Selection & Sizing

Misalignment capacity: angular, parallel and axial

A gear coupling carries three separate misalignment ratings, not one, and a selection has to satisfy all three simultaneously. The binding constraint is rarely torque — it is sliding velocity at the tooth flank, which is what actually destroys the lubricant film.

Author
Priyansh Thummar, Editor
Dates
Published · Last updated
Reading time
4 minutes

1. Three ratings, not one

Angular misalignment is the angle between the two shaft centrelines. Parallel offset is the perpendicular distance between two centrelines that remain parallel. Axial travel is movement along the common axis as the train grows and contracts. They are independent, they are published independently, and a coupling comfortably inside its torque rating can still be destroyed by exceeding any one of them.

The three misalignment modes a gear coupling accommodatesThree schematics side by side, each showing a driving shaft on the left and a driven shaft on the right joined by a coupling. In angular misalignment the two shaft centrelines meet at an angle. In parallel misalignment the centrelines stay parallel but are offset from one another. In axial travel the centrelines remain collinear while the shafts move apart along their common axis.αAngulareParallel offsetsAxial travel
Figure 1. The three modes, exaggerated for clarity. α is angular misalignment between shaft centrelines, e is parallel offset between two still-parallel centrelines, and s is axial travel along the common axis.

2. Where the limit really comes from

The limit has almost nothing to do with torque. Every degree of angular misalignment forces each hub tooth to slide back and forth along its mating sleeve tooth once per revolution. The magnitude of that sliding is set by the misalignment and the tooth pitch radius; the velocity is set by the misalignment and the speed. Sliding velocity, not transmitted load, determines whether a lubricant film survives between the flanks.

That is why misalignment ratings fall as speed rises. A coupling rated for 1.5° per mesh at a few hundred rev/min may be rated for a fraction of a degree at several thousand — on identical hardware, with identical teeth. Nothing about the torque capacity has changed. What has changed is rubbing speed at the flank, and beyond a certain value the film thins until asperities touch, local temperature spikes, and wear stops being run-in and becomes progressive.

3. Angular capacity, per mesh

Angular capacity is quoted per mesh, and this is the detail most often misread. A double-engagement coupling has two meshes, one at each hub, so its total angular capacity across the coupling is twice the per-mesh figure. A single-engagement coupling — one toothed hub, one rigid connection — has one mesh and therefore half the total.

Reading a per-mesh rating as a whole-coupling rating produces a selection that is out by a factor of two, always in the unsafe direction.

3.1 Offset from angular capacity

Parallel offset is not really an independent capability. It is what two angular misalignments in opposite directions produce when the meshes are separated by a distance: tilt the sleeve one way at the first mesh and the other way at the second, and the two shaft centrelines finish parallel but displaced.

emax ≈ L · tan αmax

Parallel offset capacity, where L is the distance between the two mesh centres and αmax is the rated angular capacity per mesh. This is why a spacer coupling tolerates so much more offset than a compact one: lengthening the spacer increases L, and the same per-mesh angular capacity converts into proportionally more offset. It costs nothing in torque capacity — only overhung moment and axial space.
Table 1 — The three modes, their source and what constrains each
ModePhysical causeWhat sets the limitConsequence of exceeding it
Angular (α)Shaft centrelines meet at an angleSliding velocity at the tooth flankProgressive flank wear, worm tracking
Parallel (e)Two opposed angular deflections across a spanAngular capacity × mesh separationSame as angular — it is angular misalignment at each mesh
Axial (s)Thermal growth and contraction of the trainAvailable sleeve tooth engagement lengthTooth disengagement, or thrust into the bearings
All three must be satisfied simultaneously. Ratings are speed-dependent — a capacity quoted without a speed is incomplete.

4. Axial travel and the thrust nobody expects

Axial travel is the mode that gets ignored, and it produces a load engineers are frequently surprised by. The hubs are free to slide within the sleeve, which is exactly what lets the train grow and contract without loading the bearings. But that sliding happens against tooth friction while the coupling is transmitting torque, and the resulting axial force is not small. It scales with transmitted torque and the friction coefficient at the flank, and it acts directly on the thrust bearings at each end of the train.

Two conditions make it worse. A coupling running dry or on degraded grease has a far higher friction coefficient, so the same movement generates several times the thrust. And a coupling that has fretted at the flanks may not slide at all until the axial force builds enough to break it free — at which point it releases suddenly. Thrust bearing failures on machines that have run for years without trouble are often traced to a coupling that stopped sliding freely, rather than to anything wrong with the bearing.

5. Cold setting for thermal growth

Alignment is set cold and the machine runs hot. Casings and pedestals grow as they reach operating temperature, and on a large machine the running centreline can sit measurably above where it was at commissioning.

Cold-set offsets exist for this: the train is deliberately misaligned at ambient, in the direction opposite to expected growth, so that it comes into alignment at operating temperature. A machine aligned perfectly cold is a machine misaligned hot — which is the condition it spends almost its entire life in.

Frequently asked

Is a gear coupling's misalignment rating per mesh or per coupling?
Per mesh, and this is the detail most often misread. A double-engagement coupling has two meshes, so its total angular capacity across the coupling is twice the per-mesh figure; a single-engagement coupling has one and therefore half the total. Reading a per-mesh rating as a whole-coupling rating produces a selection out by a factor of two, always in the unsafe direction.
Why do misalignment ratings fall as speed rises?
Because the limit is set by sliding velocity at the tooth flank, not by torque. Every degree of misalignment makes each tooth slide back and forth along its mate once per revolution; the magnitude of that sliding comes from the misalignment, and its velocity from the misalignment and the speed. Beyond a certain rubbing speed the lubricant film thins until asperities touch, and wear stops being run-in and becomes progressive. The hardware has not changed — the duty has.
How does a spacer coupling accommodate more parallel offset?
Offset capacity is angular capacity per mesh multiplied by the distance between the two mesh centres. Lengthening the spacer increases that distance, so the same per-mesh angular capacity converts into proportionally more offset. It costs nothing in torque capacity — only overhung moment on the bearings and the axial space the machine has to give up.
Why does a gear coupling put thrust into the bearings?
Because the hubs slide within the sleeve against tooth friction while transmitting torque. The resulting axial force scales with transmitted torque and the friction coefficient at the flank, and it acts directly on the thrust bearings at each end of the train. A coupling running dry or on degraded grease generates several times the thrust for the same movement, and one that has fretted may not slide at all until the force builds enough to break it free.

References

  1. AGMA 9008-B00, Flexible Couplings — Gear Type — Flange Dimensions, Inch Series, for the mesh separation that governs offset capacity.
  2. ISO 14691:2008, Petroleum, petrochemical and natural gas industries — Flexible couplings for mechanical power transmission — General-purpose applications.
  3. Editorial note: published angular, parallel and axial capacities are size- and speed-dependent properties of a particular coupling range. The 1.5° per mesh figure quoted above is a widely used order of magnitude for low-speed service, not a rating — per-size tables are to be inserted from catalogue data and confirmed at technical review.
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