Gear Pump

How a gear pump works

The counter-intuitive part is that fluid never passes through the mesh. The meshing teeth in the center form a moving seal; the fluid is carried around the outside in the pockets between the teeth and the bore. Trace one cycle from the inlet:

• Suction side: as two teeth disengage, the cavity between them expands. The growing volume drops the local pressure, and atmospheric (or charge) pressure pushes fluid in to fill it.
• Transport: each filled tooth space is sealed against the casing bore and carried bodily around the periphery — half the displacement on each gear, in opposite directions.
• Discharge side: at the outlet the teeth re-mesh. A tooth from one gear advances into the valley of the other, collapsing the cavity and forcing its trapped fluid out into the pressurized discharge line.
• The seal: the line of contact at the mesh blocks the high-pressure outlet from short-circuiting back to the low-pressure inlet. Whatever leaks past it is the pump's slip.

Only one gear is driven; the second is turned by the mesh, exactly like any gear pair. Both must rotate so their teeth move away from each other at the inlet and toward each other at the outlet — get the rotation direction wrong and inlet and outlet swap.

The governing flow equation

The defining number is displacement per revolution, D — the total volume of fluid carried around per turn (summed over both gears). For an idealized external gear pump it is well approximated by the swept annular volume:

D ≈ 2 · π · b · (R_a² − R_p²)

where:
  b   = gear face width      (m)
  R_a = addendum (tip) radius (m)
  R_p = pitch radius          (m)

Theoretical flow:   Q_th = D · N
Actual flow:        Q     = D · N − Q_slip
Volumetric eff.:    η_v   = Q / Q_th = 1 − Q_slip/(D·N)

Q is the delivered flow, N the shaft speed. The slip term Q_slip is internal leakage from outlet back to inlet through the running clearances. To first order it follows laminar flow through a thin gap:

Q_slip ≈ k · ΔP · c³ / (μ · L)

  ΔP = pressure rise across the pump (Pa)
  c  = clearance gap height          (m)
  μ  = dynamic viscosity             (Pa·s)
  L  = leakage path length           (m)
  k  = geometry constant

Three consequences fall straight out of this. Slip rises linearly with pressure, so volumetric efficiency drops as you load the pump. Slip rises with the cube of clearance, so a worn pump (clearance doubled) leaks roughly eight times as much. And slip falls with viscosity, so a gear pump delivers less of its rated flow when the oil is hot and thin, and more when it is cold and thick — the opposite of intuition for many operators.

Worked example: sizing for flow

You need 30 litres per minute of hydraulic flow at 1500 rpm. What displacement, and what does it deliver at 200 bar?

Required theoretical flow at the shaft:
  Q_th = 30 L/min ÷ η_v(assume 0.92)
       = 32.6 L/min
       = 32,600 cc/min

Displacement per rev:
  D = Q_th / N = 32,600 / 1500
    = 21.7 cc/rev   → pick a 22 cc/rev pump

Delivered flow at 200 bar (η_v falls to ~0.88):
  Q = D · N · η_v = 22 · 1500 · 0.88
    = 29,040 cc/min
    = 29.0 L/min   (just short — bump to 24 cc/rev)

Input power (hydraulic + losses, η_overall ≈ 0.85):
  P_hyd = Q · ΔP = (29.0e-3/60) m³/s · 200e5 Pa
        = 9.67 kW
  P_shaft = P_hyd / 0.85 = 11.4 kW

This is the everyday loop of gear-pump selection: pick D from the flow you need at speed, then derate for the volumetric efficiency you will actually see at working pressure, and size the prime mover for the overall efficiency.

