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
An α guide value is a mean value over a temperature range, and the range belongs to the number. For the heated outer part the mean value for 20 to 100 °C applies: α rises with temperature, so the calculated joining temperature comes out rather too high than too low, which is the safe side. For the chilled inner part the calculator uses separate, smaller values, because α falls as the temperature drops: one for 20 to −78.5 °C (dry ice) and one for 20 to −196 °C (liquid nitrogen), with interpolation over the target temperature in between. With direct input the entered value is used unchanged.
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 α:
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).
What the expansion coefficient applies to
α is not a fixed material constant but a mean value over a temperature range - and the range belongs to the number. For the heated outer part this calculator uses the mean value for 20 to 100 °C. Because α rises with temperature, the calculated joining temperature for heating comes out rather too high than too low: the part then expands more than needed and the fit certainly goes together. For cooling it is the other way round, because α falls as the temperature drops (for brass from 19 at 50 °C to 17 at −73 °C and 13 at −173 °C - these are values AT those temperatures, not mean values down to them; the mean value from 20 to −78.5 °C is 17.7). For the chilled inner part the calculator therefore uses separate, smaller mean values: one for 20 to −78.5 °C (dry ice) and one for 20 to −196 °C (liquid nitrogen), with interpolation over the target temperature in between. The range the calculated value applies to is shown below the input field and in the report.
Heating the outer part
The required temperature increase ΔT_A of the outer part (hub) follows from U_max+S_f, the expansion coefficient α_A of the outer part material and the joining diameter d:
The required joining temperature of the outer part is T_A = T_0 + ΔT_A, starting from the ambient temperature T_0.
Cooling the inner part
Analogously, the required temperature reduction ΔT_I of the inner part (shaft) follows from its expansion coefficient α_I:
The required joining temperature of the inner part is T_I = T_0 − ΔT_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 ΔT_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, the guideline value depends on the outer part material, and markedly so: 350 °C for unalloyed structural steel and cast steel, 400 °C for austenitic steel, 300 °C for grey cast iron, 200 °C for brass and only 150 °C for copper and for an age-hardened aluminum alloy - that is where artificial ageing (155 to 190 °C) takes place, the very treatment that creates the T6 condition, and above it the treatment simply continues. Up to the upper limit (450 °C for steel, 400 °C for grey cast iron, 250 °C for copper and brass, 200 °C for aluminum) microstructural change and loss of strength are possible, above it heating alone is no longer practical. These are material guideline values, not limits set by a standard. Practice grades them further by the heat treatment condition - 300 °C quenched and tempered, 250 °C case-hardened at the surface, 200 °C carburised - and because the material selection does not know that condition, the calculator shows an additional note from 200 °C onward regardless of material. 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 α = 11.5·10⁻⁶ 1/K (mean value for 20 to 100 °C).
Method: heat the outer part. ΔT_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 guideline value for unalloyed steel (green) and also below 200 °C, so the additional note for hardened parts does not appear. A hub made of an age-hardened aluminum alloy would already be in the amber range at the same temperature, with its guideline value of 150 °C. The gear is heated in an oven or by induction to about 183 °C and quickly slid onto the shaft while still hot.
The same fit calculated with cooling: the inner part does not use the warm value but the mean value down to its target temperature - for steel 8.5 instead of 11.5·10⁻⁶/K once cooling reaches the nitrogen range. ΔT_I = 0.15/(8.5·10⁻⁶·80) = 220.6 K, so T_I = 20 − 220.6 ≈ −201 °C. That is below −196 °C: this fit cannot be assembled by cooling alone, only in combination with heating. Calculated with the warm value the result would be −143 °C together with the recommendation 'liquid nitrogen' - a promise the part cannot keep.
Frequently asked questions
How hot may I heat a hub for shrink-fitting?
That depends on the material. For unalloyed structural steel and cast steel 350 °C is considered safe and 450 °C is the upper limit; below that sit austenitic steel (400/450 °C), grey cast iron (300/400 °C), brass (200/250 °C) as well as copper and age-hardened aluminum alloys with a guideline value of only 150 °C. Between the guideline value and the upper limit microstructural change and loss of strength are possible, above it heating alone is generally no longer practical. Careful with the widely quoted 350 °C: it applies to structural steel that has not been quenched and tempered. For quenched-and-tempered steels practice gives 300 °C, for surface-hardened parts 250 °C and for carburised parts 200 °C. Because the calculator does not know the heat treatment condition, it shows an additional note from 200 °C onward - 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.
Which temperature range does the expansion coefficient in the calculator apply to?
For the heated outer part the mean value from 20 to 100 °C applies, for the chilled inner part a separate mean value from 20 °C down to its target temperature. A mean linear expansion coefficient always applies to a range, and reference works print different numbers for the same material depending on that range: brass, for instance, 19.3·10⁻⁶/K for 25 to 100 °C, 21.0 for 20 to 200 °C and 21.4 for 20 to 300 °C. The warm values here are referenced to room temperature and therefore sit at the lower edge. For heating that is the safe side - the calculated joining temperature comes out slightly too high, the part expands more than strictly needed and the fit certainly goes together. A value set too high would do the opposite: the part expands less than calculated and jams during assembly. For a closer calculation, look up the mean value for the range actually covered and enter it directly.
Does the calculator use the same α for cooling as for heating?
No, and that matters: α falls with temperature. For brass the material data sheets give roughly 19·10⁻⁶/K at 50 °C, but only 17 at −73 °C and 13 at −173 °C; for steel it is 8.5 instead of 11.5·10⁻⁶/K once cooling reaches the nitrogen range. The chilled inner part therefore gets its own mean value from 20 °C down to its target temperature, based on two values per material (dry ice −78.5 °C and liquid nitrogen −196 °C) with interpolation in between. When heating, too small an α is the safe side; when cooling, too large an α is the unsafe one - with the warm value the shrinkage would be overestimated by up to 30 %, and the calculator would recommend dry ice where liquid nitrogen is needed. If you have your own values, enter them directly; they are then used unchanged.
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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