A tri-axial rotary pump is a positive-displacement pump that uses three parallel intermeshing rotors — typically one driven power rotor flanked by two idler rotors — to trap fluid in sealed cavities and move it axially from suction to discharge. Units like the Imo 3D and Leistritz L3MF push 5 to 800 L/min at pressures up to 100 bar with near-zero pulsation. The geometry exists to handle viscous, lubricating fluids quietly and continuously, which is why you see it on marine fuel-injection skids and large hydraulic elevator power packs.
Tri-axial Rotary Pump Interactive Calculator
Vary delivered flow, discharge pressure, and slip to see ideal pump flow, leakage loss, volumetric efficiency, and hydraulic power.
Equation Used
The calculator treats the tri-axial rotary pump as a positive-displacement pump with internal slip. The ideal displacement flow is the delivered flow divided by volumetric efficiency, slip flow is the internal leakage difference, and hydraulic power is pressure rise times delivered flow.
- Delivered flow is the actual outlet flow after internal slip.
- Fluid is treated as incompressible and steady.
- Pressure is differential discharge pressure in bar.
- Slip percent represents internal leakage as a fraction of ideal displacement flow.
Inside the Tri-axial Rotary Pump
The pump body holds three rotors on parallel axes — a centre power rotor that the motor drives, and two idler rotors that mesh with it on either side. As the rotors turn, the helical threads form sealed pockets between the rotor flanks and the surrounding stator bore. These pockets translate axially down the length of the rotor set, carrying fluid from the suction port to the discharge port without ever opening back up. No valves, no reciprocating parts, no churning. That is why a tri-axial rotary pump (sometimes called a three-screw pump in the marine and oil industries) delivers pulse-free flow that you can put a pressure gauge on and watch the needle sit dead still.
The geometry is chosen for one reason — the idlers are hydraulically driven, not mechanically driven. The discharge pressure pushes back on the idler threads and that pressure is what keeps them spinning in time with the power rotor. Because of this, you get very low rotor-to-rotor contact force. The mesh clearance between the power rotor and idlers must hold to roughly 0.05 to 0.10 mm on a typical 60 mm rotor set — go tighter and you get galling on cold start when the fluid is still thick, go looser and slip flow climbs and volumetric efficiency falls off a cliff.
What fails first is almost always the stator bore. If you run the pump dry for more than 30 seconds, the rotor tips score the bore, the running clearance opens up, and slip flow at high pressure climbs from a healthy 5% to 20% or worse. The other failure mode is cavitation — feed it fluid with NPSH below the rated value and you will hear a distinct rattling whine, then watch the discharge pressure drop and the suction-side rotor pit within a few hundred hours. Viscosity matters too. Below about 2 cSt the fluid no longer fills the running clearances and slip flow dominates, which is why you do not see these pumps on water service.
Key Components
- Power Rotor: The driven centre rotor coupled directly to the motor shaft. It carries the full input torque and transmits motion hydraulically to the idlers through fluid pressure on the thread flanks. Typical rotor diameters run 25 to 180 mm depending on flow rating, and the helix angle sits between 12° and 17° on most three-screw designs.
- Idler Rotors: Two driven-by-fluid rotors that mesh with the power rotor on opposite sides. They do not see torque from the shaft — they spin because discharge pressure pushes their threads forward. Mesh clearance against the power rotor must hold to 0.05 to 0.10 mm; any wider and slip flow ruins volumetric efficiency.
- Stator Bore (Pump Casing Liner): The figure-of-eight-and-a-half precision bore that surrounds all three rotors. Rotor-tip-to-bore clearance is the single most critical tolerance in the pump, typically 0.04 to 0.08 mm. A scored bore from dry running is the most common reason these pumps end up on the rebuild bench.
- Mechanical Shaft Seal: Single or double cartridge seal on the power rotor shaft only — the idlers stay submerged and never see atmosphere. On fuel-oil duty you almost always see a tungsten-carbide vs carbon face pair rated for 100 bar and 120 °C.
