The air spring suspension is shown in Figure 2a and mainly consists of air spring, shock absorber, guiding mechanism and control system. Air spring is closely related to stability and vibration damping performance. Compared with other types of spring, such as helical spring, torsion bar spring, leaf spring, air spring has good nonlinear stiffness, excellent vibration damping performance, has been widely used. At present, the air spring is mainly divided into two types of capsule air spring and membrane air spring, as shown in Figure 2b. The capsule air spring has the characteristics of large effective area change rate, high stiffness and long service life. In order to achieve good damping performance, the stiffness of the spring is reduced by increasing the auxiliary air chamber. Membrane air spring structure with small effective area change rate, low stiffness, good damping performance, self-sealing, simple structure, low cost, widely used in automotive suspension. By adding an auxiliary air chamber to the membrane air spring, the adjusting range of the spring stiffness is widened and the good damping effect is achieved. In this paper, membrane air spring is selected as the research object.

The structure of membrane air spring with double secondary air bags is shown in Figure 3a. It is mainly composed of upper cover plate, lower cover plate, main air bag, secondary air bag and pipeline system (Mo et al., 2024; Yin S et al., 2023). The secondary air bags are arranged symmetrically and installed in the main air bag. According to the change of the air spring load, the air pipeline control system controls the valve opening to inflate or deflate the secondary air bags. And the stiffness of the air spring can be changed to achieve the function of damping shock vibration.

The working process of the air spring is “Figures 3b–d”. When the external load F is less than the specified value (such as Figure 3b), the valve closes, and the main air bag acts to attenuate the random vibration. When the external load F is greater than the specified value (such as Figure 3c), the valve is opened and the main air bag inflates the secondary air bags, thereby reducing the impact stiffness of the air spring to attenuate the impact vibration. The valve opening δ is determined by the external load F, the larger F, the larger δ, the smaller impact stiffness, the better vibration reduction effect. When the external load F decreases from the maximum value to the specified value (such as Figure 3d), the valve opening δ gradually becomes smaller, and the secondary air bags release air to the main air bag. When the external load F drops below the specified value, the valve closes and the air spring is again in the working state of Figure 3b.

To enable the dual-chamber air spring to adaptively attenuate shock vibrations, this study designs an active pneumatic control system based on real-time load feedback. Its core function lies in dynamically adjusting the valve opening between the main airbag and the auxiliary chamber via an Electronic Control Unit (ECU), thereby altering the system’s equivalent volume and stiffness.

The air piping system control principle is shown in Figure 4. A force sensor is installed on the lower cover plate to collect the load data of the air spring. The ECU controls the valve opening of the air pipeline system according to the load data. When the main air bag is compressed upward, the air pressure is greater than that of the secondary air bags, and the main air bag is inflated to the secondary air bags to reduce the air pressure in the main air bag. When the main air bag is drawn down, the air pressure is lower than the air pressure of the secondary air bags, at this time the secondary air bags deflate into the main air bag, thereby increasing the air pressure in the main air bag. When the air spring load is less than the specified value, the ECU causes the valve to close. At this time, the air pressure in the main air bag is approximately equal to that in the secondary air bags.

The control system must first accurately distinguish between random vibrations and shock vibrations. This study defines a dynamic load threshold F _set as the criterion for identification, the expression is shown in Equation 1 F s e t = α · F s t a t i c (1) where F _static represents the static equilibrium load of the vehicle under the current payload, obtained through system initialization and calibration; α is the shock threshold coefficient, a design parameter greater than 1. By introducing α, F _set can adaptively adjust according to the vehicle’s load, thereby avoiding potential issues such as false triggering or delayed response associated with a fixed threshold.

When the force sensor installed at the lower end of the suspension detects a real-time load F > F _set , the condition is identified as a shock scenario, and the ECU initiates valve adjustment. The valve opening δ is determined by the following formula, the expression is shown in Equation 2 δ = min K p · e t + K i ∫ e t d t , δ max , e t = F t − F s e t (2) where e(t) represents the load deviation; K _p ​ and K _i​ are the proportional and integral gain coefficients, respectively; and δ _max​ denotes the maximum physical opening of the valve (corresponding to 100%). This proportional-integral (PI) control structure aims to achieve both rapid response and precise adjustment: the proportional term K _p ​⋅e(t) ensures that the opening is proportional to the intensity of the impact, guaranteeing immediacy; the integral term K _i​ ∫e(t)dt continuously corrects steady-state errors, particularly under prolonged or continuous impacts, enabling the system to optimize and maintain an ideal stable opening to fully utilize the volumetric effect of the auxiliary chamber. When F ≤ F _set​, the system identifies the condition as random vibration or steady-state driving, sets δ = 0, and closes the valve. In this state, the system exhibits high stiffness to provide sufficient support.

