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: /calculators/p1_1_prob.htm

Hollow shaft diameter, min, d₁mmHollow shaft diameter, max, d₁mmBore diameter, min, d₂mmBore diameter, max, d₂mmShaft wall thickness, min, smmShaft wall thickness, max, smmInterference length, min, LmmInterference length, max, LmmModulus of elasticity, min, EGPaModulus of elasticity, max, EGPaUltimate 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

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.

The computation is a literal port of the original client-side JavaScript from /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”.