Hydraulic machines exhibit many benefits that make them especially suitable for applications requiring the controlled and efficient transmission of power. Not the least of these characteristics is the positive displacement of "in-compressible fluid." When an input member moves, "rigid" fluid is positively forced from the pump. Similarly, this fluid is injected into an actuator, causing positive motion of an output member such as a motor shaft or a piston rod.

This simple interpretation is idealized and leads to a misunderstanding of the limitations and idiosyncrasies of hydraulic machinery. However, it does serve as both a good first approximation of hydrostatic phenomena and as a transition toward more accurate assessments of the phenomena.

The positive displacement phenomenon has been mechanized by inventors and designers in many ways — pistons thrust into cylinders, gear teeth mesh with gear roots, vanes sweep through angular motion and abutments. Other means exist, but all produce similar results. The ultimate necessity of producing these motions results from the practical need for rotary motion to produce positive displacement. Furthermore, reciprocation produces a non-uniform instantaneous positive displacement.

Not-so-positive displacement
As a motor or pump shaft rotates, the amount of fluid it displaces varies with every increment of shaft rotation. This is why pulsating flow and torque result. However, other phenomena also contribute to hydraulic pulsations and speed irregularities. Certainly, hydraulic fluid is not incompressible, which leads to loss of velocity (energy) and springiness in the dynamic response of hydraulic systems. The effects of fluid compressibility generally are well documented and can be included in a study without great difficulty.

Internal leakage (volumetric inefficiency) is also well known, but to date, its effects on the dynamic responsiveness of hydraulic systems have not been well documented. In this, and the next several editions of "Motion Control," we shall explore computer simulation with the intent of developing an explanation how variations in leakage resistance affect dynamic responses — especially low speed, rotational stability.

Low-speed leakage
As the shaft of a hydraulic motor rotates, the instantaneous displacement varies as does the leakage path between inlet and tank. These phenomena can react with other dynamic factors in a hydraulic system to cause irregularities in shaft rotation, especially at low speed.

A phenomenon can be observed in the operation of hydraulic motors at low speed that may seem disturbing unless effects of leakage are included. When a motor is connected to a hydraulic source of relatively low flow, the shaft will rotate with extreme smoothness throughout its entire 360° of travel. However, under load, that same motor will exhibit jerkiness and stick-slip characteristics. This can be correlated with actual test data for instantaneous motor leakage. Practically oriented motor tests will produce data that allow predicting low-speed instability.

To date, all documented explanations of irregularities in low-speed performance have been confined to variations in displacement. Tests have been devised to assess the extent of these displacement variations. For example, SAE's J746b contains a "1-rpm test" to assess the instantaneous effects of changes in motor displacement. NFPA's T 3.9.17 contains a similar test procedure, which was presented to ISO/TC-131/SC-8 at its first meeting decades ago.

For many good and practical reasons, these procedures have been separated from ISO's SC-8 emerging pump and motor test document in preference for inclusion in a special low-speed test standard. As a result of that action, more practical tests for low-speed smoothness have had an opportunity to develop. One of these is the inclusion of the measurement of instantaneous leakage flow during the low-speed test.

Model simulates low-speed operation
The ultimate objective this discussion is to determine the extent to which instantaneous variations in leakage and displacement affect low-speed operation. The two are related, but not in a way that can be correlated across the entire spectrum of motor construction types. Nonetheless, the variations in leakage flow are a more significant contributor to low-speed rotational instability than are displacement variations.

To illustrate the point, the Fluid Power Institute at Milwaukee School of Engineering developed a simulation program based on the results of actual tests in order to determine the extent to which leakage and displacement variations affect smoothness at low speed. An explanation of the model and a summary of the results will be covered in the next several editions of "Motion Control."

The purpose of the simulation is to demonstrate analytically how the leakage resistance variation of a hydraulic motor is the predominant factor contributing to low-speed instability under load. It gives a quantitative assessment of the problem. However, a qualitative assessment identifies two contributing factors:

Increased leakage takes flow away from the displacement chambers and contributes to a speed reduction.

Pressure fluctuations from leakage changes cause unwanted torque variations and thus unwanted accelerations.

Next month, we will begin examining a simulation to reveal how increases in loading affect low-speed stability when variations in leakage are present. The simulation is offered as analytical evidence of the need for an accurate test for assessing not only geometrical displacement variations, but the variations in leakage as the motor shaft rotates as well.

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