Page 356 - Automotive Engineering Powertrain Chassis System and Vehicle Body

Tyre characteristics and vehicle handling and stability C HAPTER 11.1

Fig. 11.1-31 On the stability of a trailer (Exercise 11.1.4).

limit-cycle). This is an unfortunate, possibly dangerous the introduction of this extra term will be beneficial
situation! particularly when the system to be modelled is more
complex.
Exercise 11.1.4. Stability of a trailer Assess the condition for stability for this fourth-order
system. Simplify the system by putting g ¼ f and
Consider the trailer of Fig. 11.1-31 that is towed by c 4 ¼ k 4 ¼ 0. Now find the explicit conditional state-
a heavy steadily moving vehicle at a forward speed Valong ment for the cornering stiffness C.
a straight line. The trailer is connected to the vehicle by
means of a hinge. The attachment point shows a lateral
flexibility that is represented by the lateral spring with 11.1.3.7 Vehicle dynamics at more
stiffness c y . Furthermore, a yaw torsional spring and complex tyre slip conditions
damper are provided with coefficients c 4 and k 4 .
Derive the equations of motion of this system with So far, relatively simple vehicle dynamics problems have
generalised coordinates y and 4. Assume small displace- been studied in which the basic steady-state cornering
ments so that the equations can be kept linear. The force vs slip angle characteristic plays the dominant role.
damping couple k 4 _ 4 may be considered as an external The situation becomes more complex when matters like
moment acting on the trailer or we may use the dissi- combined slip at hard braking, wheel camber, tyre tran-
2
pation function D¼ ½k 4 _ 4 and add þvD=v_ q to the left- sient and vibrational properties and e.g. obstacle cross-
i
hand side of Lag range’s equation (11.1.25). Obviously, ings are to be considered.

357