Shaft Connections Calculators

Interference fit connection

Press-fitted parts connection is obtained as a result of their preliminary thermal or mechanical deformation. This is an permanent type of connection that is used based on considerations of manufacturability. The presented calculation determines the contact pressure P of a press-fitted connection of a shaft and a bush, made of different materials and arbitrary diameters D₁, D₂ and D₃, depending on the press-fitting value Δ.

For the calculation, the elastic moduluses E_sh, E_sl and Poisson's ratios ν_sh, ν_sl of the parts should be specified.

To further calculate the stresses in the parts to be joined using the calculated contact pressure, you can use the online thick-walled pipes calculator.

Calculation of interference fit

Interference fit

INITIAL DATA

D₁ - Shaft inner diameter;

D₂ - Shaft outer diameter;

D₃ - Bush outer diameter;

Δ - Amount of interference (difference between the outer shaft radius and the inner bush radius);

Е_sh - Young's modulus of the shaft;

ν_sh - Poisson's ratio of the shaft;

Е_sl - Young's modulus of the bush;

ν_sl - Poisson's ratio of the bush.

RESULTS DATA

P - Pressure on shaft and sleeve contact surfaces.

Metric Imperial

Diameter (D₁)

Diameter (D₂)

Diameter (D₃)

Amount of interference (Δ)

Shaft Young's modulus (Е_sh)

Shaft Poisson ratio (ν_sh)

Bush Young's modulus (Е_sl)

Bush Poisson ratio (ν_sl)

Contact pressure (P)

BASIC FORMULAS

P = Δ / (([R₂/(R₃²-R₂²)]*[(1 - ν_sl)*R₂² + (1 + ν_sl)*R₃²]/Е_sl)
+([R₂ / (R₂² - R₁²)]*[(1 - ν_sh)*R₂² + (1 + ν_sh)*R₁²] / Е_sh)),

R₁, R₂, R₃ - radiuses of shaft and bush.

INITIAL DATA

D₁ - Shaft inner diameter;

D₂ - Shaft outer diameter;

D₃ - Bush outer diameter;

Δ - Amount of interference (difference between the outer shaft radius and the inner bush radius);

Е_sh - Young's modulus of the shaft;

ν_sh - Poisson's ratio of the shaft;

Е_sl - Young's modulus of the bush;

ν_sl - Poisson's ratio of the bush.

RESULTS DATA

P - Pressure on shaft and sleeve contact surfaces.

MATERIALS PROPERTIES

Material	Young’s modulus Pa (psi)	Poisson’s ratio
Steel	1.86÷2.1×10¹¹ (2.7÷3.05×10⁷)	0.25÷0.33
Cast iron	0.78÷1.47×10¹¹ (1.1÷2.1×10⁷)	0.23÷0.27
Copper	1.0÷1.3×10¹¹ (1.45÷1.9×10⁷)	0.34
Tin bronze	0.74÷1.22×10¹¹ (1.1÷1.8×10⁷)	0.32÷0.35
Brass	0.98÷1.08×10¹¹ (1.4÷1.6×10⁷)	0.32÷0.34
Aluminum alloy	0.7×10¹¹ (1.0×10⁷)	0.33
Magnesium alloy	0.4÷0.44×10¹¹ (5.8÷6.4×10⁶)	0.34
Nickel	2.5×10¹¹ (3.6×10⁷)	0.33
Titanium	1.16×10¹¹ (1.7×10⁷)	0.32
Lead	0.15÷0.2×10¹¹ (2.2÷2.9×10⁶)	0.42
Zinc	0.78×10¹¹ (1.1×10⁷)	0.27
Glass	4.9÷5.9×10¹⁰ (7.1÷8.5×10⁶)	0.24÷0.27
Concrete	1.48÷2.25×10¹⁰ (2.1÷3.3×10⁶)	0.16÷0.18
Wood (along the grain)	8.8÷15.7×10¹⁰ (12.8÷22.8×10⁶)	-
Wood (across the grain)	3.9÷9.8×10¹⁰ (5.7÷14.2×10⁶)	-
Nylon	1.03×10¹⁰ (1.5×10⁶)	-

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