Determining a Surrogate Contact Pair in a Hertzian Contact Problem

Area of Science:

• Mechanical Engineering
• Materials Science
• Tribology

Background:

• Laboratory testing of contact phenomena involving complex geometries is often prohibitively expensive.
• Existing methods lack cost-effective solutions for simulating intricate contact mechanics.

Purpose of the Study:

• To develop a method for simplifying geometrically complex contact pairs in laboratory testing.
• To enable accurate simulation of contact mechanics using inexpensive surrogate geometries.

Main Methods:

• Derived formulas to replace complicated Hertzian contact pairs with surrogate plane-spheroid pairs.
• Utilized tensor notation to represent complex surfaces as ellipsoids to second-order accuracy.
• Employed spectral decomposition of the Hessian tensor to determine surrogate spheroid geometry.

Main Results:

• Developed a surrogate pair (plane and spheroid) with equivalent contact area and pressure distribution (to second-order accuracy) as complex geometries.
• Demonstrated the theory with numerical examples of free-form surfaces.
• Validated the theory through laboratory tests on normally compressed convex surfaces.

Conclusions:

• The Hertzian contact substitution theory simplifies the testing of contact, wear, or impact for complex components and materials.
• This approach offers a cost-effective and efficient alternative for experimental contact mechanics.
• The method provides a pathway to reduce experimental costs without compromising accuracy.