Thermal Effect on Fit Calculator
Thermal Effect on Fit Calculator
What an ISO 286 fit specified at 20 °C actually becomes at operating temperature, from the two materials’ expansion coefficients — the temperature at which interference turns to clearance, the heating needed to assemble a shrink fit, and the correction for measuring the parts warm.
Thermal effect on a fit
An H7/s6 fit on a Ø50 shaft — an aluminium hub on a steel shaft — running at 100 °C, with the parts measured at 25 °C
One difference of coefficients, and everything follows
- α_hole − α_shaft
- the DIFFERENCE is what moves the fit. Same material both sides and the difference is zero, so the fit is the same at every temperature — which is the strongest argument there is for matching materials across an interference joint
- d
- the nominal size. Both ends of the tolerance band shift by the same amount, because the shift depends on the nominal and not on where in its band either part sits — an approximation good to a part in a thousand
- T − 20
- the excursion from ISO 1’s standard reference temperature, which is 20 °C for every dimensional specification whether the drawing mentions it or not
- hole tolerance
- added to the interference for the assembly temperature, because the shaft may be at its largest and the bore has to pass it with room to spare
- α
- not a constant. Published room-temperature values and wide-range means for the same material differ by up to twenty per cent, and this page prints both
Worked example
An H7/s6 fit on a Ø50 shaft — an aluminium hub on a steel shaft — running at 100 °C, with the parts measured at 25 °C
The fit at 20 °C, from ISO 286: H7 is 0 to +25 µm and s6 is +43 to +59, so the interference runs from 43 − 25 = 18 µm to 59 − 0 = 59 µm. Both ends interference, so this is a medium drive fit on the drawing
Now the temperatures. Aluminium 6061 expands at 23.6 × 10⁻⁶ per kelvin and carbon steel at 11.7, so the DIFFERENCE is 11.9 — and it is the difference that matters. Nothing else about the two materials enters this calculation
The shift: d·(α_hub − α_shaft)·ΔT = 50 × 11.9 × 10⁻⁶ × 80 = 47.6 µm, and it opens the fit because the hub is growing faster than the shaft. Both ends move by the same amount
So at 100 °C the fit runs from 11.4 µm of interference to 29.6 µm of CLEARANCE. The drawing says medium drive fit and the machine has a loose hub. That result is the page
Per 100 K the loss is 59.5 µm, which is more than the entire 18-to-59 range of an H7/s6 — so no amount of choosing within that class fixes it. The temperature at which the loose end reaches zero is 20 °C, barely above ambient, and the tight end follows at 20 °C
The fixes, in order of preference. Match the materials: with steel both sides the difference is zero and the fit is identical at every temperature. Choose the fit at the SERVICE temperature rather than at 20 °C, which here means going to u6 or beyond. Or stop relying on friction and add a key, a pin or a spline — the key and keyway dimensions page has those
Now the other half, which is assembly. To get an aluminium hub ON, the bore has to open by the maximum interference PLUS the hole's own tolerance so the shaft passes at its largest: 84 µm. ΔT = δ/(α·d) = 71 K, so about 91 °C — modest, because aluminium expands fast. A steel hub on the same fit would need 144 K
Finally the measurement, which is what ISO 1 is actually about. Clause 4 fixes the standard reference temperature at 20 °C. A 50 mm steel part measured at 25 °C reads 2.925 µm LARGE — α·L·ΔT = 11.7 × 10⁻⁶ × 50 × 5. That is 12% of the IT7 band it sits in, so on a fine grade the correction is not optional. Note that 5.8 µm, a figure that circulates for this case, corresponds to a 10 K excursion and not a 5 K one — or to an ALUMINIUM part at 25 °C, which reads 5.9 µm large
Six fits on a Ø50 joint, at 20 °C and at 100 °C with an aluminium hub on a steel shaft
| Fit | Clearance at 20 °C (µm) | At 100 °C (µm) | Class at 20 °C | Class at 100 °C | Temperature at which the tight end reaches zero (°C) |
|---|---|---|---|---|---|
| H7/g6 | 9 to 50 | 57 to 98 | clearance | clearance | 5 |
| H7/h6 | 0 to 41 | 48 to 89 | clearance | clearance | 20 |
| H7/n6 | -33 to 8 | 15 to 56 | transition | clearance | 75 |