The solenoid valve exhibits an inherent response delay of approximately T _d​ = 20 m. Without compensation, this delay would cause the stiffness adjustment to lag behind the rising edge of the impact load, thereby weakening the initial vibration mitigation effect. To address this, the system incorporates a feedforward compensation mechanism based on the load change rate. The ECU calculates the real-time load change rate dF/dt. When dF/dt exceeds a predefined impact rate threshold Rth, even if F has not yet fully surpassed F _set ​, the ECU will proactively output a feedforward opening command δ _ff ​ proportional to dF/dt, the expression is shown in Equation 3 δ f f = K f f · d F d t − R t h , d F d t > R t h (3) where K _ff ​ is the feedforward gain. This pre-emptive command is superimposed onto the opening command generated by the aforementioned PI closed-loop controller. By effectively predicting the impact trend, it partially compensates for the valve delay and optimizes the system’s transient stiffness characteristics under sudden loading, enabling the impact stiffness k _I ​ to decrease more rapidly.

The control parameters involved in this study (K _p ​, K _i​ , Rth​, K _ff ​) are initially calibrated via bench testing. The calibration principle is to align the gas flow response characteristics of the valve with the inflation/deflation dynamics of the auxiliary chamber. This ensures smooth and rapid stiffness regulation across different V _s ​ (auxiliary chamber volumes). Ultimately, by coordinating the structural parameter V _s ​​ and the control parameter δ (valve opening), this control system determines the instantaneous stiffness k _I​ of the air spring, thereby achieving effective shock and vibration attenuation performance.

The mechanical model of the air spring suspension is shown in Figure 5. The road roughness is transmitted to the vehicle body by the path “Tire-suspension”, which makes the vehicle vibrate. The one-side tire and one-side air spring form a series damping system, and the two-side damping system forms a parallel damping system, as shown in Figure 5a. According to reference (van der Seijs et al., 2016; Gao et al., 2024), the transfer function of the damping system and the stiffness of the air spring can be obtained.

The transfer function of the left damping system is H L s = H 1 L s · H 2 L s = c s l s + k s l m 1 s 2 + c t + c s s + k t + k s · 1 2 m 2 s 2 + c s l s + k s l − c s l s + k s l 2 (4) where H _1L (s) stands for the transfer function of the left tire system, H _2L (s) stands for the transfer function of the left suspension system, m ₁ stands for axle mass, m ₂ stands for the body mass, k _t stands for the tire stiffness, k _sl stands for the left suspension stiffness, c _t stands for the tire damping coefficient, c _sl stands for the left suspension damping coefficient.

The transfer function of the right damping system is H R s = H 1 R s · H 2 R s = c s r s + k s r m 1 s 2 + c t + c s s + k t + k s · 1 2 m 2 s 2 + c s r s + k s r − c s r s + k s r 2 (5) where H _1R (s) stands for the transfer function of the right tire system, H _2R (s) stands for the transfer function of the right suspension, k _sr stands for the right suspension stiffness, c _sr stands for the right suspension damping coefficient.

According to Equations 4, 5, there are many effects on the transfer function of the system, in which the parameters of tire and mass are constant. The damping parameters of suspension are mainly determined by shock absorbers, and the control method is relatively mature. The suspension stiffness is mainly determined by air spring, and the stiffness is nonlinear, which has great influence on the transfer function. Therefore, it is essential to establish a mathematical model of the air spring to analyze its mechanical properties (Zargar et al., 2012; Mendia et al., 2024; Wu et al., 2022).

For a vibration system, its dynamic characteristics are determined by the relationship between the restoring force and displacement. The air spring studied in this paper (as shown in Figure 5b) has instantaneous stiffness k as a key indicator of its resistance to deformation, defined as the derivative of the restoring force F with respect to deformation displacement x the expression is shown in Equation 6: k x = d F x d x (6)

Stiffness k(x) is a nonlinear function dependent on displacement and system state (e.g., valve opening or closing). When k(x) > 0, the system exhibits positive stiffness, meaning the restoring force increases with compressive displacement. When k(x) < 0, the system enters a negative stiffness state, where the restoring force decreases as displacement increases.

