Interference Fit and Shrink Fit Calculator

A hollow hub on a solid or hollow shaft in two different materials, by the Lamé thick-wall equations: contact pressure, torque capacity, push-out force, hub hoop stress and the assembly temperature — computed at BOTH ends of the ISO 286 interference range, with the roughness the surfaces lose on assembly subtracted the way DIN 7190 does it.

Lamé for two materials, and a range rather than a number

The interference RANGE for each fit class, in micrometres, computed from ISO 286 rather than copied

The same 30 µm interference on a 50 mm steel shaft, with the hub in each material

Friction at the interface, and why it is two numbers

What this page is, and what it is not

A range not a number, roughness in Rz not Ra, and two materials rather than one

The interference is a range, and the design has to work at one end and survive the other. An H7/s6 fit on a 50 mm shaft is not “38 µm of interference”. It is anything from 18 to 59 µm, because the hole can be anywhere in its 25 µm band and the shaft anywhere in its 16 µm band. The torque the joint carries is set by the MINIMUM, and the stress the hub sees is set by the MAXIMUM, and those two numbers differ by more than three to one. A calculation done at the mean interference is wrong twice over: it promises torque that a third of your production will not deliver and it fails to notice a hub that yields on assembly. This page computes the ISO 286 bands rather than copying them — from the standard’s own defining rules, verified against four internal identities — and reports both ends throughout.

Then take the roughness off, and take it off in R_z. The asperities on the two surfaces flatten as the parts go together, and that interference is simply gone. DIN 7190 subtracts 0.8(R_z1 + R_z2), and the figure it subtracts is the PEAK-TO-VALLEY height, not the arithmetic average. That distinction is not pedantry: R_z runs roughly four to seven times R_a for a turned or ground surface, so putting an R_a figure into that formula throws away most of the correction. On the worked example here the allowance is 10.1 µm against a minimum interference of 18 — more than half of it — and improving both surfaces from Rz 6.3 to Rz 1.6 recovers 7.5 µm, nearly doubling the effective minimum. A better finish is often the cheapest interference you can buy. Converting between R_a, R_z and N grades belongs to the converters plugin on this site and is deliberately not attempted here, because the ratio depends on the process and is not a conversion.

Two materials, which is the case the dowel-pin page does not do. Lamé’s thick-wall solution gives the radial displacement of each cylinder separately, and the interference closes when the hub’s outward movement plus the shaft’s inward movement add up to half the diametral interference. With the same material both sides the two Poisson terms cancel and the algebra collapses to the single-material form the dowel pin and hole calculator already derives — and this page’s two-material form reproduces that answer to twelve significant figures, which is how we know the extra algebra did not break anything. With different materials the results move a long way: an aluminium hub on a steel shaft develops about two fifths of the contact pressure at the same interference, needs less than half the temperature rise to assemble, and loses more interference than an H7/s6 has when the assembly warms 100 K. The whole solution here is asserted against a finite-difference solve of the axisymmetric elasticity equations at five geometries, which knows none of the algebra.

The assembly temperature, and the reason cooling the shaft is sometimes the answer. To drop a hub on, the bore has to open by the maximum interference plus enough clearance to pass the shaft at its largest — so the temperature rise is set by the maximum and not by the nominal. That is often 80 to 150 K for a steel hub, which is comfortable; above about 250 °C it stops being a heating problem and becomes a metallurgical one, because a quenched and tempered steel loses hardness, a hardened bearing ring is damaged (which is why bearing makers cap induction heating at 120 °C) and any seal, cage or coating on the part has its own limit. Cooling the shaft needs the same temperature CHANGE in the other direction, and dry ice reaches −78 °C where liquid nitrogen reaches −196, so for a modest fit it is a real alternative and for a large one it is not enough on its own.

What the fit delivers, and what it must survive. Torque capacity is p·π·d²·l·μ/2 and push-out force is p·π·d·l·μ, both linear in the pressure and therefore both computed at the minimum. DIN 7190 gives two friction coefficients for the same interface, a longitudinal one and a lower circumferential one, so a joint that will not push out can still slip in torsion — and the same source puts a shrunk joint’s coefficient above a pressed one’s, for the mechanical reason that pressing on shears the asperities off. At the other end of the band, the hoop stress at the hub bore is p(1+Q²)/(1−Q²) in tension while the equivalent stress that actually yields is 2p/(1−Q²), because the bore is in hoop tension and radial compression at once. The page reports both and says when the hub yields. The alternative connections are on the spline torque capacity calculator and the key and keyway dimensions page.