| H7/p6 | -42 to -1 | 6 to 47 | interference | clearance | 91 |
| H7/s6 | -59 to -18 | -11 to 30 | interference | transition | 119 |
| H7/u6 | -86 to -45 | -38 to 3 | interference | transition | 165 |
Expansion coefficients, and the two things they decide
| Material | Room temperature (10⁻⁶/K) | A second published figure (10⁻⁶/K) | A 50 mm length measured at 25 °C reads this much large (µm) | Interference lost against a steel shaft per 100 K on a 50 mm fit (µm) |
|---|---|---|---|---|
| Carbon steel (A36, 1020) | 11.7 | 14.0 | 2.925 | 0.0 |
| Alloy steel (4140) | 12.3 | — | 3.075 | 3.0 |
| Stainless steel, austenitic (304) | 17.2 | 17.3 | 4.300 | 27.5 |
| Stainless steel, austenitic (316) | 15.9 | — | 3.975 | 21.0 |
| Stainless steel, martensitic (410) | — | 9.9 | 2.475 | -9.0 |
| Grey cast iron | 11.4 | 10.4 | 2.850 | -1.5 |
| Aluminium 6061 | 23.6 | 23.6 | 5.900 | 59.5 |
| Brass (cartridge) | 19.9 | 20.3 | 4.975 | 41.0 |
| Bronze (phosphor) | 17.8 | 17.8 | 4.450 | 30.5 |
| Copper | 17.0 | 17.6 | 4.250 | 26.5 |
| Titanium (grade 1) | 8.6 | 8.6 | 2.150 | -15.5 |
| Magnesium (AZ31B) | 26.0 | 25.2 | 6.500 | 71.5 |
| Invar | 1.6 | 1.2 | 0.400 | -50.5 |
Which page owns which half of the interference problem
| The question | Where it is answered |
|---|---|
| What is the interference range at 20 °C? | The ISO 286 fit calculator, which derives both bands from the standard’s own rules. This page uses the same machinery |
| What does the fit become at operating temperature? | Here. Both ends of the band move by d·(α_hub − α_shaft)·ΔT, and this page reports the temperature at which each end reaches zero |
| How hot must I heat the hub to assemble it? | Here, as the raw arithmetic: open the bore by the maximum interference plus the hole’s own tolerance so the shaft passes at its largest. Note that this is the CONSERVATIVE figure |
| What contact pressure, torque capacity and hub stress does the fit give? | The interference fit and shrink fit calculator, which does the two-material Lamé solution, the hoop stress and the push-out force. That page also subtracts DIN 7190’s surface-roughness allowance from the interference before it uses it, so its shrink temperature is LOWER than this page’s — the asperities flatten on assembly and that interference never has to be opened up. Both numbers are right for what they are: this page gives the drawing limits and that one gives the joint |
| Is my measurement of the parts even valid? | Here. ISO 1 fixes the reference temperature at 20 °C, and a part measured warm reads large. On a tight grade the correction is a real fraction of the tolerance |
| How tight can the grade be before temperature governs? | The IT grade tolerance calculator, which reports the temperature change that eats the whole band for any grade and size |
Specified at 20 °C, running somewhere else
A fit is defined at 20 °C, and nothing runs at 20 °C. ISO 1:2022 fixes the standard reference temperature for every dimensional specification at 20 °C — clause 4, and it applies whether the drawing mentions it or not. So the interference or clearance on the drawing is a statement about the parts at 20 °C, and the fit the machine actually has is whatever the two materials’ expansion has made of it. The arithmetic is short: both ends of the tolerance band shift by d·(α_hole − α_shaft)·(T − 20), and it is the DIFFERENCE of the coefficients that matters. Same material both sides and the difference is zero, so the fit is identical at every temperature.
An aluminium hub on a steel shaft loosens as it heats, and by more than the fit has. Aluminium expands at about 23.6 parts per million per kelvin and steel at 11.7, so on a 50 mm joint the fit opens by 59.5 µm per 100 K. An H7/s6 on that joint has an interference range of 18 to 59 µm — so 100 K of warming does not merely loosen it, it exceeds the whole range. At 100 °C the same fit runs from 11 µm of interference to 30 µm of CLEARANCE. The joint is perfectly tight on the bench, passes every inspection, and lets go in service. That result is this page’s reason to exist, and the fixes are in order of preference: match the materials, choose the class at the service temperature, or stop relying on friction and add a key or a pin.