Considering the dual-chamber air spring described in the text, when the valve is open, the main chamber and the auxiliary chamber are connected, with the total volume being V _total​ = V _main​+V _aux​. Assuming the gas process is polytropic (with a polytropic exponent of λ), the restoring force F of the air spring can be derived based on the gas state equation and the force balance equation the expression is shown in Equation 7: F = p m a i n − P a · S (7) where, P _main represents the instantaneous air pressure in the main chamber; P _a denotes the standard atmospheric pressure; S is the effective pressure-bearing area of the air spring, which is typically a function of displacement x, i.e., S=S(x).

The pressure in the main chamber satisfies the condition shown in Equation 8, P m a i n · V m a i n λ = constant (8)

Assuming that at the equilibrium position (x = 0), the volume of the main chamber is V ₀ and the pressure is P ₀, the expression is shown in Equation 9: P m a i n = P 0 V 0 V m a i n λ (9)

The relationship between the main chamber volume and the deformation displacement is shown in Equation 10 V m a i n = V 0 − S · x + Δ V f l o w (10)

Where, ΔV _flow​ represents the gas exchange volume between the main and auxiliary chambers due to valve opening, which is controlled by the valve opening δ and the pressure difference.

The instantaneous stiffness can be obtained by taking the derivative of the restoring force F with respect to the displacement x: k a = d d x P 0 V 0 V m a i n λ − P a · S x (11)

Expanding (Equation 11) yields (Equation 12), k a = P 0 V 0 V m a i n λ − P a d S d x ⏟ Area change term + S · − λ P 0 V 0 λ V m a i n − λ − 1   d V m a i n d x ⏟ Pressure change term (12)

Where, the area variation term is typically positive, as the effective area S increases with compression (increase in x); the pressure variation term is generally negative, since compression reduces the volume, leading to an increase in air pressure.

A sufficient condition for the occurrence of negative stiffness is that the absolute value of the negative pressure variation term exceeds the positive value of the area variation term, the expression is shown in Equation 13 S · λ P 0 V 0 λ V m a i n − λ − 1   d V m a i n d x > P 0 V 0 V m a i n λ − P a d S d x (13)

In order to analyze the effect of secondary air bag volume on the stiffness of air spring, three groups of secondary air bag specimens with different volumes were made (As shown in Figure 6). Each group of 2 specimens were symmetrically installed in the main air bag. The specimen parameters are shown in Table 1. The structure and materials of the three groups of specimens are the same, which are composed of inner rubber layer, outer rubber layer, cord layer and steel wire ring.

In order to analyze the effect of valve opening of air pipeline control system on the stiffness of air spring, the specimen 2# is selected as the research object, and the valve opening is selected as 50%, 75% and 100%, respectively.

In order to measure the elastic properties of the air spring, the force, displacement, and acceleration of its upper and lower ends are measured. The positions of the sensors are shown in Figure 7a. The test includes bench test and road vibration test. The stiffness test bench is shown in Figure 7b, the loading frequency is 2.0 Hz, the loading amplitude is 0–20 mm, and the loading mode is continuous (Qin et al., 2025; Li et al., 2018). Stiffness Test Bench: Equipped with a force sensor (range: 0–50 kN, accuracy: ±0.1% FS), a displacement sensor (range: 0–50 mm, accuracy: ±0.01 mm), and a PCB accelerometer (measurement range: ±500 m/s², sensitivity: 10 mV/(m/s²), frequency response: 0.5 Hz–10 kHz).

The road vibration test is shown in Figure 7c. The PCB acceleration sensors are arranged on the upper and lower ends of the air spring, and the acceleration signal of the air spring is collected by the LMS Test. LAB system (Resolution: 0.1 Hz, Acquisition Bandwidth: 0–50 Hz). The test road chooses the pulse road surface, the height of the bump is 30 mm, the width of the lower end is 30, and the upper end is oval. The test speed is 50 km/h. Based on the acceleration data, the vibration attenuation rate, frequency response characteristic and vibration chaos phenomenon of air spring are analyzed.

