BIZOMAT MAKEOS · Materials
Differential Thermal Expansion
How does a fit clearance change when the bore and shaft materials expand differently?
Calculate how the diametral clearance between a bore and a shaft of different materials changes when both change temperature by the same amount.
Open the calculatorRuns in your browser. No account needed.
How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Nominal fit diameter | mm | Nominal diameter of the fit. |
| Bore (housing) expansion coefficient | ×10⁻⁶ /°C | Linear expansion coefficient of the housing material over the temperature range, for example about 23 × 10⁻⁶ /°C for many aluminium alloys. |
| Shaft expansion coefficient | ×10⁻⁶ /°C | Linear expansion coefficient of the shaft material, for example about 12 × 10⁻⁶ /°C for many carbon steels. |
| Uniform temperature change from assembly | °C | Temperature change of both parts from the assembly temperature; negative for cooling. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Nominal fit diameter
- What it is
- The nominal diameter where the bore and shaft meet, for example the bearing seat or hub bore size.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.1 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The clearance change is directly proportional to the diameter.
- Get it right
- Use the fit diameter itself, not the housing outside diameter.
What this means: Bore (housing) expansion coefficient
- What it is
- The linear thermal expansion coefficient of the housing or hub material that contains the bore: how much it grows per unit length for each degree of temperature change.
- Units and format
- Enter a number in ×10⁻⁶ /°C: ×10⁻⁶ /°C. The form accepts 0 ×10⁻⁶ /°C to 300 ×10⁻⁶ /°C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 23 ×10⁻⁶ /°C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher bore coefficient opens the clearance more when the parts heat up.
- Get it right
- Take it from the material data sheet for the actual alloy and temperature range; the unit is ×10⁻⁶ per °C, so type 23 for 23 × 10⁻⁶.
What this means: Shaft expansion coefficient
- What it is
- The linear thermal expansion coefficient of the shaft material: its growth per unit length for each degree of temperature change.
- Units and format
- Enter a number in ×10⁻⁶ /°C: ×10⁻⁶ /°C. The form accepts 0 ×10⁻⁶ /°C to 300 ×10⁻⁶ /°C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 12 ×10⁻⁶ /°C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher shaft coefficient closes the clearance more when the parts heat up.
- Get it right
- Enter the number before ×10⁻⁶, not the full small decimal; take it from supplier data for the actual alloy.
What this means: Uniform temperature change from assembly
- What it is
- The change in temperature of both parts together, from the temperature at assembly to the operating temperature. Both parts are assumed to reach the same temperature.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -250 °C to 1500 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 60 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The clearance change is directly proportional to the temperature change; reversing its sign reverses the effect.
- Get it right
- Enter a negative value for cooling below the assembly temperature. Use the change, not the operating temperature itself.
Method and formulas
- Growth of each part = diameter × coefficient × 10⁻⁶ × temperature change.
- Change in clearance = bore growth − shaft growth; a positive value loosens the fit.
- Example: 50 mm, 23 and 12 × 10⁻⁶ /°C and +60 °C give 0.069 − 0.036 = +0.033 mm more clearance.
Limitations
- Both parts are assumed to be at one uniform temperature. In service they often differ, which can dominate the result.
- Coefficients are constant over the range; real values change with temperature and alloy. Stresses in an interference fit are not calculated.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check whether a fit loosens or tightens at operating temperature
- Compare housing materials
- Estimate a temperature for assembly
Who it is for
- Design engineers
- Maintenance engineers
What you get
- Change in diametral clearance (mm)
- Bore and shaft growth (mm)
Interpreting the result
- Add the result to the assembly clearance to estimate the running clearance; a negative running clearance means interference.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 375–379. Topic reference; no source tables or recommended settings are reproduced.
- NPL, Fundamental Good Practice in Dimensional Metrology, GPG 80 — https://eprintspublications.npl.co.uk/3360/1/mgpg80.pdf
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Thermal contraction in assemblies
In Cryogenic Design by the Numbers
What it covers: Contraction of cryostat materials from NIST, mean coefficients for constant-property tools, fits that open, bolts that lose preload, supports that shrink, and two dowels that sheared.
BIZOMAT tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.