The reverse — how hot to heat a hub to get it on. The bore has to open by the maximum interference plus the hole’s own tolerance, so that the shaft passes at ITS largest, and ΔT = δ/(α·d). That is deliberately the conservative figure: the interference fit and shrink fit calculator on this site subtracts DIN 7190’s surface-roughness allowance first, because the asperities flatten as the parts go together and that interference never exists once they are assembled, so its answer is twenty or thirty kelvin lower. Both are right for what they are: this page gives what the drawing limits require you to open, and that page gives the joint you end up holding — along with the contact pressure, the torque capacity and the hub stress, which are not on this page at all.
And the measurement, which is what ISO 1 is really about. A warm part measures large. A 50 mm steel length measured at 25 °C reads 2.9 µm large — α·L·ΔT = 11.7 × 10⁻⁶ × 50 × 5 — which is 12 per cent of the IT7 band it sits in. At 30 °C it is 5.9 µm, and in aluminium at 25 °C it is also about 5.9. A figure of 5.8 µm circulates for “a steel part at 25 °C” and it is out by a factor of two: it is the 10 K answer, or the aluminium one. ISO 1’s Annex A makes the practical point — a measuring system is designed to report a result specified at 20 °C even when it is operating somewhere else, and the departure is additional uncertainty. Two things follow: a part just off a machine is commonly 5 to 15 K warm, and a comparative measurement against a master of the same material at the same temperature largely cancels the error, which is why a comparator beats a micrometer in a warm shop.
α is not a constant either. Two published sources for carbon steel give 11.7 and 14.0 × 10⁻⁶ per kelvin — twenty per cent apart — because the second is a mean over 21 to 427 °C and the first is a room-temperature value. Both are on this page. Over a wide excursion it is the integral of α that matters rather than any single figure, and a coefficient quoted without its temperature range is worth about one significant figure. The other approximation here is worth naming: the fit’s two ends are shifted by the same amount, because the shift is computed on the nominal size rather than on each part’s actual size. That is good to about a part in a thousand, which is far inside the uncertainty in α.
Frequently asked questions
What temperature is a fit specified at?
20 °C, always, whether the drawing says so or not. ISO 1:2022 clause 4 fixes the standard reference temperature for the specification of geometrical and dimensional properties at 20 °C. Every ISO 286 limit, every gauge, every tolerance on the drawing means what it says at 20 °C and something slightly different anywhere else. On a fine grade that difference is a real fraction of the tolerance — a 50 mm steel part is 0.6 µm bigger for every kelvin.
Why does my aluminium hub come loose when the machine warms up?
Because aluminium expands about twice as fast as steel, so the hole grows faster than the shaft and the interference disappears. On a 50 mm joint the loss is 59.5 µm per 100 K, and an H7/s6 has only 18 to 59 µm of interference to start with — so 100 K of warming exceeds the entire range of the fit. At 100 °C that fit has clearance at its loose end. Match the materials if you can; if you cannot, choose the class at the service temperature, or add a key or a pin and stop relying on friction.
How hot do I heat a hub for a shrink fit?
Enough to open the bore by the maximum interference PLUS the hole’s own tolerance, so the shaft passes at its largest: ΔT = δ/(α·d). Use the maximum and not the mean, or a proportion of your assemblies will seize halfway on. Check the material limit before the heating method: above about 200 °C a quenched and tempered steel starts losing hardness, and bearing makers cap induction heating of their rings at 120 °C. Cooling the shaft needs the same temperature CHANGE the other way, and is limited to about 98 K with dry ice and 216 K with liquid nitrogen from a 20 °C ambient.
How much does a part measure large if it is warm?
α·L·ΔT. A 50 mm steel part measured at 25 °C reads about 2.9 µm large; at 30 °C, 5.9 µm. An aluminium part of the same length at 25 °C reads about 5.9. A figure of 5.8 µm is often quoted for “a steel part at 25 °C” and it is out by a factor of two — that is the 10 K answer. The correction matters most on fine grades: 2.9 µm is 12 per cent of an IT7 band at 50 mm and more than a fifth of an IT6.
Does the same material on both sides make a fit temperature-proof?
Essentially yes, and it is the cheapest fix available. If α_hole equals α_shaft the difference is zero and the clearance is the same at every temperature — the hole and the shaft grow by the same proportion, and the clearance grows by that proportion of a very small number. Two caveats. Both parts have to actually BE at the same temperature, and a shaft inside a housing often is not, because it is closer to the heat. And the joint still has to be assembled, so the heating or cooling arithmetic still applies.
