Engineering Ring Design Considerations Installation Stress Analysis Installation stress analysis is used to check that the elastic stress limit of the ring material is not exceeded during installation. Standard parts that are assembled manually in the recommended shaft/bore and groove diameters do not require stress analysis. Custom rings assembled with special tooling may require 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 on page 128, can be used as a suitable estimate. 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 rotational capacity. After forming, a ring’s natural tendency is to return to its original state. For a ring being installed over a shaft, 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, as noted in Table 5 below. In custom designs where the installation stress exceeds the material’s elastic limit, rings can be produced to diameters that will yield a predetermined amount during assembly. Once installed, the ring will have the proper cling (grip) on the groove. Installation Stress Formulas: External Rings SE = Internal Rings SC = Eb (DS-DI) (DI+b)(DS+b) Eb (DO-DH) (DO-b)(DH-b) Example: Smalley Part Number WS-100-S02 and WH-100-S02 Where: SE = Stress due to expansion (psi) SC = Stress due to compression (psi) E = 28,000,000 psi b = .075 in DS = 1.000 in DH = 1.000 in DI = .933 in DO = 1.054 in WS-100-S02 Minimum tensile strength of the ring material: 210,000 psi 80% (Table 5) of 210,000 psi = 168,000 psi 129,845 psi < 168,000 psi Since the installation stress is less than 80% of the minimum tensile strength, permanent set is not expected. SE = SC = 28,000,000 (.075) (1.000 - .933) (.933 + .075)(1.00+.075) 28,000,000 (.075) (1.054 - 1.000) (1.054 - .075) (1.000 - .075) = 129,845 psi = 125,224 psi Application Shaft Housing Table 5 Percent of Minimum Tensile Strength 80% 100% WH-100-S02 Minimum tensile strength of the ring material: 210,000 psi 100% (Table 5) of 210,000 psi = 210,000 psi 125,224 psi < 210,000 psi Since the installation stress is less than 100% of the minimum tensile strength, permanent set is not expected. smalley.com • 847.719.5900 Order Online Easy Customization 144