- Pressure Relief Valve: Internal or externally mounted bypass that dumps flow back to suction if discharge pressure exceeds the set point — usually 110% of rated working pressure. Without it, a closed discharge valve will deadhead the pump and shear the idlers in seconds.
- Suction and Discharge Ports: Axial or radial ports at opposite ends of the rotor set. Fluid enters one end at low pressure, gets carried axially in the rotating pockets, and exits the other end at full discharge pressure. The axial flow path is what gives the pump its silent, pulse-free character.
Real-World Applications of the Tri-axial Rotary Pump
You see tri-axial rotary pumps wherever someone needs a steady, quiet, high-pressure flow of a fluid that has some lubricity to it — fuel oils, hydraulic oils, lubricating oils, asphalt, polymer melts. They are not the right answer for thin fluids like water or solvents because slip flow eats efficiency, and they cannot handle solids because the running clearances are too tight. Where they shine is on viscous fluid transfer at constant pressure, on marine and stationary diesel fuel systems, and on hydraulic power packs that cannot tolerate the pulsation of a gear or piston pump.
- Marine Propulsion: Heavy fuel oil booster modules on MAN B&W and Wärtsilä 2-stroke marine diesels — typical setup uses Imo ACE 038 three-screw pumps to deliver 380 cSt HFO at 16 bar to the injection system.
- Power Generation: Lube oil supply to the journal bearings on GE 7FA and Siemens SGT-800 gas turbines, where Leistritz L3MF pumps run continuously at 7 bar with pulse-free flow critical to bearing oil-film stability.
- Hydraulic Elevators: Power units on Otis and Schindler hydraulic passenger lifts up to 6 floors — silent operation matters because the pump room sits next to occupied space, and a tri-axial unit at 60 dB beats a gear pump at 78 dB.
- Asphalt Production: Hot bitumen transfer at 180 °C from storage tanks to mixing drums at Lafarge and Vinci road-paving plants, where Allweiler SMF screw pumps handle 50,000 cP fluid that no centrifugal pump could touch.
- Polymer and Adhesive Manufacturing: Hot-melt adhesive metering on Nordson hot-melt application heads at Procter & Gamble diaper plants, where flow steadiness directly controls bead weight on the fabric web.
- Crude Oil Pipeline Boosting: Inter-station booster duty on small-diameter heated crude lines at Husky Energy heavy oil terminals — the pump handles 800 cSt diluted bitumen at 40 bar without the maintenance burden of a triplex piston pump.
The Formula Behind the Tri-axial Rotary Pump
The flow rate of a tri-axial rotary pump is fundamentally a geometry-times-speed calculation, less the slip flow that leaks back through the running clearances. At the low end of the typical operating range — say 500 RPM — you get gentle, quiet flow but slip becomes a larger fraction of theoretical output, so volumetric efficiency drops to around 75-80%. At nominal 1750 RPM (a 4-pole motor speed) you hit the design sweet spot where efficiency runs 90-95% and the rotors are well-lubricated by the fluid film. Push past 3500 RPM and you start running into NPSH limits — the suction side cannot fill the pockets fast enough and you cavitate. The formula below tells you the actual delivered flow you can plan a system around.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| Qactual | Actual delivered volumetric flow rate | L/min | GPM |
| q | Geometric displacement per revolution of the rotor set | L/rev | in³/rev |
| N | Power rotor shaft speed | RPM | RPM |
| ηv | Volumetric efficiency (function of viscosity, pressure, and clearance) | dimensionless (0 to 1) | dimensionless (0 to 1) |
| Qslip | Internal leakage flow back through rotor clearances | L/min | GPM |
Worked Example: Tri-axial Rotary Pump in a paper-mill lube oil booster skid
You are sizing an Allweiler SMF 80 tri-axial rotary pump to circulate ISO VG 68 turbine oil from a 4000 L sump up to the journal bearings on the dryer-section drive train at a Domtar paper mill in Espanola Ontario. The bearings need 220 L/min of oil at 6 bar with absolutely steady flow — any pressure pulsation shows up as vibration in the dryer rolls and translates straight into sheet-thickness variation. The pump has a geometric displacement of 0.135 L/rev and you are pairing it with a 4-pole 1750 RPM TEFC motor.
