Hydraulic Pumps and Motors
Gear, vane and piston pumps, displacement, flow, torque, efficiency, drive power and hydraulic motors.
What a pump does
A hydraulic pump does not make pressure; it makes flow by trapping a fixed volume of oil each turn and pushing it into the system. The pressure is whatever the load needs, up to the relief valve setting. The key number is the displacement Vg in cm³ per revolution, the volume delivered per turn with no leakage.
Pump types
| Type | Pressure (bar) | Overall efficiency | Notes |
|---|---|---|---|
| External gear | up to 250 | 80 to 90 % | simple, cheap, tolerates dirt; noisy; fixed displacement |
| Internal gear / gerotor | up to 300 | 80 to 90 % | quieter, compact |
| Vane | up to 175 (280 high-pressure) | 75 to 90 % | quiet; fixed or variable displacement; sensitive to contamination |
| Axial piston (swash plate) | up to 450 | 85 to 95 % | high pressure; variable displacement; the mobile and industrial standard |
| Radial piston | up to 700 | 85 to 95 % | very high pressure, low speed, high torque |
| Screw | up to 200 | 70 to 85 % | very quiet; lubrication and marine |
Displacement, flow and torque
Q = Vg × N × ηv ÷ 1 000 (L/min) T = Vg Δp ÷ (20 π ηm) (N·m)
Drive power is P = Q p ÷ (600 ηoverall) in kW, or T ω. Both give the same answer. The speed is set by the motor, so a faster electric motor means a smaller (cheaper, lighter) pump for the same flow: that is why industrial units run at 1 450 or 1 750 rpm and mobile pumps at 2 000 to 3 000.
Worked example: sizing the press pump
Worked example: the pump for the 160 bar press
The press needs 30.2 L/min at 160 bar, driven by a motor at 1 500 rpm. Take ηv = 0.95 and ηm = 0.92 (typical for a piston pump).
- Displacement: Vg = Q × 1 000 ÷ (N ηv) = 30.2 × 1 000 ÷ (1 500 × 0.95) = 21.2 cm³/rev. Choose the next standard size, 22 cm³/rev: flow 31.4 L/min, so the press runs about 4 percent faster.
- Theoretical flow 31.7 L/min; leakage 1.6 L/min flows from the high-pressure side back inside the pump.
- Torque: T = 0.00002116 × 16 × 10⁶ ÷ (2π × 0.92) = 58.6 N·m on the motor shaft.
- Shaft power = T ω = 58.6 × 157.1 rad/s = 9.20 kW, equal to the fluid power 8.04 kW divided by the overall efficiency 0.874 (9.20 kW). A 11 kW motor is the next standard size above a 9.2 kW load.
- If the press stops and the pump keeps delivering over the relief valve, all 8.0 kW becomes heat. The idling strategy matters (see Designing a Fluid Power System).
Efficiency
Real pumps lose flow to internal leakage (which rises with pressure and falls as the oil gets thicker) and lose torque to friction. A typical piston pump is above 90 percent volumetric efficiency up to 200 bar and over 85 percent overall near the middle of its range; it is worst at low speed, at very high pressure and with very thin hot oil.
At 160 bar the example pump delivers 29.8 L/min of the 31.7 L/min that would come from a leak-free pump, and at 250 bar 28.8 L/min with an overall efficiency of 78 percent. A pump whose leakage has doubled shows up as a slower machine and a hotter oil tank: a good test (Troubleshooting and Safety).
Hydraulic motors
A hydraulic motor is a pump run backwards: oil flow in gives shaft speed, and pressure drop gives torque. N = Q ηv × 1 000 ÷ Vg and T = Vg Δp ηm ÷ (20 π). They deliver high torque from a small, lightweight unit, reverse instantly, stall without damage and can hold a load with a brake or counterbalance valve. Types: gear, vane, axial piston (fast), orbital or gerotor (slow, high torque, wheels and winches) and radial piston.
Worked example: a winch motor
- A 50 cm³/rev motor fed with 30.2 L/min at 160 bar: speed = 30.2 × 1 000 × 0.95 ÷ 50 = 573 rpm.
- Torque = 0.000050 × 16 × 10⁶ × 0.90 ÷ 2π = 114.6 N·m; shaft power 6.88 kW.
- The same motor could be replaced by an electric motor and gearbox, but would be many times heavier for that torque. That is the case for hydraulics in mobile machines.
Fixed, variable and load-sensing
- Fixed displacement: cheap; delivers constant flow, so unused flow goes over the relief valve as heat (see the idle power above). Fine for small or intermittent machines with an unloading valve.
- Pressure-compensated variable displacement: the swash plate backs off when the set pressure is reached, so at standby the pump delivers almost no flow and uses little power.
- Load-sensing: the pump delivers only the flow demanded and holds the pressure a fixed margin (10 to 20 bar) above the highest load. Big energy savings on machines with several actuators.
- Servo-pump (electric speed control): a fixed pump driven by a variable-speed servo motor delivers exactly the flow needed. Quiet and efficient, increasingly common on presses and molding machines.
Related
- Previous: Fluid Power Basics. Next: Cylinders and Actuators.
- Pump Power and Sizing Calculator (for water systems; the power relation is the same).
- Hydraulics and Pneumatics: the whole guide.
FAQ
What is displacement?
The volume of oil a pump delivers per revolution with no leakage, in cm³/rev (or in³/rev). Flow = displacement × speed × volumetric efficiency.
Why does my pump get noisy?
Usually cavitation from a restricted or too-long suction line, aeration from a leaking suction fitting, or a low or cold oil level. Keep suction velocity below 1 m/s and the suction pressure above about 0.8 bar absolute.
Can I run a pump faster than rated?
Not without checking the maximum speed and the inlet conditions: above it the pump cavitates and wears fast.
Is a bigger motor always safer?
An oversized motor is inefficient at part load; choose from the real operating pressure and flow, with a 10 to 20 percent margin.
References
- Esposito, A., Fluid Power with Applications, Pearson (pumps and motors); Rabie, M. G., Fluid Power Engineering, McGraw-Hill.
- ISO 4409 (hydraulic pumps and motors: displacement and performance determination); ISO 3019 (mounting flanges).
- Bosch Rexroth, Hydraulic Pumps and Motors technical data; Parker Hannifin pump catalogs.
Last reviewed: October 2026. Efficiencies are typical; use the maker’s curves.