# Driving Safety Improved with Control of Magnetorheological Dampers in Vehicle Suspension
## 4 Simulation Results
### Emulation of Passive Suspension  
Semi-active suspension equipped with MR dampers offers an interesting opportunity to emulate different settings of passive suspension dependent on constant values of the current controlling the damper. The damping of the vehicle suspension influences the vibration of all vehicle components, among others vibration of the wheels and body. Figure 10 presents the transmissibility characteristics evaluated from vertical road-induced excitation velocity \(v_{r}\) to vehicle body leave \(v_{s}\) or pitch \(\omega_{sp}\) velocities for constant control current \(i_{mr}\) varying from 0 to 0.33 amperes. The results were obtained for the vehicle longitudinal velocity \(v_{sx}\) equal to 5 ms\({}^{-1}\). It can be seen in Figure 10a that the suspension controlled with zero current exhibits a single dominant resonance peak at a frequency equal to 1.4 Hz. It can be seen that, for higher control currents, the damping of heave vibration is deteriorated for higher frequencies from 2 to 5 Hz. An invariant point can be noticed for currents from 0 to 0.13 A, which is independent of the current. Vibration damping for frequencies to the left of the invariant point is improved for increasing currents while damping for higher frequencies is deteriorating. Moreover, for currents greater than 0.13 A vibration damping is deteriorating over the entire frequency range. It can be noticed that the previous resonance peak is shifted to the frequency of 1.7 Hz, while a second resonance peak can be detected at a frequency that is equal to 2.2 Hz. Figure 10b presents the transmissibility characteristics evaluated for pitch velocity. Here a resonance peak is detected at a frequency equal to 1.7 Hz and is rather invariant with respect to the current. It can  
Figure 10: Transmissibility characteristics of vehicle body dynamics for passive suspension and constant vehicle longitudinal velocity equal to 5 ms\({}^{-1}\): (**a**) heave velocity, (**b**) pitch velocity. Figure 9: Time diagrams of slip ratios: (**a**) front wheel during braking, (**b**) rear wheel during accelerating. be seen that damping of pitch velocity is deteriorating for rising currents for the whole frequency range, similarly as it was noticed for heave velocity. Figure 11 presents transmissibility characteristics that were evaluated for vertical velocities of the front and rear wheel. The resonance peak of the wheel vibration can be detected for both wheels at a frequency that is equal to 1.6 Hz. For increasing currents, the resonance peak shifts slightly towards higher frequencies. This effect is more clearly visible for the front wheel, where the resonance frequency is equal to 1.7 Hz for high currents. It can be explained by the fact that for higher suspension damping vibration of wheels and vehicle body start to become coupled while the same occurs with their resonance frequencies. It was mentioned in Section 1 that the excessive vibration of the wheels can lead to alternately underdeflected and overdeflected tire, which deteriorates tire adhesion to the road surface. Thus, for the purpose of the study, variations of wheel normal forces are analysed in the frequency domain. The PSD characteristics were evaluated for different constant currents and presented for both wheels in Figure 12. It can be seen that a single resonance peak for zero control current is located at a frequency equal to 1.8 Hz for the front wheel and it is slightly shifted to 1.9 Hz for current equal to 0.33 A. Furthermore, the greater the control current, the greater PSD values of the normal force and thus the greater variations of this force. Figure 11: Transmissibility characteristics of vertical wheel velocity for passive suspension and constant vehicle longitudinal velocity equal to 5 ms\({}^{-1}\): (**a**) front wheel, (**b**) rear wheel. Figure 12: Power spectral density characteristics of wheel normal forces for passive suspension and the vehicle constant longitudinal velocity 5 ms\({}^{-1}\): (**a**) front wheel, (**b**) rear wheel.