# Research on Inertial Force Attenuation Structure and Semi-Active Control of Regenerative Suspension
## 2 The Structure and Working Principle of Energy-Regenerative Shock Absorbers
In order to improve the speed of the motor, this study applies rack and pinion to convert the vertical motion of the wheel relative to the sprung mass into rotational motion and further amplifies the rotational motion through a planetary transmission. Although the growth rate has been achieved, the equivalent inertial mass \(m_{r}\), brought about by the energy regenerative suspension and during the suspension motion process, will produce inertial force \(F_{r}\). The magnitude of inertial force is related to the acceleration \(a_{r}\) of the suspension motion, and the calculation formula is shown in Equation (2). Therefore, the inertial force generated by the equivalent inertial mass will have an impact on the motion of the wheel and the sprung mass. \[F_{r}=m_{r}a_{r} \tag{2}\]  
The parameters of the shock absorber are shown in Table 1. According to the parameters in Table 1, the equivalent inertial mass of the actuator can be calculated as shown in Equation (3). \[m_{r}=(i_{r}^{2}J_{m}+i_{r}^{2}J_{r}+J_{g})/r_{g}^{2}=58.8\text{kg} \tag{3}\]  
Figure 3: The configuration of energy-regenerative suspension. Frequency Domain and the Time Domain Characteristics of Traditional Configuration Energy Feedback Suspension  
According to the traditional configuration, the dynamic equation of the suspension system is obtained as shown in Equation (4). \[\left\{ \begin{array}{l}m_{s}\ddot{z}_{s}=k_{s}(z_{u}-z_{s})+c_{s}(\ddot{z}_{u}- \dot{z}_{s})+m_{r}(\ddot{z}_{u}-\ddot{z}_{s})\\ m_{u}\ddot{z}_{u}=k_{s}(z_{s}-z_{u})+k_{u}(z_{r}-z_{u})+c_{s}(\ddot{z}_{s}-\dot{ z}_{u})+c_{u}(\dot{z}_{r}-\dot{z}_{u})+m_{r}(\ddot{z}_{s}-\ddot{z}_{u})\end{array} \right. \tag{4}\]  
The static load of the wheels when the suspension system is balanced is \(G_{j}\); the dynamic load on the wheels during the suspension system movement is \(F_{d}\). By performing Fourier transform on Equation (4), \(\ddot{z}_{s}=\left(\mathrm{j}\omega\right)^{2}\!z_{s}\), \(\dot{z}_{s}=\mathrm{j}\omega z_{s}\), \(\ddot{z}_{u}=\left(\mathrm{j}\omega\right)^{2}\!z_{u}\), \(\dot{z}_{u}=\mathrm{j}\omega z_{u}\), the amplitude-frequency characteristics of the sprung mass acceleration \(\ddot{z}_{s}\), relative dynamic load \(F_{d}/G_{j}\), suspension dynamic deflection \(s_{d}\), and equivalent inertial mass acceleration \(a_{d}\) relative to the road excitation speed \(\ddot{z}_{r}\) of the suspension can be obtained, as shown in Equations (5)-(9). \[\left|H(\mathrm{j}\omega)\right|_{\ddot{z}_{s}\sim\dot{z}_{r}  
\(f_{u}=\sqrt{\left(k_{s}+k_{u}\right)/\left(m_{u}+m_{r}\right)}/\left(2\pi\right)\). is the frequency ratio; \(f\) is the excitation frequency of the road input, \(\lambda=f/f_{s0}\). The frequency domain characteristics of two suspension configurations are obtained. The simulation parameters are shown in Table 2. Equations (5)-(9) are calculated to obtain a comparison of the amplitude-frequency characteristics of the energy-regenerative suspension and the suspension with an equivalent inertial mass of 0 kg, as shown in Figure 4.  
In Figure 4a-c, the frequency of the intersection of suspension characteristic curves with different equivalent inertial masses on the right side of the first main frequency is \(f_{sy}\). In Figure 4c, on the right side of the second main frequency of the suspension with an inertia mass ratio of 1.35, the intersection frequency of its dynamic deflection and the dynamic deflection of the suspension with an inertia mass ratio of 0 is \(f_{uy}\). From Figure 4a, it can be seen that when the excitation frequency is less than the frequency \(f_{sy}\). The larger the equivalent inertial mass ratio, the smaller the acceleration value of the sprung mass. When the excitation frequency is higher than the frequency \(f_{sy}\), the larger the equivalent inertial mass ratio, the greater the acceleration value of the spring-loaded mass.