Figure 8 shows the dynamic stiffness curves of air spring with different secondary air bag volumes. When the excitation amplitude is less than 10 mm, the valve is closed, and the secondary air bag affects the effective volume of the main air bag, and then affects the dynamic stiffness of the air spring. The stiffness of air spring without secondary air bag is the smallest, the average value is 114.5 N/mm; the dynamic stiffness of specimen 3# is the largest, the average value is 116.6 N/mm; the dynamic stiffness of specimen 1# is 115.5 N/mm; the dynamic stiffness of specimen 2# is 116.1 N/mm. That is, under the same excitation, the larger the volume of the secondary air bag, the greater the dynamic stiffness of the air spring. When the excitation amplitude ≥10 mm, the valve is in the open state, the valve opening gradually increases, resulting in the air spring dynamic stiffness gradually decreases. The stiffness of air spring without secondary air bag is maximum, the average value is 116.5 N/mm; the dynamic stiffness of specimen 3# is the smallest, the average value is 86.5 N/mm, the dynamic stiffness of specimen 1# is 89.3 N/mm, the dynamic stiffness of specimen 2# is 87.5 N/mm. That is, under the same excitation, after the valve is opened, the greater the volume of the secondary air bag, the smaller the dynamic stiffness of the air spring. The curves also show that the larger the volume of secondary air bag, the larger the stiffness change rate of air spring, the less obvious the dynamic stiffness delay effect.

The results in Figure 8 indicate that when the excitation amplitude is less than 10 mm (valve closed), the auxiliary chamber volume regulates the dynamic stiffness by altering the effective volume of the main airbag: a larger volume increases the equivalent volume of the main airbag, enhancing gas compression resistance and thereby raising the dynamic stiffness. When the excitation amplitude reaches or exceeds 10 mm (valve open), a larger auxiliary chamber volume allows more gas flow between the main and auxiliary chambers, suppressing the rate of pressure rise in the main airbag and leading to a more significant reduction in dynamic stiffness. Simultaneously, the rapid gas flow mitigates the time lag in stiffness response, substantially weakening the dynamic stiffness hysteresis effect.

Figure 9 shows the dynamic stiffness curve of air spring with different valve opening degrees. Under the same secondary air bag volume, the valve opening degree does not affect the dynamic stiffness of the air spring, but affects the dynamic stiffness change rate. When the excitation amplitude is less than 10 mm, the dynamic stiffness of the air spring with three valve opening degrees is equivalent. When the excitation amplitude ≥10 mm, the valve opens, and the dynamic stiffness of the air spring decreases gradually. When t = 6.0 s, the minimum dynamic stiffness of 100% opening is 83.5 N/mm. When t = 7.0 s, the minimum dynamic stiffness of 75% opening is 83.7 N/mm. When t = 7.5 s, the minimum dynamic stiffness of 50% opening is 83.8 N/mm. That is, the greater the valve opening, the greater the change rate of the dynamic stiffness, and the less obvious the dynamic stiffness delay effect.

The authors conducted comprehensive experiments across the full operating range of valve openings from 10% to 100% in 10% increments. The results indicate that with a fixed auxiliary chamber volume, the valve opening does not alter the final value of the dynamic stiffness but influences the stiffness change rate by regulating the gas flow rate between the main and auxiliary chambers. When the excitation amplitude is ≥ 10 mm, a larger valve opening facilitates smoother gas flow, leading to a faster decline in the pressure of the main airbag. This results in a more rapid attenuation of dynamic stiffness and a shorter time to reach the minimum stiffness, thereby reducing the time lag in stiffness response and weakening the hysteresis effect.

Figure 10 shows the impact stiffness curves of air springs with secondary air bag volumes. Impact stiffness directly determines the ability of air spring to attenuate impact vibration, the smaller the impact stiffness, the better the damping effect. The impact stiffness without secondary air bag is the largest, the average value is 148.6 N/mm; the impact stiffness of specimen 3# is the smallest, the value is 91.8 N/mm; the impact stiffness of specimen 1# is 103.5 N/mm; the impact stiffness of specimen 2# is 97.7 N/mm. That is, under the same excitation, the larger the volume, the smaller the impact stiffness. The impact stiffness delay time affects the damping impact vibration level of air spring. The longer the delay time of the impact stiffness of air spring without secondary air bag, the worse the damping effect is. The longer the delay time of the impact stiffness of air spring with secondary air bag, the better the damping effect. The impact stiffness delay time of specimens 1#, 2# and 3# are 0.26 s, 0.32 s and 0.51 s, respectively.