Given
- q = 0.135 L/rev
- Nnom = 1750 RPM
- ηv = 0.92 dimensionless
- Qslip = 4 L/min
- Pdischarge = 6 bar
Solution
Step 1 — at the nominal 1750 RPM operating point, calculate the theoretical (geometric) flow:
Step 2 — apply the volumetric efficiency and subtract slip to get actual delivered flow at nominal speed:
That is just under your 220 L/min target — close enough that you would either accept it or shim the bypass orifice on the bearing manifold. Now look at how the pump behaves at the low end of its useful range, around 1000 RPM, where someone might run it during a winter cold-start when the oil is at 15 °C and viscosity has climbed:
At 115.8 L/min the bearings still get oil but film thickness margin is thinner than ideal — you would expect bearing temperatures to run 5-8 °C higher until the oil warms up. At the high end of the rated range, 3500 RPM (running on a VFD pushing the motor past synchronous speed, which Allweiler permits up to 3600 RPM on this frame size):
438 L/min is theoretically available but you will not see it in practice on this skid — the suction line is sized for 250 L/min and NPSH-available drops below the pump's NPSH-required around 2800 RPM, at which point the suction-side rotor starts cavitating and you hear it from across the pump room.
Result
The pump delivers 213. 4 L/min at nominal 1750 RPM and 6 bar discharge — within 3% of the 220 L/min target, which is the design sweet spot for this duty. At the 1000 RPM cold-start low end you get 115.8 L/min (lean but workable), and the theoretical 438 L/min at 3500 RPM is unreachable in practice because suction-side NPSH runs out near 2800 RPM. If you measure significantly less than the predicted 213 L/min, check three things in order: first, rotor mesh clearance — if the idlers have over 0.12 mm clearance against the power rotor, slip flow doubles and you lose 15-20 L/min; second, the internal pressure relief valve — a weak relief spring or a piece of debris on the seat will dump flow back to suction continuously and the pump will deliver maybe half rated capacity; third, suction strainer pressure drop — a clogged 100 mesh strainer will pull NPSH below the pump's tolerance and you lose flow to incipient cavitation before you ever hear it.
Choosing the Tri-axial Rotary Pump: Pros and Cons
The tri-axial rotary pump sits in a specific niche — viscous lubricating fluids, moderate to high pressure, and applications that cannot tolerate flow pulsation. Pick the wrong pump for the job and you either burn money on rebuilds or live with vibration that wrecks downstream equipment. Here is how it stacks up against the two pumps that compete for the same applications.
| Property | Tri-axial Rotary Pump | External Gear Pump | Triplex Plunger Pump |
|---|---|---|---|
| Flow pulsation | < 1% (essentially pulse-free) | 5-10% pulsation at gear-mesh frequency | 8-15% pulsation at plunger frequency |
| Typical speed range (RPM) | 500 - 3500 | 500 - 4000 | 150 - 600 |
| Maximum discharge pressure | 100 bar (3-screw); up to 280 bar on 5-screw variants | 250 bar | 700 bar+ |
| Viscosity range (cSt) | 2 - 50,000 (sweet spot 10 - 5000) | 10 - 2000 | 1 - 500 |
| Typical volumetric efficiency at nominal | 88 - 95% | 85 - 92% | 92 - 97% |
| Noise level at 1 m, rated duty | 55 - 70 dB | 75 - 88 dB | 80 - 95 dB |
| Service life between rebuilds (clean fluid) | 30,000 - 60,000 hours | 15,000 - 30,000 hours | 8,000 - 20,000 hours |
| Tolerance to particulates | Poor (10 µm filtration required) | Moderate (25 µm acceptable) | Poor to moderate (depends on valve design) |
| Capital cost (relative) | High (3-4×) | Low (1×) | Very high (5-7×) |
Frequently Asked Questions About Tri-axial Rotary Pump
You are watching slip flow grow as the running clearances wear. The dominant wear mechanism on a tri-axial rotary pump is rotor-tip-to-stator-bore wear, not the mesh between rotors. Every 0.01 mm of additional radial clearance increases slip by roughly 8-12% on a typical 60 mm rotor set at 6 bar. After 20,000 hours on dirty oil you can easily lose 30 L/min from a 220 L/min pump.
