Page 592 - Mechatronics with Experiments

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Let us consider a two track vehicle application and its two hydrostatic transmission
designs and controls. For component sizing, we need the maximum load traction force and
maximum translational speed requirements,

maximum load traction force: F ,
l,max
maximum translational speed: V .
max
In other words, it is desired to have a tracked vehicle with a specified maximum traction
force and maximum travel speed capacity.
Let us assume 100% efficiency in the components, and then take a safety factor
in component sizing after the calculations. Furthermore, if we assume no pressure loss
between pump and motor line, and that the charge circuit makes up for the flushing circuit
flow perfectly, then the pump power is equal to the motor power. In other words, with
the above assumptions, the hydraulic power of pump (converted by pump from the engine
shaft’s mechanical power into hydraulic power) is equal to the hydraulic power delivered
to the motor.
We also assume that the compressibility of fluid in the hydraulic lines is negligable,
which is a reasonably good assumption assuming that the load conditions are such that the
frequency content of the load variations are low. However, if this assumption is not accurate
enough under certain operating conditions (i.e., hitting a rigid wall or impact loading), then
fluid compressibility may need to be taken into consideration in order to better predict the
dynamic behavior of the hydrostatic transmission and accurate dynamic control.
Furthermore, we assume the flushing and charge circuit components are sized so that:
1. Flushing circuit components leak a percentage of rated flow of the circuit, so that
fluid can be cooled and filtered, and then re-introduced to the circuit by the charge
circuit,
Q = 0.1 ⋅ Q (7.712)
flush p,rated
2. The charge circuit is to make up the flushing circuit’s leak at a desired pressure,
Q charge = Q flush (7.713)
p charge = 2 MPa (7.714)
Component sizing decisions are determined by the following two key observations:
The pump determines how much power is converted from mechanical to hydraulic

power, hence the hydraulic power in the circuit at any given time. Assume we have
a constant engine speed, w eng . The power converted by the pump and delivered
to the hydrostatic transmission is determined by the pump displacement, which is
controllable, and pressure in the hydrostatic line,

Power (t) = (p (t) − p (t)) ⋅ D (t) ⋅ w eng (t) (7.715)
p
p
p
r
= T eng,p (t) ⋅ w eng (t) (7.716)
where p (t) is the pressure at the pump output line (high pressure side), p (t)isthe
p r
pressure at the pump input line (low pressure side), D (t) is the pump displacement
p
which has a range from negative to positive displacement through zero displacement
in order to provide bidirectional flow, while the mechanical input shaft speed in
unidirectional flow which is the engine speed, T eng,p (t) is the torque load on the
engine due to the pump. As a result, such a pump has a swashplate angle control
mechanism that requires two solenoids for an electronically controlled version. The
pump power must meet the load power requirement. The pump power is determined
by the engine speed, pump displacement (the controlled variable on the pump), and