Boss Stress Topics:

- Installation diagram
- D/d ratio
- Unsymmetrical boss stress
- Stress concentration factor
- Dissimilar materials

Note: In many cases the factor limiting the boss diameter will be the proof pressure requirement and not the stresses.

The success of the Lee Plug is founded upon its ability to provide high proof pressures with low, external boss stresses. If a typical installation is considered to be the equivalent of a 0.003 inch interference fit, then the hoop stresses (ST) can be expressed as a function of the Plug diameter (d), boss diameter (D), and yield point stress in tension (SY) of the boss material.

The Lee Plug lands and the boss material plastically deform, and in conjunction with the grooves, interlock to form many seals. This interlocking creates discontinuous bands of stress which quickly average out to a uniform stress at a diameter within the boss of 1.2d or more.

The boss stresses, both tangential tensile (ST) and the radial compressive (SR) vary throughout the boss. At the interface between the plug lands and the boss (Pt.#1) SR1 is high and ST1 is low. At Pt.#2, SR2 is low and ST2 has reached its maximum. At Pt.#3, the only stresses are ST3 and the values are shown on the curve of ST3 below.

**The Effect of D/d on Proof Pressures and Stresses
for Plug and Boss Materials with Similar Mechanical Properties**

A D/d ratio of 2.5 is the minimum recommended by The Lee Company

for cases in which the plug and boss are of similar materials.

For bosses that are not round the analysis is more complex, and thus a formula has been developed* to aid in the solution of this difficult problem. The following formula allows a stress concentration factor, K, to be calculated as a function of certain boss geometric parameters. The formula is reasonably accurate, somewhat conservative, and applies to the stress in the plug boss at the minimum wall thickness area.

T/ t Ratio: |
This is the ratio of the maximum boss wall thickness, to the minimum wall thickness. It is an indication of the nonsymmetry of the boss, and has a value of 1.0 for a round boss. |

Angle: |
The angle is that sector of the boss which is at the minimum wall thickness. A round boss would have an angle of 360 degrees. |

D/d Ratio: |
This is the pad ratio of the boss diameter at its minimum radius, to the plug outside diameter. |

*See Lee Technical Report No. 08-91-181 (Analytical Study to Evaluate Stresses in Unsymmetrical Lee Plug bosses).

See Figure I for examples of how the geometric parameters apply to real Lee plug bosses and Figure II for a plot of the formula results.

A typical problem is solved by using the round boss solution method with the D/d ratio as described above. The calculated stress is then multiplied by a stress concentration factor as determined from the formula.

Figure 1

These figures illustrate the applicability of the geometric parameters to variously shaped Lee Plug bosses.

NOTE: Although "t" is always the boss minimum wall thickness, "T" should be selected to be representative of the thick wall of the boss. Introduction Lee Plugs

**Stress concentration factor vs. boss angle and thickness ratio**

FIgure II

**Boss Stress – Dissimilar Materials**

When a Lee Plug is installed in a boss material of dissimilar mechanical properties, its proof pressure will be best maintained by observing the D/d ratios shown on the graph below. The stress at the O.D. of the boss will be below 40% of the tensile yield strength of the boss material when using these curves. This is a stress level that has been determined to be satisfactory in most applications.

Example: A 303 CRES Plug is being designed into a 15-5 PH CRES housing. As can be seen from the graph, a D/d ratio of 1.9 is recommended to assure the rated proof pressure of the plug. In designing the boss with a D/d ratio of 1.9, the designer achieves a weight savings of 42% relative to a boss designed with a D/d ratio of 2.5.

When a Lee Plug is installed in a weaker boss material the holding strength of the plug will be limited by the strength of the boss material. Though the rated proof pressure will most likely be maintained, the choice of a significantly weaker boss could lessen the rated proof. The Lee Company should be contacted for technical assistance if there are questions about the plug/boss strength compatibility.

When a Lee Plug is installed in a stronger boss material the surface finish of the installation hole increases in importance. If the plug is significantly weaker than the boss material, retention relies more heavily on the friction at the plug/boss interface than on the plug grooves. Though the rated proof pressure will most likely be maintained, a surface finish smoother than the recommended limit may reduce the proof pressure of the plug.