The Gerotor Pump: How Nested Rotors Meter Oil One Chamber at a Time

How it works: N inside N+1

A gerotor is an internal gear set with a one-tooth difference. The inner rotor has N lobes (teeth); the outer rotor (the ring) has N+1 lobes. Their centres are offset by a small distance e, the eccentricity. The inner rotor is driven by the shaft; because the outer has one more lobe, the two turn at different rates — the outer runs at N/(N+1) of the inner rotor speed. As the inner rotor rotates, each of its lobes stays in sliding contact with the outer profile, so at any instant the pair form a ring of N sealed chambers between them.

The single-tooth difference is what makes it a pump. As the inner rotor advances, the volume of each chamber grows on the inlet side (expanding, drawing oil in) and shrinks on the outlet side (collapsing, pushing oil out). There are no check valves: porting plates on the front and rear faces expose the expanding chambers to the low-pressure inlet kidney port and the shrinking chambers to the high-pressure outlet kidney port. One full inner-rotor revolution displaces N chambers, each cycling once — the whole rotor set breathes like a ring of tiny cylinders.

• Displacement per revolution: V_d = N · (V_max − V_min) per chamber, where V_max and V_min are the maximum and minimum chamber volumes over one cycle.
• Ideal flow: Q_ideal = V_d · n, with n the shaft speed. A common 4/5-lobe automotive rotor with V_d ≈ 10 cm³/rev at 3000 rpm gives Q_ideal ≈ 30 L/min.
• Actual flow: Q = V_d · n · η_v, where η_v is volumetric efficiency (0.85–0.95 warm, higher cold).

The geometry: epitrochoids and their conjugate envelope

The elegance of the gerotor is that the two profiles are mathematically conjugate — one is generated from the other. In the classic construction the inner rotor is an epitrochoid (or an epitrochoid whose points are replaced by circular arcs) and the outer rotor lobes are circular arcs of radius r positioned on a pitch circle. The outer profile is precisely the envelope swept by the inner rotor as it performs its planetary orbit: inner rotor spinning about its own centre while that centre orbits the outer centre at radius e.

Parametrically, an epitrochoid point on the inner rotor traces x(θ) = (R + r)cos θ − d·cos((R+r)/r · θ), y(θ) = (R + r)sin θ − d·sin((R+r)/r · θ), where R is the fixed (base) circle radius, r the rolling circle radius, and d the tracing-point offset. The design levers are the lobe count N, the eccentricity e, the outer lobe radius r_c, and the rotor thickness (axial length) L.

• Eccentricity e sets chamber travel: bigger e means larger V_max − V_min per chamber, hence more displacement, but larger sliding velocities and higher contact stress at the lobe tips.
• Lobe count N trades displacement-per-lobe against flow smoothness. Fewer lobes (2/3, 3/4) give big chambers and high displacement but chunkier flow ripple; more lobes (7/8, 9/10) give many small chambers, low ripple, quieter running, but tighter tolerances.
• Contact geometry: the theoretical profile has continuous line contact, but a small tip clearance (typ. 20–60 µm) is machined in so the parts don't seize — this clearance is the dominant leakage path.

Flow ripple, kinematics, and why it's quiet

Because several chambers deliver simultaneously and their volume rates overlap, the instantaneous outlet flow is nearly steady. The flow ripple — the peak-to-mean variation in delivery — falls sharply with lobe count. A 4/5 set has an irregularity on the order of 1–3%; a 9/10 set can be well under 1%. The fundamental pumping frequency is f = N · n / 60 (Hz) for an inner rotor of N lobes at n rpm, plus its harmonics. A 4-lobe rotor at 3000 rpm pumps at 200 Hz — right in the audible band, which is why lobe-passing tones and porting geometry matter for NVH.

Two kinematic facts drive the acoustics and durability:

• Trapped-volume compression: as a chamber crosses from inlet to outlet porting, a small pocket of oil can be momentarily sealed off. If it's connected to neither port at minimum volume, pressure spikes; the porting timing grooves (relief notches at the kidney-port ends) are tuned to bleed this pocket smoothly and kill the pressure pulse that would otherwise ring the housing.
• Sliding at the tips: the relative velocity between inner tip and outer flank is highest near the sealing contact. This is a boundary-to-mixed lubrication regime; the oil film (a few µm) separates the surfaces, and the tribology here — plus the porting design — sets both efficiency and wear life. See tribology and journal-bearing lubrication for the underlying film physics.

Sizing a gerotor: displacement, power, and torque

Design starts from the required flow at a design speed. Rearranging Q = V_d · n · η_v gives the target displacement V_d = Q / (n · η_v). Say you need Q = 12 L/min at engine idle-plus, n = 2000 rpm, η_v ≈ 0.9: V_d = 12000 cm³/min ÷ (2000 rev/min × 0.9) ≈ 6.7 cm³/rev. With that displacement fixed you choose N, then solve the geometry (e, R, r_c, L) so that N·(V_max − V_min) hits 6.7 cm³.

