Page 590 - Mechatronics with Experiments

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refers to the gain between the lever displacement (operator command signal) and the change
in the speed or force of the cylinder: speed modulation or force modulation. That gain is
built into the hydraulic circuit including the control algorithm, control valves, pump, and
cylinder parameters. Depending on the kinematic conversion relationship from the cylinder
to the tool motion, that gain is further modified. Therefore, the linkage mechanism gain as
a function of linkage angular position effects (multiplies) the control modulation capability
from the operator commands to the motion/force delivered to the tool.
In load driven motion, such as lowering a bucket, if the downward motion speed is so
high that the maximum pump flow cannot supply the other end of the cylinder, there will be
cavitation in the other end of the cylinder. In order to maintain good controllability, cylinder
cavitation should be avoided. Consider the lowering motion of the bucket lift cylinder in
the load driven case. The maximum speed that the cylinder can move without causing
cavitation in the rod-end of the cylinder is
Q max
V max = (7.707)
A Cyl,RE
⋅ D p,max ⋅ w shaft
v
= (7.708)
A Cyl,RE
Let us assume the load is W load , and the head-end area of the cylinder is A HE , and the
valve cylinder-to-tank orifice area is fully open (A v,CT ) and that valve flow rate coefficient
is known for the system, C , then the speed of the cylinder will be
d
W load
p CT = (7.709)
A HE
√
Q = C ⋅ A v,CT ⋅ p CT (7.710)
d
Q
V = (7.711)
A
HE
If V > V , there will be voiding in the rod-end of the cylinder. If the speed of the cylinder
max
exceeds that speed, there will be cavitation in the rod-end of the cylinder.

7.11 EXAMPLE: HYDROSTATIC TRANSMISSIONS

When mechanical power is transmitted from source (i.e., a diesel engine or electric motor)
to a destination load (i.e., a track or wheel) via a pair of pump and motor, it is called a
hydrostatic transmission or hydrostatic drive. Most common applications of hydrostatic
transmissions are tracked vehicles, such as excavators, dozers, agricultural harvesters,
military tanks (Figure 7.110). There are also wheeled vehicles where the wheels are powered
via a hydrostatic transmission. In track-type vehicle applications, two pairs of pump-motor
combinations drive the two tracks of the vehicle. Typically, there are three pumps connected
to the diesel engine to support the two-track hydrostatic transmission system: two pumps
to convert mechanical power to hydraulic power (one for each track), and one pump for
the charge circuit to provide replenishing fluid into the circuit. Two hydraulic motors
(one hydraulic motor for each track) convert the hydraulic power back to mechanical
power (Figure 7.111). For simplicity, the charge circuit, flushing circuit, and line relief
valves are not shown in Figure 7.111. Each hydraulic motor is connected to the track
drive sprocket via a gear reducer. Engine speed can vary between its minimum (low idle)
and maximum speed during normal operation as a function of operator commands and
load conditions. Regardless of the variations of the engine speed within its operating
range, our goal is to control position, and/or speed and/or force at the tracks. This clearly