by the following relationship,
√
Q v,ij = C ⋅ A (x ) ⋅ Δp ij (7.699)
D
ij
s
where i, j represent the ports P, T, C , C and their five possible connection possibilities
HE RE
in an open-center valve, A (x ) represents the orifice area opening as a function of spool
ij s
position between the ports, and Δp represents the pressure drop across the port, C is the
ij D
valve gain.
For a given physical valve, all five of the orifice areas as a function of spool dis-
placement are known strictly based on the valve geometry: A (x ), A (x ), A (x ),
PT s PC HE s PC RE s
A C HE T (x ), A C RE T (x ). In addition, the valve gain C is known as a specification. If it is
D
s
s
not available, C can be measured as a calibration parameter using the flow rate equation
D
above: under known pressure drop conditiond, measured flow rate, and orifice opening,
then calculate the C from the above equation. Let us assume that the pump parameters
D
(volumetric displacement D and volumetric efficiency ) are specified and the input shaft
P
v
speed of the pump (w pump )isgiven.
Let us consider two different cases: case 1 is a blocked load, and case 2 is a moving
load case with light and heavy load conditions (Figure 7.109).
Case 1: Blocked load case (force modulation curve). Since the load is blocked and the
cylinder cannot move, the hydraulic system controls the force applied on the load.
Case 2: Moving load case for light load and heavy load. In this case, we will assume the
force needed to accelerate/decelerate the load is negligable (inertial force is neglected)
for the purpose of obtaining the steady-state force and speed modulation curves.
In both cases, consider that the spool is moved from left to right starting at center
position. We can assume similar behavior in the opposite direction. Analysis of case 1 gives
us the steady-state force modulation curves for the open-center hydraulic system. In other
words, it defines in steady-state the force output at the cylinder rod (F) as a function of the
spool position (x ). As the valve moves from neutral position towards 25%, then 50% and
v
100% displacements, the orifice openings change according to the orifice functions shown
in Figure 7.108. Yet, since the load is blocked, the cylinder will not move. All of the flow