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### Force to Press Together Hub and Shaft Design Equations and Calculator

Interference Fit Force Required the Press Together Hub and Shaft Equations and Calculator

The axial force necessary to press shaft into hub under an interface pressure pc
Eq. 1
Fa = π dc l µ pc

where

µ = coefficient of friction
µ
= 0:085 to 0.125 for unlubricated surface
µ = 0.05 with special lubricants

The approximate value of axial force to press steel shaft into cast-iron hub with an interference SI Units
Eq. 2a
F = ( 4,137 x 104 ) [ ( do + 0.3 dc ) l δ ] / ( do + 6.33 dc)

where do , dc, l and δ in m, and F in N

The approximate value of axial force to press steel shaft into cast-iron hub with an interference USCS Units
Eq. 2b
F = 6,000 [ ( do + 0.3 dc ) l δ ] / ( do + 6.33 dc)

where do , dc, l and δ in in, and F in tonf

The approximate value of axial force to press steel shaft in steel hub SI
Eq. 3a
F = ( 28.41 x x 104 ) [ ( do2 + 0.3 dc2 ) l δ ] / do2

where do , dc, l and δ in m, and F in N

The approximate value of axial force to press steel shaft in steel hub USCS
Eq. 3b

F = ( 4,120 ) [ ( do2 + 0.3 dc2 ) l δ ] / do2

where do , dc, l and δ in in., and F in tonf

The transmitted torque by a press fit or shrink fit without slipping between the hub and shaft
Eq. 4
Mt = π dc2 l µ pc / 2

where
µ = 0:10 for press fit
µ = 0:125 for shrink fits

The temperature t2 in °C to which the shaft or shrink link must be heated before assembly
Eq. 5
t2 ≥ ( 2 δ / ( α dc ) + t1 )

where
t1 = temperature of hub or larger part to which shaft or shrink link to be shrunk on, °C
Mt = torque or twisting moment, Nm (lbf in)
do = hub diameter, m (in)
dc = contact surface diameter, compressive, m (in)
pc
= contact pressure MPa (psi)
δ = total change in diameter (interference), m (in)
α = coefficient of linear thermal expansion, (m/m) / °C [(in/in)/°F]

Conversion

1 newton is equal to 0.00010197162129779283 tonf.
1 tonf = .00950965 N
1 tonf = 2,204.623 lbf

Related:

Source:

Machine Design Handbook 2nd Edition, 2001
Prof. Dr. K. Lingaiah
Former Principal, Professor and Head, Department of Mechanical Engineering
University Visvesvaraya College of Engineering, Bangalore University, Bangalore