Friction clutch controlled by kinetic and upper and lower static locking friction signals
A friction clutch transfers motion and torque between two driveline axes by coupling them with friction. The Fundamental Friction Clutch block models a standard friction clutch with kinetic friction and static (locking) friction acting on the two axes. For model details, see Fundamental Friction Clutch Model.
B and F are rotational conserving ports representing, respectively, the clutch input (base) and output (follower) driveshaft axes. The clutch motion is measured as the slip ω = ωF– ωB, the angular velocity of follower relative to base.
The clutch requires three physical signal inputs (all in newton-meters):
Kinetic friction torque τK ≥ 0 (port tK)
Static friction upper limit torque τS+ (port t+)
Static friction lower limit torque τS– (port t–)
The clutch generates two physical signal outputs:
Clutch slip ω (port S)
Clutch state or mode (port M)
Select Bidirectional or Unidirectional to determine how the follower axis can turn relative to the base, in both directions or only in the forward direction, respectively. The default is Bidirectional.
Sets the minimum absolute slip ωTol above which the clutch cannot lock. Below this speed, the clutch can lock. See the diagram in Clutch State, Transition, and Variable Summary. The default is 0.001.
From the drop-down list, choose units. The default is radians/second (rad/s).
From the drop-down list, choose whether the clutch starts simulation in the Locked or the Initial Unlocked state. The default is Unlocked.
The friction clutch has two possible directionalities:
Bidirectional (ω ≤ 0 or ω ≥ 0), allowing the follower to rotate relative to the base in either direction
Unidirectional (ω ≥ 0), allowing the follower to rotate relative to the base in the forward direction only.
A unidirectional clutch is equivalent to a friction clutch connected in parallel to a one-way clutch, which disengages when the relative motion reverses.
If you want a unidirectional clutch that allows the follower to rotate relative to the base in the reverse direction only, connect the Fundamental Friction Clutch block in your driveline with reversed orientation, follower (F) to base (B).
You set the clutch velocity tolerance or threshold ωTol for each clutch individually.
The Fundamental Friction Clutch block can apply two kinds of friction to driveline motion, kinetic and static, to oppose or prevent slipping of the two axes.
The clutch applies kinetic friction torque, specified as a positive input signal, only when one driveline axis is spinning relative to the other driveline axis; that is, when the clutch is unlocked and the slip is nonzero.
The clutch applies static friction torque when the two driveline axes lock and rotate together, without slip.
You specify static friction limits as input signals. These positive upper and negative lower limits define a locked range of static friction. If the torque across the clutch remains within this range, the clutch remains locked.
The block iterates through multistep testing to determine when to lock and unlock the clutch.
When simulation starts, the state of a clutch is either Locked or Initial-Unlocked. If you change the clutch initial state default and require it to be initially locked, the simulation starts with the clutch already in the Locked state, with no initial tests of clutch conditions.
Unlike the Unlocked state, the default Initial Unlocked state lacks a direction of motion. When simulation first starts, the clutch immediately tests its condition to see if it should be:
Locked or unlocked
If unlocked, rotating forward or in reverse
Then the clutch then moves itself to the appropriate state.
The following figure shows the possible states and transitions of a bidirectional clutch. The states and transitions of a unidirectional clutch consist of just the right side of the chart.
The following diagram summarizes the physical differences between the locked and unlocked states.
The following tables summarize the clutch variables, states, and modes.
|ω||Relative angular velocity (slip)||ωF – ωB|
|α||Relative angular acceleration||dω/dt|
|ωTol||Slip tolerance for|
|First locking condition: |ω| ≤ ωTol|
|τK||Kinetic friction torque||tK||Second locking condition: τK > 0|
|τS±||Static friction torque limits||t±||Defines locked range|
|τ||Total torque transferred across clutch||Clutch remains locked if τS– < τ < τS+.|
Clutch States and Modes
|Forward or Wait Forward||+1|
|Reverse or Wait Reverse||–1|
|Initial Unlocked State||0|
A friction clutch can be in one of three physical states:
Unengaged (ω ≠ 0 and τK = 0), when the clutch applies no friction at all. The frictional surfaces are not in contact. The follower and base are independent, and no torque is transferred between them. No power is dissipated by the clutch in this state.
