What Thermal Growth Does to an Aligned Machine

Why this matters

A machine aligned cold is aligned to a geometry that exists only when it is off. Warm it up and the shaft centerlines move, by different amounts, in a direction nobody sees. The shops that get this wrong are rarely the ones who ignore it. They are the ones who computed it with the wrong temperature and applied a correction two and a half times larger than the real movement, which leaves the set further out hot than doing nothing would have. Thermal growth is three terms multiplied together, and two of the three are routinely taken from the wrong place.

Getting the temperature safely

The measurement this article depends on is the temperature of the machine's support metal at operating condition, and there is no version of that reading worth taking through a guard on a running machine. Take surface temperatures with a non-contact infrared thermometer from outside the guard line. If a contact reading is genuinely needed, install a surface probe while the machine is locked out - motor disconnect open and locked, terminals proved dead with a live-dead-live check on a known live source (29 CFR 1910.333(b)(2); NFPA 70E-2021, 120.5), rotor stopped and blocked under 29 CFR 1910.147 - and read it afterwards from the instrument, never by reaching in.

Two hazards attach to reading a hot machine. Surfaces above about 140 F burn on contact, so let the machine cool or wear gloves rated for the contact temperature before working bare-handed, and remember that a machine shut down for ten minutes is still at nearly running temperature. And do not strip insulation to get at pipe or casing metal without knowing what the insulation is: thermal system insulation installed before 1981 is treated as presumed asbestos-containing material under 29 CFR 1926.1101, with general industry work covered by 29 CFR 1910.1001, so leave it intact and have it assessed rather than pulling a section to reach a surface. Read the exposed metal you already have instead.

The relationship, and where each term comes from

Growth equals the coefficient of linear thermal expansion, times the length being heated, times the temperature rise of that length. Written short: growth equals C times L times delta T. The arithmetic is trivial. Every field error is in what you put in for L and delta T.

C: the material coefficient, with the range it was measured over

Mean coefficients of linear thermal expansion, from roughly room temperature up through a few hundred degrees F, in microinches per inch per degree F:

Those are mean values over that range, and coefficients rise as temperature rises, so a support running well above a few hundred degrees F needs the value for its actual temperature range from a materials table or the machine builder rather than the number above. Note also how much the material matters: the same machine built in austenitic stainless rather than cast iron grows about sixty percent more for the same rise.

L: the height from the shim plane to the shaft centerline

This is the term people substitute wrongly most often. L is not the overall height of the machine, not the casing diameter, and not the shaft length. It is the vertical distance from the plane where the machine is anchored - the bottom of the feet, on top of the shims - up to the shaft centerline.

The reason is that the foot is the datum. The machine is held at that plane, so expansion accumulates upward from it, and the shaft centerline rises by the expansion of the material between the two. Metal below the shim plane belongs to the base, not the machine, and metal above the shaft centerline moves the casing top without moving the shaft.

Delta T: the rise of the support metal, not the fluid and not the room

This is the term that produces the expensive errors. Delta T is the temperature rise of the metal between the shim plane and the shaft centerline, and that metal is nowhere near the process temperature.

The feet are bolted to a base that sits at or near ambient and acts as a heat sink. The support metal therefore runs a gradient: close to base temperature down at the foot, close to casing temperature up near the centerline. A pump moving 200 F water in a 70 F room does not have a 130 F support rise. It has something considerably less, and the only honest ways to get it are the machine manufacturer's published growth figures, a set of measured surface temperatures taken at several heights up the support at steady operating condition and averaged, or a hot check that measures the movement directly instead of predicting it.

The other two directions

Vertical growth is the one that dominates the coupling reading, but it is not the only movement.

Axial. A machine grows away from wherever it is anchored along its length, so a casing with a fixed foot pair and a sliding pair grows toward the sliding end. That changes the distance between shaft ends, which is a real setting on any coupling and a hard specification on a limited-end-float set with a sleeve-bearing motor. Check whether the machine's designed anchor is where you think it is before predicting which way the gap closes.

Horizontal. A symmetric machine grows outward symmetrically about its own centerline, so side-to-side movement of the shaft is usually small. It stops being small when the machine is anchored asymmetrically - a dowel pinning one foot, a bracket restraining one side - because then growth is referenced to the pinned side and the shaft walks toward the free one.