The results in Figure 10 demonstrate that the auxiliary chamber volume regulates the impact stiffness by altering the system’s equivalent volume: a larger volume allows more gas to be diverted from the main chamber to the auxiliary chamber during impact compression, thereby suppressing the pressure increase in the main chamber and reducing the impact stiffness. Simultaneously, a larger auxiliary volume extends the dynamic buffering process of gas flow, increasing the delay time of the impact stiffness response. This prolongs the interval during which stiffness declines gradually, thereby enhancing the absorption of impact energy and improving vibration damping performance.

Figure 11 shows the impact stiffness curves of air springs with different valve opening degrees. The impact stiffness of the 50% opening degree, 75% opening degree and 100% opening degree air spring is 103.7 N/mm, 96.4 N/mm and 91.8 N/mm, respectively. Under the same volume, the larger the valve opening, the smaller the impact stiffness. The impact stiffness delay time of 50% opening degree, 75% opening degree and 100% opening degree is 0.23 s, 0.29 s and 0.51 s, respectively. Under the condition of the same secondary air bag volume, the larger the valve opening, the longer the impact stiffness delay time.

The results in Figure 11 show that with a fixed auxiliary chamber volume, the valve opening influences the impact stiffness by regulating the gas flow efficiency between the main and auxiliary chambers: a larger opening reduces gas flow resistance, slows the pressure rise in the main chamber during impact, and consequently lowers the impact stiffness. Simultaneously, a larger opening prolongs the continuous gas diversion process, increasing the delay time of the impact stiffness response. This extends the interval over which the stiffness gradually attenuates, thereby more effectively buffering impact energy and enhancing vibration damping performance.

The stiffness test results indicate that when the valve is opened and the auxiliary chamber volume VauxVaux​ is integrated into the system, the total volume V _tot​ increases significantly. This volume increase notably reduces the rate of pressure change, thereby enhancing the negative effect of the pressure variation term. By controlling the gas flow ΔV _flow​ through the valve opening δ, the rate of change of V _main​ can be actively regulated during the critical moment of impact. This allows for the “shaping” of the stiffness curve within the key displacement range, inducing or strengthening negative stiffness characteristics. As discussed in Section 2.2, the matching design of control parameters (K _p​,K _i​ ) and auxiliary chamber volume V _s ​ aims to optimize the dynamic process of gas exchange. This enables the system to quickly enter and maintain a negative stiffness or near-zero low-positive-stiffness region under impact loading, thereby achieving optimal impact energy absorption.

Figure 12 shows the vibration curves of air spring suspension with different secondary air bag volumes. The vibration time-domain curves of air spring suspension are shown in Figure 12a. The vibration without secondary air bag is the largest, and the maximum acceleration is 7.3 m/s². And the bifurcation appears at the peak, which is mainly due to the large impact stiffness of the air spring, resulting in secondary impact of the air spring in deformation process. This phenomenon is not conducive to the damping performance and seriously affects the ride comfort. The vibration of specimen 3# is the smallest, and the maximum acceleration is 3.4 m/s2. The maximum acceleration of specimen 1# is 5.4 m/s². The maximum acceleration of specimen 2# is 4.8 m/s². The air spring suspension with secondary air bag has no bifurcation at the peak acceleration. Therefore, the secondary air bag is beneficial to improve the vibration damping performance. And the larger the secondary air bag volume, the better the damping effect.

Figure 12b shows the vibration frequency domain curves of the air spring suspension. The secondary air bag volume affects the natural frequency and vibration amplitude of the air spring suspension. The natural frequency of the air spring suspension without secondary air bag is 1.87 Hz, and the corresponding amplitude is 1.84 m/s². The natural frequencies of suspension with specimens 1#, 2# and 3# are 1.57 Hz, 1.54 Hz and 1.49 Hz respectively, and the corresponding amplitudes are 1.29 m/s², 1.21 m/s² and 1.15 m/s² respectively. Therefore, the larger the volume of the secondary air bag, the smaller the natural frequency of the suspension, and the better the damping effect.

