Interference fit per DIN 7190
Design cylindrical interference fits per DIN 7190: from an ISO 286 fit or a direct interference you get joint pressure, transmissible torque and axial force, safety factors against slipping and yielding, and the assembly temperature, live with every input.
Calculation
Assembly temperature (shrink fit)
Verification per DIN 7190 using the modified shear stress hypothesis (MSH). Reference values without guarantee, purely elastic design.
Results
Effective interference
- minimum U_wk
- 37 µm
- maximum U_wg
- 78 µm
Smoothing U_V = 8 µm already subtracted
Joint pressure
- minimum p_Fk
- 56.1 N/mm²
- maximum p_Fg
- 118.2 N/mm²
Transmissible at minimum interference (incl. S_R)
- Torque M_t,max
- 541 Nm
- Axial force F_ax,max
- 24,043 N
Safety factors
Permissible interference band
- required U_req
- 42.2 µm
- permissible U_allow
- 131.7 µm
The selected fit must lie with U_k above U_req and with U_g below U_allow.
Equivalent stress (MSH) at p_Fg
- Hub, bore surface
- 364 N/mm²
- Shaft
- 118.2 N/mm²
Joining
- required hub temperature
- 285 °C
- Assembly clearance (1 ‰)
- 45 µm
Intermediate values
- Q_A
- 0.5921
- Q_I
- 0
- K
- 3.0797
- U_g
- 86 µm
- U_k
- 45 µm
- U_V
- 8 µm
- p_erf
- 51.8 N/mm²
- p_zul,A
- 187.5 N/mm²
- p_zul,I
- 413.8 N/mm²
Calculation in your browser, inputs go to our server only when you export or save.
Formulas and fundamentals
Effective interference
Only part of the measured interference is load-bearing: during joining the roughness peaks of both surfaces are flattened plastically. The effective interference is:
The calculator evaluates it separately for the maximum and the minimum interference of the fit.
Joint pressure
The joint pressure follows from thick-walled cylinder theory:
The dimensionless auxiliary quantity K combines the compliances of both partners:
Transmissibility and strength verification
Transmissibility is always verified with the smallest pressure (minimum interference):
With simultaneous torque and axial force, the circumferential and axial forces are added vectorially.
The strength verification, in contrast, uses the largest pressure (maximum interference). DIN 7190 applies the modified shear stress hypothesis: at the hub bore:
This yields the permissible maximum interference U_allow; the load yields the required minimum interference U_req.
Assembly temperature
For thermal joining the calculator determines the hub temperature for the maximum interference plus an assembly clearance of 1 ‰ of the joint diameter:
Chilling the shaft (dry ice −78 °C, liquid nitrogen −196 °C) lowers the required hub temperature.
Worked example
A pinion (17CrNiMo case-hardening steel, R_e = 600 N/mm²) sits on a solid C30 shaft (R_e = 300 N/mm²) with a Ø45 H7/u6 fit. Hub outer diameter 76 mm, joint length 65 mm, Rz sum 10 µm, torque 500 Nm static, friction coefficient 0.07 (longitudinal press fit, lubricated), S_R = 1.5, S_F = 1.2.
The fit yields U_g = 86 µm and U_k = 45 µm. The smoothing loss is U_V = 0.8 · 10 = 8 µm. With Q_A = 45/76 = 0.592 and K = 3.08 the minimum interference produces a pressure of p_Fk = 56.1 N/mm² - more than the required 51.8 N/mm² from the torque; the safety against slipping is 1.62, above the required 1.5.
At maximum interference the pressure is p_Fg = 118.2 N/mm². The equivalent stress at the hub bore is σ_v = 364 N/mm², below the permissible 577 N/mm². The permissible maximum interference would be 131.7 µm, so the fit has reserve. For shrink fitting the hub must be heated to about 285 °C.
Frequently asked questions
What is the effective interference?
The measured interference (or the one following from the fit) minus the smoothing of the surface roughness during joining (per DIN 7190: 0.8 · sum of the Rz values). Only the effective interference generates joint pressure - neglecting the smoothing significantly overestimates the capacity at small diameters.
What does the transmissible torque depend on?
On the joint pressure, the joint area (diameter and joint length), and the friction coefficient of the material pairing and joining method. A safety factor against slipping is applied in addition (static 1.5, pulsating 1.8, alternating 2.2).
Why calculate with both minimum and maximum interference?
The ISO fit scatters between both limits. The slip verification must use the worst case of lowest pressure (minimum interference), the strength verification against yielding uses the highest pressure (maximum interference). Swapping the two is a classic mistake.
Which strength hypothesis does DIN 7190 use?
The modified shear stress hypothesis (MSH) with the limit (2/√3) · R_e / S_F. Calculators based on the von Mises criterion deviate by a few percent - that is not an error but a different hypothesis.
How hot must the hub be for shrink fitting?
Hot enough for the bore to expand by the maximum interference plus an assembly clearance of about 1 ‰ of the joint diameter. If the permissible hub temperature is insufficient (e.g. 200 °C for case-hardened hubs due to tempering risk), the shaft is additionally chilled with dry ice (−78 °C) or liquid nitrogen (−196 °C).
Does the calculation cover hollow shafts and different materials?
Yes. The auxiliary quantity K accounts for the shaft bore as well as different Young's moduli and Poisson's ratios of hub and shaft. Limits of the calculator: purely elastic loading, constant hub outer diameter, centrifugal force and operating temperature not considered.
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