Shaft Alignment & Thermal Growth — Why a Perfect Cold Alignment Is a Defect

The situation on site

A hot-oil pump, 180 °C, driven by a 90 kW motor. The millwright is proud of this one: laser aligned, offset 0.01 mm, angularity 0.01 mm/100 mm, printed report in the file. Best numbers he has ever produced on this unit.

Six weeks later the coupling element is cracked, the pump inboard bearing is running hot, and the vibration spectrum has a strong 2× running-speed peak with high axial amplitude — the textbook misalignment signature.

Guess first: the alignment report says 0.01 mm. Where did the misalignment come from?

The reveal: the pump shaft climbed 0.51 mm as the casing and pedestal reached temperature. The motor climbed 0.16 mm — a 0.35 mm difference at the front feet, which projects to 0.29 mm of offset at the coupling. The machine that was perfect at 25 °C is running four times its 0.07 mm tolerance out at 180 °C. The alignment report was not wrong. It was taken in the one condition the machine never operates in.

The misconception, stated plainly

"Aligned cold = aligned running. Zero is the target; anything else is sloppy work."

Let it stand. It is what every instinct says, and it is what an alignment report measures.

Then dismantle it: alignment is only meaningful at operating temperature. Everything that holds the shaft up — casing, pedestal, bearing housing, baseplate — is metal, and metal that gets hot gets taller. The two machines rarely get hot by the same amount, from the same height, in the same material. So the two shaft centrelines move by different amounts.

Which means the cold alignment must be deliberately wrong, by exactly the difference the heat is going to make, and in the opposite direction. Cold zero is not neutral. Cold zero is a decision to be misaligned hot.

The two misalignments, and why they cost money

OFFSET (parallel)   — the two shaft centrelines are parallel but not collinear.   [mm]
ANGULAR (gap)       — the two centrelines meet at an angle.                       [mm per 100 mm]

Both exist in two planes at once: vertical (fixed by shims) and horizontal (fixed by sideways moves / jack bolts). Four numbers, and a real job sets all four.

Why it matters:

• Coupling. A flexible coupling accommodates misalignment by flexing once per revolution. At 2 950 rpm that is 49 fully reversed strain cycles per second — a fatigue machine. Double the offset and you roughly double the alternating strain in the element.
• Bearings. Misalignment shows up as a steady radial reaction the bearing was not sized for. Rolling-element life runs as L10 ∝ (C/P)³ — a 25 % rise in load is a 50 % cut in life.
• Seals. The seal faces must stay square to the shaft to within a few micrometres of film thickness. Shaft deflection at the seal chamber opens and closes the face gap once per rev.
• Signature. Classic misalignment gives 2× running speed dominance and unusually high axial vibration — a good early clue that the fault is geometric, not unbalance.

Tolerance is not "as tight as possible" — it is a function of speed, because the damage is a per-revolution event:

(typical vendor / API 686 practice — always use the machine vendor's own table.)

Symbol key — every symbol on this sheet

• α (alpha) — coefficient of thermal expansion: how much 1 mm of the metal grows per °C · /°C (×10⁻⁶)
• L — growth height: shim plane (the datum that does not move) up to the shaft centreline · mm
• ΔT — temperature rise: operating metal temperature minus the temperature at which you aligned · °C
• g — thermal growth of one support = α·L·ΔT · mm
• Δg — growth difference between the two machines; this is the whole cold target · mm
• δ₁, δ₂ — required cold shim change at the movable machine's front / rear feet · mm
• A, B — distance from the coupling centre to the movable machine's front / rear feet · mm
• F, R — subscripts for front (coupling-side) and rear feet
• offset — parallel displacement of one shaft centreline from the other · mm
• angularity — relative slope of the two centrelines · mm per 100 mm
• T_amb — the metal temperature when the dial/laser reading is taken (not the weather) · °C

The one formula, applied four times

g = α · L · ΔT                (growth of one support, mm)

Apply it at each foot of each machine, because each foot can have its own height and its own temperature. Then:

cold target at the coupling   = g_stationary(coupling) − g_movable(coupling)
cold shim at movable foot i   = target evaluated at that foot's position

Sign convention that keeps you out of trouble: whichever machine grows more must start lower. A hot pump grows more than its motor, so the motor is shimmed up cold. It feels wrong every time and it is right every time.

Typical α values (×10⁻⁶ /°C): carbon/alloy steel 11.7, cast iron 10.8, 12 % Cr (410) 9.9, austenitic 304/316 17.3, aluminium 23. A stainless pedestal grows nearly 50 % more than a carbon-steel one at the same height and temperature — material choice alone can be a 0.1 mm error.

Feed real geometry into the cold-target calculator: ▶ open the interactive: rotating alignment calc — enter the two machines' materials, foot heights and operating temperatures and it returns the shim change at each foot, the cold offset and angularity you should read on the laser, and a live picture of the two centrelines cold and hot.

Worked example — 180 °C pump and its motor

Geometry (coupling centre at x = 0, motor to the right):

Pump (stationary):  shim-plane to shaft CL   L = 350 mm   carbon steel α = 11.7e-6
                    front foot 300 mm from coupling, metal 150 °C
                    rear  foot 900 mm from coupling, metal 180 °C
Motor (movable):    shim-plane to shaft CL   L = 400 mm   carbon steel α = 11.7e-6
                    front foot 250 mm, rear foot 850 mm, metal 60 °C both
Aligned at metal temperature 25 °C.  Speed 2 950 rpm.

