# Optimization of Damping in a Semi-Active Car Suspension System with Various Locations of Masses
## 4 Conclusions  
The relationship between the detected road waviness values \(w_{1}\), \(w_{2}\) and the optimized damping coefficient under various locations of vehicle load positions could be used to control damping and recommend or reduce the driving speed. The needed optimized damping value could be interpreted from a 3D gridded matrix of damping coefficients calculated at certain fixed values of speed and waviness indexes \(w_{1}\), \(w_{2}\). The surface area of the bigger values increases in the case of increasing vehicle speed and reaches maximum damping values when the speed is 70 km/h or 90 km/h and \(w_{1}\) = 6. Up to 1.5 times higher damping values are required when only the driver mass is doubled than in other cases under study. When optimizing the full-car model for the driver RMS vertical acceleration, the acceleration of the driver could be reduced up to 33% in comparison with non-optimized cases depending on driving speed and road roughness. The optimization for the driver and combined optimization for the driver and rear passenger provides results with differences less than 1%. Nevertheless, both these optimizations could result in unacceptably high values of rear-passenger RMS vertical acceleration if they are not set with a limitation. When optimizing for the whole crew, the sum of the RMS of the vertical accelerations is up to 9% smaller than when optimizing for the driver. Simultaneously, the RMS of vertical acceleration for the front passengers increases up to 10%, and it decreases to 24% for the rear passengers. The output of this research provides a reason for the new design of damping devices, which can ensure higher comfort for the vehicle crew without changing the suspension design. The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app13095371/s1](https://www.mdpi.com/article/10.3390/app13095371/s1)]([https://www.mdpi.com/article/10.3390/app13095371/s1](https://www.mdpi.com/article/10.3390/app13095371/s1)), Table S1. The optimized damping coefficients when the mass \(m_{1}\) = 80 kg; Table S2. The optimized damping coefficients when the masses \(m_{1}\) = \(m_{3}\) = 80 kg; Table S3. The optimized damping coefficients when the masses \(m_{1}\) = \(m_{4}\) = 80 kg; Table S5. The optimized damping coefficients when the masses \(m_{1}\) = 160 kg; Table S6. The optimized damping coefficients when the masses \(m_{1}\) = 100 kg, \(m_{2}\) = 60 kg, \(m_{3}\) = 50 kg, \(m_{4}\) = 40 kg; Figure S1. Dependence of the optimized damping coefficients on vehicle speed when (a) \(w_{1}\) = 1; (b) \(w_{1}\) = 2; (c) \(w_{1}\) = 4; (d) \(w_{1}\) = 6, and all masses are \(m_{1}\) = \(m_{2}\) = \(m_{3}\) = \(m_{4}\) = 80 kg; Figure S2. Dependence of the optimized damping coefficient on vehicle speed when (a) \(w_{2}\) = 0.5; (b) \(w_{2}\) = 1; (c) \(w_{2}\) = 2; (d) \(w_{2}\) = 3, and all masses are \(m_{1}\) = \(m_{2}\) = \(m_{3}\) = \(m_{4}\) = 80 kg; Figure S3. Dependence of the difference between optimized and non-optimized (a) damping coefficient; (b) RMS of vertical accelerations of the driver; on-road profile waviness \(w_{1}\) and \(w_{2}\) when masses \(m_{1}\) = \(m_{2}\) = 80 kg and vehicle speed is 20 km/h, 50 km/h, 70 km/h, 90 km/h, or 130 km/h; Figure S4. Dependence of the difference between optimized and non-optimized (a) damping coefficient; (b) RMS of vertical accelerations of the driver; on-road pro file waviness \(w_{1}\) and \(w_{2}\) when masses \(m_{1}=m_{3}=80\) kg and vehicle speed is 20 km/h, 50 km/h, 70 km/h, 90 km/h, or 130 km/h; Figure S5. Dependence of the difference between optimized and non-optimized (a) damping coefficient; (b) RMS of vertical accelerations of the driver; on-road profile waviness \(w_{1}\) and \(w_{2}\) when masses \(m_{1}=m_{4}=80\) kg and vehicle speed is 20 km/h, 50 km/h, 70 km/h, 90 km/h, or 130 km/h; Figure S6.