Research on Efficient Suspension Vibration Reduction Configuration for Effectively Reducing Energy Consumption

Abstract

Reducing vehicle energy consumption is crucial for sustainable development, especially in the context of energy crises and environmental pollution. Energy regenerative suspension offers a promising solution, yet its practical implementation faces challenges like inertial mass issues, cost, and reliability concerns. This study introduces a novel suspension configuration, optimizing shock absorber technology with energy regenerative principles. The objective is to drastically cut energy consumption. Through a frequency domain analysis, this study identifies the root causes of increased energy consumption and worsened vibration in traditional suspensions. This study presents a comparative analysis of the frequency-domain characteristics between the novel suspension configuration and the traditional one. This study reveals that the new configuration exhibits a low-pass filtering effect on the shock absorber’s velocity, effectively minimizing vibrations in the low-frequency range, while mitigating their impact in the high-frequency range. This approach mitigates the trade-off between increased energy consumption and worsened vibration in the high-frequency range, making it a promising solution. Simulations show that this configuration significantly reduces acceleration by 7.04% and suspension power consumption by 10.47% at 60 km/h on the D-level road, while maintaining handling stability. This makes it a promising candidate for future energy-efficient suspension systems.

1. Introduction

Energy conservation and consumption reduction are not only for protecting the environment, but also for achieving sustainable development. Numerous studies have examined the energy consumption of diverse vehicle systems. In vehicle operations, the engine exhaust contributes to 33% of the total fuel energy, the cooling system dissipates 29%, and mechanical driving consumes 38% of the total fuel energy [1]. Roughly 20–30% of the mechanical system’s energy is utilized to overcome road friction and air drag resistance. Additionally, the suspension system consumes approximately 3–12% of the total fuel energy [2,3,4].

Reducing the energy consumption of vehicles is advantageous for curbing emissions and enhancing fuel efficiency, which is beneficial for global sustainability. To this end, technologies such as waste thermal energy harvesting have been explored and developed to enhance engine efficiency [5,6]. Furthermore, regenerative braking systems have been researched and developed to improve the efficiency of mechanical drive systems [7,8,9]. Additionally, to minimize the energy consumption of suspension systems, regenerative suspensions with energy-harvesting shock absorbers have undergone extensive research and development [10,11,12].

In the past two decades, the regenerative suspension equipped with an energy-harvesting shock absorber has garnered extensive research attention. This is primarily due to its exceptional dynamic characteristics, as well as its ability to convert wasted vibration energy into electrical energy. Zuo Lei et al.’s research [13] revealed that regenerative shock absorbers with a 1:2 ratio prototype can generate 16~64 W of power at suspension velocities of 0.25~0.5 m/s RMS. Li Zhongjie et al. [14] found that a single prototype shock absorber can peak at 68 W and average 19 W when a vehicle travels at 48 km/h on smooth roads. Additionally, regenerative suspension systems can provide over 1 kW of collectable power for heavy-duty and off-road vehicles [15].

The regenerative suspension has the advantage of harvesting energy, thereby enhancing the fuel efficiency of vehicles. This efficiency is achieved as the shock absorber captures energy from vibrations caused by road irregularities. Consequently, the shock absorber serves as the regenerative suspension’s core component and is classified into two main types: electromagnetic actuators and electrohydraulic actuators [16,17]. Electromagnetic actuators offer a lower energy density and damping force, whereas electrohydraulic actuators exhibit a higher energy density and damping force. To enhance the damping force, the motor’s output torque is typically boosted via a transmission mechanism, such as a rack and pinion, worm gear, hydraulic motor, or planetary gearbox. However, this transmission increases the actuator’s inertial mass, resulting in poorer suspension performance and reduced reliability [18,19,20].

Despite numerous studies [21,22,23] offering potential solutions to mitigate the negative impacts of inertial mass, these have yet to be experimentally verified. Consequently, the regenerative suspension faces significant challenges in its practical application, primarily due to concerns over reliability. Additionally, high costs and the system’s heavy weight further hinder its widespread adoption.

To minimize suspension energy consumption and enhance practicality, a reassessment of traditional passive suspension is imperative. Despite the advancements in semi-active and active suspension technologies over the years, passive suspension remains prevalent in vehicles due to its simplicity, high reliability, and low cost. This type of suspension consists of hydraulic dampers and springs arranged in parallel, effectively buffering the vibration energy through springs and dissipating it as thermal energy via dampers.

The continuous evolution of passive suspension dampers provides valuable insights for addressing existing suspension challenges. Early shock absorber applications revealed issues such as insufficient oil replenishment due to rapid volume changes during high-velocity piston rod movement, resulting in air travel, cavitation, performance distortions, and safety hazards [24]. To address untimely oil filling, inflatable hydraulic shock absorbers were developed, incorporating low-pressure nitrogen gas at 0.4~0.6 MPa within their double tubes. This innovation reduced empty strokes, enhanced vibration reduction, and minimized noise and impact. Subsequently, single-cylinder inflatable shock absorbers with a floating piston structure emerged, filled with nitrogen to create a high-pressure chamber of 2.0~2.5 MPa. These performed superior to double-cylinder designs [25], avoiding damping characteristic distortions, effectively suppressing high-frequency vibrations and noise, improving wheel grounding, and enhancing driving smoothness [26]. In essence, the air chamber within the inflatable hydraulic shock absorber, connected in series with the damping element, functions as a low-pass filter, shaping the suspension model where the damping element is serially connected to the elastic element and then arranged in parallel with the suspension elastic element.

To address the issue of high-frequency inertial force in energy-harvesting suspensions, numerous studies [21,22,23,27] have consecutively advocated for the integration of a buffer in series between the wheel and the energy-harvesting damper. This approach aims to mitigate the negative impact of inertial mass, thereby enhancing the overall performance of the suspension system. This approach is designed to alleviate the negative impacts of inertial mass. It can also be broadened to enhance traditional passive suspension configurations. This is akin to upgrading a shock absorber to an inflatable version and serially connecting it with an elastic element. By harnessing the low-pass filtering effect of spring components, the benefits of hydraulic or regenerative dampers can be maximized. Simultaneously, this approach minimizes their weaknesses. This approach satisfies the requirement for substantial damping force in the low-frequency range. Additionally, it reduces both the damping force and inertial force within the higher-frequency spectrum.

Drawing upon the research into traditional suspension systems and energy feedback suspension configurations, this paper introduces a novel suspension configuration which boasts efficient vibration reduction. This paper establishes a vibration transmission model and, through rigorous frequency domain analysis and time domain simulation, validates that this novel suspension configuration effectively reduces energy consumption.