The results in Figure 12 demonstrate that the auxiliary chamber enhances vibration damping performance through a dual mechanism of “reducing impact stiffness and adjusting natural frequency”: In the time domain, a larger auxiliary chamber volume allows more complete gas diversion from the main chamber during impact, leading to lower impact stiffness; This helps avoid acceleration bifurcation caused by secondary impacts, significantly reducing the peak vibration amplitude. In the frequency domain, the auxiliary chamber increases the system’s equivalent volume, which attenuates the suspension’s natural frequency while also lowering vibration amplitude, thereby reducing the risk of resonance. Under the synergistic effect of these two mechanisms, a larger auxiliary chamber volume results in stronger suppression of impact vibrations and improved vehicle ride comfort.

Figure 13 shows the vibration curves of air spring suspension with different valve opening degrees. In the time-domain curve of Figure 12a, the vibration with 50% opening degree is the largest, and the maximum acceleration is 5.1 m/s 2. The vibration with 100% opening degree is smallest, and the maximum acceleration is 3.4 m/s². The maximum acceleration with 75% opening degree is 4.5 m/s². That is, under the same secondary air bag volume, the larger the valve opening, the best damping effect of suspension.

In Figure 13b, the natural frequencies of air spring suspension with 50% opening degree, 75% opening degree and 100% opening degree are 1.56 Hz, 1.51 Hz and 1.49 Hz respectively, and the corresponding amplitudes are 1.42 m/s²,1.27 m/s² and 1.15 m/s² respectively. Therefore, the larger the valve opening, the smaller the natural frequency, the better the damping effect.

The results in Figure 13 indicate that with a fixed auxiliary chamber volume, the valve opening optimizes vibration damping performance by regulating gas flow efficiency. In the time domain, a larger valve opening facilitates smoother gas exchange between the main and auxiliary chambers, leading to a faster reduction in impact stiffness and a lower vibration peak. In the frequency domain, an increased valve opening dynamically enhances the system’s equivalent volume, lowering the natural frequency, reducing vibration amplitude, and mitigating the risk of resonance. Under the combined effect of these two mechanisms, a larger valve opening results in stronger attenuation of impact vibrations by the suspension system.

Figure 14 shows the maximum deformation of air spring suspension with different secondary air bag volumes, the deformation of air spring suspension without secondary air bag is the smallest, which is 8.9 mm and the corresponding time is 1.46 s. The deformation of air spring suspension with specimen 3# is the largest, which is 16.8 mm and the corresponding time is 1.13 s. The deformation of the suspension with specimen 1# is 12.6 mm and the corresponding time is 1.28 s. The deformation of the suspension with specimen 2# is 14.4 mm, and the corresponding time is 1.22 s. That is, the larger the volume of secondary air bag, the larger the deformation of air spring, the shorter the dynamic response time.

The results in Figure 14 indicate that the auxiliary chamber volume regulates deformation and response by altering the system’s stiffness characteristics: a larger volume reduces the equivalent stiffness of the air spring, enabling greater deformation to buffer energy during impact. Simultaneously, the increased volume accelerates gas flow between the main and auxiliary chambers, allowing the system to reach a state of force balance more quickly, thereby shortening the dynamic response time. Combined, these effects mean that a larger auxiliary chamber volume enhances the suspension’s energy absorption capacity during impact, accelerates its response, and improves its overall buffering performance.

Figure 15 shows the maximum deformation of air spring suspension with different valve opening degrees,and the loading time of shock excitation is 1.0 s, the deformation of air spring suspension with 50% opening degree is the smallest, which is 11.4 mm and the corresponding time is 1.31 s. The deformation with 100% opening degree is the largest, which is 16.8 mm and the corresponding time is 1.13 s. The deformation with 75% opening degree is 12.3 mm and the corresponding time is 1.24 s. That is, under the same secondary air bag volume, the larger the valve opening, the larger the suspension deformation, the shorter the dynamic response time.

The results in Figure 15 indicate that with a fixed auxiliary chamber volume, the valve opening influences deformation and response by regulating the efficiency of gas flow: a larger valve opening reduces the resistance to gas exchange between the main and auxiliary chambers. As a result, the pressure rise in the main chamber during impact becomes more gradual, the equivalent stiffness of the spring decreases, and greater deformation is achieved for energy buffering. Simultaneously, the accelerated gas flow hastens the system’s progression toward force equilibrium, thereby shortening the dynamic response time. These combined effects enhance the suspension’s efficiency in buffering impacts, with larger valve openings yielding superior buffering performance.