Page - 42 - in Maximum Tire-Road Friction Coefficient Estimation

3 Vehicle model For all manoeuvres and all model parameters, both the friction potential µmax and the vehicle’s speed vx are varied. The mean relative deviation for each state variable and each manoeuvre is then displayed as a function of bothµmax and vx, see Figure 3.3 as an example. The state variables investigated for longitudinal and lateral manoeuvres are not necessarily the same, see Section 3.1.2. It has to be noted that the criterion of mean relative deviation works very well when a variation of the model setup results in a change of amplitude of the investigated variable, but it fails in the rare cases when the variation of the model setup results in a phase shift, such as for quantifying the influence of dynamic tire forces, e.g. Table 3.2 and Table 3.3. Thus, for high mean relative deviation values, the time signals of the respective variable is also examined regarding phase shift. In these cases, the phase shift ∆φw of a variablew is a second evaluation criterion. The limits for the mean relative deviation was set at 5 % for all variables and 0.05 s for maximum phase shift in a signal. 3.1.2. Investigated manoeuvres Three manoeuvres are investigated, including either dynamic longitudinal or dynamic lateral excitation. To assess lateral dynamics, the double lane change manoeuvre (DLC) according to ISO 3888-1 was chosen, [fSI99]. In this manoeuvre, the vehicle model fol- lows a trajectory based on the track dimensions in ISO 3888-1 using a lateral control. However, only the difference in the vehicle reaction for the different model parameters was evaluated. It has not been studied whether the course defined in ISO 3888-1 could be followed by the vehicle in every condition, as this was not an assessment of the mod- elled vehicle. The investigated variables include the vehicle’s rotational speed bωz, which charac- terises the course of the vehicle. The mean relative deviation ∆ωz between the reference model andthe simplifiedmodelhas tobe small, inorder to ensureahighaccuracyof the simplified model. As a measure of the accuracy of modelled driving stability, the side slip angleβ is used. Additionally, the mean deviation ∆ay of the lateral acceleration is evaluated. The lateral acceleration depends on both the yaw rate and the side slip rate β˙ as another measure of driving stability, cf. Weber, [Web04, p.73]. Since the vehicle model has to be suitable for the analysis of different friction potentials, the tire loadFz,i and the lateral tire forceFy,i are also examined for each tire i. To ensure that the lateral control to follow the given trajectory is working properly in the model setups compared, the steering wheel angles are compared using its mean relative deviation ∆δS. It is a prerequisite for the comparison of the other state variables for every simulation that this 42