"Knockdowns" Help Calculate Bearing Stress in Common Mechanical Designs

Designing bearings seems a straightforward matter of sizing pins and shafts. Yet the load placed on mating plates is also significant. Calculating only shear and breakthrough loads misses a problem common with high-cycle mating plate designs. This is the gradual elongation of a hole toward a load over time, a process called wallowing.

One way to attack wallowing (as well as pin failures) is to find the endurance limit of the bearing material. The endurance limit uses empirical evidence on wear to adjust a material’s tensile strength downwards through a series of “knockdowns” that provide a truer picture of how a material stands up to long-term fatigue.

Take, for example, a pin and matching plate made of AISI 4130 carbon steel with tensile strength of 80,000 psi and shear strength of 28,000 psi. Assuming the mating plate is 0.5 inch thick and must withstand repeating/reversing loads of 1,000 psi, how thick should we make the pin?

We could derive the pin diameter using stress equals force/area (S=F/A). The allowable stress would be the shear strength of 28,000 psi, and the force 1,000 psi.

The area would equal the thickness of the mating plate (0.5 inches) multiplied by the diameter of the pin. This would yield a pin diameter of 0.072 inch. Apply a safety factor of two and the pin diameter is still less than 0.15 inch in diameter.

The endurance limit produces very different results. The calculations apply such knockdown factors as surface finish, size effects, temperature, and stress concentrations to tensile (break) strength. In AISI 4130 steel, this produces

a corrected endurance limit of 11,120 psi.

Then comes another calculation informed by empirical evidence. When calculating the area of the pin, include only the 60 percent of the pin diameter (the middle cross-section minus top and bottom) that transfers force to the mating plate. When combined with the endurance limit, this produces a pin diameter of 0.30 inch. This is four times thicker than the original calculation, enough to prevent fatigue, wallowing, and pin deformation.

Material properties may change significantly with temperature. For example, the shear strength of AISI 316 stainless steel at room temperature is 12,500 psi. At 1,000 °F, however, it falls to 12,000 psi after 10,000 hours and to 7,500 psi after 100,000 hours. Starting with temperature-corrected properties before applying knockdown factors ensures a material will maintain its original safety factors and not creep or fail over its service life.

Some designs use a bushing or flange bearing pressed into the link arm. These parts are often made of bronze or hardened brass, which have lower yield strength than the material used in the link or pin. When calculating maximum stresses for these material stacks, use the properties of the weakest material as the starting point for the endurance limit.

Finally, do not forget the pin itself. Engineers need to double-check pin material, diameter, and clamp load to validate fully the link connection.

Editor’s note: Originally published in Mechanical Engineering magazine in March 2010, page 3 and 4, https://www.MEMAGAZINE.org, Fred Finkelstein is a mechanical engineering consultant at Iron Designer, Diamond Bar, Calif. This section was edited by Associate Editor Alan S. Brown. TECH FOCUS SECTION, Power Transmission & Motion Control Section