Thick Wall Cylinder Press or Shrink Fits Equations and Calculator

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Thick Wall Cylinder Press or Shrink Fits Equations and Calculator

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Thick Wall Cylinder Press or Shrink Fits Interference and Pressure Equations and Calculator

If two thick-walled cylinders are assembled by either a hot/cold shrinking or a mechanical press-fit, a pressure is developed at the interface between the two cylinders. At the interface between the two cylinders, at a radius (R), the outside cylinder, or collar, increases an
amount (δ_c) radially, and the inside cylinder, or shaft, decreases an amount (δ_s) radially.

Figure 1
Geometry of press fit cylinders

Preview: Thick Walled Cylinder Press Fit Interference Calculator

Using the geometry of Figure 1, the increase in the outside cylinder, or collar, radially (δ_c) is given by:

Eq. 1
δ_c = ( ( p R ) / E_c ) [ ( r²_o + R² ) / ( r²_o - R² ) + v_c ]

decrease in the inside cylinder, or shaft, radially (δ_s ) is given by:

Eq. 2
δ_s = ( ( p R ) / E_s ) [ ( R² + r²_i ) / ( R² - r²_i ) + v_s ]

The difference between the radial increase (δ_c) of the collar, a positive number, and the radial decrease (δ_s ) of the shaft, a negative number, is called the radial interference (δ) at the interface (R) and is given by:

Eq. 3
δ = δ_c + | δ_s | = ( ( p R ) / E_c ) [ ( r²_o + R² ) / ( r²_o - R² ) + v_c ] + ( ( p R ) / E_s ) [ ( R² + r²_i ) / ( R² - r²_i ) + v_s ]

When the radial interference (δ) is determined from a particular fit specification, Eq. 3

If the collar and shaft are made of the same material, then the modulus of elasticity’s and Poisson ratio’s are equal and so Eq. (3) can be rearranged to give an expression for the interface pressure (p) given in Eq. (4).

Eq. 4
p = ( E δ ) / R [ ( ( r²_o + R² ) ( R² - r²_i ) ) / ( 2 R² ( r²_o + r²_i ) )]

If the inner shaft is solid, meaning the inside radius (r_i) is zero, then Eq. (4) for the interface pressure (p) simplifies to the expression in Eq. (5).

Eq. 5
p = ( E δ ) / ( 2 R ) [ 1 - ( R / r_o )² ]

Where:

E_c = Modulus of elasticity collar (psi, MPa),
E_s = Modulus of elasticity shaft (psi, MPa),
v_c = Poisson's ratio collar,
v_s = Poisson ratio shaft,
δ = radial interference (in, m),
R = Interface radius (in, m),
r_i = inside radius (in, m),
r_o = external radius (in, m)

Source:

Marks' Calculations for Machine Design,
Thomas H. Brown, Jr. Ph.D., PE
Faculty Associate
Institute for Transportation Research and Education
NC State University
Raleigh, North Carolina