Sign convention (vertical): rim TIR positive = movable shaft reads high at the coupling; face TIR positive = gap wider at the top. Results: positive = add shims / for horizontal, move toward the reference side marked on your sketch. Read the convention section below before trusting a sign.
The Calculation, Explained
The geometry
Two dial readings describe the whole misalignment. The rim reading (TIR) is twice the parallel offset between the two shaft centrelines at the coupling. The face reading (TIR across the dial's sweep diameter) is the angularity — a slope, in mm per mm. If you know the offset at the coupling and the slope, similar triangles give the correction at any distance along the machine:
Apply it at the front feet (distance X) and rear feet (distance X + Y), in both planes. The vertical result is a shim pack; the horizontal result is a lateral move. Negative means the reverse: remove shims, move the other way.
Sign convention — the part that ruins alignments
- Vertical rim TIR is entered positive when the movable shaft sits high relative to the stationary shaft at the coupling (top reading minus bottom reading, taken as a signed quantity after the 180° check).
- Vertical face TIR is entered positive when the coupling gap is wider at the top than at the bottom.
- With those conventions, a positive computed shim means add shims. Horizontal signs follow the same logic in the side plane; mark your reference side on the sketch before you start, and keep it.
- Different textbooks flip both signs together — which is harmless if you are consistent, and catastrophic if you mix conventions mid-job. The protection is the verification pass: after correcting, re-measure. The readings must come back near zero by the same convention.
Assumptions and applicability
- Soft foot first. If any foot rocks, the machine distorts as you tighten and no arithmetic survives it. Correct soft foot before taking readings — and suspect it whenever corrections refuse to repeat.
- Bracket sag must be measured (roll the rig on a pipe) and compensated in the rim readings; unmeasured sag writes itself straight into the vertical plane.
- Readings assume both shafts rotated together with the coupling engaged, TIRs taken after the 0°/90°/180°/270° consistency check (opposite readings summing to the same TIR). Readings that fail that check are dirt, looseness or a bent shaft — not data.
- This is cold alignment. Machines that grow thermally need deliberate cold offsets — compute the growth with the Thermal Expansion Calculator and aim off-target on purpose.
- Typical acceptance at 1,500 rpm (good industrial practice): offset ≤ 0.05 mm and angularity ≤ 0.05 mm per 100 mm at the coupling — tighter for high-speed machines, per the OEM where specified.
Worked example (the defaults above)
Vertical: rim TIR +0.10 mm → offset +0.05 mm; face TIR +0.15 mm over 150 mm → slope 0.001 mm/mm (0.10 per 100). Front feet at 250 mm: 0.05 + 0.001 × 250 = +0.30 mm of shims. Rear feet at 750 mm: 0.05 + 0.001 × 750 = +0.80 mm. Horizontal readings (−0.06 rim, −0.09 face) give moves of −0.18 mm (front) and −0.48 mm (rear). Shim the vertical, move the horizontal, re-measure, and expect the next pass to be a fraction of the first — that convergence is how you know the convention held.
References
Standard rim-and-face method as taught in machinery alignment practice (e.g. Piotrowski, Shaft Alignment Handbook); tolerance guidance per ANSI/ASA S2.75 and OEM coupling documentation.
Related reading: Inside a 60,000-Hour Overhaul — where this arithmetic earns its keep.
Related calculators: Thermal Expansion · Bolt Torque & Preload