Hydraulic-Electric Analogies, Part 2: Voltage and Pressure

May 13, 2014
In Part 2 of this report, we look at how voltage and pressure are similar, but not identical forces for electricity and fluid motion, respectively.
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Last month’s discussion illustrates how voltage and pressure provide the motivating forces for their respective fundamental elements — electrons and molecules of fluid. Voltage is a measure of the difference in potential energy per unit of charge between two points in a circuit or some other electrical space. The unit of voltage is the volt. Voltage is the energy per unit of electrical charge, measured as Newton-meter per coulomb. What’s important is the force element (Newton).

Voltage is represented by two different algebraic symbols: V and E. The source of the V should be obvious, but where does the E come from? The archaic name for voltage was electromotive force and is still, at times, abbreviated as emf. The earliest electrical concepts used fluid flow as analogous and identical processes. Only after Georg Simon Ohm asserted that current and voltage are linearly related did scientists understand that fluid and electrical properties are similar, but not identical mathematically.

Figure 3. This diagram shows that a differential pressure transducer or differential pressure gauge needs two connections because pressure is a measure of the difference in potential between two points in the circuit.

Many people usually reserve the letter E for voltage sources, such as batteries and generators, whereas V is generally reserved for voltage losses — generally caused by resistance and other impeding elements. The use of upper and lower-case letters usually differentiates steady-state values (upper case) and time-varying quantities (lower case).

Pressure, like voltage, is a measure of the potential energy difference between two points in a circuit or in space. It is expressed as force per unit of area, such as lb/in.2 (psi) or N/m2 (Pascal). The Pascal is such a tiny amount of pressure that we generally use it with the mega prefix (MPa).

Pressure can be viewed as related to potential energy by a simple manipulation of the units. For example, multiplying both the numerator and denominator of psi by inches yields energy per unit volume:

psi × in./in. = lb-in./in.3

The key word with pressure is difference, because it is a measure of the potential difference between two points in the circuit.

Measuring voltage and pressure

Voltage and pressure are measured with voltmeters and pressure gauges, respectively. Both are two-terminal devices. That is, two connections must be made to the instrument. This fact is often lost on pressure gauges because of the way they are built and the way we choose to teach students how to use them.

To illustrate the point, consider first, a differential pressure transducer or differential pressure gauge. The schematic symbol is shown in Figure 3. The transducer construction is not carried in the symbol. It could be a Bourdon tube with purely a mechanical display, or it could be an electromagnetic sensing element with a deflectable diaphragm and electrical signal output. We don’t know, and at this point, we don’t care. But it has two input connections because pressure is a measure of the difference in potential between two points in the circuit.

If the positive terminal is connected to, say, the output port of an operating pump, and the negative terminal is not connected to anything, the pressure reading will be a measure of the difference between the pump output pressure and atmospheric pressure. On the other hand, if the negative terminal is connected to a near-perfect vacuum, the reading will be a measure of the absolute pressure of the pump outlet. If the negative terminal is connected to the output port of some control valve, the reading will be the difference in pressure between the pump output and the valve output. Normally, this would be the pressure drop across the valve’s metering element. The point is that the instrument has two terminals, but the user connects both or only one. Doing so determines the meaning of the pressure difference reading.

Figure 4. The digital multimeter is the instrument of choice in the well-equipped electrohydraulic tool kit.

How, then, is the common single-port Bourdon-tube pressure gauge a pressure-difference device? Clearly, there is no second plumbing port. The key to understanding its difference measurement is to consider the mechanical aspects of the Bourdon-tube sensing element. The active port is connected into the fluid-power circuit, and pressure inside the tube causes the tip to straighten. At the same time, atmospheric pressure acts on the outside of the tube and, if the atmosphere is at some absolute pressure, that pressure will attempt to push the tube back to its relaxed state, trying to undo what the internal pressure is doing. If the tube was surrounded by a leak-free enclosure, and that enclosure was outfitted with an external fitting, the instrument would become a fully functioning differential pressure transducer with both ports accessible by the user.

An absolute pressure transducer is a differential sensing device. However, one port is always connected to an internal chamber at almost a perfect vacuum. Thus, it reads the absolute pressure of whatever the one port is connected to.

A voltmeter always has two connections available to the user. Electrohydraulic practitioners will likely use a handheld digital multimeter. One of the two connections is labeled +, V, A, or O and connected to a red lead wire. The other is labeled “COMM” and is connected to a black lead wire. This practice helps keep the algebraic sign straight, which can be important, especially if automatic control systems will be used. The bottom line is that both leads must be connected to the circuit being tested in order to get a usable voltage reading. The digital multimeter is the instrument of choice in the well-equipped electrohydraulic tool kit.

