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358 Multibody Systems Approach to Vehicle Dynamics
REVOLUTE
TORQUE
Dummy transmission
part
COUPLER
REV
REV
Driven
wheels
Fig. 6.34
Simple drive torque model
The rotation of the front wheels is coupled to the rotation of the dummy
transmission part shown in Figure 6.34. The coupler introduces the following
constraint equation:
s 1 r 1 s 2 r 2 s 3 r 3 0 (6.16)
where s 1 , s 2 and s 3 are the scale factors for the three revolute joints and r 1 ,
r 2 and r 3 are the rotations. In this example suffix 1 is for the driven joint and
suffixes 2 and 3 are for the front wheel joints. The scale factors used are
s 1 1, s 2 0.5 and s 3 0.5 on the basis that 50% of the torque from the
driven joint is distributed to each of the wheel joints. This gives a constraint
equation linking the rotation of the three joints:
r 1 0.5r 2 0.5r 3 (6.17)
Note that this equation is not determinant. For a given input rotation r 1 ,
there are two unknowns r 2 and r 3 but only the single equation. In order to
solve r 2 and r 3 this equation must be solved simultaneously with all the
other equations representing the motion of the vehicle. This is important
particularly during cornering where the inner and outer wheels must be
able to rotate at different speeds.
6.11 Other driveline components
The control of vehicle speed is significantly easier than the control of vehicle
path inside a vehicle dynamics model. In the real vehicle, speed is influenced
by the engine torque, brakes and aerodynamic drag. As discussed
earlier these are relatively simple devices to represent in a multibody systems
model, with the exception of turbochargers and torque converters.
Even these latter components can be represented using differential equations
of the form:
T T Tˆ
(6.18)
BOOST
2
BOOST
d T1
( T2
) ( tboostT2
)
dt
k
2
(6.19)