Effects of the drive configuration
According to the linearised analysis, the drive forces do not affect the stability as long as the net yaw moment contribution is zero. This is the case with open differentials, where the left and right wheel torques are equal in magnitude (Azad, Khajepour and McPhee, 2007). The results from previously published multibody dynamic simulations are not unambiguous, as it has been stated by some authors that the longitudinal forces are small compared to the lateral forces and hence do not affect the snaking stability (Azad, Khajepour and McPhee, 2005b), whereas other studies on a roughly similar vehicle indicate that front-wheel drive results in improved lateral stability compared to all-wheel drive (Dudzinski and Skurjat, 2010). Hence, the influence of longitudinal forces warrants further investigation. The influence of front- and rear-wheel drive has been investigated with the scale model vehicle by disconnecting the front or rear drive shafts, thus achieving a single-axis drive configuration. Results from these tests are shown in figure 25. The tests were performed at an initial velocity of 1.9 m/s and with added masses at the front and rear, to provide a response that is close to neutrally stable. Figure 8 (a) shows the results for the baseline vehicle with all-wheel drive, displaying a slowly divergent response at this velocity. Figure 8 (b) shows the response of the vehicle with front- and rear-wheel drive. It is seen that rear-wheel drive makes the vehicle unstable, as the articulation angle diverges quickly after the initial steering input. Interestingly, it can also be seen that front-wheel drive seems to result in deteriorated stability as well, although the response is different from that of the rear-wheel drive vehicle. Rather than experiencing the divergence seen in the rear-wheel drive case, the front-wheel driven vehicle enters a stable limit cycle after the initial disturbance.
It is clear from the results seen above that the driveline configuration influences the snaking oscillations of the vehicle. These experiments also show that linearised analysis is insufficient for lateral stability analysis when longitudinal forces are considered.
3.4.2 Effects of wheel suspension
The scale model vehicle can also be modified with various types of suspended wheel axles. This allows investigation of the influence of suspension on the snaking stability. Two suspension configurations have been analysed here. The first configuration includes independent front wheel suspension, using individual suspension arms and coil springs as the suspension elements. The rear axle pivots as in the baseline configuration, but with added rubber elements to provide roll stiffness. In the second configuration, individual suspension arms and steel coil springs are used for all the wheels, thus providing fully independent front and rear suspension. The roll frequency for both configurations is estimated to be about 6.0 Hz, based on tests with a stationary vehicle. The roll damping for the suspended vehicle is rather high, despite the low damping of the suspension springs. This is possibly due to high friction in the suspension linkages. Using data from stationary roll tests, the relative damping can be estimated to about 0.5, based on the time history of the lateral acceleration, which is measured above the roll centre. The two suspension setups show approximately the same damping rate. The stability of the suspended vehicle is evaluated in the same way as that of the baseline configuration, initiating a steering disturbance when going straight at 1.9 m/s. The resulting responses can be seen in figure 9. All-wheel drive is used.
Comparing the results for the suspended vehicle to the baseline results in figure 8 (a), it is seen that both the suspended configurations display a slightly stronger divergence in the articulation angle, hence indicating a reduced stability margin. The frequency of the snaking oscillations is about 1.0 Hz for the suspended vehicle, as compared to about 1.3 Hz for the baseline vehicle. As in the multibody dynamics simulations (figure 4), it can be seen that the suspended mass roll seems to decrease the frequency of the snaking oscillations.
Generally, the results from the suspended vehicle seem to be in agreement with the multibody simulation results. It is seen that suspended configurations display slightly decreased stability compared to the unsuspended vehicle, but that the influence is less than that of other parameters such as mass, inertia and steering system properties. The responses of the two suspended configurations seem to be similar despite the differences in the suspension geometry. It should be noted that the modification of the wheel suspension removes about 0.5 kg of mass from each frame. As the changes are symmetric and close to the respective centres of gravity, the effect of these mass changes on the snaking stability should not be critical.