The paper is structured as follows: Section 2 formulates a vibration transmission model for traditional suspension, examines the impact of varying damping ratios on suspension characteristics, and identifies the frequency range where traditional passive suspension consumes energy yet degrades vibration performance. Section 3 introduces the design of the novel suspension configuration, establishing a theoretical model incorporating a high-frequency damping structure. It delves into the mechanisms behind the new configuration’s low energy consumption and enhanced smoothness, and conducts a comparative analysis of the frequency-domain characteristics between the novel and traditional suspension configurations. The study reveals that the novel suspension effectively acts as a low-pass filter for shock absorber velocity, significantly reducing vibrations in the low-frequency range while suppressing the shock absorber’s effects in the high-frequency range, thus preventing energy wastage without compromising vibration performance. Section 4 explores the implementation of the high-frequency damping structure and compares the suspension characteristics of both configurations through time domain simulations. The results indicate that the novel suspension configuration significantly reduces the acceleration of the spring-loaded mass while substantially lowering suspension power consumption. Notably, it does so without compromising the vehicle’s handling stability. Section 5 concludes the paper, summarizing the benefits of the novel suspension configuration and highlighting the limitations of the high-frequency damping structure.

2. Energy Consumption Analysis of Traditional Suspension

The traditional suspension system, as shown in Figure 1, involves sprung mass, a suspension system, unsprung mass, a wheel, and road disturbance.

Each of these elements holds a pivotal position in enhancing the overall performance and ride quality of the vehicle. The sprung mass comprises the section of the vehicle that is suspended, encompassing the body and passengers. This mass is crucial in determining the vehicle’s dynamics and comfort level. The suspension system itself is responsible for damping vibrations and providing a smooth ride, while the unsprung mass refers to the components that are not supported by the suspension, such as the wheels and axles. The wheel interfaces with the road, transmitting forces and absorbing impacts, while road disturbance represents the irregularities and obstacles encountered by the wheel as it rolls over the road surface.

The symbols utilized in the suspension configuration are defined as follows: $m_s$ denotes the sprung mass, $m_u$ denotes the unsprung mass, $k_s$ denotes the suspension spring stiffness, $k_u$ denotes the wheel stiffness, $c_s$ denotes the suspension damping coefficient, $c_u$ denotes the wheel damping coefficient, $z_s$ denotes the sprung mass displacement, $z_u$ denotes the unsprung mass displacement, and $z_r$ denotes the road excitation displacement. Drawing upon the traditional configuration, the dynamic equation of the suspension system is derived and presented in Equation (1).

$$\left\{\begin{array}{l}{m}_s{\ddot{z}}_s=k_s(z_u-z_s)+c_s({\dot{z}}_u-{\dot{z}}_s)\\ m_u{\ddot{z}}_u=k_s(z_s-z_u)+k_u(z_r-z_u)+c_s({\dot{z}}_s-{\dot{z}}_u)+c_u({\dot{z}}_r-{\dot{z}}_u)\end{array}\right.$$

(1)

To evaluate suspension characteristics, sprung mass acceleration ${\ddot{z}}_s$ serves as a crucial indicator for evaluating the smoothness of a vehicle. A lower value of this indicator translates into a more comfortable ride for passengers. Additionally, the relative dynamic load $F_d/G_j$ serves as an indicator for evaluating vehicle smoothness. Furthermore, the suspension dynamic deflection $s_d$ acts as a measure to determine if the suspension has reached its limiter, thereby assessing the reasonableness of the suspension travel. Furthermore, the velocity of the shock absorber $v_d$ and the velocity of wheel deformation $v_{ur}$, both being crucial factors in assessing the dissipation power of the suspension, are considered evaluation indicators. Therefore, a thorough analysis of the recurrence rate-dependent amplitude behavior of these characteristic indicators provides valuable insights into the suspension characteristics, which is useful in gaining a deeper understanding of its performance.

Upon the application of the Fourier transform to Equation (1), ${\ddot{z}}_s={(\mathrm{j}\omega )}^2{z}_s$, ${\dot{z}}_s=\mathrm{j}\omega z_s$, ${\ddot{z}}_u={(\mathrm{j}\omega )}^2{z}_u$, ${\dot{z}}_u=\mathrm{j}\omega z_u$, the amplitude-frequency characteristics of the sprung mass acceleration ${\ddot{z}}_s$, relative dynamic load $F_d/G_j$, suspension dynamic deflection $s_d$, shock absorber velocity $v_d$, and wheel deformation velocity $v_{ur}$, relative to the road excitation velocity ${\dot{z}}_r$, can be determined. These relationships are presented in Equations (2)–(6).

$${\left|H(\mathrm{j}\omega )\right|}_{{\ddot{z}}_s~{\dot{z}}_r}=\omega \left|\frac{X_{zs}}{X_{zr}}\right|$$

(2)

$${\left|H(\mathrm{j}\omega )\right|}_{(F_d/G_j)~{\dot{Z}}_r}=\frac{{\omega }_{s0}}{\omega (1+\mu )g}\left|\gamma {\omega }_{s0}+2\epsilon \xi \omega \mathrm{j}\right|\left|\frac{X_{Fd}}{X_{zr}}\right|$$

(3)

$${\left|H(\mathrm{j}\omega )\right|}_{s_d~{\dot{z}}_r}=\frac{1}{\omega }\left|\frac{X_{sd}}{X_{zr}}\right|$$

(4)

$${\left|H(\mathrm{j}\omega )\right|}_{v_d~{\dot{z}}_r}=\left|\frac{X_{sd}}{X_{zr}}\right|$$

(5)

$${\left|H(\mathrm{j}\omega )\right|}_{v_{ur}~{\dot{z}}_r}=\left|\frac{X_{zur}}{X_{zr}}\right|$$

(6)

$$\begin{array}{c}{X}_{zs}=A_{su}{A}_r,X_{zr}=A_s{A}_u-A_{su}^2,X_{Fd}=A_s{A}_u-A_{su}^2-A_s{A}_r,\\ X_{sd}=(A_{su}-A_s)A_r,X_{zur}=A_s{A}_r-(A_s{A}_u-A_{su}^2),\\ A_s=1-{\lambda }^2+2\mathrm{j}\xi \lambda ,A_{su}=1+2\mathrm{j}\xi \lambda ,A_u=1+\gamma -\mu {\lambda }^2+2\mathrm{j}\xi \lambda +2\mathrm{j}\epsilon \xi \lambda ,A_r=\gamma +2\mathrm{j}\epsilon \xi \lambda .\end{array}$$

