Electrohydraulics: hydraulic power and proportional control

Executive summary

Electrohydraulics joins two worlds: the brute force of hydraulics and the intelligence of electrical control. A cylinder turns pressure into force following F = p·A, and the power that moves the machine is P = p·Q (pressure times flow). A proportional valve or a servo valve takes an electrical signal and meters it into dosed flow or pressure, closing a position, velocity or force loop. Here you get the fundamentals with formulas, a worked example with exact numbers, and the honest criterion for when hydraulics still wins over electric actuation: when you need a lot of force in very little space.

Who this is for

For maintenance, project and plant engineers working with presses, injection machines, press brakes, shears, mobile or process machinery driven by hydraulic cylinders and motors. If you have to size a hydraulic power unit (HPU), choose between a hydraulic and an electric drive, or understand why your power pack draws the power it draws, this article gives you the calculation framework. It is not a treatise; it is the numerical baseline used on the plant floor every day.

The real problem on the plant floor

The most expensive mistake is not a badly chosen valve: it is oversizing the hydraulic power unit without understanding the power chain. A large electric motor is specified "just in case", the pump delivers more flow than needed, the excess dumps across the relief valve and turns into heat. The result is a system that spends kilowatts heating oil, demands extra cooling and wears seals. The opposite mistake also happens: choosing hydraulics where an electric servo drive would do the same job at half the consumption. Both errors come from not separating three things: the force the load demands, the flow the speed imposes, and the power that results from multiplying them.

Engineering fundamentals

All of electrohydraulics rests on three equations. First, cylinder force:

F = p · A

where p is the port pressure and A the effective piston area. On the extend stroke, A is the full bore circle; on retract, it is the annular area (bore minus rod). Second, rod velocity comes from the incoming flow:

Q = A · v

more flow, more speed; at equal flow, a larger-area cylinder moves more slowly. Third, hydraulic power is the product of pressure and flow:

P = p · Q

In practical units, with p in bar and Q in litres per minute, this becomes P[kW] = p · Q / 600. The 600 is no magic: it is the constant that converts bar·(L/min) into kilowatts (Hydraulics Online, 2024). There is an elegant check: the mechanical power the cylinder delivers to the load is P = F · v, and since F = p·A and Q = A·v, it follows that F·v = p·A·v = p·Q. Hydraulic and mechanical power coincide except for the cylinder's real losses (seal friction, backpressure), which typically subtract 5–15 %.

The electrical layer is built on top of this. A proportional valve receives a signal (for example 0–10 V or 4–20 mA), moves its spool continuously and passes a flow or sets a pressure proportional to that signal, with a linear relationship and low hysteresis. A servo valve does the same with much higher speed and precision (wider bandwidth, near-zero overlap), in exchange for higher cost and a demand for very clean oil (Bosch Rexroth, 2024). That is how a loop closes: a sensor measures position or force, the controller compares it against the setpoint and trims the valve.

How to apply it step by step

• 1. Define the load: what maximum force F must the cylinder overcome? Add margin for friction and peaks.
• 2. Pick the area and solve for pressure: set a bore diameter, compute area A and get the working pressure p = F / A. It must stay below the cylinder rating (for example 160 bar in the ISO 6020-2 series).
• 3. Turn speed into flow: with the desired rod speed v, the flow is Q = A · v. That is the flow the pump must deliver.
• 4. Compute the hydraulic power: P = p · Q / 600 in kW. That is the power the pump puts into the fluid.
• 5. Climb the chain to electrical power: divide by the pump efficiency and then by the motor efficiency to get the power pack's real draw.
• 6. Choose the control: fixed flow (on/off valve) for simple cycles; a proportional or servo valve if you need to meter velocity, position or force in a closed loop.

Worked example with numbers

A hydraulic press must exert a force of F = 120 kN with a cylinder of 100 mm bore diameter, extending at v = 0.10 m/s over a 0.5 m stroke. We compute the full power chain step by step:

Assumptions: extension on the full bore stroke (not annular), practically incompressible oil, no line losses, overall pump efficiency 0.85 and electric motor efficiency 0.90. The 152.8 bar pressure stays below a 160 bar cylinder, so the chosen diameter is valid; had it come out higher, simply increasing the diameter would lower the pressure. The overall electrohydraulic efficiency to the load is 12.0 / 15.69 = 76.5 %: for every 15.69 kW the motor draws, 12.0 kW reach the load as useful work and the rest is lost as heat. The 0.5 m stroke at 0.10 m/s takes 5.0 s. Note the defining trait: we picked the area first, and pressure and flow followed from it; power does not depend on the cylinder but on the force × velocity product.

