Coulomb damping is a type of constant mechanical damping in which the system's kinetic energy is absorbed via sliding friction (the friction generated by the relative motion of two surfaces that press against each other). Coulomb damping is a common damping mechanism that occurs in machinery.
Coulomb damping was so named because Charles-Augustin de Coulomb carried on research in mechanics. He later published a work on friction in 1781 entitled "Theory of Simple Machines" for an Academy of Sciences contest. Coulomb then gained much fame for his work with electricity and magnetism.
Coulomb damping absorbs energy with friction, which converts that kinetic energy into thermal energy, i.e. heat. Coulomb friction considers this under two distinct modes: either static, or kinetic.
Static friction occurs when two objects are not in relative motion, e.g. if both are stationary. The force exerted between the objects does exceed—in magnitude—the product of the normal force and the coefficient of static friction :
|F\rm|<\mu\rmN
Kinetic friction on the other hand, occurs when two objects are undergoing relative motion, as they slide against each other. The force exerted between the moving objects is equal in magnitude to the product of the normal force and the coefficient of kinetic friction :
|F\rm|=\mu\rmN
Regardless of the mode, friction always acts to oppose the objects' relative motion. The normal force is taken perpendicularly to the direction of relative motion; under the influence of gravity, and in the common case of an object supported by a horizontal surface, the normal force is just the weight of the object itself.
As there is no relative motion under static friction, no work is done, and hence no energy can be dissipated. An oscillating system is (by definition) only dampened via kinetic friction.
Consider a block of mass
m
k
F=kx
where
x
N=mg
As stated earlier,
F\rm
m\ddotx =-F-(sgn{
| x}) |
Fk=-kx-(sgn{
| x}) |
\mu\rmmg
Above,
| x |
\ddotx
| sgn{x} |
A real-life example of Coulomb damping occurs in large structures with non-welded joints such as airplane wings.
Coulomb damping dissipates energy constantly because of sliding friction. The magnitude of sliding friction is a constant value; independent of surface area, displacement or position, and velocity. The system undergoing Coulomb damping is periodic or oscillating and restrained by the sliding friction. Essentially, the object in the system is vibrating back and forth around an equilibrium point. A system being acted upon by Coulomb damping is nonlinear because the frictional force always opposes the direction of motion of the system as stated earlier. And because there is friction present, the amplitude of the motion decreases or decays with time. Under the influence of Coulomb damping, the amplitude decays linearly with a slope of
\pm2\mumg\omega\rm/(k\pi)