Can a clearance fit close up and seize?
Yes, whenever the shaft expands faster than the housing — a steel shaft in an Invar or a ceramic housing, or any assembly where the shaft runs hotter than the part around it, which is usual in a bearing or a bush. It is worse than it sounds because it runs away: a journal bearing needs its clearance for the oil film, closing it raises the temperature, and that closes it further. This page reports the temperature at which the tight end of the band reaches zero clearance, which is the number to design against.
How accurate is this calculation?
The arithmetic is exact for a linear coefficient, and the linearisation itself is very good: exp(α·ΔT) − 1 differs from α·ΔT by less than 0.06 per cent over 100 K. The real uncertainty is in α, which is not a constant — two published figures for carbon steel differ by twenty per cent because one is a room-temperature value and the other a mean to 427 °C, and both are printed here. The other approximation is that both ends of the tolerance band are shifted by the same amount, computed on the nominal size rather than each part’s actual size, which is good to about a part in a thousand.
Related calculators
References
- ISO 1:2022, Geometrical product specifications (GPS) — Standard reference temperature for the specification of geometrical and dimensional properties. Its freely published preview was fetched during this batch. Clause 4: “The standard reference temperature value for the specification of geometrical and dimensional properties shall be fixed at tₐ₀ = 20 °C.” Annex A adds the part that matters for measurement: most measuring systems “are designed to produce measurement results specified at the standard reference temperature value of 20 °C, even though they might be operating at a different temperature”, and a departure from it is additional measurement uncertainty.
- AmesWeb. Thermal expansion coefficient (CTE) of metals. The source for the room-temperature coefficients on this page: carbon steel 11.7, alloy steel 12.3, austenitic stainless 304 17.2 and 316 15.9, grey cast iron 11.4, aluminium 6061 23.6, cartridge brass 19.9, phosphor bronze 17.8, copper 17.0, titanium grade 1 8.6, magnesium AZ31B 26.0 and Invar 1.6, all in 10⁻⁶/°C.
- The Engineering ToolBox. Metals — temperature expansion coefficients. The second source, and the reason this page says that α is not a constant. It gives carbon steel as 14.0 against AmesWeb’s 11.7 — 20 per cent higher — because its figure is a MEAN over 21 to 427 °C where AmesWeb’s is a room-temperature value. It also gives grey cast iron 10.4, martensitic 410 stainless 9.9, copper 17.6, magnesium 25.2 and Invar 1.2. Where the two disagree, both are printed.
- ISO 286-1:2010, Geometrical product specifications (GPS) — ISO code system for tolerances on linear sizes — Part 1: Basis of tolerances, deviations and fits. Cited by number; the standard is copyrighted and its tables are not reproduced here. What this page uses from it is its STRUCTURE, which is not a table: the standard tolerance factor i = 0.45·∛D + 0.001·D evaluated at the geometric mean of each nominal size step, the grade multipliers (IT5 = 7i, IT6 = 10i, IT7 = 16i, IT8 = 25i, IT9 = 40i, IT10 = 64i, IT11 = 100i and so on), the rule that IT(n+5) is ten times IT(n) from IT7 upward, the formulas for each letter’s fundamental deviation, and the Δ correction for hole letters J to ZC. Every one of those is checked here against a published table rather than trusted.
- DIN 7190, Interference fits — calculation and design rules. Cited for the one thing this page hands over rather than computes: the roughness allowance 0.8(R_z1 + R_z2) that has to come off an interference before it is real. That correction, and the two-material Lamé solution, live on the interference-fit page on this site, which is why the shrink-fit temperature here is the raw-interference figure and the one there is lower.
- Machining Doctor. Tolerance charts by fundamental deviation letter (one page per letter, hole and shaft, stated as ISO 286-1:2010). The source for the fundamental deviations of c, d, e, f, g, k, m, n, p, r, s and u on this page, fetched one letter at a time so a shifted column could not hide in a wide table. Every row of every letter satisfies es − ei = IT(grade) exactly — 220 independent checks — and its N7 hole column reproduces the Δ = IT(n) − IT(n−1) rule at all thirteen size steps. Its u6 column also agrees with the interference-fit page already on this site at all sixteen steps that page covers, which cross-validates both.