Shrink Fit of Links or Anchors of Length Equations

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Shrink Fit of Links or Anchors of Length Equations

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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
σ_c = F / ( A_b A_r )^0.5

The tensile stress in link formula
Eq. 2
σ_t = ( L_f - L_o ) / L_o

The total load on link formula
Eq. 3
F = [ ( L_f - L_o ) E A ] / L_o

The compressive stress in rim formula
Eq. 4
σ_c = [ ( L_f - L_o ) / L_o ] ( E A ) / ( A_b A_r )^0.5

The original length of link
Eq. 5
L_o = L / [ 1 + ( 1 + ( E A ) / ( A_b A_r )^0.5 ) ( σ_r / E ) ]

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

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

Eq. 8
b / a = 2 to 3

Eq. 9
σ_d 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
A_b = area bearing surface rim, m², in²
A_r = area rim, m², in²
L_o = original length, m (in)
L_f = 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)

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