Page 545 - Mechatronics with Experiments

October 9, 2014 8:41 254mm×178mm
Printer: Yet to Come
JWST499-c07
JWST499-Cetinkunt
ELECTROHYDRAULIC MOTION CONTROL SYSTEMS 531
(t ) and fluid volume in the
where the initial conditions of the accumulator pressure p acc 0
(t ) should be specified, K
accumulator V acc 0 acc is the flow rate gain across the valve between
the accumulator and the line. Then, the dynamic behavior of the accumulator state (its
pressure and fluid volume at any given time) can be predicted by solving the initial value
problem.
As an analogy to electrical systems, the capacitance C acc of the accumulator (as an
energy storage device) is defined as
( )
V disch
C = (7.404)
acc
p − p
max min
similar to electrical capacitance defined as C = (∫ i(t)dt)∕V = Q∕V, where fluid volume
in the accumulator is analogous to the electron charge accumulated in a capacitor, and
pressure is analogous to voltage.
Notice that the sign function and absolute value of the pressure differential in the
flow rate equation expresses that flow can flow into the accumulator from the line or from
accumulator to the line. The pressure p line is the line pressure connected to the accumulator.
If the accumulator is placed on the pump-valve side, this can be taken as the pump pressure.
Likewise, if the accumulator is connected to the cylinder-valve side, then the line pressure
is the pressure of the corresponding cylinder line.
In summary, the accumulator design variables and operating variables are as follows:
The accumulator is designed to operate within the range of [p , p ] pressure, with
min max
initial precharge pressure of p , and accumulator discharge volume capacity V and
pre disch
total accumulator volume V . Given the accumulator valve flow gain K , and initial
acc,g acc
conditions of the accumulator volume and pressure, (V (t ), p (t )), and the line pressure
acc 0 acc 0
condition p line (t), the state of the accumulator can be calculated using the above flow rate
(Q acc (t)) volume (V acc (t))and pressure (p acc (t)) relations.
p – maximum operating pressure, above which the line relief valve should open.
max
p min – minimum operating presssure, below which the bladder would start to contact

the accumulator valve and is not desirable.
p – precharge pressure is the gas (i.e., nitrogen) pressure in the accumulator before
pre
having any fluid on the liquid side.
V – accumulator volume at the gas side at precharge condition (this is also the

acc,g
total accumulator volume).
V – accumulator discharge volume, the maximum fluid the accumulator can

disch
discharge.
K acc – flow coefficient of the accumulator poppet valve.

Q acc (t) – flow rate in or out of the accumulator to/from the line.

(t ) – liquid volume in the accumulator and its initial condition value.
V acc (t), V acc 0

p acc (t), p acc 0
(t ) – pressure in the accumulator and its initial condition value.

p line (t) – line pressure, the pressure of the hydraulic circuit line the accumulator is

connected to.
Summary of Hydraulic Equations The algebraic sum of flow rate in and out of
a cross-section (a node) is equal to zero. This is the analogy of Kirchoff’s current law: the
algebraic sum of currents at a node is zero.
∑ ∑
Q − Q out = 0 (7.405)
in
∑ ∑
i − i out = 0 (7.406)
in