1.4 Integration of a Subsystem Level in the Derivation
1.4.2 Deriving Properties from Full Vehicle to Subsystem
In the following section, the full vehicle targets described in the previous section are derived using the model approach given in Sect.1.3.
The basic principle for the cascading process is to define full vehicle targets as reference when varying subsystem characteristics. In this context, a useful approach is to design subsystem parameters from lower to higher frequency with respect to the influence of characteristics to a corresponding phenomenon. Thereby proce- dures can be found for defining individual parameters within the scope of different full vehicle targets. However, boundary conditions concerning interdependencies within the same discipline and other disciplines need to be considered. By parallel application of models simulating characteristics of all disciplines, an optimum on full vehicle level can be found.
The procedure will be exemplified on vertical and longitudinal stiffness of the suspension. As already described in Sect.1.3.2the vertical stiffness influences ride comfort in a wide frequency range. Starting at low frequencies this shall be one of the first parameters to be designed. The representation in a subsystem model can be carried out with a characteristic curve, as shown in Fig.1.9.
The curve can be divided into three main regions: rebound stop, linear region and progressive region. In this case, the region of the rebound stop is considered as irrelevant for ride comfort, as the deflection amplitudes in associated maneuvers are too small for reaching this area. The suspension predominantly operates within the subsequent linear section. In this case, linear corresponds to a constant increase of the vertical force related to the vertical deflection. With higher amplitudes additionally a progressive increase becomes obvious in the curve, limiting the maximum deflection when compressing the axle. Under these conditions, two boundaries for specifying the
design area of the suspension in vertical direction can be found. At zero force the wheel lifts off the ground, limiting the vertical deflection in rebound direction. In direction of compression a point can be defined where a specific maximum force occurs at a maximum deflection, predominantly specifying the desired limit for axle compression. Both values define the suspension travel in vertical direction, being an important criterion on subsystem level for defining vertical stiffness. Within this range an optimum curve for reaching full vehicle targets needs to be defined.
As wheel load distribution is provided in early phases of the development process, in the linear region a constant stiffness can be found by changing the parameter until the natural frequency of the body defined on full vehicle level is reached. In this context the damping can also be varied for reaching the defined amplitude of the vibration. The procedure is conducted for front and rear axle.
However, interdependencies between full vehicle targets in the same discipline as also other disciplines need to be considered, when conducting this procedure.
When changing a parameter having differing effects on characteristic values, trade-offs are occurring. Within ride comfort the magnitude of the transfer function between body and road when varying damping characteristics can be used as an example, as shown in Fig.1.10.
With rising damping the magnitude of the transfer function decreases in the resonance area and increases in the isolation area. This trade-off needs to be optimized based on full vehicle properties for an optimum solution. As the deflec- tion amplitude of the suspension generally changes with the excitation frequency under operating conditions, an important factor for resolving the shown trade-off can be found in the nonlinearity of the damper curve, which allows the definition of different damping ratios at various amplitudes.
Fig. 1.9 Significant properties describing the shape of the characteristic curve between vertical force and vertical deflection
On top of that, the influence on full vehicle characteristics of other disciplines needs to be considered. In this case, the correlation to other models described in Sect.1.3.1is of importance as the parametrization should be similar for ensuring maximum comparability of the results.
An example is given by the influence of vertical stiffness on ride comfort and driving dynamics. Decreasing stiffness reduces coupling between wheel and road which partially results in better ride comfort. In driving dynamics on the other hand the roll angle gradient is rising with lower vertical stiffness, as shown in Fig.1.11.
This correlates with a lower score in subjective evaluation of driving dynamics for this characteristic value. Additionally changing load has a higher impact on ride height and the operating point is shifting towards the progressive region, depicted in Fig.1.9. By modifying the alternate vertical stiffness, the effects in driving dynam- ics can partially be resolved. However, this also causes higher dynamic roll accelerations when driving over asymmetric road profiles.
Fig. 1.10 Influence of damping on the magnitude of the transfer function between body and road
Fig. 1.11 Influence of vertical stiffness on roll angle gradient in driving dynamics
Under the described conditions the vertical stiffness can be designed indepen- dently of longitudinal stiffness, whose influence on the vertical body natural frequency can be neglected. As already described in Sect.1.3.2, the longitudinal stiffness comes into effect when the tire transfers longitudinal forces into the suspension, which is a phenomena at higher frequencies in ride comfort, for instance when a cleat is passed. In this case, longitudinal stiffness influences the step response in longitudinal direction while the support angle between vertical and longitudinal direction transfers an additional force in vertical direction. As the vertical stiffness of the axle has an important influence on the step response in vertical direction, the parameter also needs to be designed for this application.
Therefore after designing vertical stiffness for low frequency phenomena, as described above, the parameter needs to be optimized with respect to phenomena at higher frequencies as well, to find an optimum solution.
In addition to vertical and longitudinal stiffness, the described procedure is conducted as already proposed with rising frequency incorporating an increasing amount of parameters and full vehicle targets.