The Mystery and Clarity of Leonardo da Vinci's Coefficient of Friction

Abstract

The science of friction has been using the coefficient of friction as the main quantitative characteristic of the friction process for more than five centuries. The concept of the coefficient of friction as a characteristic of the resistance to the movement of rubbing surfaces in a hidden form was formulated by Leonardo da Vinci: "Each rubbing body exerts a friction resistance equal to one quarter of its weight, provided that the flat plane is in contact with the polished surface". Two centuries later, the coefficient of friction appeared explicitly, in the form of a formula, in the works of G. Amontons. It is clear that the coefficient of friction is a convenient friction parameter, easily determined in the experiment. However, what is the physical meaning of resistance to the movement of rubbing surfaces? Modern engineering believes that the coefficient of friction has no physical meaning. Thermodynamic analysis of the friction process is performed. The evolutionary patterns of the behavior of the friction contact are shown. A structural-energy interpretation of the logic of the coefficient of friction (resistance) is proposed: accumulation of potential energy of defects in the crystal structure of the deformable volume by friction contact. The static potential energy of the formed defects in the crystal structure of the contact is a measure of the decrease in the kinetic energy of the relative motion of the rubbing surfaces. Such a formulation of resistance to movement under friction has a deep physical and clear meaning for a scientist and engineer. The substantiation of Leonardo da Vinci's formulation of friction that the friction resistance should be equal to 0.25 is given. The interpretation of this rule is given for the case of friction in mechanisms (machines).