Represent friction clutch with kinetic and static friction and controlled by pressure signal
A friction clutch transfers torque between two driveline axes by coupling them with friction. The Controllable Friction Clutch block models a standard friction clutch with kinetic friction and static (locking) friction acting on the two axes. The motion is measured as the slip of follower (F) axis relative to base (B) axis, ω = ωF – ωB.
The clutch requires a dimensionless input pressure signal P that modulates the applied kinetic friction. This signal should be positive or zero. A signal P less than zero is interpreted as zero. A signal P of unity corresponds to the full normalized kinetic friction.
The Controllable Friction Clutch is based on the Fundamental Friction Clutch block. See the Fundamental Friction Clutch block reference page for more about:
Use the blocks of the Dynamic Elements library as a starting point for vehicle modeling. To see how a Dynamic Element block models a driveline component, look under the block mask. The blocks of this library serve as suggestions for developing variant or entirely new models to simulate the same components. Break the block's library link before modifying it and creating your own version.
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.
Number of friction-generating contact surfaces inside the clutch. The default is 6.
The effective moment arm radius, in meters (m), that determines the kinetic friction torque inside the clutch. The default is 0.04.
The maximum force, in newtons (N), normal to the frictional surfaces in the clutch. This value normalizes the Simulink® input signal P for clutch pressure and determines the maximum kinetic friction torque. The default is 1000.
Dimensionless kinetic friction factor μ as a function of the angular velocity in tabular form. The table is a matrix whose rows are vectors of length 2, separated by semicolons. Each two-component vector specifies a pair of values, an angular velocity ω and a corresponding μ value, in that order. The simulation automatically interpolates a cubic spline from these values.
The default matrix is [0 1; 1e8 1], which is a constant μ of value 1. The angular velocity values are in units of radians/second.
Ratio of the static friction limit for clutch locking to the kinetic friction. The default is 1.1.
Minimum normalized pressure Pth that activates clutch friction. If the normalized pressure input signal P is less than this threshold, the clutch applies no friction. The default is 0.
Select to require this clutch to use the driveline-wide velocity tolerance ωTol specified in the Driveline Environment block connected to the driveline. The default is selected.
If you unselect this check box, you enable the Use automatic clutch velocity tolerance for variable-step solvers check box and the Clutch velocity tolerance field (see following).
Sets the minimum angular velocity ωTol above which the clutch cannot lock. Below this velocity, the clutch can lock. (See Simplified Friction Clutch Model following.) The units are radians/second. The default is 1e-3.
For a fixed-step solver, this clutch always uses this value, if you do not specify a default velocity tolerance through the Driveline Environment block.
This field is enabled only if the Use default clutch velocity tolerance from the Driveline Environment block check box is unselected.
Select to require this clutch to compute the velocity tolerance ωTol automatically from solver settings. The default is selected.
This check box is enabled only if the Use default clutch velocity tolerance from the Driveline Environment block check box is unselected.
Select to start the simulation with the clutch already locked. The default is unselected.
Select to make available the Simulink outport for the clutch slippage signal. The default is unselected.
The clutch slippage is the relative angular velocity ω of the two coupled driveline axes. The signal measures the clutch slippage in radians/second.
Select to make available the Simulink outport for the power dissipation signal. The default is unselected.
The signal measures the power, in watts (W), being dissipated by friction torques applied by the clutch to the driveline axis.
Select to make available the Simulink port for the discrete clutch mode signal. The default is unselected.
The signal value is a function of the clutch state. See the table, Clutch States and Modes, following.
The Controllable Friction Clutch is based on the Fundamental Friction Clutch. Consult the Fundamental Friction Clutch block reference page for the complete friction clutch model. This section discusses the simplified model implemented in the Controllable Friction Clutch.
When you apply a pressure signal above threshold (P ≥ Pth), the Controllable Friction Clutch 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 are locked and spin together. The block iterates through multistep testing to decide when to lock and unlock the clutch.
These tables summarize the clutch variables, states, and modes.
|ω||Relative angular velocity||ωF – ω B|
|α||Relative angular acceleration||dω/dt|
|ωTol||Relative angular velocity tolerance for clutch locking||See text following|
|P, Pth||Normalized clutch pressure and threshold||Dimensionless input pressure applied to clutch discs; threshold clutch pressure. Usually, 0 ≤ P, Pth ≤ 1.|
|Pfric||Clutch friction capacity||max[(P – Pth), 0]|
|reff||Effective torque radius||Effective moment arm of clutch friction force|
|μ||Kinetic friction coefficient||Dimensionless coefficient of kinetic friction of clutch discs, function of ω|
|τK||Kinetic friction torque||See text following|
|τS||Static friction torque limit||(static friction peak factor)·(kinetic friction torque for ω → 0) (See text following)|
Clutch States and Modes
|Forward or Wait Forward||+1|
|Reverse or Wait Reverse||-1|
|Default Initial State||0|
Instead of requiring the kinetic and static friction limit torques as input signals, the Controllable Friction Clutch calculates these from the fixed clutch parameters and the input normalized pressure signal P.
The kinetic friction torque is a product of five factors:
τK = μ·(number of friction
(peak normal force)·Pfric ≥ 0
The effective torque radius reff is the effective radius, measured from the driveline axis, at which the frictional forces are applied at the frictional surfaces. It is related to the geometry of the friction surface by
ro and ri are the outer and inner radii, respectively, of the friction surface, modeled as a disk.
You specify the kinetic friction coefficient μ as a tabulated discrete function of relative angular velocity ω. This function is assumed to be symmetric for positive and negative values of the relative angular velocity, so that you need to specify μ for positive values of ω only.
The peak normal force is the normal force applied to the frictional surfaces when the normalized clutch friction capacity signal P – Pth is one. The pressure signal should be nonnegative. If P is less than Pth, the clutch applies no friction at all.
The static friction limit is a product of two factors:
τS = (static friction peak factor)·τK(ω → 0)
The block computes the kinetic friction torque with the kinetic friction coefficient μ interpolated to zero relative angular velocity with a cubic spline.
The static friction peak factor measures how much larger the static friction has to be to unlock the clutch, as a ratio to the kinetic friction at the instant of unlocking, when ω = 0.
The static friction torque limits or range is then defined symmetrically as:
τS ≡ τS+ = –τS–
The Wait state of the Controllable Friction Clutch is identical to the Wait state of the Fundamental Friction Clutch, with the replacement of the positive kinetic friction condition (τK > 0) by the positive clutch friction capacity condition (P ≥ Pth).
The power dissipated by the clutch is |ω·τK|. The clutch dissipates power only if it is both slipping (ω ≠ 0) and applying kinetic friction (τK > 0).
These SimDriveline™ example models contain working examples of controllable friction clutches used to change gear couplings: