VM-WB-MECH-025

VM-WB-MECH-025
Stresses Due to Shrink Fit Between Two Cylinders

Overview

Reference:	Timoshenko, S. P. Strength of Materials, Part 2 - Advanced Theory and Problems (3rd ed., pp. 208-214).
Solver(s):	Ansys Mechanical
Analysis Type(s):	Linear Static Structural Analysis
Element Type(s):	Solid

Test Case

One hollow cylinder is shrink fitted inside another. Both cylinders have length L and both the flat faces of each cylinder are constrained in the axial direction. They are free to move in radial and tangential directions. An internal pressure of P is applied on the inner surface of the inner cylinder. To get accurate results, apply a global element size of 0.8 inches.

Find the maximum tangential stresses in both cylinders.

Material Properties

Geometric Properties

Both cylinders are made of the same material

E = 3 x 10⁷ psi

ν = 0

ρ = 0.28383 lbm/in³

Inner Cylinder:

r_i = 4"

r_o = 6.005"

R_i = 6"

R_o = 8"

Length of both cylinders = 5"

P = 30000 psi

Analysis Assumptions and Modeling Notes for Ansys Mechanical

The following figure shows the finite element model in Ansys Mechanical:

Figure 28: Schematic

Note: Tangential stresses can be obtained in the Mechanical application using a cylindrical coordinate system.

To simulate interference, set Contact Type to Rough with interface treatment set to add offset with Offset = 0.

Results Comparison for Ansys Mechanical

Results	Target	Mechanical	Error (%)
Maximum normal y stress, inner cylinder (psi)	35396.67	35756	1.01515
Maximum normal y stress, outer cylinder (psi)	42281.09	42299	0.042359

Note: Here y corresponds to θ direction of a cylindrical coordinate system.