Shrink Fit Joining Temperature Calculator (Heating/Cooling)
Determine the required temperature for thermally assembling an interference fit: from the joining diameter, maximum interference and joining clearance the tool derives the temperature the outer part must be heated to, or the inner part cooled to, so the parts can be assembled without binding - as heating, cooling, or a combination of both, live with every input.
Calculation
Model: simplified thermal expansion calculation (Roloff/Matek) for thermally assembling interference fits. Applies to purely elastic joining and does not account for temperature loss during the assembly process itself. Sizing tool for mechanical engineering.
Results
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Formulas and fundamentals
Why an additional joining clearance?
The interference U_max alone is exactly compensated by the thermal expansion in theory - but as soon as the heated or cooled part is handled, it starts losing temperature again during transport to the joining location. An additional joining clearance S_f is therefore added so the parts can still be assembled without binding after this temperature loss. Rule of thumb: S_f ≈ 1 µm per mm of joining diameter.
Basic thermal expansion equation
The length change of a part under a temperature change follows from the linear expansion coefficient alpha:
For the joining case the reference length L is replaced by the joining diameter d: the outer part must expand by the maximum interference U_max plus the joining clearance S_f (or the inner part must shrink by the same amount).
Heating the outer part
The required temperature increase Delta-T_A of the outer part (hub) follows from U_max+S_f, the expansion coefficient alpha_A of the outer part material and the joining diameter d:
The required joining temperature of the outer part is T_A = T_0 + Delta-T_A, starting from the ambient temperature T_0.
Cooling the inner part
Analogously, the required temperature reduction Delta-T_I of the inner part (shaft) follows from its expansion coefficient alpha_I:
The required joining temperature of the inner part is T_I = T_0 − Delta-T_I.
Combination: cooling plus residual heating
If the lowest practically achievable inner-part temperature (dry ice −78.5 °C, liquid nitrogen −196 °C, or a freely chosen target) is not enough on its own, the shrinkage achieved at that temperature is subtracted from U_max+S_f; the remainder is provided by additionally heating the outer part:
If the remainder is zero or negative, cooling alone is already sufficient - no additional heating of the outer part is needed. Otherwise Delta-T_A follows as in pure heating, but referred to the remainder instead of U_max+S_f.
Limits: tempering risk and physically achievable temperatures
For heating, a joining temperature up to 350 °C is considered safe for quenched-and-tempered steels; between 350 °C and 450 °C a tempering effect (microstructural change, loss of hardness) becomes possible, above that the temperature is no longer practical for most tempered or hardened parts. From 200 °C onward, an additional note is shown for hardened or case-hardened parts. For cooling, dry ice is sufficient down to −78.5 °C, lower temperatures down to −196 °C require liquid nitrogen; below that, the temperature is no longer physically achievable with common coolants - here only a combination with heating the outer part helps.
Worked example
Given: a gear (hub, outer part) made of steel is shrink-fitted onto a shaft (inner part, also steel) with a joining diameter d = 80 mm. Maximum interference U_max = 70 µm (from the interference fit calculator), required joining clearance S_f = 80 µm (rule of thumb 1 µm/mm at d = 80 mm). Ambient temperature T_0 = 20 °C, steel expansion coefficient alpha = 11.5·10⁻⁶ 1/K.
Method: heat the outer part. Delta-T_A = (70+80)·10⁻³/(11.5·10⁻⁶·80) = 0.15/9.2·10⁻⁴ = 163.0 K.
Joining temperature T_A = 20 + 163.0 ≈ 183 °C. That is below the 350 °C limit (green, pass), but above 200 °C - for a hardened gear the calculator would additionally flag possible tempering effects. The gear is heated in an oven or by induction to about 183 °C and quickly slid onto the shaft while still hot.
Frequently asked questions
How hot may I heat a hardened hub for shrink-fitting?
Up to 350 °C the joining temperature is considered safe for quenched-and-tempered steels. Between 350 °C and 450 °C a tempering effect with microstructural change and loss of hardness becomes possible, above 450 °C heating alone is generally no longer practical. For hardened or case-hardened parts the calculator shows a note starting at 200 °C already, because depending on the material's tempering temperature a measurable drop in hardness can already begin there - when in doubt, look up the specific material's tempering temperature.
Why isn't the interference U_max alone enough - why do I also need the joining clearance S_f?
The maximum interference U_max describes the geometric overlap in the cold state. Right after heating or cooling, however, the part immediately starts approaching ambient temperature again - during transport to the joining location and the actual assembly, part of the expansion is already lost again. The additional joining clearance S_f (rule of thumb 1 µm per mm of joining diameter) ensures the parts can still be assembled without binding even after this temperature loss.
Dry ice or liquid nitrogen - when do I need which?
Dry ice (carbon dioxide sublimation) reaches about −78.5 °C and is sufficient for most cooling cases with moderate interference. If that is not enough, liquid nitrogen at about −196 °C is required. Below −196 °C no further temperature reduction is possible with common coolants - here only a combination of cooling and additional heating of the outer part remains. When working with liquid nitrogen, appropriate personal protective equipment (cold-protection gloves, face shield, adequate ventilation) is essential.
Where do I get the maximum interference U_max for my fit?
The maximum interference follows from the chosen tolerance pairing of bore and shaft, or from the interference fit design per DIN 7190. The interference fit calculator on this site derives U_max directly from the joining diameter, tolerance classes and the required safety factors against slipping and yielding; the result can then be carried over here for the joining temperature.
Induction heating or an oven - what's the difference?
An oven heats the part evenly and slowly all the way through, so it suits thick-walled or geometrically complex hub parts well, but needs time and energy for the entire part volume. Induction heating puts heat into the joining zone quickly and locally, with short cycle times and lower total energy input, but requires a suitable induction coil and usually more process experience so the part is heated evenly.
What happens when the assembled part cools down - do shrink stresses build up?
Once the parts are assembled and equalize to the common operating temperature, the actual interference fit forms with the joining pressure determined by the interference fit calculator. With very large temperature differences between joining and operation, or different expansion coefficients of hub and shaft, the effective joining pressure can shift compared with the room-temperature design - this should be checked separately with the interference fit calculator for the relevant operating temperature.
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