Related Resources: mechanics machines

### Shrink Fit of Links or Anchors of Length Equations

Shrink Fit of Links or Anchors of Length Equations

Shrink-fit connections utilizing a link or anchor are widely used in machine design and construction.

The average compression in the part of rim affected according to C. D. Albert
Eq. 1
σc = F / ( Ab Ar )0.5

The tensile stress in link formula
Eq. 2
σt = ( Lf - Lo ) / Lo

Eq. 3
F = [ ( Lf - Lo ) E A ] / Lo

The compressive stress in rim formula
Eq. 4
σc = [ ( Lf - Lo ) / Lo ] ( E A ) / ( Ab Ar )0.5

Eq. 5
Lo = L / [ 1 + ( 1 + ( E A ) / ( Ab Ar )0.5 ) ( σr / E ) ]

The necessary linear interference δ for shrink anchors
Eq. 6
δ = σd l / L

The force exerted by an anchor
Eq. 7
F = a b σd

Eq. 8
b / a = 2 to 3

Eq. 9
σd design stress based on a reliability factor of 1.25

Figure 1 Shrink links or anchors

where

F = load , kN (lbf)
E = modulus of elasticity or Young’s modulus, Pa [psi (lb/in2)]
A = cross section area, m2, in2
Ab = area bearing surface rim, m2, in2
Ar = area rim, m2, in2
Lo = original length, m (in)
Lf = final length, m (in)
l = effective length of anchor, m (in)
ρ = mass density, kg/m3 (lbm/in3)
v = Poisson's ratio
u = displacement, m (in)

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