External, internal and gerotor

	External gear	Internal gear (crescent)	Gerotor
Layout	Two equal external-tooth gears side by side	Small external gear inside a larger ring gear, crescent divider	Inner rotor with one fewer lobe orbiting inside an outer rotor
Pressure capability	High — up to ~250 bar	Medium — up to ~150 bar	Low–medium — up to ~100 bar
Flow ripple / noise	Highest (pulses per tooth)	Lower, smoother	Smoothest, quietest
Viscosity handling	Good for thin oils	Excellent for thick fluids	Excellent, self-priming
Cost / compactness	Cheapest, most compact per kW	Moderate	Low cost, very compact
Typical use	Hydraulic power packs, fuel, lube	Asphalt, resin, food, high-viscosity transfer	Engine oil pumps, fuel-injection feed

External gear pumps dominate raw hydraulic power because they pack the most displacement into the smallest, cheapest casing and tolerate high pressure. Internal and gerotor designs win where smoothness, quiet running, or thick fluids matter — which is why nearly every automotive engine-oil pump is a gerotor sitting on the crankshaft nose.

Real-world numbers

• Engine oil pump (gerotor): ~10–15 cc/rev, 2–6 bar, driven at crankshaft speed; pushes 30–60 L/min of hot oil through the bearings of a passenger car.
• Mini power pack (external gear): 0.8–8 cc/rev, 150–230 bar, 1450 rpm motor — the unit inside a tail-lift, scissor lift or dock leveller.
• Mobile machine main pump: 30–100 cc/rev, up to 250 bar, delivering 60–250 L/min for excavator and tractor hydraulics.
• Chemical / food transfer (internal gear): moves fluids from thin solvents to 100,000 cP chocolate or asphalt with the same casing, because positive displacement does not care about viscosity for output, only for slip.

Trade-offs versus a centrifugal pump

Property	Gear pump (positive displacement)	Centrifugal pump (dynamic)
Flow vs. pressure	Flow ~constant; pressure rises until relief opens	Flow falls as head rises; self-limiting
Self-priming	Yes — draws its own suction	No (needs prime / flooded suction)
Viscous fluids	Excellent	Poor — efficiency collapses
Best at	High pressure, low–moderate flow	High flow, low–moderate head
Dead-head a closed valve	Dangerous — must have a relief valve	Tolerable for short periods
Flow smoothness	Ripples at tooth-passing frequency	Very smooth
Tolerance to solids	Poor — tight clearances clog/wear	Better with open impellers

The single most important operational rule follows from the first row: a positive-displacement pump will not stop pushing fluid just because the outlet is closed. With nowhere for the trapped slug to go, pressure spikes until a seal, a hose, or the pump itself fails — so every gear-pump circuit needs a pressure-relief valve set below the weakest component's rating.

Failure modes and design trade-offs

• Cavitation erosion. Starved suction lets the inlet pressure fall below vapor pressure; bubbles form and then implode at the outlet, pitting the gear faces and bore. Cure: low inlet velocity, generous suction lines, controlled fluid temperature, adequate net positive suction head.
• Pressure-driven slip and efficiency loss. As pressure rises, axial and radial leakage climb. Good pumps add pressure-loaded side plates that push harder against the gear faces as outlet pressure rises, shrinking the axial clearance to hold efficiency — a self-compensating trick.
• Wear and clearance growth. Slip scales with clearance cubed, so wear is self-accelerating: a worn pump runs hotter, the oil thins, slip grows, it gets hotter still. Dirty fluid (abrasive particles in the 5–30 µm clearance) is the usual culprit; clean fluid is the cheapest life-extender.
• Trapped-volume pressure spikes. During mesh, fluid can be momentarily trapped in a closing cavity before it can escape, generating local pressure spikes, noise and load on the bearings. Relief grooves machined into the side plates vent this trapped volume.
• Shaft seal and bearing failure. High discharge pressure pushes the gears apart radially, loading the bearings and the shaft seal; oversized or hydrodynamic bearings and balanced porting manage the side load.
• Flow ripple and acoustic whine. Pulsation at tooth-passing frequency (speed × tooth count) radiates as noise and can excite hose and structure resonances. Helical gears and higher tooth counts smooth the ripple at some cost in axial thrust.