For the purpose of facilitating research, the ratio between the wheel damping coefficient and the suspension damping coefficient is denoted as $\epsilon$, $\epsilon =c_u/c_s$. The ratio of the wheel stiffness coefficient to the suspension stiffness coefficient is denoted as $\gamma$, $\gamma =k_u/k_s$. The quotient of the unsprung mass and the sprung mass is defined as $\mu$, $\mu =m_u/m_s$. Additionally, the suspension damping ratio is denoted as $\xi$, $\xi =c_s/2\sqrt{k_s{m}_s}$. The bias frequency pertaining to the sprung mass is denoted as $f_{s0}$, $f_{s0}=(\sqrt{k_s/m_s})/2\pi$, while the bias frequency of the unsprung mass is denoted as $f_{u0}$, $f_{u0}=\sqrt{(k_s+k_u)/m_u}/(2\mathsf{\pi })$. The bias circular frequency of the sprung mass is denoted as ${\omega }_{s0}$, ${\omega }_{s0}=2\pi f_{s0}$. The bias circular frequency of the unsprung mass is denoted as ${\omega }_{u0}$, ${\omega }_{u0}=2\pi f_{u0}$.

Finally, the frequency offset ratio between the excitation frequency $f$ and the sprung mass is represented by $\lambda$, $\lambda =f/f_{s0}$.

Using the simulation parameters outlined in

Table 1. Suspension simulation parameters.

Parameters	Value	Description
$m_s$	2400 kg	Sprung mass
$m_u$	125 kg	Unsprung mass
$k_s$	154 N/mm	Suspension stiffness coefficient
$c_s$	9613 N·s/m	Suspension damping coefficient
$k_u$	1940 N/mm	Wheel stiffness coefficient
$c_u$	786 N·s/m	Wheel damping coefficient
$\mu$	0.052	Unsprung mass to sprung mass rate
$\gamma$	13.3	The ratio of wheel stiffness coefficient to suspension stiffness coefficient
$\epsilon$	0.081	The ratio of wheel damping coefficient to suspension damping coefficient
fs0	1.27 Hz	The bias frequency of the sprung mass
fu0	20.60 Hz	The bias frequency of the unsprung mass

, Equations (2)–(4) are computed to assess and compare the amplitude-frequency characteristics of the suspension. The results from these calculations are graphically presented in Figure 2.

As depicted in Figure 2a, when the excitation frequency $f$ is below the turning frequency $f_{sy}$, an increase in the damping ratio $\xi$ leads to a decrease in the acceleration value of the sprung mass. Conversely, when $f$ exceeds $f_{sy}$, a greater damping ratio $\xi$ corresponds to a higher acceleration value of the sprung mass. This observation suggests that the optimal damping characteristics for a suspension system entail a high damping ratio at low frequencies (i.e., frequencies below the turning frequency $f_{sy}$) and a low damping ratio at high frequencies (i.e., frequencies above the turning frequency $f_{sy}$).

The zone surpassing the turning frequency $f_{sy}$ constitutes the energy dissipation and vibration deterioration region for the shock absorber. Within this frequency range, the shock absorber not only fails to mitigate the vibration of the sprung mass, but paradoxically enhances it. Furthermore, a greater damping force correlates directly with a more severe vibration of the sprung mass, which concurrently consumes energy which is crucial for driving the vehicle.

As depicted in Figure 2b, the amplitude of the relative dynamic load exhibits a declining trend with an increase in the damping ratio when the excitation frequency $f$ is below the frequency $f_{sy}$ or exceeds the frequency $f_{uz}$. However, when the excitation frequency $f$ lies between $f_{sy}$ and $f_{uz}$, an increase in the damping ratio leads to a corresponding rise in the amplitude of the relative dynamic load.

As observed in Figure 2c, the suspension’s dynamic deflection decreases noticeably with an increase in the damping ratio, particularly in the first and second main frequency regions. However, in other regions, the amplitude of the suspension’s dynamic deflection remains largely unchanged regardless of the damping ratio. This suggests that, in contrast to the significant impact in the first and second main frequency regions, variations in the damping ratio have a relatively minor effect on the suspension’s dynamic deflection in other frequency bands. This is a distinctive characteristic of traditional suspension systems.

The analysis above reveals that the primary contradiction in traditional suspension design exists within the [$f_{uz}$,100] frequency band. Within this frequency range, the sprung mass acceleration increases with the damping ratio, while the comparative dynamic load reduces with the damping ratio. This tendency contributes to an enhanced handling stability, but compromises the ride smoothness. The magnitude of suspension dynamic deflection has a direct bearing on the driving smoothness and handling stability of a vehicle. Excessive deflection can lead to significant vibrations and shaking during driving, thus compromising ride comfort. Additionally, excessive dynamic deflection can also affect the handling stability of the vehicle, making it more prone to rolling and swaying at high speeds.

The shock absorber’s dissipated power $P_c$ is calculated using Equation (7) [28]. Notably, given a fixed damping coefficient, a lower velocity of the shock absorber results in reduced dissipated power. This observation suggests that optimizing the shock absorber’s velocity can lead to more efficient energy utilization within the suspension system.

$$P_c=c_s{v}_d^2$$

(7)

To reduce the suspension’s consumption energy, measures should be taken to reduce energy consumption in a frequency band greater than $f_{sy}$, while ensuring that the relative dynamic load of the frequency band [$f_{uz}$,100] does not increase.

When ${\xi }_1=0.2$, ${\xi }_3=0.6$, the values of frequency $f_{sy}$ and $f_{uz}$ can be calculated using Equations (8) and (9). Utilizing the parameters outlined in Table 1, the solution of this equation results in the following three real roots: 2.09 Hz, 29.6 Hz, and 30.95 Hz. The first real root is the frequency at which two curves intersect on the right side of the first main frequency, and the second and third real roots are the frequency points at which they intersect on the left and right sides of the second main frequency. According to Figure 2, the turning frequency is determined as $f_{sy}=2.09\mathrm{Hz}$.

$$\left|\frac{X_{zs}\left({\xi }_1\right)}{X_{zr}\left({\xi }_1\right)}\right|=\left|\frac{X_{zs}\left({\xi }_3\right)}{X_{zr}\left({\xi }_3\right)}\right|$$

(8)

$$\left|\gamma {\omega }_{s0}+2\epsilon {\xi }_1\omega \mathrm{j}\right|\left|\frac{X_{Fd}\left({\xi }_1\right)}{X_{zr}\left({\xi }_1\right)}\right|=\left|\gamma {\omega }_{s0}+2\epsilon {\xi }_3\omega \mathrm{j}\right|\left|\frac{X_{Fd}\left({\xi }_3\right)}{X_{zr}\left({\xi }_3\right)}\right|$$

(9)

3. The Novel Suspension Configuration with Efficient Vibration Reduction

3.1. The Novel Configuration Suspension

The suspension principle of the new configuration is shown in Figure 3. The new suspension configuration adds a high frequency vibration reduction structure (HVRS) between the shock absorber and the wheel in the traditional suspension configuration.

