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valves in their design which makes it impossible for them to operate in motoring mode.
Similarly, some motor designs are such that the hydraulic motor cannot operate in pumping
mode even under over-running (regenerative) load conditions (Figure 7.32).
An over-center motor means that when the swash plate is moved in the opposite
direction relative to its neutral position, the direction of the output shaft speed of the motor
changes even though the input–output hydraulic ports stay the same. An over-center pump
means that when the swash plate is moved in the opposite direction relative to its neutral
position, the direction of the hydraulic fluid flow changes (input port becomes output port,
and output port becomes input port), while the direction of the mechanical input shaft speed
stays the same.
Given the displacement (D , fixed or variable) of a rotary hydraulic motor, the motor
m
output speed (w) is determined by the flow rate (Q) input to it,
w = Q∕D (7.136)
m
Similarly, for linear cylinders, the same relationship holds by analogy,
V = Q∕A c (7.137)
where w is the speed of motor, V is the speed of cylinder, D is the displacement of the
m
motor (volume∕rev), A is the cross-sectional area of the cylinder. If we neglect the power
c
conversion inefficiencies of the actuator, the hydraulic power delivered must be equal to
mechanical power at the output shaft, for the rotary motor
Q ⋅ ΔP = w ⋅ T (7.138)
L
and for the cylinder
Q ⋅ ΔP = V ⋅ F (7.139)
L
where ΔP is the load pressure differential acting on the actuator (cylinder or motor)
L
between its two ports (A and B), T is the torque output, F is the force output. Hence, the
developed torque/force, in order to support a load pressure ΔP ,is
L
T =ΔP ⋅ D m (7.140)
L
F =ΔP ⋅ A (7.141)
L c
If the rotary pump and motor are the variable displacement type, and an input–output
model is desired from the commanded displacement to the actual displacement, a first or
second-order filter dynamics can be used between the D and D cmd ,
m
1
D (s) = D cmd (s) (7.142)
m
( m1 ⋅ s + 1)( m2 ⋅ s + 1)
There are applications which require extremely high pressures with a small flow rate which
cannot be directly provided by a pump. In these cases, pressure intensifiers are used. The
basic principle of the pressure intensifier is that it is a hydraulic power transmission unit,
like a mechanical gear. Neglecting the friction and heat loss effects, the input power and
output power are equal. The only function it performs is that it increases the pressure while
reducing the flow rate. It is the analog of a mechanical gear reducer (increases the output
torque, reduces the output speed). Figure 7.42 shows a pressure intensifier in a hydraulic
circuit. The ideal power transmission between B and A pressure chambers means,
Power = Power A (7.143)
B
F ⋅ V cyl = F ⋅ V cyl (7.144)
A
B
p ⋅ A ⋅ V cyl = p ⋅ A ⋅ V cyl (7.145)
B
A
A
B
p ⋅ A = p ⋅ A A (7.146)
B
A
B