Page 588 - Mechatronics with Experiments

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(i) Low load (ii) High load
F
mg
.
C RE -T X
C RE -T

P-C HE
P-C HE
P-T
P-T

.
X - speed
Low load
P relief * A C he
F max
High load

X s 25% 100% X s
(a) (b)
FIGURE 7.109: Open-center hydraulic system, operating conditions: (a) blocked load and
steady-state force modulation curve, (b) moving load (low and high load cases) and
steady-state speed modulation curves.

has to go through the P–T port, until the relief valve pressure is reached. As a result, from
the flow equation, since we know the orifice opening and the flow rate that must go through
the P–T orifice, we can determine the pressure drop developed across the P–T port. This
same pressure is applied on the cylinder head-end as well. Hence, the applied force can be
calculated as a function of spool displacement. The resulting force as a function of spool
displacement is called the force modulation curve.

Q = ⋅ D ⋅ w (7.700)
s v p pump
√
Q = C ⋅ A (x ) ⋅ p − p = Q (7.701)
PT D PT s P T s
F (x ) = A ⋅ p (x ) (7.702)
s s Cyl,HE P s
From these equations, we can calculate the force modulation curve as a function of the
spool displacement (Figure 7.109). For a given constant Q and spool position x , we know
s s
A (x ). Then p can be determined as a function of x . Since A (x ) is large when x is
PT s P s PT s s
small, and gets smaller when x increases (Figure 7.108), the p (x ) gets larger as x gets
s P s s
larger (Figure 7.109a). Notice that p ≤ p relief , which defines the maximum force that can
P
be applied,
(F ) = A Cyl,HE ⋅ p relief (7.703)
s max
Notice that the modulation curve is also a function of the engine speed, hence the modulation
can be also affected by changing the engine speed. This is not possible in a load sensing
(closed-center) hydraulic system.