To clearly demonstrate the significance of the HVRS, Figure 3 presents a visualization of the filtering effect of various suspension configurations on road excitation. When compared to the traditional suspension, the addition of the HVRS introduces an additional level of vibration reduction. This enhanced configuration effectively filters out high-frequency excitation, thus preventing the shock absorber from unnecessarily consuming energy in the high-frequency range, while simultaneously reducing the sprung mass acceleration.

In Figure 3, $m_h$ denotes the mass of the HVRS, $k_h$ denotes the rigidity factor of the HVRS, $c_h$ denotes the parameter of damp of the HVRS, and $z_h$ denotes the positional change of the HVRS.

For the convenience of research, the ratio of the stiffness coefficient of the HVRS to the suspension stiffness coefficient is defined as $\delta$, $\delta =k_h/k_s$; The ratio of the damping coefficient of the HVRS to the damping coefficient of the wheels is defined as $\chi$, $\chi =c_h/c_s$. The ratio of the mass of the HVRS to the unsprung mass is defined as $\varsigma$, $\varsigma =m_h/m_u$.

In accordance with Figure 3, the HVRS remains operational. The HVRS remains functional as long as its deformation remains below the designated stroke $L_h$ limit. Equation (10) defines the kinetic behavior of the HVRS. Supposing that no collision occurs during the time take for the HVRS to reach the endpoint of its stroke during extension or compression, the new structure demonstrates equivalent characteristics to a traditional suspension system. Furthermore, its motion equation is represented by Equation (1).

The model is founded on the following assumptions: The stiffness coefficient, damping coefficient, wheel stiffness coefficient, and wheel damping coefficient of the suspension remain constant throughout the analysis. The impact of the stopper on the system’s behavior is negligible. Friction forces are disregarded in this model.

Utilizing the schematic diagram of the model, the study derives an equation, presented as Equation (10), which forms the basis for subsequent analysis.

$$\left\{\begin{array}{l}{m}_s{\ddot{z}}_s=k_s(z_u-z_s)+c_s({\dot{z}}_h-{\dot{z}}_s)\\ m_h{\ddot{z}}_h=k_h(z_u-z_h)+c_h({\dot{z}}_u-{\dot{z}}_h)-c_s({\dot{z}}_h-{\dot{z}}_s)\\ m_u{\ddot{z}}_u=k_s(z_s-z_u)+k_u(z_r-z_u)+k_h(z_h-z_u)+c_u({\dot{z}}_r-{\dot{z}}_u)+c_h({\dot{z}}_h-{\dot{z}}_u)\end{array}\right.$$

(10)

By subjecting Equation (10) to Fourier transformation, one can derive the amplitude-frequency profiles of various parameters including the sprung mass acceleration ${\ddot{z}}_s$, relative dynamic load $F_d/G_j$, dynamic deflection of the suspension system $s_d$, shock mitigation velocity $v_{sh}$, shock mitigation velocity of the HVRS $v_{hu}$, and wheel deformation $v_{ur}$ in comparison to the road’s excitation velocity ${\dot{z}}_r$, as delineated in (11) to (16).

$${\left|H_h(\mathrm{j}\omega )\right|}_{{\ddot{z}}_s~{\dot{z}}_r}=\left|\frac{{\ddot{z}}_s}{{\dot{z}}_r}\right|=\omega \left|\frac{{{\rm X}}_{zsh}}{X_{zrh}}\right|$$

(11)

$$\left|H_h{(\mathrm{j}\omega )}_{(F_d/G_j)~{\dot{Z}}_r}\right|=\left|\frac{{\omega }_{s0}(\gamma {\omega }_{s0}+2\epsilon \xi \omega \mathrm{j})}{(1+\mu )g}\right|\left|\frac{X_{Fdh}}{X_{zrh}}\right|$$

(12)

$$|H_h(\mathrm{j}\omega ){|}_{s_d~{\dot{z}}_r}=\frac{1}{\omega }\left|\frac{X_{sdh}}{X_{zrh}}\right|$$

(13)

$$|H_h(\mathrm{j}\omega ){|}_{v_{sh}~{\dot{z}}_r}=\left|\frac{X_{vsh}}{X_{zrh}}\right|$$

(14)

$$|H_h(\mathrm{j}\omega ){|}_{v_{hu}~{\dot{z}}_r}=\left|\frac{X_{vhu}}{X_{zrh}}\right|$$

(15)

$$|H_h(\mathrm{j}\omega ){|}_{v_{ur}~{\dot{z}}_r}=\left|\frac{X_{zhur}}{X_{zrh}}\right|$$

(16)

$$\begin{array}{c}{{\rm X}}_{zsh}=A_{hr}{A}_{hb}+A_{hr}{A}_{ha}{A}_{ua},\\ X_{zrh}=A_{ub}{A}_{sa}{A}_{hb}-A_{ub}{A}_{ha}{A}_{sb}-A_{hb}-A_{ha}{A}_{ua}-A_{hc}{A}_{sb}-A_{hc}{A}_{sa}{A}_{ua},\\ X_{Fdh}=X_{zrh}-A_{hr}{A}_{sa}{A}_{hb}+A_{hr}{A}_{ha}{A}_{sb},\\ X_{sdh}=A_{hr}(A_{hb}+A_{ha}{A}_{ua})-A_{hr}(A_{sa}{A}_{hb}-A_{ha}{A}_{sb}),\\ X_{vsh}=A_{hr}(A_{hb}+A_{ha}{A}_{ua})-A_{hr}(A_{sa}{A}_{ua}+A_{sb}),\\ X_{vhu}=A_{hr}(A_{sb}+A_{sa}{A}_{ua})-A_{hr}(A_{sa}{A}_{hb}-A_{ha}{A}_{sb}),\\ X_{zhur}=X_{z_{rh}}-A_{hr}{A}_{sa}{A}_{hb}-A_{hr}{A}_{ha}{A}_{sb},\\ A_{sa}=1-{\lambda }^2+2\xi \lambda \mathrm{j},A_{ha}=2\xi \lambda \mathrm{j},A_{sb}=2\xi \lambda \mathrm{j}/\delta ,A_{ua}=1+2\chi \epsilon \xi \lambda \mathrm{j}/\delta ,\\ A_{hb}=1-\varsigma \mu {\lambda }^2/\delta +2\xi \lambda \mathrm{j}/\delta +2\chi \epsilon \xi \lambda \mathrm{j}/\delta ,A_{hc}=\delta +2\epsilon \xi \lambda \mathrm{j},\\ A_{ub}=1+\gamma +\delta -\mu {\lambda }^2+2\epsilon \xi \lambda \mathrm{j}+2\chi \epsilon \xi \lambda \mathrm{j},A_{hr}=\gamma +2\epsilon \xi \lambda \mathrm{j}+2\chi \epsilon \xi \lambda \mathrm{j}.\end{array}$$

