Page 594 - Mechatronics with Experiments

JWST499-Cetinkunt
JWST499-c07
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From conservation of power between pump and motor (assuming perfect efficiency), the
speed conversion ratio between engine speed and motor output shaft speed is,
Power (t) = Power (t) (7.729)
p m
p (t) ⋅ D (t) ⋅ w (t) = p (t) ⋅ D (t) ⋅ w (t) (7.730)
p p eng p m m
D (t)
p
w (t) = ⋅ w eng (t) (7.731)
m
D (t)
m
Similarly, the effective gear ratio between the load torque at each track and reflected load
on the engine is
T eng,p (t) ⋅ w eng (t) = T (t) ⋅ w (t) (7.732)
m
m
w (t)
m
T eng,p (t) = (t) ⋅ T (t) (7.733)
m
w eng
D (t)
p
= ⋅ T (t) (7.734)
m
D (t)
m
D (t)
m
T (t) = ⋅ T eng,p (t) (7.735)
m
D (t)
p
Notice that the ratio of pump displacement and motor displacement defines the effective
transmission gear ratio between engine speed and motor speed. The gear ratio that can be
realized with continuous variability is in the range of
D p,min D p D p,max
≤ N = ≤ (7.736)
tr
D m,max D m D m,min
where D , D are minimum and maximum pump displacements, and D , D
p,min p,max m,min m,max
are minimum and maximum motor displacements. Maximum motor speed, when the engine
is operating at a rated speed, can be determined by using the pump and motor displacements
that are maximum. It should be checked whether it meets the specified maximum track
speed requirement.
In short, pump displacement D (t) must be controlled to meet the power demand (i.e.,
p
maximize the available hydraulic power at all times, or only to meet the current demand,
or limit the load on the engine so that engine does not stall, or a combination of all of the
above), whereas the motor displacement D (t) is controlled to deliver the proper traction
m
torque (or force) to meet the load torque demand or commanded speed.
For a given load force, each track needs to deliver half of it, and the torque each track
motor must provide can be determined from,
1
T (t) = ⋅ R ⋅ (F (t)∕2) (7.737)
t
l
m
N g
= D (t) ⋅ p line (7.738)
m
Since, we need to meet the maximum load demand with the maximum motor displacement
condition, then the selected motor should have a maximum displacement that meets the
following condition,
T (t)
m
D ≥ (7.739)
m,max
p
relief
Once a particular motor is selected, then we would know the minimum and maximum
displacements of the motor, [D m,min , D m,max ]. Then for a given load force condition