INTERFERENCE (PRESS & SHRINK) FIT CALCULATOR

An interference (press & shrink) fit is a frictional shaft-hub 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.

Interference (press) fit representation

Calculator:

INPUT PARAMETERS
Parameter/Definition Symbol Value Unit
Working Conditions
Torque to be transmitted T
Axial force to be transmitted F
Coefficient of friction μ  
Operation temperature To
Rotation speed w rpm
Engagement length L
Hub Parameters
Hub outside diameter Dho
Hub inside diameter Dhi
Inside diameter upper deviation Δh,+tol
Inside diameter lower deviation Δh,-tol
Stress concentration factor Kt  
Modulus of elasticity Eh
Yield strength Sy
Poisson's ratio vh  
Coefficient of thermal expansion αh
Density ρh
Shaft Parameters
Shaft outside diameter Dso
Shaft inside diameter Dsi
Outside diameter upper deviation Δs,+tol
Outside diameter lower deviation Δs,-tol
Stress concentration factor Kt  
Modulus of elasticity Es
Yield strength Sy
Poisson's ratio vs  
Coefficient of thermal expansion αs
Density ρs
Shrink Fit Design
Desired clearance to be able to make assembly (clearance obtained between shaft and hub after thermal process) Δd
Standard reference temperature(reference temperature for geometrical product specification and verification defined by ISO and ANSI) Ta
Design Factors
Design factor against sliding * nds  
Design factor against yielding (Hub) * ndy,h
Design factor against yielding (Shaft) * ndy,s
       

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
Interference Parameters
Minimum required interface pressure (interface pressure required to transmit torque and force) rpi ---
Limit values for diametrical interference (minimum and maximum diametrical interference values possible for input parameters entered) delta Max Min
--- ---
Limit values for resultant interface pressure due to diametrical interference (pressure values for minimum and maximum interference condition) P --- ---
Factor of safety against sliding [= Pmin / rpi]* foss ---
Assembly Parameters For Shrink Fit
Required temperature of shaft for assembly if cooling shaft Tr,s ---
Required temperature of hub for assembly if heating hub Tr,h ---
Assembly Parameters For Press Fit
Assembly force range to press fit for calculated interference range Fpf Max Min  
--- ---
Hub Results
Radial displacement of inner surface uinner
Radial press fit stress at inside diameter σr,pressure
Circumferential press-fit stress at inside diameter σθ,pressure
Axial stress from applied axial force σz
Shear stress from applied torque τ
Max radial centrifugal stress σr,centrifugal
Max circumferential centrifugal stress σθ,centrifugal
Max Von Mises stress σmises
Factor of safety against yielding of hub * fosy,h
Shaft Results
Radial displacement of outer surface uouter
Radial press fit stress at outside diameter σr,pressure
Circumferential press-fit stress at outside diameter σθ,pressure
Axial stress from applied axial force σz
Shear stress from applied torque τ
Max radial centrifugal stress σr,centrifugal
Max circumferential centrifugal stress σθ,centrifugal
Max Von Mises stress σmises
Factor of safety against yielding of shaft * fosy,s

* Shall be larger than relevant design factor. Green color means safe, red color means not safe according to input parameters.

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: Al6061-T6: 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 286-1 (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

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