When the damping ratio is set to 0.25, the maximum amplitude of the first dominant frequency in the amplitude frequency characteristics of the suspension dynamic deflection is M. The HVRS stroke is L_h, the suspension stroke is Ls, then the percentage of buffer stroke is u_h = L_h/L_s, and the maximum amplitude reached by the HVRS is M_h = M(L_h /L_s). The probability of the HVRS working is P(H) [29].

Let the size of HVRS distortion be S_h. When S_h ≤ M_h, the HVRS operates at full capacity with a probability of 100%, as indicated in (17). However, when S_h > M_h, the HVRS functionality is compromised. The damping likelihood is expressed as depicted in (18) [29].

$$P(H)=1(S_h\le M_h)$$

(17)

$$P(H)=M_h/S_h(S_h>M_h)$$

(18)

The amplitude of the sprung mass acceleration ${\ddot{z}}_s$, relative dynamic load $F_d/G_j$, dynamic deflection $s_d$, shock mitigation velocity $v_{sh}$, shock mitigation velocity of the HVRS $v_{hu}$, and wheel deformation $v_{ur}$ at any frequency point on the suspension amplitude frequency characteristic curve is the sum of the amplitude with the HVRS multiplied by probability and the amplitude without the HVRS multiplied by probability, as shown in Equations (19)–(24).

$${\left|H_{hx}(\mathrm{j}\omega )\right|}_{{\ddot{z}}_s~{\dot{z}}_r}=\omega \left|\frac{{{\rm X}}_{zsh}}{X_{zrh}}\right|P(H)+\omega \left|\frac{X_{zs}}{X_{zr}}\right|(1-P(H))$$

(19)

$$\left|H_{hx}{(\mathrm{j}\omega )}_{(F_d/G_j)~{\dot{z}}_r}\right|=\left|\frac{{\omega }_{s0}(\gamma {\omega }_{s0}+2\epsilon \xi \omega \mathrm{j})}{(1+\mu )g}\right|\left(\left|\frac{X_{Fdh}}{X_{zrh}}\right|P(H)+\left|\frac{X_{Fd}}{X_{zr}}\right|(1-P(H))\right)$$

(20)

$$|H_{hx}(\mathrm{j}\omega ){|}_{s_d~{\dot{z}}_r}=\frac{1}{\omega }\left|\frac{X_{sdh}}{X_{zrh}}\right|P(H)+\frac{1}{\omega }\left|\frac{X_{sd}}{X_{zr}}\right|(1-P(H))$$

(21)

$${|H_{hx}(\mathrm{j}\omega )|}_{v_{sh}~{\dot{z}}_r}=\left|\frac{X_{vsh}}{X_{zrh}}\right|P(H)+\left|\frac{X_{sd}}{X_{zr}}\right|(1-P(H))$$

(22)

$${|H_{hx}(\mathrm{j}\omega )|}_{v_{hu}~{\dot{z}}_r}=\left|\frac{X_{vhu}}{X_{zrh}}\right|P(H)$$

(23)

$$|H_{hx}(\mathrm{j}\omega ){|}_{v_{ur}~{\dot{z}}_r}=\left|\frac{X_{zhur}}{X_{zrh}}\right|P(H)+\left|\frac{X_{zur}}{X_{zr}}\right|(1-P(H))$$

(24)

3.2. Novel Configuration’s Spectral Attributes

Table 1 and

Table 2. Suspension and HVRS simulation parameters.

Parameters	Value	Description
$\xi$	0.25	Suspension damping ratio
$u_h$	0.1	The percentage of buffer stroke
$M$	0.35	The maximum amplitude of suspension dynamic deflection
$\chi$	5	The ratio of the HVRS damping coefficient to wheel damping coefficient
$\delta$	1.5	The ratio of HVRS stiffness to suspension stiffness
$\varsigma$	0.01	The ratio of the mass of the HVRS to the unsprung mass

provide an outline of the modeling parameters. Utilizing (18) to (20), we derive the frequency-dependent amplitude curve with the HVRS and juxtapose it against the behavioral graph of the traditional suspension. The results of this comparative analysis are visually presented in Figure 4.

As depicted in Figure 4a, when the excitation frequency falls below the threshold frequency $f_{sy}$, the sprung mass acceleration of the new configuration suspension with the HVRS exhibits a slight increase when compared to the traditional suspension in the initial main frequency range. This increment is attributed to the deformation of the HVRS within this range, which diminishes the shock absorber’s effectiveness relative to traditional suspension, consequently resulting in a minor elevation in the sprung mass acceleration.

Conversely, when the excitation frequency surpasses the turning frequency $f_{sy}$, a marked reduction in the sprung mass acceleration is observed for the new configuration suspension with the HVRS, particularly within the range between $f_{sy}$ and the second main frequency. This significant decrease is due to the deformation of the HVRS in the second main frequency range, which significantly slows down the shock absorber’s velocity when compared to traditional suspension. This reduction in velocity leads to a decrease in the damping force and energy consumption of the shock absorber, ultimately resulting in a substantial drop in the amplitude of the sprung mass acceleration. This pattern aligns with the trend exhibited in Figure 2a.

Observing Figure 4b, it is evident that, in the first main frequency range, where the excitation frequency is below the threshold frequency $f_{sy}$, the relative dynamic load of the new configuration suspension with the HVRS undergoes a slight increase when compared to the traditional suspension. This increase is attributed to the deformation of the HVRS within this frequency range, which diminishes the shock absorber’s effectiveness relative to the traditional suspension, thereby resulting in a minor elevation in the relative dynamic load.

However, as the excitation frequency rises above the turning frequency $f_{sy}$ and remains below the frequency $f_{uz}$, the relative dynamic load of the new configuration suspension with the HVRS experiences a significant reduction when compared to the traditional suspension. This notable decrease is due to the deformation of the HVRS in this frequency range, which significantly slows down the shock absorber’s velocity, effectively reducing its damping ratio. Consequently, the damping force output by the shock absorber decreases significantly, leading to a substantial reduction in the amplitude of the relative dynamic load. This pattern aligns well with the trend displayed in Figure 2b.

