Press Fit Calculator Formula

Understand the math behind the press fit calculator. Each variable explained with a worked example.

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Formulas Used

Interface Pressure

interface_p = interference * e_mpa / (shaft_dia * (1 / (1 - k_ratio)))

Assembly Press Force

assembly_force = pi * shaft_dia * fit_length * (interference * e_mpa / (shaft_dia * (1 / (1 - k_ratio)))) * friction_coeff / 1000

Variables

VariableDescriptionDefault
interferenceDiametral Interference (delta)(mm)0.05
shaft_diaNominal Shaft Diameter (d)(mm)50
hub_odHub Outer Diameter (D)(mm)100
fit_lengthFit Length (L)(mm)40
modulusElastic Modulus (E)(GPa)200
friction_coeffFriction Coefficient0.15
e_mpaDerived value= modulus * 1000calculated
k_ratioDerived value= pow(shaft_dia / hub_od, 2)calculated

How It Works

Press Fit (Interference Fit) Analysis

A press fit creates a joint by assembling a slightly oversized shaft into a slightly undersized hole.

Simplified Formula (solid shaft, same material)

p = delta E (1 - (d/D)^2) / d

where delta is the radial interference (diametral/2), d is shaft diameter, D is hub OD, and E is the elastic modulus.

Assembly Force

F = pi d L p mu

where L is the engagement length and mu is the friction coefficient.

Worked Example

A 50 mm shaft pressed into a hub (OD=100 mm) with 0.05 mm diametral interference, 40 mm long, steel.

interference = 0.05shaft_dia = 50hub_od = 100fit_length = 40modulus = 200friction_coeff = 0.15
  1. 01k = (50/100)^2 = 0.25
  2. 021/(1-0.25) = 1.333
  3. 03p = 0.05 x 200,000 / (50 x 1.333) = 10,000 / 66.67 = 150 MPa
  4. 04F = pi x 50 x 40 x 150 x 0.15 / 1000 = 141.4 kN

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