Page 572 - Mechatronics with Experiments

JWST499-Cetinkunt
JWST499-c07
558 MECHATRONICS Printer: Yet to Come October 9, 2014 8:41 254mm×178mm
Remark on Component Size Matching in Design The above parameters
represent the size of the components of the hydraulic system. It is important for a good
design to have component sizes selected to match each other. That is the pump, valve, and
cylinder sizing must be matched. A simple calculation can determine if the components are
properly sized. For this purpose, one should compare the following size information:

Pump flow capacity: Q = D ⋅ w shaft = 1.0 ⋅ 10 m ∕s
−3 3
p
p
Servo valve rated flow at rated pressure drop across the valve:

3
Q = 1.0 ⋅ 10 −3 m ∕s at p = 1000 psi (6.895 MPa) (7.622)
rv
r
Speed and force requirements of the cylinder:

V max <= Q ∕A a (7.623)
rv
F load < (p max − p ) ⋅ A + (m + m ) ⋅ ̈ y max (7.624)
p
l
a
r
At rated valve flow, the maximum cylinder speed is
V max = Q ∕A a (7.625)
rv
−3
= 1.0 ⋅ 10 ∕0.001 (7.626)
= 1.0m∕s (7.627)
The difference between the
[(p max − p ) ⋅ A − F load ] (7.628)
a
r
is the hydraulic force available for accelerating the inertia and friction losses. Hence,
at most the acceleration we can support is
̈ y = [(p − p ) ⋅ A − F ]∕(m + m ) (7.629)
max max r a load p l
assuming no loss for friction. This “head-room” in hydraulic force available deter-
mines the maximum acceleration the EH system can support at rated conditions and
affects the quality of transient response.
For instance if

3
Q = 1.0 ⋅ 10 −3 m ∕s (7.630)
p
3
Q = 10.0 ⋅ 10 −3 m ∕s (7.631)
rv
at rated pressure drop, this would mean that the valve is too large for this pump, or the pump
is too small for the valve. Likewise, the relief valve should be set to limit the line pressure
to a desired value, and should be sized to so that it has the rated flow capacity to be able
to dump the pump flow capacity when the servo valve is in neutral position. Similarly, if
the desired maximum cylinder speed is larger than the one afforded by rated flow rate, the
pump–valve combination is too small to be able support the desired motion, that is if the
required maximum cylinder speed is V max = 2m∕s, and Q = Q , matched pump–valve,
p
rv
but Q ∕A = 1m∕s. In order to meet the cylinder speed requirement, we can either
a
rv
1. Reduce the cylinder cross-sectional area by a factor of two, hence increase the cylinder
speed by two for the same flow rate. But this in turn reduces the force output capacity
of the cylinder by two.
2. Increase the pump and valve size such that their flow rate is increased by two.