Steady state response

Figure 4-2 refers to the comparison o f the steady-state yaw rate response to steering angle input o f the rigid vehicle layouts o f Config-Ol to Config-04, as they are the most common configurations o f heavy goods rigid vehicles seen on highways these days. From the figure it can be observed that yaw rate gain is an increasing function o f vehicle velocity. From the rigid vehicle lot congif-01 and congif-02 are commonly found on the American and European roads and are characterized by a significantly undefsteering behaviour, which is particularly evident for the steady state yaw rate gain o f Config-02 layout (shown in blue in Figure 4-2).

It is reported from the figure that steady state yaw rate gain for the two-axle vehicle (config-01 shown in red) is found to be higher than that any other rigid layout in the group but a moderate un­ dersteering behaviour is also observed for the whole range o f vehicle velocity simulated. As compared with the two-axle vehicle, three-axle truck shows increased understeering characteristics but lower yaw rate gain on the other hand this enhanced understeering performance is due to the increased vehicle stability induced by the double (tandem) rear axles. This improved stability is achieved as the lumped cornering stiffness is increased on the rear end o f the vehicle as a result o f increased number o f axles hence increased number o f tyres. The high stability o f this layout is also confirmed by the reduced rate o f vehicle sideslip angle variation [43]. Therefore increasing the number o f rear axles o f a rigid vehicle may improve the stability, but increase in road tyre surface

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stress may also be observed for such vehicles for low speed turning, to deal with such conditions multi-steered axle vehicle are also discussed.

£ Î — — Config 01 — — Config 02 — Config 03 — — Config 04 100 Vehicle speed (km/h)

Figure 4-2: Steady-state yaw rate comparison o f rigid vehicles

The layouts characterised by rigid vehicle with the double steering axles (config-03 shown in green and config-04 shown in pink) present potential oversteering at high velocities, related to the kinematics o f their steering system for the second steering axle. For the simulations, a constant gain between the steering angle o f the front axle and the steering angle o f the second steering axle is considered (in counter-phase for the rear steering axle). Though the two layouts (config-03 and config-04) are similar in dimensions/kinematics and payload terms but the vehicle with rear- steered axle (config-04) demonstrates higher yaw rate gain and also an increased degree o f over­ steering as compared with the one having second front axle steered. It may also be reported that the yaw rate gain o f the rear steered axle supersedes all the other vehicles in the batch for high vehicle velocity values (around 97 km/h) which could not be considered technically good for the stability o f the vehicle. Hence a very small or no multi-steering is recommended for high speed manoeu­ vring, but a reasonable multi steering technique could be an advantage for low speed curve negotiation on the other hand. Therefore it can be concluded that the benefit o f increasing the num ­ ber o f rear axles o f a rigid commercial vehicles has two main benefits. First it enhances the payload carrying capacity; second it also improves the stability o f the vehicle, but may also reduce

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the responsiveness o f the vehicle.

4.1.1.2 A rticulated vehicles

The second category o f heavy good commercial vehicles is articulated vehicles (i.e. Config-05 to Config-08, shown in Figure 4-1), Figure 4-3 and Figure 4-4show the steady state yaw rate to steering angle gain and steady state articulation angle to steering angle gain for the articulated con­ figurations, respectively.

It can be observed that in general articulated vehicles with larger numbers o f rear tractor axles and semi-trailer axles have higher steady state yaw gain (Figure 4-3) and higher negative values for tractor body sideslip angles are also noticed [43]. Moreover all the articulated vehicles are also re­ ported to have good steady state directional stability as the behaviours o f the vehicles are found to be understeering for the whole range o f vehicle speed considered in this activity. Particularly Con- fig-07 has proven a prominent difference in steady state yaw rate to steering angle gain showing that increased number o f axles for articulated vehicle improves the handling but at the cost o f high trailer swings which is also discussed here.

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Figure 4-3: Steady-state yaw rate comparison o f articulated vehicles

Another parameter o f interest, as a handling performance measure, in the case o f articulated ve-

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h id es may be the articulation (hitch) angle. It is also apparent that steady state hitch angle is di­ rectly proportional to the number o f tractor rear axles that is more rear axles on the truck tend to generate larger steady state hitch angle, especially for low vehicle speeds (Figure 4-4). This is be­ cause o f the difference o f moment o f tractor and semi-trailer along vertical axis, particularly the increased number o f axles o f semitrailer is showing higher values o f hitching angle.

The gradient o f hitching angle with respect to vehicle speed is similar for three vehicle cases (Config-05,Config-06and Config-08), except the vehicle layout Config-07, which has two rear ax­ les o f the tractor and two axles o f the semitrailer. The rate o f change o f articulation angle, for the articulated vehicle Config-07 is rapidly decreasing as the vehicle speed is increased and the value o f hitch angle attains the same value as o f the vehicle configuration with lower number o f axles (Config-05 and Config-06), hence the semitrailer becomes more stable as the vehicle speed is in­ creased. In general increasing the increasing the vehicle

I 2.4 — Config 05 — Config 06 — Config 07 Config 08 30 100 Vehicle speed (km/h)

Figure 4-4: Steady-state articulation angle response, comparison o f articulated vehicles