Frequently asked questions

Related calculators

References

1. DIN 7190-1:2017, Interference fits — Part 1: Calculation and design rules for cylindrical self-locking pressfits. Cited by clause; not fetched. The two things this page takes from it, via the eAssistant handbook below, are the roughness allowance and the assembly-temperature relation. The elastic theory itself is Lamé’s and is derived here.
2. GWJ Technology. eAssistant Handbook, chapter “Interference Fit According to DIN 7190”. The source for the roughness allowance — the effective interference is the nominal interference less s = 0.8(R_zA + R_zI) — and for the assembly-temperature and press-force relations. Note carefully that the standard’s allowance is in R_z, the peak-to-valley height, and NOT in R_a: R_z runs about four to seven times R_a for a turned or ground surface, so using R_a in that formula understates the loss by most of it. It also carries the friction coefficients and the external-load relations p_r = F_r/(d_F·l_F) and p_b = (9/2)·M_b/((2 − Q_W)·D_F·l_F²).
3. 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 clause; not fetched. Its defining relations are what this page computes from: the standard tolerance factor i = 0.45 D^(1/3) + 0.001 D at the geometric mean of each size band, the grade multipliers IT6…IT11 = 10i, 16i, 25i, 40i, 64i, 100i, and the fundamental-deviation rules for the interference letters. The table values were checked against those relations rather than trusted, and the two relations disagree below 6 mm because the standard rounds small sizes to convenient numbers.
4. Machining Doctor. Engineering Fits & Tolerances — Calculator & Charts, fundamental-deviation-of-shafts chart. The source for the p, r, s, t and u lower deviations over the sixteen bands this batch uses, with the split sub-bands above 10 mm printed separately. Four independent identities from ISO 286-1 check it: p = IT7 + (0 to 5) at every band above 3 mm; s = IT8 + (1 to 4) up to 50 mm and s = IT7 + 0.4 D above it, which reproduces all seven bands above 50 mm to a quarter of a micrometre; r = √(p·s) at all fifteen bands above 3 mm; and u = IT7 + D at all eleven bands from 18 mm up.
5. Dalloway Precision. ISO 286 Tolerance Grade Chart — IT5 to IT11 in Microns. The source for the IT table. Its column HEADINGS come through in the order IT5 IT6 IT8 IT7 while its VALUES are in the order IT5 IT6 IT7 IT8; the R5 ratio settled which reading is right, because each grade step must be about 10^(1/5) = 1.585 and 10 → 1.67 satisfies that where 14 → 2.33 does not. Every one of the 78 values was then checked against the tolerance-factor formula.
6. ISO 286-2:2010, Part 2: Tables of standard tolerance classes and limit deviations for holes and shafts. Its freely published sample pages carry Tables 1 to 3 in full, which is where the D-hole fundamental deviation on this page comes from: EI = 20, 30, 40, 50, 65 and 80 µm for the first six bands, reproduced to better than 1.5 µm by 16 D^0.44. The fetch returned the D11 upper-deviation column beside the correct EI column; ES − EI = IT caught it at every row, and only EI, which is grade-independent, was taken.
7. Schaeffler (INA/FAG). Technical tables: dimension and tolerance symbols, shaft and housing fits. Fetched as the intended cross-check on the p6, r6 and s6 deviations and DISCARDED: the extract came back with three different row offsets in three columns, so its “30–50 mm r6” row carried the 18–30 mm values while its p6 column was offset the other way. ES − EI = IT6 caught it. Nothing on this page is attributed to it.
8. This plugin’s own dowel-pin-and-hole calculator. The single-material Lamé pressure it derives is the degenerate case of the two-material form used here, and the two agree to twelve significant figures when both moduli and both Poisson ratios are set equal and the shaft is solid. That is the check that this page’s extra algebra did not break the case the site already had right.