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Brake Torque, including Lock-up Behavior
A brake applied to a non-spinning wheel behaves differently than the same brake when applied to
a spinning wheel. The spinning wheel has a dynamical degree of freedom; the locked-up wheel
does not.
When applied to a spinning wheel, the brake torque is mainly a function of the applied fluid
pressure and serves to resist the spin by dissipating energy. However, when applied to a non-
spinning wheel, the brake torque reacts as needed to prevent wheel spin, without dissipating
energy or doing any work.
When the wheel is spinning, brake torque is defined as a Configurable Function of fluid pressure
and possibly temperature. Details for the thermal model are described later. In the case of the
model that does not include thermal effects, the torque is calculated directly from the actuator
pressure.
The CarSim/TruckSim brake models account for the non-spinning state by representing the
locked brake with a torsional spring and damper that winds up as needed to react to tire/ground
forces. This change in the model equations occurs when the spin rate reaches zero. At that time,
the equations are activated for the torsional spring and damper to allow the wheel to achieve a
true static equilibrium in the locked state. The properties of the spring and damper applied at this
step are determined automatically by the math model to meet requirements of numerical stability,
based on the frequency and damping parameters LOCK_BK_R_FREQ and LOCK_BK_ZETA (see
lines 415 – 417, Figure 1, page 2). These parameters are not represented in the GUI; however,
advanced users may set them using a miscellaneous yellow field.
The brake remains locked as long as the magnitude of the torque from the spring/damper system
is less than the magnitude of the current value of the applied brake torque. If the spring/damper
torque exceeds the applied torque, then the spring/damper is disabled.
Configurable Functions in the Brake Model
Configurable functions are used to describe the nonlinear relationships in the system. Table 1 lists
the libraries used to specify datasets for configurable functions with standard editing and viewing
controls as described in detail in the VehicleSim Browser Reference Manual. The tabular datasets
are identified for the solver programs by keywords based on the root names listed in the table.
These are also identified in the Echo file (see lines 389-391, Figure 1, page 2).
Brake System Screens
The main brake system screen in CarSim is named Brakes: Four-Wheel System. In TruckSim,
brake properties are specified on a per-axle basis using the datasets from the library Brakes:
Two-Wheel System.
Another library is provided in CarSim named Brakes: Trailer Two-Wheel System. It is similar
to the other two, but has no user controls for setting the top-level controls.
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