coulombdemping

Coulombdemping is a term used to describe a non-linear damping mechanism inspired by Coulomb (dry) friction, in which the damping force has a roughly constant magnitude and acts opposite to the direction of motion. In many descriptions, it corresponds to the idealized model of friction where the resistive force is F = -μN sign(v) for motion with nonzero velocity, with a range of static friction when the system is at rest. The coefficient μ is the coefficient of friction and N is the normal force; the static friction threshold μsN determines whether motion resumes when external forcing is applied.

In a simple single-degree-of-freedom oscillator, Coulombdemping is incorporated into the equation of motion as m dv/dt = -k x - μN sign(v) for v ≠ 0 (with sign indicating direction of motion). If v = 0, the friction force can take any value up to μN in magnitude, so the body may remain at rest unless an external force overcomes the static friction threshold. This leads to a non-smooth, piecewise dynamics that contrasts with viscous damping, where the resisting force is proportional to velocity.

Key characteristics include its velocity-independent damping magnitude, potential for stick-slip behavior, and discontinuities in the acceleration at zero velocity. Energy dissipation is tied to the slip distance rather than the slip speed, and the rate of amplitude decay in oscillations depends on the friction threshold and excursion amplitude. Numerically, Coulombdemping can cause chattering and requires careful handling of sign changes and static-friction conditions.

Applications and considerations involve modeling frictional losses in mechanical components and vibration systems, where a simple dry-friction model captures essential damping behavior but must be complemented by other damping mechanisms for realism.