Temperature Effects

Part of Precision Measurement

Understanding and compensating for thermal expansion in precision measurement and machining.

Why This Matters

Everything expands when heated and contracts when cooled. For rough woodwork, this does not matter. For precision metalwork, it is one of the most important sources of measurement error — and the one most often overlooked by beginners.

Steel expands about 11 micrometers per meter per degree Celsius. This sounds tiny. But a 500 mm steel shaft measured when it is 5°C warmer than the measuring instrument will read 0.027 mm larger than its true size. That is nearly three times the tolerance on a precision bearing fit. An entire morning’s machining work can be invalidated by temperature effects if you do not account for them.

Understanding, measuring, and compensating for thermal effects is not optional at the precision level. It is the difference between reproducible, reliable results and mysterious inconsistency.

Coefficients of Thermal Expansion

All materials expand at characteristic rates, expressed as the coefficient of linear thermal expansion (CTE), usually in micrometers per meter per degree Celsius (µm/m/°C):

Material	CTE (µm/m/°C)
Invar (36% Ni steel)	1.2
Glass, borosilicate	3.3
Granite	5–9
Cast iron	10–11
Carbon steel	11–12
Stainless steel	10–17
Copper	17
Brass	18–20
Aluminum	23
Lead	29
Concrete	10–12

Key insight: If the workpiece and the measuring instrument are made of the same material and at the same temperature, thermal expansion cancels out — the instrument expands with the work, and the reading is correct. Problems arise when:

• Workpiece and instrument are at different temperatures
• Workpiece and instrument are made of different materials

Calculating Thermal Error

Formula: ΔL = L × CTE × ΔT

Where:

• ΔL = dimensional change (mm)
• L = nominal length (mm)
• CTE = coefficient in µm/m/°C (= mm/m/°C × 10⁻³)
• ΔT = temperature difference (°C)

Example: A 300 mm steel shaft is 8°C warmer than the steel micrometer used to measure it.

ΔL = 0.300 m × 11 µm/m/°C × 8°C = 26.4 µm = 0.026 mm

The micrometer will read 0.026 mm larger than the shaft’s true cold size.

Example 2: A 150 mm aluminum part is measured with a steel rule when the part is 3°C warmer than the rule.

Aluminum CTE = 23; Steel CTE = 11. Differential CTE = 23 - 11 = 12 µm/m/°C. ΔL = 0.150 m × 12 µm/m/°C × 3°C = 5.4 µm = 0.005 mm

Less dramatic, but still meaningful for close-tolerance work.

Standard Measurement Temperature

International standard: 20°C (68°F)

All precision measurements are, by convention, referred to 20°C. If you measure at a different temperature, you should either:

1. Correct your measurements to 20°C, or
2. Ensure workpiece and instrument are at the same temperature

Allowing equilibration:

• A machined part that has just been cut will be warm from the cutting operation
• Allow it to cool to room temperature before measuring (typically 15–30 minutes for small parts)
• For large parts (over 1 kg), allow longer — the thermal mass requires more time to equilibrate

Hand Warmth

Your hands are ~35°C. Holding a micrometer for 5 minutes transfers enough heat to cause 0.003–0.005 mm of error. Hold micrometers by the insulated grip only, or let them rest on the surface plate between measurements.

Controlling the Measurement Environment

Ideal: A temperature-controlled room at 20°C ± 0.5°C. Most large precision work is done in such rooms.

Practical for rebuilding: Measure in the coolest time of day (early morning). Avoid measuring in direct sunlight. Let parts and instruments stabilize together before measuring.

Practical checks:

1. Measure the same dimension twice with a 30-minute gap
2. If the readings agree within your target tolerance, temperature effects are not significant
3. If they differ, let everything equilibrate longer

The thermometer rule: Keep a thermometer near your measuring station. Record temperature with important measurements. If a re-check gives a different result, temperature records may explain why.

Differential Expansion in Machine Design

Temperature effects matter not just for measurement but for machine performance:

Spindle growth: A lathe spindle running hot (from bearing friction) grows in length. This shifts the tool tip toward the workpiece, making parts progressively smaller with each pass. Good machining practice allows the spindle to reach thermal equilibrium before taking finish cuts.

Structural distortion: A machine frame that is warm on one side and cool on the other will bow slightly. Surface grinders and precision lathes are sensitive to this — measure in the morning after everything has equalized, not on one side after a window was open all night.

Different materials in an assembly: If a steel shaft runs in a brass bearing, the brass expands faster with temperature. The clearance between shaft and bearing changes with temperature. A fit that is correct at 20°C may seize at 40°C or rattle at 0°C. This must be designed for.

Invar and Low-Expansion Materials

For applications where thermal expansion cannot be tolerated:

Invar (36% nickel-iron alloy): CTE of only 1.2 µm/m/°C versus steel’s 11. Used for:

• Precision reference bars
• Survey equipment
• Optical mounts
• Bimetallic thermometer compensation

Making Invar: Requires controlled alloying — not achievable in a basic forge. However, if pre-collapse Invar stock is available, preserve it carefully for standards applications.

Alternative: Granite reference surfaces — very low CTE (5–9 µm/m/°C depending on composition), naturally occurring, no fabrication required beyond grinding flat.

Record Keeping

When recording precision measurements:

• Always note the temperature at time of measurement
• Note the material of the workpiece
• Note whether the workpiece had time to equilibrate
• Flag any measurements taken under non-standard conditions

This habit pays off when investigating discrepancies between batches of parts, when comparing measurements taken by different operators, and when diagnosing why a part that measured in tolerance at one stage is out of tolerance at the next. Temperature is surprisingly often the hidden culprit.