Page 595 - Mechatronics with Experiments

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JWST499-c07
JWST499-Cetinkunt
ELECTROHYDRAULIC MOTION CONTROL SYSTEMS 581
(i.e., worst case) F , we can calculate the line pressure developed when the motor is at
l
its maximum displacement,
1
T (t) = ⋅ R ⋅ (F (t)∕2) (7.740)
m
t
l
N g
T (t)
m
p line = (7.741)
D m,max (t)
And the line pressure under the same load condition when the motor is at its minimum
displacement is
1
T (t) = ⋅ R ⋅ (F (t)∕2) (7.742)
m t l
N
g
T (t)
m
p = (7.743)
line
D (t)
m,min
In other words, when track conditions face a load condition, T , depending on the value of
m
the motor displacement at any given time, line pressure will be at a value in the following
range, never exceeding the relief pressure since relief valves would open at that condition,
( )
T m T m
≤ p line ≤ min , p relief (7.744)
D D
m,max m,min
Another way to view the dynamics of the system is in terms of the maximum traction that
can be developed at the tracks and ground contact. If the ground conditions are such that a
smaller value of traction force can be developed, then the tracks would start slipping when
the the torque output from the motors exceeds the maximum torque that can be supported
by the track-ground conditions. This may happen even before relief pressure is reached.
For instance, in poor traction conditions (i.e., muddy and slippery ground conditions with
poor friction, hence poor traction capacity), we quickly observe slipping of the tracks.
Track slip condition should be minimized since it represents the wasted energy condition.
Component Sizing for Hydrostatic Transmissions Let us consider a
numerical example for a hydrostatic transmission circuit component sizing. Given hydro-
static transmission specifications for an application, such as an excavator model,
the hydrostatic drive should be able to deliver traction force of F l,max = 100 000 N,

and
a linear speed of V max = 10 km∕h.

Based on this specification, a designer must select a pair of hydraulic pump-motors, as well
as the sprocket radius, final drive gear ratio, and charge pump.
The sprocket radius and final gear reducer ratio are typically chosen from a range of
standard values depending on the power levels involved in the application. Let us assume
that the final drive gear ratio and sprocket radius are
N = 50 (7.745)
g
R = 0.5 m (7.746)
s
Let us assume that the flushing circuit is sized to approximately flush about 10% of
the flow rate in the line. Then, the charge pump should be sized to provide this flow rate at
the nominal charge pressure. Hence, the selection criteria for the charge pump is
Q flush = 0.1 ⋅ Q p,rated (7.747)
Q charge = Q flush (7.748)
p charge = 2 MPa (7.749)