Fundamental Friction Clutch

Friction clutch with kinetic and static-limit friction torques as inputs




This block represents a friction clutch, a mechanism that transmits rotational power through friction. The clutch contains two friction plate sets, each rigidly connected to a driveshaft, that come into contact in order to engage. Once in contact, the plates experience frictional torques that enable power to flow between the driveshafts.

The clutch can be bidirectional or unidirectional. A bidirectional clutch can slip in the positive and negative directions. A unidirectional clutch can slip only in the positive direction. The slip direction is positive if the follower shaft spins faster than the base shaft and negative if it spins slower. The block defines the slip velocity as the difference



  • ω is the slip velocity.

  • ωF is the angular velocity of the follower driveshaft.

  • ωB is the angular velocity of the base driveshaft.

Clutch States

The clutch can be in three states:

  • Locked — Real clutch state in which the friction plates spin as a unit. A locked clutch has one rotational degree of freedom. It experiences no power losses due to friction.

  • Unlocked — Real clutch state in which the friction plates slip with respect to each other. An unlocked clutch has two rotational degrees of freedom. It experiences power losses equal to the product of the slip velocity and the kinetic friction torque.

  • Wait — Virtual clutch state that maintains the motion of the previous state while testing for locking and unlocking. The clutch degrees of freedom and power losses depend on the previous clutch state.

The schematic shows the conditions under which the clutch is locked and unlocked. The clutch is generally locked if the torque it transfers lies between its static friction torque limits and the magnitude of the slip velocity is smaller than its velocity tolerance. The clutch unlocked otherwise.

In the schematic:

  • τ is the torque transferred between the clutch plates.

  • τS- and τS+ are the static friction torque limits.

  • τK is the kinetic friction torque between the clutch plates.

  • ωTol is the slip velocity tolerance of the clutch.

  • ω is the slip velocity between the clutch plates.

The block identifies the clutch state through physical signal port M using values -1, 0, and +1. The table summarizes the correspondence between the states and the output values.

State Value
Unlocked Forward or Wait Forward+1
Unlocked Reverse or Wait Reverse-1
Locked or Unlocked Initial State0

State Transitions

At the start of simulation, the clutch is in one of two states—locked or initial unlocked. The initial unlocked state is unique in that it lacks a direction of motion. The clutch remains in this state until the clutch slip velocity becomes nonzero. The clutch then transitions to the appropriate state—unlocked reverse or unlocked forward—according to the schematic.

During simulation, the clutch tests various dynamic conditions to determine the appropriate state transitions, if any. The schematic shows the possible transitions, their dynamic conditions, and the resulting states. If the clutch is unidirectional, the schematic reduces to the right half. The variable α is the slip acceleration between the clutch plates.

Dialog Box and Parameters


Slip directions the clutch allows between its plates. A bidirectional clutch allows positive and negative slip velocities. A unidirectional clutch allows only positive slip velocities. The default setting is Bidirectional.

The unidirectional clutch is equivalent to a friction clutch connected in parallel to a one-way clutch that disengages only when the slip velocity becomes positive. To model a unidirectional clutch with slip in the negative direction, reverse the base and follower port connections.

Clutch velocity tolerance

Slip velocity below which the clutch can lock. The clutch locks if, after falling below the clutch velocity tolerance, the kinetic friction torque is nonzero and the transferred torque is between the static friction torque limits. The default value is 0.001 rad/s.

Initial state

Clutch state at the start of simulation. The clutch can be in one of two states, locked and unlocked. A locked clutch constrains the base and follower shafts to spin at the same velocity, i.e., as a single unit. An unlocked clutch allows the two shafts to spin at different velocities, resulting in slip between the clutch plates. The default setting is Unlocked.

A clutch that starts simulation unlocked lacks a direction of motion. For this reason, after checking that the unlocked state is valid, the block automatically determines the appropriate direction of motion based on the driveline dynamics. Based on the direction of motion, the clutch then transitions to an unlocked-reverse or unlocked-forward state.


  • B — Rotational conserving port that represents the base driveshaft

  • F — Rotational conserving port that represents the follower driveshaft

  • tK — Physical signal input port for the kinetic friction torque

  • t+ — Physical signal input port for the upper static friction torque limit

  • t- — Physical signal input port for the lower static friction torque limit

  • S — Physical signal output port for the clutch slip velocity

  • M — Physical signal output port for the clutch state

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