Disc Friction Clutch
Friction clutch with disc plates that engage when plate pressure exceeds threshold
Libraries:
Simscape /
Driveline /
Clutches
Description
The Disc Friction Clutch block represents a friction clutch with two flat friction plate sets that come into contact to engage. The clutch engages when the applied plate pressure exceeds an engagement threshold pressure. Once engaged, the plates experience frictional torques that enable them to transmit power between the base and follower 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 slips slower. The block defines the slip velocity as the difference
where:
ω is the relative angular velocity or slip velocity.
ωF is the angular velocity of the follower driveshaft.
ωB is the angular velocity of the base driveshaft.
The block provides a physical signal input port P for the applied pressure between the clutch plates. The applied pressure must be greater than or equal to zero. If the input signal falls below zero, the block treats the plate pressure as zero.
Equations
The Disc Friction Clutch block is a simplified implementation of the Fundamental Friction Clutch block. The Fundamental Friction Clutch requires the kinetic and static friction limit torques as input signals. The Disc Friction Clutch does not require the input data. Instead, the block calculates the kinetic and static friction from the clutch parameters and the input pressure signal P.
When you apply a pressure signal above threshold, such that the applied pressure equals or exceeds the pressure threshold, that is, , the block can apply two kinds of friction to the driveline motion, kinetic and static. The clutch applies kinetic friction torque only when one driveline axis is spinning relative to the other driveline axis. The clutch applies static friction torque when the two driveline axes lock and spin together. The block iterates through multistep testing to determine when to lock and unlock the clutch.
The kinetic friction torque opposes the relative slip and is applied with an overall minus sign. Mathematically, the kinetic friction is the positive sum of viscous drag and surface contact friction torques:
τK is the kinetic friction torque.
μ is the viscous drag coefficient.
ω is the relative angular velocity, or slip velocity.
τcontact is the contact torque.
The contact friction is a product of six factors such that
where:
kK is the dimensionless coefficient of kinetic friction of clutch discs, which is a function of ω.
D is the clutch de-rating factor.
N is the number of friction surfaces.
reff is the effective torque radius, that is, the effective moment arm of clutch friction force.
Pfric is the clutch friction capacity, such that .
A is the engagement surface area.
You specify the kinetic friction coefficient, kK, as either a constant or a tabulated discrete function of relative angular velocity ω. The tabulated function is assumed to be symmetric for positive and negative values of the relative angular velocity. Therefore, specify kK for positive values of ω only.
The clutch applies a normal force from its piston as the product of the clutch friction capacity, Pfric, and engagement surface area, A, on each of N friction surfaces. The pressure signal, P, should be nonnegative. If P is less than the pressure threshold. Pth, the clutch applies no friction at all.
The effective torque radius, reff, is the effective moment arm of clutch friction force, measured from the driveline axis, at which the kinetic friction forces are applied at the frictional surfaces. It is related to the geometry of the friction surface by:
where, for a friction surface, modeled as an annular disc:
ro is the outer disc radius.
ri is the inner disc radius.
The clutch de-rating factor, D, accounts for clutch wear. For a new clutch, D is one. For a clutch approaching a uniform wear state:
The static friction limit is related to the kinetic friction, setting ω to zero and replacing the kinetic with the static friction coefficient:
where:
τS is the static friction torque limit, which is the product of the static friction peak factor and the kinetic friction torque as ω approaches 0.
kK is the dimensionless coefficient of static friction of clutch discs.
D is the clutch de-rating factor.
N is the number of friction surfaces.
reff is the effective torque radius, that is, the effective moment arm of clutch friction force.
Pfric is the clutch friction capacity, such that .
A is the engagement surface area.
, so that the torque τ needed across the clutch to unlock it by overcoming static friction is larger than the kinetic friction at the instant of unlocking, when .
The static friction torque range or limits are then defined symmetrically as
The Wait state of the Disc Friction Clutch is identical to the Wait state of the Fundamental Friction Clutch, with the replacement of the positive kinetic friction condition, , by the positive clutch friction capacity condition, the applied pressure equals or exceeds the pressure threshold, that is, .
The power dissipated by the clutch is the absolute value of the product of slip velocity, ω, and the kinetic friction torque, τK, that is, . The clutch dissipates power only if it is both slipping, , and applying kinetic friction, .
Velocity-Dependent and Temperature-Dependent Friction Models
You can model the effects of rotational velocity change by selecting a
velocity-dependent model. To choose a velocity-dependent model, in the
Friction settings, set the Friction
model parameter to Velocity-dependent kinetic
friction coefficient
. For information about a friction model
that depends on both velocity and temperature, see Thermal, Velocity-Dependent Model.
For the velocity-dependent model these related parameters become visible in the Friction settings:
Relative velocity vector
Kinetic friction coefficient vector
Friction coefficient interpolation method
Friction coefficient extrapolation method
You can model the effects of heat flow and temperature change by selecting a
temperature-dependent model. To choose a temperature-dependent model, in the
Friction settings, set the Friction
model parameter to Temperature-dependent friction
coefficients
. For information about a friction model that
depends on both velocity and temperature, see Thermal, Velocity-Dependent Model.
You can model the effects of rotational velocity change and heat flow by
selecting a velocity-dependent and temperature-dependent model. To choose a
model that depends on both velocity and temperature, in the
Friction settings, set the Friction
model parameter to Temperature and
velocity-dependent friction coefficients
.
Faults
To model a fault in the Disc Friction Clutch block, in the Faults section, click the Add fault hyperlink next to the fault that you want to model. For more information about fault modeling, see Fault Behavior Modeling and Fault Triggering.
You can choose either or both of these settings for block faulting. When you trigger a fault, the block responds according to the setting of the Behavior when faulted parameter for the remainder of the simulation. The fault options are:
Cannot transmit power
Cannot unlock