Step 1 — growth at each foot.

pump front  g = 11.7e-6 × 350 × (150−25) = 0.512 mm
pump rear   g = 11.7e-6 × 350 × (180−25) = 0.635 mm
motor both  g = 11.7e-6 × 400 × ( 60−25) = 0.164 mm

Step 2 — project each shaft line to the coupling. The pump line rises 0.512 mm at x = −300 and 0.635 mm at x = −900, so its slope is (0.635 − 0.512)/(−600) = −0.000205 mm/mm and at the coupling it has risen 0.512 − 0.000205 × 300 = 0.451 mm. The motor is flat: 0.164 mm.

Step 3 — the cold target.

target at coupling = 0.451 − 0.164 = +0.287 mm      (motor HIGH by 0.29 mm, cold)
target slope       = −0.000205 mm/mm = −0.021 mm per 100 mm

Step 4 — turn it into shims. Evaluate the target line at each motor foot:

front foot (x = 250):  0.287 − 0.000205 × 250 = +0.236 mm   → add 0.24 mm shim
rear  foot (x = 850):  0.287 − 0.000205 × 850 = +0.113 mm   → add 0.11 mm shim

Step 5 — sanity-check against tolerance. At 2 950 rpm the acceptable offset is ~0.07 mm. The cold target is 0.287 mm — four times the tolerance, and that is correct. A cold report reading 0.29 mm offset is the passing report here. A cold report reading 0.01 mm is the failure.

Watch the same thing happen in three dimensions: ▶ open the interactive: rotating alignment 3d — drive the temperature slider with "aligned cold" selected and the shafts break apart as they heat; select "cold target set" and they walk into line.

Before you align anything: soft foot and pipe strain

Two site conditions make every number above meaningless.

Soft foot — the machine does not sit flat, so tightening the bolts bends the frame and moves the shaft. Check it with a dial on each foot while you loosen that bolt alone; > 0.05 mm (0.002 in) of movement is a soft foot and must be corrected before alignment, not after. Four kinds worth knowing apart:

• Parallel — a uniform gap under one foot. Shim it.
• Angular — the foot is not parallel to the base. A stack of flat shims makes it worse; machine the base or use a stepped/tapered shim.
• Squishy — too many shims, rust, paint or burrs; the stack compresses. Rule of thumb: max 4 shims per foot, cleaned, thickest at the bottom, precut stainless.
• Bolt-bound / induced — the hold-down bolt is jammed in its hole, or piping is pulling the frame. Shimming cannot fix either.

Pipe strain masquerading as misalignment. This is the crossover with the nozzle-load topic — piping that exceeds the API 610 allowable distorts the casing, and the distortion reads on the laser as misalignment you then "correct" with shims. You have now shimmed a bent machine.

The test is simple and is written into API 686 practice: put indicators on the coupling, then slacken the suction and discharge flange bolts. If the shaft moves more than 0.05 mm (0.002 in), the pipe is imposing strain — fix the pipe, not the shims. The flange faces should come together parallel and concentric without being pulled, and no bolt should need a lever.

Common pitfalls

• Aligning to zero cold on any machine that runs hot — the defect this topic exists to kill.
• Using ambient air temperature instead of the metal temperature at the moment of alignment.
• Measuring L from the floor instead of from the shim plane, then wondering why the answer is 3×.
• Forgetting the pump and motor can be different materials — 304 pedestals grow 48 % more than steel.
• Ignoring the rear-foot temperature difference, which is what generates the angular target.
• Fixing an apparent misalignment with shims when the real cause is soft foot or pipe strain.
• Leaving bar sag uncompensated on reverse-dial jobs, or mixing a sag-checked and non-checked set.
• Re-aligning after a hot run without re-checking that the machine has actually cooled and returned to its cold datum — a half-cooled machine gives a half-wrong reading.
• Treating the coupling as a "misalignment allowance". Its catalogue rating is a survival limit for upsets, not a design target; bearings and seals see the load long before the coupling complains.

Outcome

• Alignment is a hot condition. The cold setting is a deliberate, computed offset in the opposite direction to the expected relative growth.
• Growth at every support is g = α·L·ΔT, with L measured from the shim plane to the shaft centreline and ΔT relative to the alignment-day metal temperature. Only the difference between machines matters.
• Whichever machine grows more starts lower: a hot pump means the motor is shimmed up cold.
• Different front/rear foot temperatures create an angular cold target, not just an offset.
• Tolerance scales with speed because the damage is per-revolution; 3 000 rpm allows roughly half what 1 000 rpm allows.
• Cure soft foot (> 0.05 mm) and prove there is no pipe strain (> 0.05 mm shaft movement when the flange bolts are slackened) before you trust any alignment number.
• Tools: ▶ open the interactive: rotating alignment calc (cold shims per foot from real geometry) and ▶ open the interactive: rotating alignment 3d (watch the shafts come into line as they heat).

Open items

• Add horizontal (sideways) thermal targets for single-side-restrained casings.
• Add a vendor-supplied growth-target case (turbines are usually specified, not calculated).
• Cross-link the pipe-strain test to the nozzle-load checker so a failed flange-bolt test can be converted straight into an estimated nozzle load.

Educational teaching material — simplified and illustrative. Not for engineering design use.
© EPiC Circle · provided by PipeAxis