Page 121 - Fluid Power Engineering

Hydraulic Pumps 95

The effect of leakage is expressed by the volumetric efficiency, η ,
v
defined as follows:
Q Q − Q L Q L P
t
1
1
η = = =− =− (4.7)
v
Q Q Q RV n
t t t L g
The volumetric efficiency of displacement (geometric) pumps ranges
from 0.8 to 0.99. Piston pumps are of high volumetric efficiency, while
vane and gear pumps are, in general, of lower volumetric efficiency.
The friction is the second source of power losses. The viscous friction
and the mechanical friction between the pump elements dissipate ener-
gy. A part of the driving torque is consumed to overcome the friction
forces. This part is the friction torque, T . It depends on the pump speed,
F
delivery pressure, and oil viscosity. Therefore, to build the required pres-
sure, a higher torque should be applied. The friction losses in the pump
are evaluated by the mechanical efficiency, η , defined as follows:
m

ω T −( T ) T − T
η = F = F (4.8)
m ωT T
where T = Actual pump driving torque, Nm
T = Friction torque, Nm
F
T – T = Torque converted to pressure, Nm
F
ω = Pump speed, rad/s
The third source of power losses in the pump is the pressure losses in
the pump’s inner passages. The pressure, built inside the pumping
chamber, P , is greater than the pump exit pressure, P. These losses
C
are caused mainly by the local losses. The hydraulic losses are of neg-
ligible value for pumps running at speeds less than 50 rev/s, and
mean oil speeds less than 5 m/s. For greater speeds of oil, the pressure
losses are proportional to the square of the flow rate. These pressure
losses are evaluated by the hydraulic efficiency, η .
h

η = QP = P (4.9)
h QP P
C C
where P = Pressure inside the pumping chamber, Pa
C
P = Pump exit pressure, Pa
An expression for the total pump efficiency, η , is deduced as follows:
T
−
QP Q TT P QP QP
η = = F tC = ηη η tC (4.10)
T − v m h ω(TTT−
(
ωT Q T P ω TT ) )
t C F F