INTERFERENCE (PRESS & SHRINK) FIT CALCULATOR

An interference fit (press fit & 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 are 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 fit calculator has been developed to calculate interference parameters such as press fit 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:

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	T_o
Rotation speed	w		rpm
Engagement length	L
Hub Parameters
Hub outer diameter	D_ho
Hub inner diameter	D_hi
Inner diameter upper deviation	Δ_h,up
Inner diameter lower deviation	Δ_h,low
Stress concentration factor	K_t
Modulus of elasticity	E_h
Yield strength	Sy
Poisson's ratio	v_h
Coefficient of thermal expansion	α_h
Density	ρ_h
Shaft Parameters
Shaft outer diameter	D_so
Shaft inner diameter	D_si
Outer diameter upper deviation	Δ_s,up
Outer diameter lower deviation	Δ_s,low
Stress concentration factor	K_t
Modulus of elasticity	E_s
Yield strength	Sy
Poisson's ratio	v_s
Coefficient of thermal expansion	α_s
Density	ρ_s
Shrink Fit Design
Desired clearance to be able to make assembly (clearance obtained between shaft and hub after thermal process)	Δ_d
Standard reference temperature(reference temperature for geometrical product specification and verification defined by ISO and ANSI)	T_a
Design Factors
Design factor against sliding *	nd_s
Design factor against yielding (Hub) *	nd_y,h
Design factor against yielding (Shaft) *	nd_y,s

Note: Use dot "." as decimal separator.

* Appropriate design factor shall be selected to cover material non-uniformity, 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 press-fit 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 press-fit 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.

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 tolerances and fits charts (ISO)	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 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