Interestingly, when the excitation frequency surpasses frequency $f_{uz}$, particularly in the vicinity of the second main frequency, the relative dynamic load of the new configuration suspension with the HVRS undergoes a significant increase. This rise is attributed to the maximum variation of the HVRS within this frequency range, which suppresses the shock absorber’s effectiveness. However, since the damping force of the HVRS is smaller than that of the traditional suspension, it results in a comparatively larger amplitude of the dynamic load.

Upon the analysis of Figure 4c, it becomes apparent that the dynamic deflection of the new configuration suspension with the HVRS exhibits a slight increase relative to traditional suspensions, specifically at the first and second main frequencies. This increment is attributed to the deformation of the HVRS within these primary frequency regions, which diminishes the efficacy of the shock absorbers when compared to traditional setups. Consequently, the damping ratio is reduced, leading to a slight uptick in the suspension’s dynamic deflection. This trend aligns precisely with the pattern observed in Figure 2c.

A quantitative analysis of the frequency-domain suspension characteristic amplitude changes between the two suspension configurations reveals the amplitudes of the sprung mass acceleration, relative dynamic load, and dynamic deflection, as presented in

Table 3. Comparison of the average amplitude of suspension characteristics.

Comparison of Suspension Characteristics	Average Amplitude in Frequency Domain
	${\ddot{\mathit{z}}}_{\mathit{s}}/{\dot{\mathit{z}}}_{\mathit{r}}$	$({\mathit{F}}_{\mathit{d}}/{\mathit{G}}_{\mathit{j}})/{\dot{\mathit{z}}}_{\mathit{r}}$	${\mathit{s}}_{\mathit{d}}/{\dot{\mathit{z}}}_{\mathit{r}}$
Without HVRS	2.0204	0.4050	0.0081
With HVRS	1.6836	0.4195	0.0086
Change (%)	−16.67	+3.58	+6.17

.

Notably, the sprung mass acceleration underwent a significant reduction of 16.67%, while the relative dynamic load increased by 3.58%, and the dynamic deflection increased by 6.17%. This suggests that the novel suspension configuration exhibits significant potential in minimizing the acceleration of the sprung mass, while maintaining relatively stable dynamic load and deflection levels.

3.3. Comparison of Energy Consumption in Frequency Domain between Two Suspension Configurations

By utilizing Equations (5), (6) and (22)–(24), a comparative analysis of the reducer velocities for two distinct suspension configurations can be conducted. The results of this comparison are graphically represented in Figure 5, providing a clear visualization of the differences in the velocity profiles between the two systems.

As depicted in Figure 5a, it is evident that, when the excitation frequency falls below the frequency $f_{sh}$, the velocity of the shock absorber in the new configuration suspension equipped with the HVRS remains largely unaltered when compared to traditional suspension. Notably, the velocity of the shock absorber within the HVRS is significantly lower, indicating its low-pass filtering function. In the primary frequency range, the HVRS exhibits minimal influence on the energy consumption of the shock absorber, thus enabling it to fully optimize its shock-absorbing capabilities.

As the excitation rate exceeds the frequency $f_{su}$, the velocity of the HVRS shock absorber gradually exceeds that of the suspension shock absorber, reaching a peak in the region of the second principal frequency. This suggests that the HVRS shock absorber gradually becomes effective at higher frequencies, dissipating more power than the suspension shock absorber, which is beneficial for attenuating high-frequency vibrations and reducing suspension energy consumption.

When the excitation rate surpasses the $f_{hu}$, the HVRS shock absorber’s velocity gradually exceeds that of the traditional suspension shock absorber. This indicates that, when compared to the traditional suspension, the HVRS shock absorber functions to filter low frequencies and block high frequencies, reducing the energy consumption of the traditional suspension in the high-frequency range, thereby facilitating further vibration reduction.

In Figure 5b, it is apparent that, when the excitation frequency is below $f_{su}$, the deformation velocity of the wheels remains virtually identical in both suspension configurations. However, as the excitation frequency surpasses $f_{su}$ but remains below $f_{hu}$, the deformation velocity of the wheels in the HVRS-configured suspension significantly drops in comparison to the traditional suspension. Conversely, once the excitation frequency exceeds $f_{hu}$, the deformation velocity of the wheels in the HVRS-configured suspension increases markedly, surpassing that of the traditional suspension. Nevertheless, as the excitation frequency surpasses the second principal frequency, the deformation velocity of the wheels in the HVRS-configured suspension gradually decreases, ultimately approaching the characteristics of the traditional suspension.

To assess the potential of the HVRS in reducing suspension energy consumption, a comparative analysis of the energy consumption of two suspension configurations was conducted in the frequency domain. Since the energy consumption of the suspension is solely determined by its internal components, it suffices to analyze the energy dissipation of the shock absorbers, wheels, and HVRS shock absorbers.

After determining the vehicle speed $v$ based on random inputs from different road surfaces, different road roughness coefficients $G_q(n_0)$, and reference spatial frequency $n_0$, the mean square value of the relative velocity ${\sigma }_{vsh}^2$ of the shock absorber with the novel configuration suspension can be obtained, as shown in Equation (25).

$${\sigma }_{vsh}^2=G_{\dot{q}}{\displaystyle {\int }_0^{\infty }{\left(\left|\frac{X_{vsh}}{X_{zrh}}\right|P(H)+\left|\frac{X_{sd}}{X_{zr}}\right|(1-P(H))\right)}^{2}df}$$

(25)

In the formula, $G_{\dot{q}}$ is the power spectral density of the vertical velocity of the road surface, whose value is $G_{\dot{q}}=4{\pi }^2{G}_q(n_0)n_0^{2}v$.

