A clutch makes two shafts spinning at different rates spin at a single rate by applying torques that tend to accelerate one shaft and decelerate the other. The most common way for a clutch to accomplish this action is with surface friction. Such a clutch can operate in one of these modes of motion:
Disengaged: the clutch applies no friction at all.
Engaged but unlocked: the clutch applies kinetic friction, and the two shafts spin at different rates.
Engaged and locked: the clutch applies static friction, and the two shafts spin together.
A clutch consists of mated frictional surfaces overlapping one another and connected on either side to a shaft. If the clutch is disengaged, the frictional surfaces have no contact and the shafts spin independently. To engage the clutch, contact between two surfaces is induced by applying pressure normal to the clutch surfaces. The two surfaces in contact and moving relative to one another experience kinetic friction, which causes them to narrow their relative velocity. The friction acts to reduce the relative motion between the two clutch plates and their connected shafts. At some critical combination of reduced relative speed and pressure (normal force), the clutch locks, so that the two shafts are spinning at the same rate. The shafts remain locked together as long as the transmitted torque remains less than the static friction, which is proportional to the applied normal force. If the clutch unlocks but is still engaged, it again applies kinetic rather than static friction.
The transition between unlocked and locked states is discontinuous. Modeling a clutch locking or unlocking event requires searching for the correct combination of pressure and torque acting on the clutch. The locking and unlocking events are determined during simulation by repeated and accurate zero-crossing detection. On simulating events and solving constraints together with dynamics in Simscape™ models, see Desktop Simulation (Simscape).