4569846498

Modelling and assembly of the full vehicle 353
For the most common brake rotor material, cast iron, the specific heat versus
temperature characteristic can be approximated in the working range
(0–730°C) by the expression:
c 320 0.15T 1.164 10 9 T 4 (6.15)
Note that in the above expression, temperature T is in centigrade (Celsius)
and not Kelvin. The brake torque and temperature models may be used easily
within a multibody system model using a combination of design variables
(declared in MSC.ADAMS using the ‘variable create’ command) and
run-time variables (declared in MSC.ADAMS using ‘data_element create’
variable) as shown in Table 6.1 where we are using for the first time here an
input format that corresponds to a command language used in MSC.ADAMS.
Note the need for an explicit iteration since the temperature depends on the
heat capacity and the heat capacity depends on the temperature. When
modelling such behaviour in a spreadsheet, it is sufficient to refer to the
temperature of the preceding time step. Although this is possible within
many multibody system packages, it can be awkward to implement and can
also lead to models with some degree of numerical delicacy.
Note also that it is common practice within brake manufacturers to separate
the brake energizing event from the brake cooling event for initial design
calculations, leading to a systematic overestimation of the temperature during
fade/recovery testing. This conservative approach is unsurprising given
the consequences of brake system underdesign. The example given is a relatively
simple one, with convection characteristics that are independent of
vehicle velocity and no variation of brake friction with brake temperature.
Although in practice these simplifications render the results slightly inaccurate,
they are useful when used for comparative purposes – for example, if
the brake temperature model is used with an ESP algorithm it can rank
control strategies in terms of the energy added to individual brake rotors.
Similar modelling is of course possible for other frictional systems within
Joules
2.0E005
1.5E005
1.0E005
50000.0
brake_rotor_heat_in.Q
brake_rotor_heat_out.Q
degrees Celsius
120.0
100.0
80.0
60.0
40.0
rotor_temperature_estimate_2
metres/second
0.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Analysis: Last_Run Time (sec) 2003-08-25 16:02:49
30.0
25.0
vehicle_velocity.Q
20.0
15.0
10.0
5.0
0.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Analysis: Last_Run Time (sec) 2003-08-25 16:02:49
Joules/kilogram/K
20.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Analysis: Last_Run Time (sec) 2003-08-25 16:02:49
340.0
335.0
330.0
325.0
rotor_heat_capacity_estimate_2.Q
320.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Analysis: Last_Run Time (sec) 2003-08-25 16:02:49
Fig. 6.29 Output from the brake temperature model shown in Table 6.1
during a 60 mph–0 stop