How to size a gear coupling

1. Four checks, not one calculation

Sizing a gear coupling is arithmetic, but it is four separate pieces of arithmetic, and a selection is only valid when all four pass:

• Continuous torque — whether the teeth survive normal running.
• Peak torque — whether they survive the start, the trip and the upset.
• Bore capacity — whether the coupling physically fits the two shafts it has to join.
• Speed — whether the selection needs balancing, and whether it can be run at that speed at all.

Engineers reliably do the first and reliably skip at least one of the other three. The order below is deliberate in one respect only: bore is worth checking early, because when it governs, it governs, and everything upstream has to be redone.

2. Nominal torque from power and speed

Power and speed give torque directly. For power in kilowatts and speed in revolutions per minute, the working form carries a constant of 9550 — which is simply 60 000 ÷ 2π, folded in so the units come out in newton metres.

2.1 Rated power or absorbed power?

The correct input is the driver's rated power, not the power the driven machine absorbs in normal service. A motor will deliver its rated torque into a fault, and during a direct-on-line start it delivers a substantial multiple of it — entirely independently of what the pump was drawing the moment before.

Sizing on absorbed power produces a coupling that is adequate for the duty as described and inadequate for the event that actually breaks couplings. The exception that proves the rule: where the driver is deliberately oversized for future capacity, sizing on the full rating is still correct, because the day the capacity is used, nobody re-selects the coupling.

3. Applying the service factor

The service factor is routinely misread as a safety margin. It is not. It describes the character of the load rather than its magnitude. A centrifugal pump and a reciprocating compressor drawing identical average power impose entirely different peak loading on the tooth flanks, because one applies torque smoothly and the other applies it in pulses with a reversal component.

It is not there to cover uncertainty in the power figure. Inflating it because the load is poorly understood hides a question rather than answering it — and the honest response to an unknown duty is to characterise the duty, not to multiply by a larger number.

4. The peak check is separate

Gear couplings carry a peak or momentary rating distinct from the continuous one, and the events checked against it are transient: direct-on-line motor starting, a short circuit at the terminals, compressor surge, a two-phase reclosure, a driven machine seizing.

The magnitudes are large. Direct-on-line starting alone commonly produces two to two and a half times full-load torque at the shaft, and electrical transients can produce considerably more for a few cycles. The check therefore has to be made against the worst credible event for that train, not against a generic multiplier — a soft-started motor and a direct-on-line motor of identical rating impose entirely different peak duties on the same coupling.

5. Bore — where selections actually fail

Every coupling size has a maximum bore, set by the material left between the bore surface and the root of the hub teeth. That limit does not scale with torque capacity in the same proportion, so on a great many drives the shaft diameter demands a larger coupling than the torque does.

A 132 kW four-pole motor in a standard frame carries an 80 mm shaft. The coupling has to accept that bore regardless of the fact that the torque calculation would have been satisfied by something smaller. When the two hubs sit on different shaft diameters — the normal case, not the exception — each is bored to its own shaft, and the size is governed by the larger of the two.

Keyway practice enters here too. The keyway removes material from the same wall the bore limit is protecting, so a shaft calling for a deeper-than-standard keyway can push a bore past the size's capability even when the nominal diameter is within it. The bore and keyway conventions themselves come from whichever standard governs the order — see AGMA 9002 for the inch-series practice and IS 3238 for the domestic metric convention.

6. Speed and the balance threshold

Every size carries a maximum speed, and beyond a threshold that varies by manufacturer and size, couplings require dynamic balancing. Running an unbalanced coupling above that threshold puts a rotating force into bearings that were never intended to carry it.

On a 1480 rev/min drive this check passes trivially. On a compressor train at ten thousand it governs the entire selection — and it is the reason high-speed service moves away from lubricated gear teeth altogether, toward the dry flexible elements covered in the gear versus disc comparison.

7. The example, end to end

A 132 kW, four-pole squirrel-cage motor at 1480 rev/min, started direct-on-line, driving a centrifugal blower. Motor shaft 80 mm, blower shaft 75 mm. Both machines on a common baseplate, ambient service, indoor.

The size call is then made by reading down a manufacturer's rating table for the first size that satisfies all of: continuous rating ≥ 1278 N·m, peak rating ≥ 2130 N·m, maximum bore ≥ 80 mm, maximum speed ≥ 1480 rev/min. If the first size satisfying the bore requirement also satisfies the torque requirements — as it does here — the selection is complete, and there is nothing to be gained by going larger.

Two things remain before the order is placed, and neither is a torque question. The misalignment capacity at the chosen size has to cover the angular, parallel and axial movement the installation will actually see, and the axial travel has to cover thermal growth of the train between cold and running conditions.

Working the same arithmetic against a specific range rather than in the abstract? Our publisher, Super Mech Industries, runs a gear coupling torque calculator against their own catalogue sizes. This article is the method; that is the tool.