Worked example: a pump and motor, computed twice

A cast-iron centrifugal pump on 200 F service, motor driven, in a 70 F mechanical room.

Pump. Shim plane to shaft centerline: 12.0 inches. Cast iron, so C equals 6.0 microinches per inch per degree F, which is the mean value over the range this support actually runs in. Support metal rise, measured at three heights at steady condition and averaged: 70 F. Growth equals 12.0 times 6.0 times 70, in microinches, which is 5,040 microinches, or 5.0 mils.

Motor. Shim plane to shaft centerline: 8.0 inches. Steel frame, C equals 6.5. The motor is not heated by the process at all; its rise comes from its own winding and bearing losses, measured at 40 F. Growth equals 8.0 times 6.5 times 40, which is 2,080 microinches, or 2.1 mils.

Differential. The pump shaft rises 5.0 mils, the motor shaft rises 2.1 mils, so at operating temperature the pump shaft sits 2.9 mils higher relative to the motor than it did cold. That 2.9 mils is the number that matters. Neither machine's individual growth means anything on its own, because both moving together by the same amount would leave the joint untouched.

Now compute it the way it usually gets computed. Take the fluid rise, 200 F minus 70 F ambient, as the pump's delta T: 12.0 times 6.0 times 130 equals 9,360 microinches, or 9.4 mils. Differential comes out 9.4 minus 2.1, which is 7.3 mils, against a real value of 2.9. That is 2.5 times the actual movement.

Why the over-estimate is worse than no estimate. Apply a cold offset of minus 7.3 mils, meaning you set the pump shaft 7.3 mils low cold, expecting it to rise 7.3. It rises 2.9. Hot position is minus 7.3 plus 2.9, which is minus 4.4 mils: the set is 4.4 mils out, in the opposite direction, at operating temperature. Had nobody compensated at all, it would have run zero cold and plus 2.9 mils out hot. The careful, wrong calculation left the machine 4.4 mils out where doing nothing left it 2.9. Over-correcting is not a conservative error.

What flips the sign entirely. Put the same pump on chilled water at 45 F in the same 70 F room and the support metal runs below ambient. The pump support contracts, the motor still grows from its own losses, and the differential reverses: the pump shaft ends up lower relative to the motor hot than it was cold, so the cold offset goes the other way. Any machine on a cold service needs the sign checked rather than assumed, and it is the single most common sign error in the field.

What makes the number unusable. A machine that runs in short cycles never reaches thermal steady state, so its actual growth sits somewhere between zero and the computed value and moves every time the duty changes. On those, a computed offset is a guess dressed as arithmetic, and the right answer is a hot check or the manufacturer's figure rather than a calculation. Same conclusion for an outdoor machine, where the base and the ambient swing seasonally and the differential you measured in July is not the one running in January.

How to verify the prediction against reality

The only real verification is a hot check, and it has to be run honestly. Bring the machine to steady operating condition, shut down, isolate and lock out the motor circuit and the process lines, and take the coupling readings as quickly as the safe sequence allows. The machine begins cooling the moment it stops, so the reading you take is already smaller than the true hot condition, and the elapsed minutes from shutdown to reading is part of the measurement. Write it on the record next to the numbers. A hot check with no elapsed time recorded cannot be compared to the next one.

Compare the hot reading against the cold reading taken under the recorded cold conditions. The difference between them is the actual differential growth of your machine, on your service, in your room, and it beats any calculation in this article. Once you have it, the calculated value's only remaining job is to tell you whether the measurement is plausible.

References

• 29 CFR 1910.147 for mechanical isolation and stored energy; 29 CFR 1910.333(b)(2) with NFPA 70E-2021, 120.5, for the motor circuit; 29 CFR 1926.1101 for presumed asbestos-containing thermal system insulation installed before 1981, and 29 CFR 1910.1001 for the general industry asbestos standard.
• Machine manufacturer documentation for published thermal growth figures, the designed anchor point, and the between-shaft-ends dimension.
• Published mean coefficients of linear thermal expansion by material and temperature range, from a materials reference or the machine builder.
• See related: "How to Allow for Thermal Growth When You Align Cold"; "The Alignment That Was Perfect Cold and Wrong Hot"; "How to Set Up a Shaft Alignment and Know It Held".