You may have conducted this experiment in school: Your science teacher gives you a plastic syringe. With the syringe full of air and the plunger retracted, she tells you to block the outlet with your finger, then attempt to push the plunger forward. You discover you are able to compress the air in the syringe by a significant amount.
She then tells you to repeat the experiment with the syringe full of water. This time, the result is different. No matter how hard you try, you cannot compress the water in the syringe.
Seeing is believing, and to a 12-year old, this experiment demonstrates that gases are highly compressible and liquids are apparently incompressible. By the way, if you didn't perform this experiment at school, you can try it at home!
Figure 1. Pressure vs. Volume
The effectiveness of this simple physics experiment is illustrated by the fact that in my work as a fluid power engineer, I regularly meet people who believe liquids, including hydraulic oil, are completely incompressible. But this is not their fault.
I don't remember my science teacher qualifying the obvious results of this experiment by explaining that compared to gases; liquids are highly incompressible - but compressible nonetheless!
In the July-August 2007 issue of Machinery Lubrication, I discussed the topic of the perfect hydraulic fluid with respect to viscosity. This ideal fluid would have a constant viscosity of 25 centistokes, regardless of its temperature.
Another property of this ideal but nonexistent hydraulic fluid would be perfect stiffness, similar to the apparent stiffness of the water in the syringe in the school science experiment.
A fluid's compressibility is defined by its bulk modulus of elasticity, which is the reciprocal of compressibility. Meaning, as the bulk modulus of elasticity increases, the compressibility decreases.
The bulk modulus of a fluid is also nonlinear, meaning when the change in volume with pressure is plotted on a graph, the result is a curve rather than a straight line.
Tangent bulk modulus relates to the slope of the curve at any given point and, therefore, the true rate of change in volume at a particular working pressure.
Secant bulk modulus is the ratio of total change in pressure to total change in volume, given by the slope of the line from the origin to a particular point on the curve.
Bulk modulus is further defined as isothermal, where the heat associated with compression is dissipated (constant temperature), or isentropic, where the heat associated with compression is not dissipated and so both pressure and thermal expansion are considered.
Isentropic can be viewed as dynamic bulk modulus and isothermal as static bulk modulus. The former is typically pertinent to modern, high-response hydraulic systems.
Bulk modulus is an inherent property of the oil and, therefore, an inherent inefficiency of the hydraulic system. The fluid in the pipeline and actuator must be pressurized, and consequently compressed, before it will move a load. (Compression of 0.4 to 0.5 percent by volume per 1,000 psi - up to 4,000 psi, is typical for mineral oil).
Because this compression of the fluid requires work at the input — which cannot be converted to useful work at the output — it is lost work and therefore a contributing factor to the overall inefficiency of the hydraulic system. The larger the actuator and the faster the required response time, the higher the inefficiency attributable to bulk modulus.
And in high-performance, closed-loop electrohydraulic systems, deforming oil volumes affect dynamic response, causing possible stability problems such as self-oscillation.
Bulk modulus varies with base stock. For example, naphthenic oils have a higher bulk modulus than paraffinics, and unlike viscosity index, bulk modulus cannot be improved with additives. However, hydraulic equipment users can take steps to minimize the inefficiencies and potential control problems associated with compression of the fluid.
The first step to minimizing these problems is to ensure hydraulic equipment doesn't run hot. Compressibility of the fluid increases with temperature. Mineral hydraulic oil is approximately 30 percent more compressible at 100°C than it is at 20°C. Of course, there are many reasons why one should never allow hydraulic equipment to run hot - most of which I have discussed in this column. Reduced bulk modulus is an additional reason.
The second step is to prevent conditions that cause aeration. The school science experiment explains that air is 10,000 times more compressible than oil. One percent of entrained air by volume can reduce the isothermal tangent bulk modulus of oil to as low as 25 percent of the normal value.
At this point, it is important to distinguish between entrained air (bubbles typically with a diameter of less than one millimeter dispersed within and throughout the bulk fluid) and dissolved air. Hydraulic oil typically contains between six and 12 percent of dissolved air by volume. This dissolved air has no measurable effect on bulk modulus (or viscosity) provided it stays in solution.
While controlling aeration is largely a design issue - for example, the amount of dwell time the fluid has in the tank - proper maintenance also plays an important role.
Dissolved air comes out of solution as temperature increases, which is another reason to maintain appropriate and stable operating temperatures. Oxidative degradation and water contamination inhibit the oil's ability to release air, often resulting in an increase in entrained air volume and thus compressibility.
Given that the perfect hydraulic fluid — one with infinite stiffness, exists only in our imagination, and in view of the current trend toward hydraulic equipment with higher operating pressures, higher power density and faster response — it's more important than ever to consider the operational effects of fluid compressibility on hydraulic equipment.