Quick diagnostic — pull the suction screen, run the pump deadheaded against the relief valve for 10 seconds, and watch the relief flow back to tank. If relief flow is normal but delivered flow is low, the issue is internal slip, not the relief valve. The fix is a stator and rotor set replacement, which Imo and Leistritz both supply as a matched cartridge.
You can, but you need to pick the right rotor material and accept the lower pressure rating. Diesel fuel sits around 2-4 cSt, which is at the very bottom of the pump's useful viscosity range — slip flow runs 2-3× higher than on lube oil and volumetric efficiency drops to 70-80%. Manufacturers like Imo derate maximum discharge pressure on light-fuels duty by roughly 40% to keep slip from overheating the fluid.
If you are pumping anything below 1.5 cSt (gasoline, light naphtha) walk away from this pump style entirely — there is not enough fluid film between the rotor flanks and you will get metal-on-metal contact within hours.
The decision comes down to pressure and flow steadiness. A 3-screw pump tops out around 100 bar in standard build because the idlers carry pressure-induced bending loads that scale with discharge pressure. A 5-screw design adds two more idlers, which support the power rotor against bending and let the pump push 200-280 bar. You pay for it in cost (roughly 1.5×) and in tighter manufacturing tolerances.
Rule of thumb — below 60 bar use 3-screw, above 100 bar use 5-screw, between 60-100 bar look at your duty cycle. Continuous duty above 80 bar wears a 3-screw fast enough that the 5-screw pays back inside two years.
That is almost always cold-oil cavitation on the suction side. When ISO VG 68 oil drops below 10 °C, viscosity climbs to over 1000 cSt and the suction line cannot supply the pump fast enough to fill the rotor pockets. Vapour and entrained air collapse on the discharge side of the rotor mesh and you hear it as a marbles-in-a-coffee-can rattle.
If it clears within a few minutes as the oil warms, you are fine. If it persists past 10 minutes or returns at full operating temperature, check NPSH-available — most likely the suction strainer is partially clogged or the suction line is undersized. Persistent cavitation pits the leading edge of the suction-side rotor flanks and you will see flow loss within 500 hours.
The relief valve has a finite response time and a finite flow capacity. On a tri-axial rotary pump running at 1750 RPM, the rotors displace fluid in roughly 30 ms per revolution — faster than most spring-loaded relief valves can fully open. You will see a brief pressure transient (sometimes 130-150% of set point) for 50-200 ms before the relief stabilises.
If the spike is permanent, not transient, the relief is undersized for the pump's full displacement or the relief is recirculating into a restricted return line. Size the relief return path for at least full pump displacement at 1.5× rated pressure drop, and confirm the relief opens before the motor's overload trip point.
VFD operation is fine over a wide range — typically 25% to 110% of rated speed — and most marine and industrial installations run them this way. The idlers stay hydraulically balanced as long as discharge pressure stays above roughly 2 bar, because that is what loads the idler threads against the power rotor.
The trap is running too slow with no back pressure. Below about 400 RPM with discharge pressure under 1 bar, the idlers can lose their hydraulic timing for a moment and tick against the power rotor. You will hear a faint metallic click. Either keep minimum speed above 500 RPM or maintain at least 2 bar minimum discharge pressure with a back-pressure regulator.
10 µm absolute (β10 ≥ 200) on the suction or pressure side, full flow. The running clearances inside the pump are 40-80 µm, and any particle larger than half that clearance acts as a lapping compound between the rotor and stator. Run with 25 µm filtration and you will see clearances open up at 3-4× the rate of a 10 µm system.
The published 30,000-60,000 hour figures assume ISO 4406 cleanliness code 18/16/13 or better. If your oil sample comes back at 20/18/15, expect to halve the rebuild interval. Pull an oil sample every 2000 hours and trend the particle count — it is the cheapest insurance you can buy on this style of pump.
References & Further Reading
- Wikipedia contributors. Screw pump. Wikipedia
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