DIN 7190-1 Interference Fit Calculator

How does an interference fit work?

Before assembly the inner part is slightly larger than the bore of the outer part; that difference in diameter is the interference. Joining elastically compresses the inner part and expands the outer part. Both then remain permanently stressed and press against each other with the joint pressure pF. This normal pressure creates friction over the cylindrical contact area, and that friction alone transfers circumferential force — and therefore torque — as well as axial force, with no keyway, pin or other form lock involved. More interference means more joint pressure and more capacity, but also higher stress in both parts. Designing the joint therefore always has two sides: a lower bound from the required capacity and an upper bound from the material strength.

Interference fit vs. press fit vs. shrink fit

The three terms do not mean the same thing. Interference fit is the joint principle: a connection created purely by the difference in diameter. Press fit and shrink fit describe how the parts are actually joined.

In a press fit the parts are forced axially into one another. In a shrink fit the dimensions are changed temporarily — the hub is heated, the shaft cooled, or both — so the parts slide together without force. Once temperatures equalise, both routes leave the same cylindrical interference joint.

That does not make the methods interchangeable, though: the joining process affects surface condition, roughness smoothing, lubrication and therefore the usable friction coefficient. A pressed-in and a shrink-fitted joint of identical geometry can carry different loads.

What does “purely elastic” mean?

Purely elastic means both parts stay below the onset of plastic deformation. Only then is the deformation fully reversible and the linear relation between interference and joint pressure valid. The calculator checks this by comparing the joint pressure against the elastic pressure limits of inner and outer part.

This is a limit of the implementation, not of the standard: alongside the purely elastic procedure DIN 7190-1 also contains an elastic-plastic one, in which limited yielding of the hub is permitted and tracked in the calculation. That procedure is not implemented here. Once utilization exceeds 1.0 the calculator therefore no longer returns a valid result but a warning.

Formula and variables

pF = ξw · EA / K

• Uw = U − 0.4 · (RzI + RzA)
• ξw = (Uw / 1000) / DF
• qi = DiI / DF · qa = DF / DaA
• K = EA/EI · ((1 + qi²)/(1 − qi²) − νI) + (1 + qa²)/(1 − qa²) + νA
• pperm,A = (1 − qa²) · ReA / (√3 · SpA)
• pperm,I = (1 − qi²) · ReI / (√3 · SpI) · solid shaft: 2 · ReI / (√3 · SpI)
• Mt = π/2 · DF² · lF · pF · µT / Sr
• Fax = π · DF · lF · pF · µA / Sr

Choose the inputs correctly

Fit diameter DF and joint length lF, the inner part's bore DiI and the outer part's outside diameter DaA, interference U with the roughness depths RzI and RzA, plus Young's moduli, Poisson ratios, yield strengths with their plasticity safety factors, and the friction coefficients for circumferential and axial direction with the slip safety Sr. Interference creates the interface pressure needed for friction, but also raises assembly force and plasticity risk. Diameter ratio, Young's modulus and Poisson ratio share the deformation between shaft and hub.

How to use the calculator

Enter fit diameter and joint length, plus the inner part's bore (0 for a solid shaft) and the outer part's outside diameter. Add the interference of the unassembled parts and both roughness depths, the material data of both parts, and the friction coefficients and safety factors. The calculator returns effective interference, joint pressure, the elastic pressure limits of both parts with the utilization, and the transmissible torque and axial force.

Worked example

The annex example of the standard: DF = 50 mm, lF = 40 mm, solid shaft, DaA = 100 mm, U = 75 µm, RzI = RzA = 6 µm, both parts steel with E = 215,000 MPa and ν = 0.3, ReI = 200 MPa, ReA = 300 MPa, plasticity safety factors 1.1. This gives Uw = 70.2 µm, K = 2.667 and pF = 113.2 MPa. The hub governs at 118.1 MPa (shaft: 209.9 MPa), so utilization is 0.96 — purely elastic, but with little margin.

How to interpret the result

Joint pressure pF is the mean normal pressure at the cylindrical interface; everything else follows from it. Torque and axial capacity are the resulting slip limits in circumferential and axial direction — each on its own, not usable together. The two elastic pressure limits say whether the purely elastic model still applies at all: the lower of the two governs, and utilization must not exceed 1.0. Not covered by a passing result are shaft fatigue strength, edge stress peaks at the ends of the joint, rotating bending, centrifugal effects at high speed, form and position error of the mating surfaces, and galling during assembly. Operating and assembly temperatures can change the effective interference, particularly for dissimilar materials; thermal effects are not included in this calculator and must be checked separately. For the shaft itself, the DIN 743 Shaft Verification calculator provides the strength assessment.

