Double-Shoe Brake
Frictional brake with two pivoted shoes diametrically positioned about a rotating drum with triggered faulting
Libraries:
Simscape /
Driveline /
Brakes & Detents /
Rotational
Description
The Double-Shoe Brake block represents a frictional brake with two pivoted rigid shoes that press against a rotating drum to produce a braking action. The rigid shoes sit inside or outside the rotating drum in a diametrically opposed configuration. A positive actuating force causes the rigid shoes to press against the rotating drum. Viscous and contact friction between the drum and the rigid shoe surfaces cause the rotating drum to decelerate.
Double-shoe brakes provide high braking torque with small actuator deflections in applications that include motor vehicles and some heavy machinery. The model employs a simple parameterization with readily accessible brake geometry and friction parameters.
You can also enable faulting. When faulting occurs, the belt will exert a user-specified force. Faults can occur at a specified time or due to an external trigger at port T.
Equations
In the schematic, a) represents an internal double-shoe brake, and b) represents an external double-shoe brake. In both configurations, a positive actuation force F brings the shoe and drum friction surfaces into contact. The result is a friction torque that causes deceleration of the rotating drum. Zero and negative forces do not bring the shoe and drum friction surfaces into contact and produce zero braking torque.
The model uses the long-shoe approximation. The equations for the friction torque that the leading and trailing shoes develop are:
where for ,
and for ,
Where:
TLS is the brake torque the leading shoe develops.
TTS is the brake torque the trailing shoe develops.
μ is the effective contact friction coefficient.
pa is the maximum linear pressure in the leading shoe-drum contact.
pb is the maximum linear pressure in the trailing shoe-drum contact.
rD is the drum radius.
θsb is the shoe beginning angle.
θs is the shoe span angle.
θa is the angle from hinge pin to maximum pressure point.
c is the arm length of the cylinder force with respect to the hinge pin.
rp is the pin location radius.
θp is the hinge pin location angle.
ra is the actuator location radius.
The model assumes that only Coulomb friction acts at the shoe-drum surface contact. Zero relative velocity between the drum and the shoes produces zero Coulomb friction. To avoid discontinuity at zero relative velocity, the friction coefficient formula employs the hyperbolic function
where:
μ is the effective contact friction coefficient.
μCoulomb is the contact friction coefficient.
ωshaft is the shaft velocity.
ωthreshold is the angular velocity threshold.
Balancing the moments that act on each shoe with respect to the pin yields the pressure acting at the shoe-drum surface contact. The equations for determining the balance of moments for the leading shoe are
and
where:
F is the actuation force.
MN is the moment acting on the leading shoe due to normal force.
MF is the moment acting on the leading shoe due to friction force.
c is the arm length of the cylinder force with respect to the hinge pin.
pa is the maximum linear pressure at the shoe-drum contact surface.
rp is the pin location radius.
θp is the hinge pin location angle.
ra is the actuator location radius.
The model does not simulate self-locking brakes. If brake geometry and friction parameters cause a self-locking condition, the model produces a simulation error. A brake self-locks if the friction moment exceeds the moment due to normal forces, that is, when MF > MN.
The balance of moments for the trailing shoe is
The net braking torque is
where μvisc is the viscous friction coefficient.
Faults
When faults are enabled, a belt force is applied in response to one or both of these triggers:
Simulation time — Faulting occurs at a specified time.
Simulation behavior — Faulting occurs in response to an external trigger. This exposes port T.
If a fault trigger occurs, the input force is replaced by the Belt force
when faulted value for the remainder of the simulation. A value of
0
implies that no braking will occur. A relatively large
value implies that the brake is stuck.
You can set the block to issue a fault report as a warning or error message in the Simulink Diagnostic Viewer with the Reporting when fault occurs parameter.
Thermal Model
You can model the effects of heat flow and temperature change by exposing the optional thermal
port. To expose the port, in the Friction settings, set the
Thermal Port parameter to Model
.
Exposing the port also exposes or changes the default value for these related settings,
parameters, and variables:
Friction > Temperature
Friction > Static friction coefficient vector
Friction > Coulomb friction coefficient vector
Friction > Contact friction coefficient vector
Thermal Port > Thermal mass
Variables > Temperature
Variables
Use the Variables settings to set the priority and initial target values for the block variables before simulating. For more information, see Set Priority and Initial Target for Block Variables.
Variable settings are visible only when, in the Friction settings, the
Thermal port parameter is set to
Model
.
Limitations and Assumptions
Contact angles smaller than 45° produce less accurate results.
The brake uses the long-shoe approximation.
The brake geometry does not self-lock.
The model does not account for actuator flow consumption.
Ports
Input
Conserving
Parameters
Extended Capabilities
Version History
Introduced in R2012b