# Optimization of Damping in a Semi-Active Car Suspension System with Various Locations of Masses
## 3 Results and Discussion
The dependence of RMS values of the optimized vertical acceleration of the driver, the difference between the RMS of the vertical accelerations of the driver when optimized and non-optimized, and the RMS of the non-optimized vertical accelerations of the driver on the road profile and speed when all masses are 80 kg are shown in Figure 1b-d, respectively. Other differences between the optimized and non-optimized RMS of the vertical accelerations of the driver are presented in Figures 2b and 3b. One can observe the maximum RMS of the driver acceleration increasing as the speed shifts from lower \(w_{2}\) values to higher (see Figure 1b,d). We obtained all smaller driver acceleration values after optimization for all cases (Figures 1c, 2b, 3b, 3b, 5 ab, 55b and 56b). For example, the change varies from 0 m/s\({}^{2}\) up to 0.66 m/s\({}^{2}\) when all masses are 80 kg, and up to 1 m/s\({}^{2}\) when mass is 160 kg. This means that the acceleration of the driver could be reduced by up to 33% in comparison with non-optimized cases, depending on driving speed and road roughness. According to the ISO 2361 standard, the comfort level is very low when the total values of overall vibration magnitudes are from 1.25 m/s\({}^{2}\) up to 2.5 m/s\({}^{2}\) and becomes extremely uncomfortable when they are greater than 2.5 m/s\({}^{2}\)[73]. When optimized acceleration is still high, we could recommend additionally a lower speed value. Thus, combining information about speed, masses and their locations from car sensors, optimal damping, RMS of vertical acceleration stored in a microcomputer or the cloud, and road information, we could control damping and recommend or reduce the driving speed [40,74]. The calculated differences between the sums of the RMS of the vertical accelerations of the crew both when optimized for the driver and non-optimized, as presented in Figure 4a, show that it varies from 0.3 m/s\({}^{2}\) down to \(-\)4.4 m/s\({}^{2}\) (or in the range \(-\)35-6%). More detailed analysis showed that although driver acceleration was reduced, in a few situations the acceleration of the front-right passenger increased less than 0.1%. Meanwhile, the acceleration of the rear passengers decreased to 41% or increased to 31%. The biggest reduction of the rear passengers' acceleration was observed when the sum of the accelera  
Figure 3: Dependence of the difference between optimized and non-optimized (a) damping coefficient and (b) RMS of vertical accelerations of the driver on-road profile waviness \(w_{1}\) and \(w_{2}\) when mass \(m_{1}=160\) kg and vehicle speed is 20 km/h, 50 km/h, 70 km/h, 90 km/h, or 130 km/h. Black dotted line shows values of major ticks. Black solid line is zero. tion decreased more than 10%. Moreover, the positive values of the differences between the sums of the RMS of the vertical accelerations are related to the bigger increase of the acceleration of the rear passengers. The question is, what is the most suitable to ensure the best driving comfort for all passengers and the driver. Usually, suspension systems have not one, but multiple different damping values in the front and rear of the vehicle. The combined RMS vertical accelerations of the driver and rear-left passenger were chosen to optimize the suspension settings for ride comfort [75]. In addition, we optimized for the driver and front passenger or for the whole crew. The differences between the sum of the RMS of the vertical accelerations when optimized for the driver and front passenger or the whole crew, and when optimized for the driver, are presented in Figure 4b,c. The optimization for the driver only or for driver and front-right passenger give nearly the same results (the differences are less than 1%). In addition, it is true not only for the sum of the accelerations but also for the individual passenger's acceleration. Consequently, both these optimizations could result in unacceptably high RMS vertical acceleration values for the rear passengers if left unchecked.