Diameters and joint length in millimetres, interference and roughness in micrometres, Young's moduli, yield strengths and joint pressure in MPa, torque in N·m, axial force in N. Poisson ratio, friction coefficients, safety factors and utilization are dimensionless.

Why does surface roughness reduce effective interference?

No mating surface is perfectly smooth. During joining the asperity peaks of both surfaces are partially flattened, and that share of the geometrical interference never becomes elastic deformation of the two bodies.

DIN 7190-1:2017 accounts for this with a flat deduction of 0.4·(RzI + RzA) from the measured interference. The smoothing factor was changed from 0.8 in the previous edition to 0.4. The effect is far from negligible: two surfaces at Rz = 16 µm each already cost 12.8 µm of interference.

The governing parameter is explicitly the mean roughness depth Rz, not Ra. The factor cannot be transferred to other roughness parameters.

What limits the interference?

From below, the capacity: too little effective interference means too little joint pressure, too little friction and a risk of slip. From above, the material strength: too much interference drives the joint pressure past the elastic pressure limit of shaft or hub. “More interference” is therefore not automatically better.

How narrow that window is depends on geometry. Hub wall thickness enters through the ratio qa = DF/DaA: a thin hub is more compliant and builds less pressure at the same interference, while its elastic limit falls with (1 − qa²) at the same time. A hollow shaft acts in the same direction through qi = DiI/DF. Both effects are in the calculator and can be read off directly by varying DaA and DiI.

How do ISO 286 fits relate to DIN 7190?

ISO 286 defines tolerance zones and therefore the possible actual sizes of shaft and bore. A standard fit such as H7/p6 or H7/s6 consequently gives not a single interference value but a range between minimum and maximum interference.

DIN 7190 then evaluates what a specific interference means mechanically: joint pressure, material limits and transmissible load. Both ends of the range matter, but for different things — minimum interference usually governs frictional transmission and slip resistance, maximum interference governs material stress and plasticity.

Calculate the minimum and maximum interference from an ISO 286 fit with the ISO 286 fits calculator; the interference range it reports is the input for this page.

What friction coefficient should I use?

The friction coefficient enters torque and axial force linearly and is therefore the single most influential assumption in the whole calculation: raised from 0.10 to 0.15 it increases the calculated capacity by 50 % at unchanged joint pressure. That is exactly why it is not a material constant.

It depends on material pairing, surface finish, cleanliness, lubrication and the joining process. The tooltips of the two input fields quote guideline values from DIN 7190 — for a steel-steel pairing assembled with mineral oil, or a normally heated shrink fit, for example. Treat those as example values for orientation, not as universal recommendations for your own joint.

Circumferential and axial direction are entered separately because joining can give the contact surface a preferred direction: an axially pressed joint has a different history along its length than around its circumference.

Torque and axial force at the same time

Both capacities come from the same contact area and the same joint pressure. They are separate limiting cases: one for pure torsion, the other for pure axial load. When both act together the friction force is the vector sum of a circumferential and an axial component, and neither individual limit is then fully available.

Combined-load verification is not implemented in this calculator. The displayed torque and axial capacities are individual limiting cases and must not both be applied at 100 % simultaneously; combined loading needs a separate assessment.

Typical applications

Sizing an interference fit for a required torque or axial force, checking an existing interference against the elastic limits of shaft and hub, and understanding what a chosen ISO 286 fit means mechanically.

Assumptions, limits and common mistakes

DIN 7190-1:2017-02 covers cylindrical self-locking interference fits made of metallic materials and contains both a purely elastic and an elastic-plastic procedure. This implementation covers the purely elastic case with a cylindrical contact surface of equal length only. Edge stress peaks, centrifugal force, the interaction of axial force and torque, and thermal effects are not included.

Common mistake: Don't use the measured interference directly as the effective one — roughness smoothing removes 0.4·(RzI + RzA), which for two surfaces at Rz 16 µm is already 12.8 µm. Nor may torque and axial capacity be used in full at the same time: both come from the same contact area and are separate limiting cases. And a purely elastic result just below the limit is not a margin — manufacturing scatter of the interference feeds straight through to joint pressure.