When it applies and when it does not

Choose hydraulics when you need very high force in little space: presses, injection, forging, mobile machinery, shears. Its edge is power density: an axial-piston motor can approach 10 kW per kilogram, far above a typical industrial electric motor (0.05–0.1 kW/kg) (Mobile Hydraulic Tips, 2023). It also holds a static load without drawing power and tolerates overloads. Choose an electric drive (servo motor + ball screw) when energy efficiency, cleanliness (no oil leaks), repeatable position accuracy and cycles with lots of positioning and little force dominate. The boundary has shifted: electric is advancing in mid-size machines, but hydraulics remains irreplaceable at the extreme of peak force and stiffness.

Common mistakes

• Oversizing the power unit: more flow than needed dumps across the relief and becomes heat; you pay for it in energy and cooling.
• Confusing pressure with power: high pressure with no flow is little power; consumption is set by the p·Q product, not by the gauge alone.
• Forgetting the annular area: on retract the force and speed change because the area is smaller; sizing only for extension leaves the return badly calculated.
• Fitting a servo valve where a proportional will do: you pay the price and the filtration demand for nothing; most machine control is solved by a proportional valve.
• Ignoring the chain efficiency: computing only the hydraulic power and not dividing by the pump and motor efficiencies underestimates the real electrical draw.

Decision checklist

• Do you know the real maximum load force, with margin for friction and peaks?
• Does the working pressure p = F/A stay below the cylinder rating?
• Did you compute the flow Q = A·v from the required speed?
• Did you get the power as P = p·Q / 600 and check it against F·v?
• Did you climb the chain by dividing by the pump and motor efficiencies?
• Does the control (on/off, proportional or servo valve) match the accuracy the process actually needs?

Frequently asked questions

How do you calculate the hydraulic power of a cylinder?

It is pressure times flow. In practical units, P[kW] = p[bar] × Q[L/min] / 600, where the 600 only converts units. If you know force and speed, the same value appears as P = F × v, because the cylinder's mechanical power is the hydraulic power minus losses. A cylinder pushing 120 kN at 0.10 m/s delivers 12.0 kW, which is the p·Q the pump must supply.

When is a hydraulic actuator better than an electric one?

When you need a lot of force in little space. Hydraulics wins on power density: since F = p·A and pressures reach 160 or 250 bar, a compact cylinder exerts hundreds of kN. Electric wins on overall efficiency, cleanliness and position accuracy; hydraulics wins on peak force, stiffness and holding a static load without drawing power.

What is the difference between a proportional valve and a servo valve?

Both convert an electrical signal into proportional flow or pressure. The servo valve is faster and more precise (wider bandwidth, lower hysteresis, near-zero overlap), but costs more and demands very clean oil. The proportional valve covers most industrial position, velocity and force control with good linearity and more tolerance to contamination. You pick a servo valve only when the loop needs very fast response and fine accuracy.

SEMHYS tools

The same P = p · Q structure that governs electrohydraulics rules any fluid system: in water pumping, power is also pressure times flow (written there as power = ρ·g·Q·H). If your work is on the water side —centrifugal pumps, head, NPSH, operating point—, our free pump calculator gives you the total dynamic head, the cavitation margin and the power to size the equipment properly. And if your case is a machine hydraulic drive or a hydraulic-vs-electric decision you want reviewed with engineering judgement, see the advisory options in the SEMHYS shop.

References

1. Bosch Rexroth (2024). Proportional and servo valves — Industrial Hydraulics (product technical documentation).
2. Esposito, A. (2013). Fluid Power with Applications (7th ed.). Pearson.
3. Hydraulics Online (2024). Hydraulic Calculations and Formulas (technical resource; formula P[kW] = p·Q/600).
4. Mott, R. L. (2015). Applied Fluid Mechanics (7th ed.). Pearson. Reference cylinder standards: ISO 6020-2 / ISO 6022; NFPA (National Fluid Power Association).