Viscous Friction

Friction proportional to relative speed — the faster something turns, the more resistance it meets.

Viscous friction is a resistive force proportional to speed, in its simplest form F = −b·v, where v is the relative velocity (angular velocity, for a joint), b is the viscous friction coefficient, and the negative sign indicates the force opposes the motion. It arises from the internal friction (viscosity) within a fluid layer such as lubricating oil, and unlike Coulomb friction — whose magnitude is roughly independent of speed and depends only on the normal force — it vanishes when speed is zero. In robot joints, the friction in motors, gearboxes, and bearings is usually modeled as several parts together: Coulomb friction plus viscous friction, with the Stribeck effect added at low speed. Once b is identified, it can be fed forward in the controller to make joint torque control more accurate. Simulators also use it to model energy loss at a joint: MuJoCo's joint damping parameter is exactly this viscous damping coefficient, producing a passive force opposite the joint's velocity; when transferring from simulation to a real robot, this coefficient is often identified from the real hardware or randomized during training.

ExampleIf a joint has a viscous coefficient of b = 0.2 N·m·s/rad, then rotating at 1 rad/s produces a viscous friction torque of 0.2 N·m, and rotating at 2 rad/s produces 0.4 N·m; the Coulomb-friction portion, by contrast, is nearly the same at both speeds.

Also called

Viscous Damping

Related

Coulomb Friction · Static Friction (Stiction) and Stribeck Effect · Damping · Friction Compensation · Dynamic Parameter Identification · Dynamics Randomization

Sources

Sorrentino et al., Physics-Informed Learning for the Friction Modeling of High-Ratio Harmonic Drives (arXiv:2410.12685)
MuJoCo Documentation: Computation (Passive forces / damping)
Wikipedia: Friction