Interference fit of a thin-walled hollow shaft (min/max tolerances)

Deterministic (worst-case) and probabilistic (±1.96σ) contact pressure, mounting force and transmissible torque for an interference fit of a thin-walled hollow shaft in a bore, stressed into the plastic regime, from the min/max tolerance bands of every dimension.

✓ validated against legacyoriginal: /engineering-abc/calculators/p1_1_prob.htm

Bore diameter, min, d₂mmBore diameter, max, d₂mmShaft wall thickness, min, smmShaft wall thickness, max, smmInterference length, min, LmmInterference length, max, LmmUltimate tensile stress, min, RmMPaUltimate tensile stress, max, RmMPaFriction coefficient, min, μFriction coefficient, max, μ

Contact pressure, worst-case min, p88.85572139303481 MPa

Contact pressure, worst-case max, p109.74874371859298 MPa

Mounting force, worst-case min, F_f11.05455901816963 kN

Mounting force, worst-case max, F_f20.894539507397177 kN

Transmissible torque, worst-case min, T_f109.99286223078781 kNm

Transmissible torque, worst-case max, T_f209.99012204934166 kNm

Contact pressure, probabilistic min, p92.47717859613157 MPa

Contact pressure, probabilistic max, p106.12728651549624 MPa

Mounting force, probabilistic min, F_f12.760155636302404 kN

Mounting force, probabilistic max, F_f19.188942889264403 kN

Transmissible torque, probabilistic min, T_f127.32572059933713 kNm

Transmissible torque, probabilistic max, T_f192.6572636807923 kNm

The legacy source also collects the hollow shaft’s own inner diameter (d₁, min/max) and modulus of elasticity (E, min/max) as descriptive geometry, but never uses either in the pressure/force/torque formulas — confirmed against the original: only the wall thickness (s) and bore diameter (d₂) drive the result. Not exposed here, matching how other calculators in this port omit fields the legacy source reads but never computes with.

Method & references

The compressive stress in one of the elements is set to the ultimate tensile stress, assuming plastic deformation.
±2.5% one-sided failure probability (95% two-sided) — 95% of assemblies fall between the probabilistic min and max values.
Thin-walled components stressed in the elastic regime should instead use the standard interference-fit calculator.

ISO 286-2 hole & shaft tolerance reference tables

The computation is a literal port of the original client-side JavaScript from /engineering-abc/calculators/p1_1_prob.htm. Results are verified equal to the original by an automated golden-master test. No formula has been re-derived or “improved”.