BIZOMAT MAKEOS · Materials
Linear Thermal Growth
How much does an unrestrained dimension change with temperature?
Estimate signed linear growth using a supplied constant expansion coefficient and temperature change.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Initial length | mm | Dimension at the initial temperature. |
| Expansion coefficient | µm/(m·K) | Material supplier data over the temperature range; 12 is an illustrative input. |
| Initial temperature | °C | Temperature at which the initial length applies. |
| Final temperature | °C | Uniform final part 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: Initial length
- What it is
- The length of the part or feature at the initial temperature, before it heats or cools.
- 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 1000 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Growth is directly proportional to the initial length.
- Get it right
- Use the length at the initial temperature you enter, not at some other measurement temperature.
What this means: Expansion coefficient
- What it is
- The material’s mean linear thermal expansion coefficient over the temperature range: growth in micrometres per metre of length for each kelvin of temperature change.
- 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
- Growth is directly proportional to the coefficient.
- Get it right
- µm/(m·K) gives the same number as ×10⁻⁶ /K; take it from supplier data for the alloy and range.
What this means: Initial temperature
- What it is
- The temperature at which the entered length is true, such as the inspection or assembly temperature.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -273.14 °C to 10000 °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
- Growth depends on final minus initial temperature, so raising it reduces the growth.
- Get it right
- Enter the actual temperature in °C; the tool works out the change.
What this means: Final temperature
- What it is
- The uniform temperature the whole part reaches at the condition you are checking.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -273.14 °C to 10000 °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 higher final temperature gives more growth; below the initial temperature the part contracts.
- Get it right
- The model assumes the whole part is at this one temperature and free to expand.
Method and formulas
- Temperature change = final − initial temperature.
- Length change = initial length × coefficient × 10⁻⁶ × temperature change.
- Final length = initial length + change. Example: 1000 mm, 12 µm/(m·K), 20 to 60°C grows 0.48 mm.
Limitations
- Constant coefficient, uniform temperature and unrestrained expansion only.
- No phase changes, gradients, constraint stresses or temperature-dependent properties are modelled.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- thermal expansion
- temperature correction
- dimensional growth
Who it is for
- Designers
- Maintenance engineers
- Metrologists
What you get
- Temperature change
- Signed length change
- Final length
Interpreting the result
- For a fit, calculate both mating parts under their actual thermal conditions.
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.
Method explained here · BIZOMAT original book
Shrink fitting with liquid nitrogen
In Cryogenic Liquids by the Numbers
What it covers: Check a fit against its torque, find a shaft’s real contraction from NIST’s integrated data, the temperature it needs and the time to assemble, and a constant-coefficient mistake.
Method explained here · BIZOMAT original book
Use motion, thermal and flow studies as load sources
In Design Simulation by the Numbers
What it covers: Derive loads from a motion study, check them by hand, apply temperature with the right restraint and decide when a flow study earns its place in the plan.
Method explained here · BIZOMAT original book
Thermal Expansion by the Numbers
What it covers: Calculate how parts, pipes, liquids and gases change with temperature: growth, measuring at 20 °C, thermal stress, pipe loops, shrink fits, expansion vessels, gas pressure and machine design.
Useful alongside · BIZOMAT original book
Distortion, cracks and residual stress
In Induction Hardening by the Numbers
What it covers: Why a hardened journal grows, bows and is left in compression, where quench cracks start, why the end of the case matters for fatigue, grinding after hardening, and a cross-drilled hole that cracked.
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