Engaged, but not locked (ω ≠ 0 and τK > 0), when the clutch applies kinetic friction as the frictional surfaces touch and slip past one another. The follower and base remain independent, but some torque is transferred between them.
The clutch dissipates power only in this state. The power dissipated is |ω·τK|.
Locked (ω = 0 and τK > 0), when the clutch applies static friction. The frictional surfaces lock together and do not slip. The follower and base effectively form a single axis. This state transfers the maximum torque possible. Because static constraints do no work, no power is dissipated by the clutch in this state.
There is also a fourth, virtual state called the wait state. See the diagram in Clutch State, Transition, and Variable Summary.
Locking requires that the:
Relative speed (absolute slip) |ω| be smaller than a velocity threshold ωTol.
Kinetic friction torque τK be positive.
The static friction torque controls the unlocking of a friction clutch. When the clutch is locked, it remains locked unless the torque transferred across the clutch exceeds the static friction torque limits.
If it locks, a Fundamental Friction Clutch block imposes a constraint on your driveline by requiring that two otherwise independent angular velocities be equal. A locked clutch thus reduces the number of independent degrees of freedom by one.
By the same principle, a clutch unlocking restores one independent degree of freedom to a driveline.
A locking clutch imposes a dynamic constraint because its constraint can appear and disappear during the simulation.
The kinetic friction torque τK applied between the base and follower driveshafts is specified by the incoming signal at the tK inport. This signal should be positive or zero.
The Fundamental Friction Clutch applies this torque as long as the clutch remains unlocked.
Once the friction clutch locks, it remains locked as long as the total torque τ transferred across the clutch remains within the range defined by the static friction torque limits:
τS– < τ < τS+ .
You specify the static friction torque limits τS± by the incoming signals at the t+ and t– inports. τS+ and τS– are independent, as long as
τS– < 0 < τS+ .
The locking and unlocking of a friction clutch proceed through an intermediate Wait state.
The Wait state is a virtual state that continues the motion of the clutch's previous state but tests for locking or unlocking.
If the clutch moved to Wait from Locked, it remains locked while in Wait.
If the clutch moved to Wait from Unlocked, it remains unlocked while in Wait.
The friction clutch locks the two connected driveline axes together when both these conditions hold:
Either of these conditions:
|ω| ≤ ωTol
τ changes sign while the clutch is unlocked
If the ω changes sign while the clutch is unlocked, but τK = 0, the clutch enters the Wait state. While the clutch is in the Wait state, the driveshafts continue to slip relative to one another, subject to τK. While in the Wait state, if the clutch locking conditions become true, the clutch moves to Locked.
If the total torque across the two driveline axes moves outside the static friction limit range, the clutch enters the Wait state. While the clutch is in the Wait state, it remains locked but tests for unlocking.
The unlocking of a friction clutch is a conditional, multistep process implemented internally through mode iteration. The Wait state encompasses the steps that test the entire driveline for unlocking.
The block first checks the relative acceleration α = dω/dt of the two driveline axes, based on the torques present when the clutch enters the Wait state.
The clutch returns to the Locked state if:
The whole driveline requires the axes to turn in the relative forward direction, but α is negative.
The whole driveline requires the axes to turn in the relative reverse direction, but α is positive.
If the clutch remains in the Wait state instead of returning to Locked, the relative acceleration is integrated in time to obtain the absolute value of the virtual angular speed. The block checks this result against angular velocity tolerance ωTol. If the result is less than ωTol, the clutch returns to the start of the Wait state and the relative acceleration check. If the result exceeds ωTol, the clutch unlocks.
In the Unlocked state, the clutch begins applying kinetic friction again.
Tip For more information about mode iteration and solving constraints in Simscape™, see Simulation.