Shaft thermal growth
How far a machine's shaft rises as it heats up — the offset you build into a cold alignment so the coupling runs true hot, not cold. Height times expansion coefficient times temperature rise.
Shaft thermal growth · vertical centerline rise
ΔL = L × α × ΔT
What this gives you
When a machine runs, its casing and shaft heat up and the shaft centerline rises above where it sat cold. Align a pump to its motor cold and dead-on, and the coupling can be badly misaligned once both machines reach operating temperature. This calculator estimates that vertical rise so you can build an intentional cold offset into the alignment — the shafts are deliberately set “off” cold so they run true hot. The growth is ΔL = L × α × ΔT, where L is the height from the machine feet to the shaft centerline, α is the material’s coefficient of thermal expansion, and ΔT is the temperature rise from cold to running.
Reading the result
The main number is the growth in mils — thousandths of an inch, the unit alignment tools and dial indicators speak in. One mil is 0.001 in. A few mils of vertical rise is typical for a warm pump; a hot turbine or a tall motor can move 10 mils or more. The value assumes the whole support height sits at the temperature rise you enter — real machines have a gradient, so treat this as a starting target and confirm with a hot alignment check or the OEM’s published thermal-growth figures when they exist. Pick the shaft material — carbon steel, cast iron, 304 or 316 stainless, aluminum or brass — and enter the temperature rise in either °F or °C; the °C value is scaled by 1.8 before the per-°F expansion coefficient is applied.
Field note — the offset goes on the machine that grows more
Thermal growth only matters as a difference between the two machines. If a motor and pump both rise the same amount, the coupling stays aligned and no offset is needed. In practice the driven machine — a pump handling hot product, say — usually grows more than its motor, so you set the motor low by the difference in growth, not by either machine’s absolute rise. Switch the tool to Differential (motor vs pump) mode to enter both machines at once and read the net vertical offset directly, or run each separately and subtract.
Worked example
A pump with its shaft centerline 10 in above the feet, carbon steel (α ≈ 6.5 µin/in·°F), running 50 °F above ambient: growth is 10 in × 6.5 µin/in·°F × 50 °F = 3,250 µin = 0.00325 in, or 3.25 mils. If its motor grows only 1 mil, you would set the motor about 2.3 mils low cold so the two centerlines meet when everything is hot.