Through Equation (25), the dissipated power $P_{sh}$ of the shock absorber of the novel configuration suspension can be calculated as Equation (26). Similarly, the power $P_{hu}$ of the shock absorber of the HVRS of the novel configuration suspension, the power $P_{hur}$ of the wheels of the novel configuration suspension, the power $P_{su}$ of the shock absorber of the traditional suspension, and the power $P_{ur}$ of the wheels of the traditional suspension can be obtained, as shown in Equations (27), (28), (29) and (30), respectively.

$$P_{sh}=c_s{({\dot{z}}_s-{\dot{z}}_h)}^2=c_s{\sigma }_{vsh}^2$$

(26)

$$P_{hu}=c_h{({\dot{z}}_h-{\dot{z}}_u)}^2=c_h{G}_{\dot{q}}{\displaystyle {\int }_0^{\infty }{\left(\left|\frac{X_{vhu}}{X_{zrh}}\right|P(H)\right)}^{2}df}$$

(27)

$$P_{hur}=c_u{({\dot{z}}_u-{\dot{z}}_r)}^2=c_u{G}_{\dot{q}}{\displaystyle {\int }_0^{\infty }{\left(\left|\frac{X_{zhur}}{X_{zrh}}\right|P(H)+\left|\frac{X_{zur}}{X_{zr}}\right|(1-P(H))\right)}^{2}df}$$

(28)

$$P_{su}=c_s{({\dot{z}}_s-{\dot{z}}_u)}^2=c_s{G}_{\dot{q}}{\displaystyle {\int }_0^{\infty }{\left(\left|\frac{X_{sd}}{X_{zr}}\right|\right)}^{2}df}$$

(29)

$$P_{ur}=c_u{({\dot{z}}_u-{\dot{z}}_r)}^2=c_u{G}_{\dot{q}}{\displaystyle {\int }_0^{\infty }{\left(\left|\frac{X_{zur}}{X_{zr}}\right|\right)}^{2}df}$$

(30)

The parameters are presented in Table 1 and Table 2, covering frequencies ranging from 0.1 to 100 Hz. Employing Equations (26)–(30), the energy consumption of both suspension configurations with and without the HVRS are calculated to determine the dissipation power of the suspension, damper, wheels, and the HVRS, across various speeds on D-level road surfaces. These results are graphically repesented in Figure 6a. Additionally, Figure 6b illustrates the energy consumption of each damping component of the new configuration suspension when travelling at 60 km/h on the D-level road.

As depicted in Figure 6a, as the vehicle speed increases, the dissipated power of the suspension damping components rises accordingly. Notably, the dissipated power of the shock absorber without the HVRS exceeds that with the HVRS. Conversely, the dissipated power of the wheels with the HVRS is greater than that without the HVRS. This phenomenon follows a pattern, as outlined in Equation (31).

$$P_{su}>P_{sh}>P_{hu}>P_{hur}>P_{ur}$$

(31)

To assess the energy consumption reduction capabilities of the new suspension configuration in the frequency domain, we compile and present the power consumption data of both configurations across various driving speeds under D-level road conditions in

Table 4. Suspension energy consumption under the D-level road.

Status	Suspension Energy Consumption (W)
	20 km/h	40 km/h	60 km/h	80 km/h
Without HVRS	1504	3007	4511	6014
With HVRS	1344	2688	4032	5376
Change (%)	−10.64	−10.61	−10.62	−10.61

. Upon analyzing this data, it becomes evident that the new configuration suspension can achieve a reduction in energy consumption exceeding 10% without compromising suspension characteristics.

4. Time-Domain Characteristics of Suspension with the HVRS

4.1. The Implementation Form of the HVRS

The frequency domain analysis has shown that incorporating the HVRS into the suspension configuration is advantageous in reducing the energy consumption of suspension systems. To confirm this conclusion, it is imperative to validate the performance of the new configuration suspension through time-domain simulations and to conduct a comparative analysis with the traditional suspension.

The fundamental principles of the HVRS are analyzed, depicted in Figure 7a, which comprises two elastic elements and two damping elements. When the suspension is statically balanced, the two elastic and damping components of the HVRS are not under any force and exist in a free state. However, when the suspension undergoes compression, the elastic and damping elements positioned between b and a1 become active. Similarly, during extension or compression between b and a2, the corresponding elastic and damping elements between b and a2 engage. Notably, in the HVRS of the suspension, both a1 and a2 are connected to the suspension damper.

The engineering implementation of the HVRS, depicted in Figure 7b, involves connecting the upper and lower oil ports of the suspension shock absorber to a one-way throttle valve and a nitrogen-filled accumulator, respectively. During suspension motion, the oil from the shock absorber flows into the one-way throttle valve and the accumulator of the HVRS. This arrangement enables the HVRS to function as a low-pass filter, effectively reducing suspension energy consumption. The incorporation of a one-way throttle valve is crucial as it facilitates the rapid return of oil from the accumulator to the shock absorber when the shock absorber moves in the opposite direction, thus preventing oil insufficiency within the shock absorber.

In Figure 7b, the stiffness $k_h$ of the HVRS is nonlinear, which is different from Equation (9). The magnitude of stiffness $k_h$ is determined by the gas constant $m$, initial inflation pressure $p_0$, initial gas column length $L_0$, accumulator piston diameter $D$, and displacement of piston $s$. Due to the sharp increase in stiffness at the end of the accumulator’s stroke, it is equivalent to the end-stopper, which is an advantage of using gas springs. The stiffness calculation of the HVRS is shown in Equation (32).

$$k_h=\frac{\pi D^{2}m{p}_0{L_0}^m}{4{(L_0-s)}^{m+1}}$$

(32)

4.2. Time Domain Comparison of Two Suspension Configurations

In the time domain, the simulation models for both traditional and new configuration suspensions using the parameters detailed in Table 1, Table 2 and

Table 5. HVRS simulation factors.

Parameters	Value	Description
$m$	1.27	The gas constant
$p_0$	4 MPa	Initial inflation pressure
$L_0$	15 mm	Initial gas column length
$D$	40 mm	Accumulator piston diameter

are constructed. These models are driven by standard Class D road profiles at a speed of 60 km/h. By inputting the corresponding suspension configurations, simulated results are generated for comparison.

Through simulation, curves representing time-varying data for the sprung mass acceleration, relative dynamic load, and suspension dynamic deflection of the two distinct suspension are derived, as depicted in Figure 8.

Additionally, spectral density analysis is conducted on these parameters for both configurations, yielding the comparative spectral density curves depicted in Figure 9.

Upon the analysis of Figure 8 and Figure 9, it is evident that both suspension configurations display similar characteristics in terms of relative dynamic load and time-dependent dynamic distortion. Notably, there is a significant reduction in the sprung mass acceleration. However, discrepancies arise in their frequency-domain characteristics, although they closely resemble those described in Figure 4.

In terms of the sprung mass accelerations, it is noted that, below a certain threshold frequency $f_{sy}$, the spectral density within the primary frequency band experiences a slight increase within the novel configuration featuring the HVRS as compared to the traditional suspension. However, beyond the threshold $f_{sy}$, the spectral distribution of the sprung mass acceleration within the HVRS suspension undergoes a significant reduction relative to the traditional suspension. This reduction is particularly pronounced within the frequency range spanning from $f_{sy}$ to the second principal frequency, exhibiting the most prominent decrease.

