BIZOMAT MAKEOS · Materials
Differential Thermal Fit
How does clearance change at different part temperatures?
Calculate signed diametral clearance after hole and shaft undergo separate uniform temperature changes from one reference.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Hole diameter at reference temperature | mm | Actual or selected limit hole diameter at the reference temperature. |
| Shaft diameter at reference temperature | mm | Actual or selected limit shaft diameter at the same temperature. |
| Hole-material expansion coefficient | µm/(m·K) | Validated mean linear expansion coefficient for the hole material over its range. |
| Shaft-material expansion coefficient | µm/(m·K) | Validated mean coefficient for the shaft material over its range. |
| Common reference temperature | °C | Common temperature at which both entered diameters apply. |
| Hole operating temperature | °C | Uniform temperature of the hole-carrying part. |
| Shaft operating temperature | °C | Uniform operating shaft temperature. |
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: Hole diameter at reference temperature
- What it is
- The diameter of the bore at the common reference temperature, either a measured size or the limit size you want to check.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50.02 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger hole adds directly to the clearance.
- Get it right
- Use the size at the reference temperature; a hole measured warm already includes some expansion.
What this means: Shaft diameter at reference temperature
- What it is
- The diameter of the shaft at the same reference temperature as the hole, measured or chosen from its tolerance limits.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.001 mm to 1000000 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
- A larger shaft reduces the clearance one-for-one.
- Get it right
- Check worst-case fits by entering the largest shaft with the smallest hole, and the reverse.
What this means: Hole-material expansion coefficient
- What it is
- The mean linear thermal expansion coefficient of the material carrying the hole over the temperature range: its growth in micrometres per metre per kelvin.
- Units and format
- Enter a number in µm/(m·K): micrometres per metre per kelvin. The form accepts -1000 µm/(m·K) to 1000 µm/(m·K). Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 23 µm/(m·K) as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher hole coefficient increases clearance when the hole heats above the reference.
- Get it right
- µm/(m·K) has the same number as ×10⁻⁶ /K; take it from validated supplier data for the alloy.
What this means: Shaft-material expansion coefficient
- What it is
- The mean linear thermal expansion coefficient of the shaft material over its temperature range, in micrometres per metre per kelvin.
- Units and format
- Enter a number in µm/(m·K): micrometres per metre per kelvin. The form accepts -1000 µm/(m·K) to 1000 µm/(m·K). Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 12 µm/(m·K) 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 reduces clearance when the shaft heats above the reference.
- Get it right
- Use the value for the actual alloy and temperature range, not a generic family value.
What this means: Common reference temperature
- What it is
- The temperature at which both entered diameters are true, often the inspection or assembly temperature.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -273.14 °C to 2000 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Each part grows in proportion to its own temperature minus this reference.
- Get it right
- Both diameters must apply at this one temperature; it is not an operating temperature.
What this means: Hole operating temperature
- What it is
- The uniform temperature the part containing the hole reaches in operation.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -273.14 °C to 2000 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 80 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A hotter hole part grows more, opening the clearance.
- Get it right
- Enter the temperature itself, not the rise above reference; the tool works out the difference.
What this means: Shaft operating temperature
- What it is
- The uniform temperature the shaft reaches in operation, which can differ from the hole’s temperature.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -273.14 °C to 2000 °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
- A hotter shaft grows more, closing the clearance.
- Get it right
- Shafts often run hotter or cooler than housings; use a measured or estimated shaft value.
Method and formulas
- For each part: diameter at temperature = reference diameter × [1 + coefficient × 10⁻⁶ × temperature change].
- Signed diametral clearance = hole − shaft. Positive is gap; negative is geometric interference.
- Example: 50.02 mm hole with coefficient 23 and 50 mm shaft with coefficient 12, referenced at 20°C and operating at 80°C and 60°C, gives 50.0890276 and 50.024 mm. Clearance = 0.0650276 mm.
Limitations
- Uniform, unrestrained isotropic expansion with constant mean coefficients; gradients, coatings and constraint are excluded.
- Interference is geometric, not a contact-pressure or assembly-force result.
- Coefficients are user-supplied, and the examples do not select materials. Tolerance/temperature corner cases require separate evaluation.
- Default values are worked examples, not recommended settings or material properties.
Typical uses
- operating clearance
- differential expansion
- thermal interference
Who it is for
- Design engineers
- Maintenance engineers
What you get
- Operating diameters
- Reference and operating signed clearance
- Thermal clearance change
Interpreting the result
- Check minimum and maximum clearance across credible size and temperature conditions.
- Verify material data over the complete temperature range.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 375–379. Topic reference; implementation and examples are original, and no source tables are reproduced.
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