Stress Analysis

The equations provided are used to check that the elastic stress limit of the ring material is not exceeded by stress due to installation. Standard parts that are assembled manually in the recommended shaft/bore and groove diameters do not require stress analysis. Custom rings, or rings being assembled with custom tooling, require stress analysis.

To select a safe stress value, it is necessary to estimate the elastic limit of the raw material. The minimum tensile strength, as shown in the materials table of the catalog, can be used as a suitable estimate. As with any theoretical calculation, a closer analysis of the actual application may reveal that these stress values can be exceeded. However, particular consideration must be made to functional characteristics such as installation method, the number of times the ring will be installed and removed, thrust load and/or centrifugal capacity.

After forming, the ring’s natural tendency is to return to its original state. This places the inner edge of the radial wall in residual tension and the outer edge in residual compression. To account for the residual stress in the ring when expansion is taking place, only 80% of the minimum tensile strength should be used to compare to the installation stress; see the table below. In custom designs, where the installation stress exceeds the material’s elastic limit, rings can be produced to diameters which will yield a predetermined amount during assembly. Once installed, the ring will have the proper cling on the groove.

Nomenclature

S_E = Stress due to expansion (psi)
S_C = Stress due to compression (psi)
E = Modulus of elasticity (psi)
b = Radial wall (in)
D_S = Shaft diameter (in)
D_H = Housing Diameter (in)
D_I = Free inside diameter, minimum (in)
D_O = Free outside diameter, maximum (in)