INTERFERENCE
(PRESS & SHRINK) FIT CALCULATOR
An interference (press
& shrink) fit is a frictional shafthub connection. Joint pressure in
the friction surface is necessary for the torque (force) transmission and this
pressure is generated by the deformation of shaft and hub. Suitable assembly
method shall be selected between shrink fit and press fit. In the
press fit case, assembly operation is done with large amount of forces and
forcing shaft into the hub. In the
shrink fit case, assembly operation is done by relative size change of parts
with the help of heat treatment. Typical examples of press fit is fitting shafts
into the bearing and bearings into the housings.
For
the preferred interference tolerances for shaft & hub connection in metric and inch fits, visit
"Supplements" section.
The Interference (press & shrink) fit calculator was developed to calculate
interference parameters such as assembly (press) force, required temperature for
shrink fit, Von Mises stresses occurred on shaft and hub, factor of safety
values.

Note: For more information on interference fits, please refer to pages 387  399 of the Precision Machine Design.
Calculator:
Note: Use dot "." as decimal separator.
* Appropriate design factor shall be selected to cover material nonuniformity,
uncertainty of service conditions, calculation and analysis inaccuracy etc.
RESULTS 
Parameter 
Symbol 
Value 
Unit 
Dimensional Parameters 
Max. shaft outer diameter 
d_{so_max} 



Min. shaft outer diameter 
d_{so_min} 


Max. hub inner diameter 
d_{hi_max} 


Min. hub inner diameter 
d_{hi_min} 


Limit values for diametrical interference (minimum and maximum diametrical
interference values before assembly. Not include rotation, thermal, poisson's
effects) 
delta 
Max 
Min 




Limit values for diametrical interference (minimum and maximum diametrical
interference values during operation. Includes rotation, thermal, poisson's
effects) 
delta 




Interference Parameters 
Minimum required interface pressure (interface pressure required to transmit
torque and force) 
rpi 



Limit values for resultant interface pressure due to diametrical interference
(pressure values for minimum and maximum interference condition) 
P 





Factor of safety against sliding [= P_{min}
/ rpi]* 
fos_{s} 


 
Assembly Parameters For Shrink Fit (For Max. Diametrical Interference) 
Required temperature of shaft for assembly if cooling shaft 
T_{r,s} 



Required temperature of hub for assembly if heating hub 
T_{r,h} 


Assembly Parameters For Press Fit 
Assembly force range to press fit for calculated interference range 
Fpf 
Max 
Min 






Hub Results (For Max. Diametrical Interference) 
Radial displacement of inner surface 
u_{inner} 


Radial press fit stress at inner diameter 
σ_{r,pressure} 


Circumferential pressfit stress at inner diameter 
σ_{θ,pressure} 

Axial stress from applied axial force

σ_{z} 

Shear stress from applied torque at inner diameter 
τ 

Max radial centrifugal stress 
σ_{r,centrifugal} 

Max circumferential centrifugal stress

σ_{θ,centrifugal} 

Max Von Mises stress 
σ_{mises} 

Factor of safety against yielding of hub * 
fos_{y,h} 

 
Shaft Results (For Max. Diametrical Interference) 
Radial displacement of outer surface 
u_{outer} 


Radial press fit stress at outer diameter

σ_{r,pressure} 


Circumferential pressfit stress at outer diameter 
σ_{θ,pressure} 

Axial stress from applied axial force 
σ_{z} 

Shear stress from applied torque at outer diameter 
τ 

Max radial centrifugal stress 
σ_{r,centrifugal} 

Max circumferential centrifugal stress

σ_{θ,centrifugal} 

Max Von Mises stress 
σ_{mises} 

Factor of safety against yielding of shaft * 
fos_{y,s} 

 
* Shall be larger than relevant design factor. Green color means safe, red color
means not safe according to input parameters.
Selection of Unit System for Graphs:



Shaft 
Hub 
Definitions:
Design factor (nd): The ratio of failure stress to allowable stress.
The design factor is what the item is required to withstand .The design factor is defined for an application
(generally provided in advance and often set by regulatory code or policy) and is not an actual calculation.
Factor of Safety (Safety Factor):
The ratio of failure stress to actual/expected stress. The difference between the factor of safety (safety factor)
and design factor is: The factor of safety gives the safety margin of designed part against failure. The design factor
gives the requirement value for the design. Safety factor shall be greater than or equal to design factor.
Modulus of elasticity (Young’s
modulus): The rate of change of unit tensile or compressive stress with respect to unit tensile or compressive strain
for the condition of uniaxial stress within the proportional limit. Typical values: Aluminum: 69 GPa, Steel: 200GPa.
Poisson’s ratio: The ratio of lateral unit strain to longitudinal unit
strain under the condition of uniform and uniaxial longitudinal stress within the proportional limit.
Press fit: Assembly of parts with very large amounts of force. Assembly operation
is done with presses.
Proportional Limit:
The largest value of stress up to which a linear relation still exist between stress and strain (Hooke’s Law).
Shear stress: A form of a stress acts parallel to the surface (cross section)
which has a cutting nature.
Shrink fit: Assembly of parts by
relative size change with the help of heat treatment. This is usually achieved
by heating and cooling one component before assembly and allowing it to return
to the ambient temperature after assembly.
Shrink fit machine: A type of machine generally used to insert cutting tools
inside the tool holders with shrink fit. When tool change is required, same machine is used to remove cutting tool.
Shrink fit machines use induction heating to increase the temperature of tool holder.
Stress: Average force per unit area which results strain of material.
Stress Concentration Factor:
Dimensional changes and discontinuities of a member in a loaded structure causes
variations of stress and high stresses concentrate near these dimensional
changes. This situation of high stresses near dimensional changes and
discontinuities of a member (holes, sharp corners, cracks etc.) is called stress
concentration. The ratio of peak stress near stress riser to average stress over
the member is called stress concentration factor.
Von Mises: A theory used to
estimate the yielding of ductile materials. The Von Mises criteria states that failure occurs when the energy of distortion
reaches the same energy for yield failure in uniaxial tension test.
Yield strength: The stress at which a material
exhibits a specified permanent deformation or set. Example: Al6061T6: 145 Mpa
Supplements:
Link 
Usage 
Limits, fits and tolerances calculator (ISO system)

For the design of interference fit, it can be first referred to
limits, fits and tolerances
calculator to select and calculate shaft/hole tolerances according to ISO and
ANSI standard. After selection of the fit, deviations which are calculated for
selected fit can be used as input parameters to interference fit calculator. 
Preferred fits advised by ISO and ANSI standard (Metric) 
Preferred fits advised by ISO 2861 (2010) and ANSI B4.2 (1978) standard are
given to help user about the selection of fit. Whenever possible, selection of
tolerance class shall be done among these tolerances to avoid too many numbers of
tools and gauges. 
ANSI standard limits and fits
calculator

For the design of interference fit, it can be first referred to ANSI standard
limits and fits calculator to select and calculate shaft/hole tolerances according to ANSI standard. After selection of the fit, deviations
which are calculated for
selected fit can be used as input parameters to interference fit calculator. 
List of Equations:
List of equations and calculation steps for interference (press & shrink) fit calculations

Slocum, A. H., Precision Machine Design, © 1995, Society of Manufacturing
Engineers, Dearborn, MI. (first published by Prentice Hall in 1992), pp 387399