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A hydrostatic transmission (HST) exists any time a hydraulic pump is connected to and dedicated to one or more hydraulic motors. Versatility is achieved by making either or both the pump and motor(s) variable displacement. The result is a continuously variable transmission (CVT).
An HST is preferred over shifted gear transmission in many cases because of the stepless way in which the HST's speed ratio can be changed. Many such CVTs are manually changed, while others change automatically. A popular automatic configuration uses a manually adjusted pump displacement with a pressure compensated motor. This configuration results in the so-called "constant output power" transmission. These transmissions produce a speed-torque characteristic that is hyperbolic, and they are used primarily to prevent lugging of the prime mover. There are others, but the aim here is to concentrate on the implementation of the models.
Establishing a model
Figure 1 shows the first step in connecting Type 2 pump and motor models when configuring a hydrostatic transmission. Input torque to drive and power the pump is from some unspecified source at the left in Figure 1. Similarly, the motor output shaft is supplying power to some unspecified rotational load to the right.
The A and B Port nomenclature of the two machines is not standard in either ISO or US standards. Rather, it's been copied from the standardized practice used with valves. In fact, I'll sometimes refer to them as the work ports of the pump and motor, as is common with directional valves.
The A port of the pump connects to the A port of the motor, the CD ports of pump and motor are connected together, as are the B ports of the pump and motor. In this way, the output of the pump feeds and powers the motor, and the spent fluid from the B port of the motor supplies the inlet ( B port) of the pump. Meanwhile, internal leakage that makes its way into the pump and motor cases is combined to also feed the pump inlet through internal leakage passages.
Real-world conditions
In a perfect world, this configuration might be practical. But it is not, for at least two reasons.
First, the internal leakage that empties into the respective cases can only escape by...