Page 450 - Mechatronics with Experiments

JWST499-Cetinkunt
JWST499-c07
436 MECHATRONICS Printer: Yet to Come October 9, 2014 8:41 254mm×178mm
y ·

Q Main valve
acc
w (t) Q P p Q V
P
in
Q r A B

P relief
A A

T

y ·

s
7.5 15 22.5 30

FIGURE 7.23: A hydraulic circuit with a fixed displacement pump, main valve, cylinder, and
accumulator. The desired cyclic motion profile is shown below the figure. The pump is sized for
average flow requirement, and the accumulator is sized to support the peak flow requirement.

has to be made up by the accumulator. The discharge volume needed from the accumulator
during up and down motion is the difference between the volume of fluid needed and the
volume of fluid the pump can provide,

V disch = (V cyl up + V cyl down ) − (Q ave ∗ (7.5 + 7.5)) (7.74)
= 687 in 3 (7.75)
The necessary accumulator size is calculated from the empirical formula, where we will
assume a precharge pressure of 90% of minimum pressure, and n = 1.4. Then,
1 1∕1.4
V = 687 ⋅ ∕(1 − (1500∕3000) ) (7.76)
acc
0.9
3
= 1954 in = 8.5 gallon (7.77)
Selecting a 10 gallon accumulator would be a good choice with sufficient safety margin for
the needed volume. During the part of the cycle when there is no motion in the cylinder, the
pump flow is used to recharge the accumulator. It is important to check that the pump flow
and charge time available are sufficient to recharge the accumulator for continuous cyclic
operation. The pump can charge the following volume when the cylinder is in waiting mode,
3
V charge = 45.8in ∕s ∗ 15 s (7.78)
= 687 in 3 (7.79)