Absolute zero pressure and voltage

The idea of a condition of absolute zero pressure is imaginable, if not actually achievable. If you could completely remove all the gas molecules from a sealed container, the pressure within the container would be at absolute zero. For all practical purposes, enough of the gas molecules can be removed so that a practical perfect vacuum can be achieved, and absolute pressure instruments can be built.

Voltage is different, and this is where analogies begin to break down. There is no such thing as a condition of absolute zero voltage. The most important consequence of this reality is that cavitation in electrical circuits cannot exist. Voltage can be as negative as necessary to satisfy the physical laws of electricity. Not so with pressure. If a region in a hydraulic circuit gets low enough, gases begin to emerge from the fluid (outgassing) and the pressure can never become less than absolute zero. Gases in the hydraulic fluid can lead to serious failure of hydraulic machines of all types.

In contrast, voltage will reach as far into negative values as is necessary to satisfy all the pertinent physical laws. The concepts of meter-in and meter-out are essentially meaningless in electrical circuits. If you want to shut off an electric motor, a switch can be placed in either of the motor’s two terminals — not so with the hydraulic motor.

Figure 5 contains a simple direct current, electric motor circuit and an equally simple hydraulic motor circuit. The electric motor circuit has two control switches, and the hydraulic motor circuit has two on-off valves. The idea is to compare how the two motors are brought to a stop and how the choice of switch or valve differs in the two circuits.

Let’s begin with the two power supplies powered up, the switches and valves in the positions shown, and the motor shafts rotating. Both electrical switches as shown in their closed positions (they are conducting), whereas both hydraulic valves are in their open positions (they, too, are conducting). Therefore, a closed electrical switch is analogous to an open hydraulic valve, and vice-versa.

Valves and switches

Now assume both switches are closed, the motor is powered up and running normally and we open Switch 1. That is, the circuit is interrupted by moving the switch’s movable member. This action removes electrical power from the motor, so it will coast to a stop. While it is coasting to a stop, the motor operates as a generator from the energy stored in the inertia of the rotor and/or load inertia. When all the inertial energy is dissipated, the motor will stop. If we open Switch 2 instead of Switch 1, the result is the same. Power is removed from the motor, and it coasts to a stop when all the inertial energy is dissipated. If we need to bring the motor to a stop suddenly, a more robust method must be used, called dynamic braking. Dynamic braking recovers electrical energy from the rotating motor, creating a load that decelerates the motor.

Figure 5. Two switches in the electric motor circuit and two valves in the hydraulic motor circuit are used to illustrate the ways in which the stopping of the two motors differs from one another.

Stopping a hydraulic motor is much more complex: Valve 1 is referred to as a meter-in valve because it is located in the power inlet circuit of the motor. Valve 2 is referred to as a meter-out valve because it is located at the outlet of the motor. Now, with the motor running normally and the valves in the positions shown, suddenly shifting Valve 1 to its blocked (closed) position removes power from the motor. Because of the inertia of the motor (which is low compared to the inertia of an electrical motor rotor) and its load, the motor will continue to turn, and pressure in the line between Valve 1 and the motor makes precipitous drop toward vacuum conditions. The low pressure results in outgassing in the upper part of the circuit as its fluid is pulled out of the lines while the coasting motor runs as a pump on the inertial effects. Eventually, the fluid is pumped out of the circuit and the motor coasts to a stop on inertial energy.

The external action of the hydraulic motor is similar to that of the electric motor. However, outgassing must be avoided because the air pulled out of solution will find its way into the reservoir, where it can be ingested by the pump, resulting in cavitation damage. Outgassing can be prevented by using a simple fix called an anticavitation circuit.

But what happens if, instead, we shift Valve 2 to its blocked position? The reaction of the motor is not totally predictable without knowing much more about the circuit. However, some insight is useful in pointing out the problems. If the valve is blocked suddenly, the pressure on the “low pressure side” of the motor rises suddenly as the load and motor inertias cause the motor to operate as a pump. The positive displacement of the motor, now in a pumping mode, will cause the low-pressure side to rise to a level that could be damaging to the motor and/or the circuitry. Possible damage can be breakage of the motor shaft when the load inertia is high or rupture of the plumbing on the so-called “low-pressure side.” The point is, a one-for-one analogy between the electrical and hydraulic circuits creates problems in the hydraulic circuit. Neither valve in Figure 5 will do a safe and effective job of stopping the motor.

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