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Press Fit Bushings into Lug Stresses Calculator and Equations

Machine Design Application, Equations and Calculators

Stresses Due to Press Fit Bushings into Lug or Ring Calculator and Equations

Preview calculator: Press Fit Bushing Design Calculator

Pressure between a lug and bushing assembly having negative clearance can be determined from consideration of the radial displacements. After assembly, the increase in inner radius of the ring (lug) plus the decrease in outer radius of the bushing equals the difference between the radii of the bushing and ring before assembly.

Eq. 1

${\displaystyle \mathrm{\delta <!--\; \delta \; -->}=u_{ring}-<!--\; -\; -->u_{bushing}}$

where

δ = difference between outer radius of bushing and inner radius of the ring.
u = radial displacement, positive away from the axis of ring or bushing.

Radial displacement at the inner surface of a ring subjected to internal pressure p is

Eq. 2

${\displaystyle u=\frac{D_p}{E_{ring}}[\frac{C^2+D^2}{C^2-<!--\; -\; -->D^2}+{\mathrm{\mu <!--\; \mu \; -->}}_{ring}]}$

Radial displacement at the outer surface of a bushing subjected to external pressure p is

Eq. 3

${\displaystyle u=-\frac{B_p}{E_{bush}}[\frac{B^2+A^2}{B^2-<!--\; -\; -->A^2}+{\mathrm{\mu <!--\; \mu \; -->}}_{bush}]}$

where

A = inner radius of bushing
B = outer radius of bushing
C = outer radius of ring (lug)
D = inner radius of ring (lug)
E_ring = Modulus of elasticity ring
E_bush = Modulus of elasticity bushing
µ_ring = Poisson's ratio
µ_bush = Poisson's ratio
D_p = external pressure on outer ring
B_p = internal pressure on inner ring
p = pressure

Figure 1, Bushing Press Fit Annotation

Substitution of the previous two equations into the first yields:

Eq. 4

${\displaystyle p=\frac{\mathrm{\delta <!--\; \delta \; -->}}{\frac{D}{R_{ring}}(\frac{C^2+D^2}{C^2-<!--\; -\; -->D^2}+{\mathrm{\mu <!--\; \mu \; -->}}_{ring})+\frac{B}{E_{bush}}(\frac{B^2+A^2}{B^2-<!--\; -\; -->A^2}-<!--\; -\; -->{\mathrm{\mu <!--\; \mu \; -->}}_{bush})}}$

Maximum radial and tangential stresses for a ring (lug) subjected to internal pressure occur at the inner surface of the ring (lug) and are

Eq. 5

${\displaystyle f_r=-<!--\; -\; -->p}$

Eq. 6

${\displaystyle f_t=p\left(\frac{C^2+D^2}{C^2-<!--\; -\; -->D^2}\right)}$

Positive sign indicates tension.

The maximum shear stress at this point is

Eq. 7

${\displaystyle f_s=\frac{f_t-<!--\; -\; -->f_r}{2}}$

The maximum radial stress for a bushing subjected to external pressure occurs at the outer surface of the bushing is

Eq. 8

${\displaystyle f_r=-<!--\; -\; -->p}$

The maximum tangential stress for a bushing subjected to external pressure occurs at the inner surface of the bushing and is

Eq. 9

${\displaystyle f_t=-<!--\; -\; -->\frac{2p{B}^2}{B^2-<!--\; -\; -->A^2}}$

The allowable press fit stress should be based on stress corrosion, static fatigue, fatigue life, and the ultimate strength.

Reference:

• Bell Helicopter Structural Design Manual, 1977

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