# Research on Inertial Force Attenuation Structure and Semi-Active Control of Regenerative Suspension
## 5 The Verification of HVRS Suspension Characteristics
### Comparison of Vibration Shock Absorber Diagram  
In order to compare the characteristics of two different shock absorbers, the dissipation resistor is configured as \(R_{d}=60\)\(\Omega\). Through a single degree of freedom test, the upper end of the shock absorber is fixed and a vertical sine signal with a frequency of 1 H and an amplitude of 50 mm is input into the end of the shock absorber. The force-displacement curve and force-velocity curve with and without the HVRS are obtained as shown in Figure 12.  
Figure 11: Quarter-vehicle test setup.  
Due to the presence of gaps in the meshing of gear and rack, when the shock absorber is reversing, it will produce an idle stroke. At this time, the equivalent inertial mass has a large acceleration, resulting in a large inertial force. The inertial force causes the damping force of the shock absorber to oscillate. From Figure 12, it can be seen that the shock absorber with an HVRS can eliminate the oscillation of the force curve compared to the shock absorber without an HVRS, making the damping force change of the force-displacement curve smooth, which is conducive to improving reliability and comfort.  
From Figures 7 and 12, it can be seen that the HVRS does not attenuate inertial forces in the first main frequency region of the suspension, which is beneficial for suspension vibration reduction.  
In order to further verify the attenuation effect of the HVRS on high-frequency inertial forces, the load resistance \(R_{r}\) in Figure 8 was disconnected. According to Equation (26), the damping coefficient of the suspension was essentially 0 at this time. Due to the fact that the damping force of the shock absorber was essentially 0, the shock absorber only output inertial force at that time. We input a vertical sine signal with a frequency of 10 H and an amplitude of 10 mm to the end of the shock absorber to obtain the inertial force-displacement curve and inertial force-velocity curve with and without the HVRS, as shown in Figure 13.  
From Figure 13, it can be seen that the inertial force curve of the damper without an HVRS shows oscillation, and the inertial force that is generated when the shock absorber  
Figure 12: (**a**) Damping force–displacement curve of shock absorber; (**b**) damping force–velocity curve of shock absorber.  
Figure 13: (**a**) Inertial force–displacement curve of shock absorber; (**b**) inertial force–velocity curve of shock absorber.  
changes direction is much greater than that of the shock absorber with an HVRS. The inertial force of the shock absorber with an HVRS is significantly attenuated.  
From Figures 7 and 13, it can be seen that in the second and higher frequency regions of the suspension, the HVRS significantly reduces the inertial force, thereby improving the suspension performance.  
It can be seen that the HVRS can not only eliminate the oscillation of the shock absorber force curve but also significantly attenuate the inertial force in the high-frequency region. From the perspective of energy recovery, after the application of the HVRS structure in the energy regenerative suspension, the recovered energy is mainly concentrated in the low-frequency region of suspension vibration, that is, the first main frequency region.