# Driving Safety Improved with Control of Magnetorheological Dampers in Vehicle Suspension
## 4 Simulation Results
### Road Holding  
The road holding index describes the susceptibility of the wheels to separation from the road surface. It was calcuated for the vehicle that alternately accelerates, drives, and brakes. The road holding index is based on instantaneous wheel normal force \(F_{n}\). The static normal force, which is denoted as \(F_{ns}\), is assumed to be optimized for each wheel and related to the static tire pressure. It is assumed that any deviation from static normal force during the ride worsens the ability to stay on the road and the ability to follow the desired driving trajectory. This behaviour is described by a road holding weighting function \(w_{rh}(F_{n})\), as presented in Figure 17.  
Figure 16: Power spectral density characteristics of wheel normal forces for Skyhook control of the body vibration modes (Skyhook-2 DOF) and vehicle longitudinal velocity equal to 5 \(\mathrm{ms}^{-1}\): (**a**) front wheel, (**b**) rear wheel. Figure 17: Weighting function dedicated to assessment of tire from road separation for the front and rear wheel. The weighting function is based on the quadratic relationship, where the greatest value equal to 1.0 can be obtained for the wheel normal force that is equal to the static normal force \(F_{ns}\). For the model under consideration value of the wheel normal force cannot drop below zero since it indicates separation of the wheel from the road surface. Likewise, the presented weighting function is not defined below \(F_{n}\) equal to zero. Moreover, significantly increased wheel normal force is also not recommended for the vehicle, since it can lead to deteriorated road holding and it can speed up the tire wear. Thus, for \(F_{n}\) above the static normal force \(F_{ns}\), the weighting function is decreasing and it takes the value zero for double static normal force. The function is quadratic in order to make the function still tolerate small deviations of the wheel normal force. As a result, the road holding index denoted as \(J_{rh}\) is defined as a mean value of the weighting function \(w_{rh}(F_{n})\) calculated for the normal force of a selected wheel over time and consecutive accelerating or braking phases:  
\[J_{rh}=\frac{1}{M\cdot N}\sum_{m=1}^{M}\sum_{i=1}^{N}w_{rh}[F_{n}(i)], \tag{32}\]  
where \(M\) denotes the number of accelerating or braking phases and \(N\) is the number of signal samples included in a single phase. Further discussion on road holding is carried out in comparison to the results that were obtained for constant currents. A normalized value of \(J_{rh}\), denoted as \(J_{rh,n}\), was evaluated for each simulation case. The results obtained for zero current were assumed as reference value for the normalized \(J_{rh,n}\). It is worth noting that the higher road holding index corresponds to the better road holding. Figure 18 presents the values of the normalized road holding index for different suspension settings and vehicle longitudinal velocity equal to 5 ms\({}^{-1}\). The results obtained for the front wheel are presented for braking phases, since it is dependent on the front wheel while the accelerating phase was related to the rear wheel since the rear axle is driving. It can be stated that, for rising values of constant current, the road holding is deteriorating. As was mentioned previously, it is caused by stronger coupling between the wheels and the body, which results in worse matching of wheel movement to the shape of road surface. The reason of this effect is the same as in the case of constant control currents, i.e., the suppression of wheel vibration does not necessarily lead to an improvement of road holding and may even worsen it. Figure 18: Comparison of road holding for different suspension settings: passive, separate and coupled Skyhook control for vehicle longitudinal velocity of 5 ms\({}^{-1}\): (**a**) front wheel during braking, (**b**) rear wheel during acceleration.