The legacy of Coulomb and generalized laws of friction
The simple formulation of “Coulomb's law of friction” which can be found in most textbooks—the force of friction is proportional to the normal force and does not depend on the contact area and velocity—has little to do with the real work of Coulomb. On the contrary, Coulomb found that Amontons' law, as well as the independence of the coefficient of friction on velocity, normal force, contact area and roughness are only a first, very rough approximation. He differentiated between material couples (e.g. metal-metal), where Amontons' law is a good approximation, and other (wood on metal or wood on wood), where there are significant deviations from Amontons' law. In all cases, however, the dependencies are relatively weak. In contemporary language, we would say they are of logarithmic character: the geometric and loading parameters have to be changed by several orders of magnitude to achieve a change in the coefficient of friction by a factor of two. Coulomb also gives simple two-term relations, which empirically summarize these experimental findings.
Published in: Proceedings in Applied Mathematics and Mechanics (PAMM), 10.1002/pamm.202000062, Wiley