FORMULAS FOR INTERFERENCE (PRESS & SHRINK) FIT CALCULATIONS


The formulas used in Interference Fit Calculator are given below. For more information on interference fits, please refer to pages 387 - 399 of the Precision Machine Design.

Calculation Steps and list of equations for Interference (Press & Shrink)  Fit:

Step Parameter/Condition Symbol Equation
Dimensional Parameters
1 Differential radial interference due to Poisson’s effect of axial force upoisson Equation for differential radial interference due to Poisson’s effect of axial force
2 Differential thermal radial interference due to different operation and assembly temperatures for different materials uthermal Equation for differential thermal radial interference due to different operation and assembly temperatures for different materials
3 Hub radial displacement due to rotation uh,cfg Equation for hub radial displacement due to rotation
4 Shaft radial displacement due to rotation us,cfg Equation for shaft radial displacement due to rotation
5 Maximum diametrical interference Equation for maximum diametrical interference in interference fit
Pressure Parameter
6 Interference pressure as a result of diametrical interference P Equation for interference pressure as a result of diametrical interference
Pressure & Stress Parameters (Hub)
7 Radial stress on hub due to interference pressure σr,pressure Equation for radial stress on hub due to interference pressure
8 Circumferential stress on hub due to interference pressure σθ,pressure Equation for circumferential stress on hub due to interference pressure
9 Axial stress on hub due to axial force σz Equation for axial stress on hub due to axial force
10 Shear stress on hub caused by torque τ Equation for shear stress on hub caused by torque
11 Circumferential stress on hub due to centrifugal effect σθ,cfg Equation for circumferential stress on hub due to centrifugal effect
12 Von Mises stress at the hub surface σVM Equation for Von Mises stress at the hub surface
Pressure & Stress Parameters (Shaft)
13 Radial stress on shaft due to interference pressure σr,pressure Equation for radial stress on shaft due to interference pressure
14 Circumferential stress on shaft due to interference pressure σθ,pressure Equation for circumferential stress on shaft due to interference pressure
15 Axial stress on shaft due to axial force σz Equation for axial stress on shaft due to axial force
16 Shear stress on shaft caused by torque τ Equation for shear stress on shaft caused by torque
17 Circumferential stress on shaft due to centrifugal effect σθ,cfg Equation for circumferential stress on shaft due to centrifugal effect
18 Von Mises stress at the shaft surface σVM Equation for Von Mises stress at the shaft surface
List of Parameters :



Symbol Parameter
F Axial force to be transmitted
T Torque to be transmitted
νh Poisson’s ratio of hub
νs Poisson’s ratio of shaft
Dhi Hub inner diameter
Dho Hub outer diameter
Dsi Shaft inner diameter
Dso Shaft outer diameter
Eh Hub elastic modulus
Es Shaft elastic modulus
ΔT Temperature difference between operating and assembly conditions
αs Thermal expansion coefficient of shaft
αh Thermal expansion coefficient of hub
ρ Density of the shaft/hub material


Supplements:



Link Usage
Interference (press & shrink) fit calculator Calculates press fit force, required temperatures for shrink fit, fit stresses and other parameters necessary for interference fit design

Reference:

  • Slocum, A. H., Precision Machine Design, © 1995, Society of Manufacturing Engineers, Dearborn, MI. (first published by Prentice Hall in 1992), pp 387-399