The hydraulic and shaft numbers follow directly:

• Hydraulic power: P_hyd = Δp · Q. At Δp = 500 kPa and Q = 12 L/min = 2.0×10⁻⁴ m³/s, P_hyd = 5×10⁵ × 2.0×10⁻⁴ ≈ 100 W.
• Shaft power: P_shaft = P_hyd / η_o, with overall efficiency η_o = η_v · η_m ≈ 0.75–0.85; here ≈ 120–130 W.
• Drive torque: T = P_shaft / ω. At 2000 rpm, ω = 2π·2000/60 ≈ 209 rad/s, so T ≈ 130/209 ≈ 0.6 N·m. Equivalently T ≈ (Δp · V_d)/(2π · η_m).

Key scale check: displacement scales with rotor thickness L linearly and with e and R roughly as e·R·L, so a modest bump in eccentricity or length buys flow cheaply — until tip stress, sliding speed, and inlet velocity push you into cavitation.

Real hardware: where gerotors live

The gerotor is the default engine oil pump in the overwhelming majority of modern passenger cars and motorcycles — often crank-nose-driven, so it runs at engine speed. Because lube demand doesn't scale with engine speed, high-rpm oversupply is dumped over a spring-loaded relief valve (a parasitic loss), which is why variable-displacement gerotor pumps — where a control ring shifts eccentricity to modulate V_d — have become common for fuel-economy gains, actively regulating gallery pressure to ~150–350 kPa instead of dumping.

• Automatic transmissions: a gerotor charge pump pressurizes the ATF circuit (clutch apply, torque-converter charge, cooling) at 0.5–2 MPa.
• Fuel systems: low-pressure lift/transfer pumps and diesel priming pumps use gerotors; high-pressure common-rail generation is left to other topologies.
• Dry-sump & aerospace: multi-stage gerotor scavenge pumps pull oil-air froth from the sump; here the pump must tolerate high entrained-air fractions.
• Materials: rotors are commonly sintered powder-metallurgy steel (net-shape, cheap, self-lubricating porosity) or hardened tool steel for high pressure; housings in aluminum or cast iron. Powder-metallurgy net-shape forming is what makes the complex trochoidal profile economical at scale.

Failure modes, cavitation, and design limits

The gerotor's Achilles' heel is the inlet. As a chamber expands it must fill in the time available; if oil can't rush in fast enough, local pressure drops below the vapour/gas-release pressure and the chamber only partially fills. The metrics that govern this:

• Cavitation / incomplete filling: at high speed and cold, high-viscosity oil, filling lags. Symptoms are a flow curve that falls off above a threshold rpm, noise, and vapour-bubble collapse that erodes rotor tips and porting. Fixes: larger inlet kidney port, lower inlet velocity (<~5–8 m/s), adequate NPSH, and limiting shaft speed. See cavitation and NPSH.
• Aeration: entrained air (foamy scavenge oil, low sump level) makes the fluid compressible, collapsing η_v and delivery pressure — the pump can't build head on a spongy, gas-rich charge.
• Wear & leakage: tip and face clearances open with wear; because internal leakage Q_leak ∝ Δp·h³/µ (a Poiseuille gap flow, cubic in clearance h), a clearance that doubles from 25 to 50 µm can raise leakage ~8×, tanking η_v — most acute hot and at low speed.
• Cold-start torque: at −20 °C, oil viscosity can be 100–1000× warm value; drive torque and housing stress spike, and the relief valve may pin open. Rotors and drives are sized for this transient.

Best practice: keep tip clearance in the 20–60 µm band, generous inlet porting, add porting relief grooves to control trapped-volume pressure spikes, choose N≥5 where quiet operation matters, and use a pressure-relief or variable-displacement scheme rather than deadheading the outlet. Well-designed automotive gerotors routinely exceed 300,000 km of service.

Gerotor vs. external gear pump vs. crescent internal gear pump for low-to-medium pressure oil transfer

Attribute	Gerotor (trochoidal)	External gear pump	Crescent internal gear
Moving parts	2 (inner + outer rotor)	2 meshing gears	3 (gear, ring, crescent)
Contact points / chamber seal	Continuous multi-tooth line contact	Single mesh line	Gear-ring mesh + crescent seal
Typical pressure	0.3–2 MPa (spec. to 20 MPa)	up to 25–30 MPa	up to ~17 MPa
Speed range	high (to 6000+ rpm)	high (to 3500 rpm)	moderate
Flow ripple / noise	Low ripple, quiet	Higher ripple, whine	Low ripple
Cost / compactness	Very low, very compact	Low	Moderate, longer axially