Regarding the relative dynamic loads, when the excitation rate is below $f_{sy}$ within the primary frequency band, the spectral density of the relative dynamic loads within the novel structure with the HVRS shows a slight increase when compared with the traditional suspension. When the excitation frequency is higher than the frequency $f_{sy}$ but lower than the frequency $f_{uz}$, the relative dynamic load spectrum density of the new configuration suspension with the HVRS is significantly reduced when compared to traditional suspension. Upon surpassing $f_{uz}$, the spectral density of the relative dynamic loads within the novel suspension structure with the HVRS notably increases within the range of the second principal frequency.

For dynamic deflection, the spectral density of the dynamic deflection of the new configuration suspension with the HVRS remains relatively unchanged when compared to traditional suspension.

A comparative analysis of the energy consumption of each damping component for two suspension configurations on a D-level road surface at 60 km/h is presented in Figure 10.

Additionally, Figure 11a illustrates a comparison of the average power consumption across each damping component. Furthermore, Figure 11b depicts the percentage breakdown of energy consumption for each damping component in the new suspension configuration.

Table 6. Comparative evaluation of the suspension time-domain characteristics.

Status	${\mathit{\sigma }}_{{\ddot{\mathit{z}}}_{\mathit{s}}}/{\mathbf{m}/\mathbf{s}}^2$	${\mathit{\sigma }}_{{\mathit{F}}_{\mathit{d}}/{\mathit{G}}_{\mathit{j}}}$	${\mathit{\sigma }}_{{\mathit{s}}_{\mathit{d}}}/\mathbf{m}$	${\overline{\mathit{P}}}_{\mathit{s}}/\mathbf{W}$	${\overline{\mathit{P}}}_{\mathit{c}}/\mathbf{W}$	${\overline{\mathit{P}}}_{\mathit{u}}/\mathbf{W}$	${\overline{\mathit{P}}}_{\mathit{h}}/\mathbf{W}$
Without HVRS	3.3484	0.4161	0.0314	4508	4284	225	0
With HVRS	3.1126	0.4241	0.0319	4036	3134	304	598
Change (%)	−7.04	+1.92	+1.59	−10.47	−26.84	+35.11

provides a comprehensive comparison of various parameters between the two suspension configurations, including the root mean square values of the sprung mass acceleration ${\sigma }_{{\ddot{z}}_s}$, relative dynamic load ${\sigma }_{F_d/G_j}$, dynamic deflection ${\sigma }_{s_d}$, as well as the averages of the suspension power consumption ${\overline{P}}_s$, shock absorber power consumption ${\overline{P}}_c$, wheel power consumption ${\overline{P}}_u$, and HVRS power consumption ${\overline{P}}_h$.

The analysis indicates that the novel suspension configuration not only mitigates the sprung mass acceleration, but also achieves a substantial reduction in energy consumption. This offers a viable solution to the issue of the traditional suspensions’ increased energy usage above certain frequencies, often accompanied by a deterioration in the sprung mass acceleration.

Comparatively, the new configuration exhibits a 7.04% reduction in the sprung mass acceleration when compared to the traditional setup. While the relative dynamic load and dynamic deflection have increased slightly by 1.92% and 1.59%, respectively, these increments have a minimal impact on the vehicle’s handling stability.

Furthermore, the new configuration maintains similar characteristics to the traditional suspension but boasts a notable 10.47% reduction in energy consumption. The energy usage pattern of each damping component in both configurations adheres to the trend outlined in Equation (31). Notably, the HVRS configuration results in a slightly higher wheel power consumption when compared to the traditional setup.

Crucially, the energy consumption breakdown of each damping component in the new configuration, derived from time-domain simulations, closely aligns with the results obtained from the frequency-domain calculations. This validation underscores the accuracy and reliability of the theoretical model underlying the new suspension configuration.

It is indeed true that the novel suspension configuration offers a significant energy consumption reduction. However, this advancement comes with the necessity of incorporating the high-frequency vibration reduction structure (HVRS), which understandably raises costs. Furthermore, the addition of the HVRS complicates the suspension structure, making it more challenging to maintain and manage. Additionally, the long-term durability of the HVRS structure, which is responsible for absorbing high-frequency vibrations, remains a concern that needs to be addressed. Nevertheless, these challenges are areas that the research and development team of the novel suspension configuration will actively explore and seek to overcome in the future, aiming to deliver an optimal balance between performance, cost, and durability. In the future, the integrated HVRS shock absorber, which boasts superior performance, low cost, and high reliability, will emerge as a significant research direction.

The introduction of this new suspension configuration is expected to bring significant alterations to the control strategy when compared to traditional suspensions. Specifically, the employment of the HVRS significantly reduces the high-frequency vibrations received by the shock absorber, facilitating the implementation of active suspension control. Furthermore, for semi-active control, the low-pass filtering effect of the HVRS in the high-frequency range considerably attenuates the shock absorber’s speed, necessitating significant modifications to the semi-active control algorithm. Consequently, active/semi-active control strategies tailored for HVRS suspensions represent a crucial research direction.

5. Conclusions

Drawing from research concerning traditional suspension systems and energy feedback suspension configurations, this study introduces an innovative suspension configuration to mitigate the energy consumption of traditional suspensions. Both frequency and time domain analyses confirm that this novel suspension configuration effectively reduces energy consumption while enhancing vibration damping capabilities. The specific conclusions can be summarized as follows:

(1) The traditional suspension setup leads to a surge in the sprung mass acceleration and energy usage beyond the f_sy frequency.

(2) The novel suspension configuration outperforms the traditional one, decreasing both the sprung mass acceleration and suspension power consumption in frequency domain.

(3) Time-domain simulations reveal a 7.04% reduction in the sprung mass acceleration with the new configuration, as compared to the traditional one. While the relative dynamic load and deflection exhibit slight increases of 1.92% and 1.59%, respectively, these are outweighed by the overall energy savings.

(4) Time-domain simulations show that, when traveling at 60 km/h on a D-level road, the new suspension configuration consumes less power than the traditional one, achieving a 10.47% reduction in suspension power consumption.

(5) The integrated HVRS damper with superior performance, low cost, and high reliability will be an important research direction in the future.

(6) Active/semi-active control based on the HVRS suspension will be an important research direction.

In the future, extensive research into HVRS suspension and control algorithms will be undertaken, focusing on achieving high cost-effectiveness and reliability, ultimately maximizing the performance potential of the HVRS suspension configuration.