§1The last machine element
Misalignment is not a fault a machine reports — it is a hidden preload it pays for continuously, at exactly the addresses this section has spent its pages protecting.
Bolt a motor a few tenths off its pump’s line and nothing dramatic happens; the flexible coupling absorbs it, as its catalogue promised. But absorbs means flexes under it every revolution — fatigue duty the couplings page priced — and the reaction to that flexing arrives as steady radial and axial force on four bearings that never appear on any load calculation, feeding the bearing page’s cube law around the clock: a load increment invisible at commissioning, halving lives silently. Seals wear eccentric orbits; the vibration pages’ once- and twice-per-revolution signatures rise; on a hot day the loosest joint in the drive announces the sum. Alignment is therefore treated here as the section’s closing element: a manufactured property with a specification (§6), a measurement system (§3), an installation arithmetic (§4) and even a thermal design case (§5) — the discipline that turns a shelf of correctly chosen components into the machine their catalogues described. It is also, agreeably, the cheapest element on the shelf: a dial, patience, and a box of shims.
Contents§2The two errors
However tangled two shafts look, their misalignment reduces to exactly four numbers: an offset and an angle, in the vertical plane and the horizontal.
Extend both shaft centrelines to the coupling and compare them there — the convention that makes every method’s numbers commensurable. Parallel offset is the perpendicular distance between the lines at the coupling plane: the shafts point the same way but run on different rails, and the hero draws its vertical case. Angular misalignment is the difference in direction — the lines converge or diverge — expressed most usefully as a slope, millimetres per hundred millimetres or per metre, because a slope multiplies by distance in §4’s triangles without ceremony. Each error lives independently in two planes: vertical, corrected with shims under feet, and horizontal, corrected by sliding the machine sideways against its jacking screws — four numbers, two correction tools, and the complete state of the joint. Real machines present mixtures, and the coupling’s gap-and-rim geometry feels them differently (offset works the coupling in shear each revolution, angle works it in bending), but the method never changes: measure until the four numbers are known, then move one machine — by convention the motor, the light, adjustable, expendable partner — until all four sit inside §6’s targets.
Contents§3Measuring
The measurement ladder runs from straightedge to laser, but its arithmetic was settled in the dial-indicator era — and three corrections separate a number from a mistake.
| Reading | Raw | Rule | Result |
|---|---|---|---|
| Rim sweep (offset) | TIR 0.30 mm | the dial sees the offset twice → halve it | offset 0.15 mm |
| Face sweep (angle) | TIR 0.10 mm on a Ø100 face | divide by the sweep diameter | 1 mm/m angularity |
| Bar sag | rigid-pipe test reads 0.06 mm | the test reads 2 × sag → apply the test value to every bottom rim reading | sag 0.03 mm, corrected |
| Soft foot | one foot lifts 0.08 mm as its bolt is cracked | anything past ~0.05 mm is a rocking base | shim that foot flat first |
| The ladder around the table: a straightedge and feeler across the coupling rims gets a rough set within a tenth or two; rim-and-face dials read offset and angle directly as above; reverse-dial sweeps a rim from each shaft, cancelling face-reading errors and suiting couplings that cannot be reached across; and the laser is the same triangles with the sag, sign conventions and arithmetic automated — which is why the dial-era rules remain the literacy: the laser’s screen is only trustworthy to someone who could have computed its answer. And the fourth row outranks the first three in sequence forever: measuring a machine that rocks on a soft foot is measuring the rock. | |||
§4The shim arithmetic
With the four numbers known, the correction is one similar-triangle line evaluated at each pair of feet — the whole craft of alignment compressed into primary-school geometry.
The §3 readings say the motor’s shaft sits 0.15 mm high at the coupling and slopes 0.5 mm/m rising toward the motor. Its front feet stand 0.3 m behind the coupling plane, its rear feet 0.9 m. Evaluate the line: front feet −(0.15 + 0.5 × 0.3) = −0.30 mm; rear feet −(0.15 + 0.5 × 0.9) = −0.60 mm — remove shims, twice as much at the back, and both offset and angle vanish in one move. The same triangles run sideways for the horizontal plane, with jacking screws and the dial watching in real time instead of a shim calculation. The craft around the arithmetic: correct vertical first (shimming disturbs horizontal less than sliding disturbs vertical), use clean stainless shims few and thick rather than a pastry of thin ones, snug the hold-down bolts in a consistent pattern, and re-measure after every move — the triangles are exact, but bases flex, bolts walk work sideways, and the dial is the only witness that counts. Two or three patient iterations is the honest norm.
§5Hot, cold and pipes
Machines are aligned cold and run hot — so the true target is a deliberate cold misalignment that thermal growth will close — and pipework must arrive with empty hands.
A machine’s shaft centreline stands on its frame, and frames grow: 300 mm of steel warming 30 °C rises αLΔT = 12 × 0.300 × 30 µm = 0.108 mm. If the driven machine runs hot while the motor stays near ambient, perfect cold alignment becomes a 0.11 mm offset at temperature — so the procedure aligns to cold targets, here parking the hot machine’s partner about 0.11 mm low, exactly as the manufacturer’s thermal-growth figures or a hot-alignment check prescribe. The second thermal citizen is pipe strain, alignment’s classic saboteur: flanges that need the bolts to pull them home are hanging their fabrication error on the machine casing, pre-loading the shafts before the coupling is even connected — and growing worse as the pipe heats. The acceptance test is simple and merciless: leave dials on the shaft while the flange bolts are tightened; if the needles move more than a whisker, the pipework — not the alignment — gets corrected. Alignment is a property of the whole installation; the shims only finish what the steelwork and pipework either respected or ruined.
§6Tolerances and the payback
How straight is straight enough is a speed question — and the answer’s payback is written in the ledgers of every preceding page, which is why this page closes the section.
Tolerance scales with speed because the coupling flexes and the bearings feel the error once per revolution: a 3000-rpm-class machine wants offsets held to a few hundredths of a millimetre and angles to a few hundredths per hundred, while a slow drive tolerates several times that — the machine maker’s or coupling maker’s table governs, and “the coupling can take it” is a statement about survival, not about §1’s hidden preload. Procedure finishes the job the triangles started: verify at final bolt torque (torquing moves machines), record the as-left numbers and the thermal targets on the machine’s card, and re-check after the first thermal cycles. Then the payback, collected from this section’s own accounts: bearing load taken off the cube-law meter; coupling elements flexing within their fatigue budget instead of consuming it; seals running centred; §3’s vibration signatures quiet; energy not spent flexing steel. It is the fitting last entry in a Machine Elements section — the element that is pure workmanship, costing a morning and a box of shims, whose entire output is that every other element on these pages finally behaves exactly as its page promised.
Contents§7Quick reference
The working core of the page on one card rack.
Four numbers
offset + angle × two planes
stated at the coupling
Readings
TIR/2 = 0.15 · face/Ø = 1 mm/m
sag: pipe test = 2× · soft foot > 0.05
Shims
−(offset + slope·x)
−0.30 front · −0.60 rear
Thermal
growth 0.108 mm worked
align to cold targets · no pipe strain
Payback
bearings · couplings · seals
the section, kept honest