Shaft Alignment Tolerance Calculator

There is no international standard for shaft alignment tolerance, so the working rule is that acceptable offset is 110 divided by the running speed in millimetres, acceptable angularity is 75 divided by the speed in millimetres per 100 mm, and excellent is half of each. Below 600 rpm the tolerance stops tightening and is held at the 600 rpm value.

The rule, and where it comes from

A given offset does not become any larger when the machine runs faster. Two things change instead. The coupling elements, the bearings and the seals are worked through that same offset more often in every hour the machine runs, so the cycles accumulate faster. And the parts have to be accelerated through the same displacement in less time, so the same offset generates more force. Both push the same way, which is why the permissible offset has to fall as speed rises. That single idea produces every published alignment table in the trade, and the tables differ only in where they were rounded.

Written as constants in millimetre-rpm:

Those four numbers are common industry practice, not a standard, and they apply to short flexible couplings. Every figure the calculator prints comes from them and from nothing else, which is the only claim worth making for them.

What that gives at real speeds

Every figure below is the arithmetic above and nothing else.

Angularity is a slope, so its units are millimetres per 100 mm of axial length: 100 mm travelled along the shaft, not 100 mm of coupling diameter. Read the same way as offset it is meaningless: a slope of 0.05 says nothing until you know over what distance.

Below 600 rpm the tolerance is held at the 600 rpm row. The formula would keep granting a larger and larger allowance on a slow machine, and past a point that stops being an alignment tolerance and becomes permission to leave the machine misaligned.

Which figure governs

A general rule like this one is the last of four places to look, not the first.

1. The site’s own alignment specification, where the plant has written one.
2. The machine manufacturer, or the coupling maker for the coupling itself.
3. The contract, where a tolerance was written into it.
4. A published general guideline, used only when the first three are silent.

Whichever figure is used, write it on the alignment record together with where it came from. A tolerance without a source cannot be defended later, and the next person to work on the machine has no way of knowing whether to keep it.

Spacer shafts and membrane couplings are more forgiving of offset and less forgiving of angle than a short flexible coupling, and they are worked to their own numbers rather than to this rule.

The other case that falls outside the rule is any machine whose alignment target is not zero. That covers anything with meaningful thermal growth, which is most hot pumps, most compressors and most turbines. On those machines the tolerance is a band around a deliberate cold offset, not a band around zero.

Signs, and which machine you are describing

Readings describe the position of the movable machine relative to the stationary one.

• Vertical offset is positive when the movable shaft sits high.
• Vertical angularity is positive when the axis of the movable machine rises as it goes away from the coupling, towards its own far end. That is the same condition as a coupling gap open at the bottom.
• Horizontal offset is positive when the movable shaft sits to the right, viewed from behind the movable machine looking towards the coupling.
• Horizontal angularity is positive when that axis moves towards the same right-hand side as it goes away from the coupling, which leaves the gap open on the left.

The angularity sign is the one that catches people, so it is worth stating twice: a positive result means the axis of the machine being measured rises as it goes away from the coupling. That is what makes the projection below work, because the slope has to carry the shaft further from zero as the distance to the foot grows.

Any consistent convention works, but a convention swapped halfway through a job produces shim corrections in exactly the wrong direction, and that failure looks like a measurement error rather than a bookkeeping one.

From coupling readings to foot moves

The coupling is where the tolerance lives. The feet are where the work happens, and they are not in the same place.

Where the movable shaft sits at a given foot is the offset at the coupling plus the slope carried along the shaft to that foot:

• Position at the foot = offset + (angularity / 100) × distance from the coupling centre

The move required is the negative of that, because the whole point is to bring the position back to zero. Positive means add shim vertically or move right horizontally; negative means remove shim or move left.

This is the step that makes a small angularity expensive. A slope that looks negligible at the coupling has been multiplied by the distance to the far foot by the time it reaches the shims, and on a long machine the far foot move is often several times the offset reading that raised the alarm.

A worked example

A machine running at 1480 rpm. The near foot is 250 mm from the coupling centre and the far foot 700 mm. The readings are 0.12 mm vertical offset, 0.06 vertical angularity, −0.04 mm horizontal offset and 0.02 horizontal angularity.

The tolerances at that speed are 110 / 1480 = 0.074 mm acceptable offset, 55 / 1480 = 0.037 mm excellent, 75 / 1480 = 0.051 acceptable angularity and 37.5 / 1480 = 0.025 excellent.

The moves follow from the offset plus the slope:

• Near foot, vertical: −(0.12 + 0.0006 × 250) = −0.27 mm, so remove 0.27 mm of shim
• Far foot, vertical: −(0.12 + 0.0006 × 700) = −0.54 mm, so remove 0.54 mm of shim
• Near foot, horizontal: −(−0.04 + 0.0002 × 250) = −0.01 mm, so move left 0.01 mm
• Far foot, horizontal: −(−0.04 + 0.0002 × 700) = −0.10 mm, so move left 0.10 mm

The vertical error at the coupling was 0.12 mm and the shim change at the far foot is 0.54 mm. That ratio is the normal state of affairs, and it is why alignment is judged at the coupling and corrected at the feet.