Dynamic Characteristics Analysis of Vehicle Incorporating Hydraulically Interconnected Suspension System with Dual Accumulators

A novel roll-resistant hydraulically interconnected suspension with dual accumulators on each fluid circuit (DHIS) is proposed and dynamic characteristics of vehicle incorporating DHIS subsystem are studied in this paper. A 10-degrees-of-freedom (DOFs) vehicle model coupled with DHIS subsystem is established and validated. Four physical parameters of DHIS subsystems which are crucial to vehicle responses are selected with prescribed variation ranges to explore their relationships with the vehicle performance. Simulations of vehicle conducting sine-wave steering maneuvers are carried out to evaluate handling performance with roll angle and vertical tyre force for DHIS subsystem with the parameters varying, compared with the results for vehicle with the original spring-damper suspension and conventional hydraulically interconnected suspension (HIS). On the other hand, ride comfort performance indicated by total weighted root mean square accelerations at the center of gravity is studied when vehicle is excited by three different types of road pavements when the four parameters vary in the prescribed ranges. Simulation results are compared to investigate the special merits of DHIS subsystem, and the parameters that influence the handling performance and ride comfort most are identified. Overall, the DHIS subsystem can effectively enhance the vehicle handling performance compared with the original spring-damper suspension, and it can also benefit much to the ride comfort in contrast to the HIS subsystem.


Introduction
Vehicle rollover is the leading cause of fatalities in road crashes.According to the statistics of National Highway Traffic Safety Administration (NHTSA), 33% of all deaths from passenger vehicle crashes are related to rollover accidents in 2002.As a consequence, research studies on suspension system aiming at improving handling performance and reducing rollover propensity has found prosperity in terms of both active/semiactive controlled and passive suspensions [1][2][3][4][5][6][7][8].Many active/semiactive control strategies, such as H ∞ control strategies and sliding-mode control strategies, have been utilized onto vehicle to enhance handling performance and ride comfort [9][10][11][12][13][14][15][16].However, they are too expensive for ordinary passenger cars.erefore, some inexpensive passive suspension systems, which can also benefit vehicle dynamic performance, have been widely studied, such as hydraulic suspension subsystems, to investigate their effects on vehicle dynamics [17,18].
A large number of researches have been focused on the hydraulic suspension subsystems.Moulton and Best introduced a hydroelastic suspension system, consisting of four hydroelastic units, which are connected in the pitch plane by pipes [19].Félez and Vera applied the bond-graph method for the design of hydropneumatic suspension [20].El-Demerdash and Crolla studied the slow active control strategy of hydropneumatic suspension on quarter vehicle model with a previewed road profile [21].Els and Grobbelaar studied the effects of heat transfer on the spring characteristics of hydropneumatic suspension [22].Schumann and Anderson utilized the hydragas suspension to improve vehicle ride performance on off-road [23].Sridhar and Sekar applied the hydrogas suspension onto tracked vehicle to suit for many different road profiles [24].Solomon and Padmanabhan applied the skyhook control theory to improve ride performance of a tracked vehicle [25,26].
e researches above mainly discussed the hydraulic suspension subsystems with independent spring and damping units on vehicle performances.However, the hydraulic suspension with spring and damping effects integrated into one chamber has barely been investigated.Cao et al. proposed this novel type of hydraulic suspension, with each oil chamber employing a gas chamber to adjust the spring effects and with two valves, namely, compression and rebound valves, to adjust the damping effects [27,28].In 2010, Cao et al. studied a number of interconnection patterns of hydropneumatic suspension in full-vehicle scale, aiming at finding appropriate fluidic couplings to enhance roll-and pitch-mode stiffness and damping effects, but simultaneously have little effects on bounce-and warp-mode properties [17].Later on Cao et al. studied the dynamic responses of vehicle with X-shaped hydropneumatic suspension system in the situation of braking-in-a-turn maneuver [29].
Abovementioned researches have studied many types of hydraulic suspensions and their improvements, mainly focused on the utilization on heavy trucks, which take the handling performance and load-bearing capacity as the principal considerations in the design procedure.However, hydraulic suspensions can also be utilized on light vehicles with the emphases mainly on improvement of handling performance at the same time giving more consideration on ride comfort.Different from the hydraulic suspensions mentioned above, hydraulically interconnected suspension (HIS) system does not necessarily remove or replace the original spring-damper suspension system, but works as an auxiliary device to benefit vehicle performances.Zhang et al. took an investigation on the background and modeling of HIS subsystem and introduced a novel type of hydraulic suspension, with all the chambers interconnected with two oil circuits, for the purpose of improving roll motion performance [30].Smith et al. studied the characteristics of handling performances with fishhook steering input and half-sine bump input [19].Ding et al. extended the application of HIS subsystem on vehicle with two axles to that with three axles, using the transfer matrix method to generate the final dynamic equations of HIS subsystem [31].Wang and coworkers developed a motion-mode energy method to identify the contribution of HIS subsystem on vehicle motion modes, which could be used to decouple vehicle dynamic energy distribution on each motion mode [32].Ding et al. investigated characteristics of the pitch-plane HIS subsystem on two-axle vehicles to formulate feasible regions for subsystem parameters [33].Liang et al. introduced an interval analysis method for uncertain-but-bounded parameters of HIS subsystem to investigate the influences of uncertain parameters on vehicle's dynamic responses [34].
However, literatures above mainly focused the vehicle characteristics with only one accumulator on each fluidic circuit in HIS subsystem and barely discussed HIS subsystem with dual accumulators on each fluidic circuit.However, DHIS subsystem possesses its own distinctive characteristics comparing with conventional HIS subsystem, such as providing much wider ranges for stiffness and damping adjustment, and alterations of stiffness and damping properties in each mode motion with the help of the variable damping valves adjacent to the additional accumulators.Consequently, a novel DHIS subsystem in roll plane is presented in this paper.e characteristics of DHIS subsystem are numerically investigated in terms of some physical parameters, such as precharged oil pressure, damping coefficients, chamber section area difference, and ratio in the cylinders at front axle.
e rest of the paper will be arranged as follows: Section 2 presents the modeling of vehicle coupled with DHIS in roll plane; in Section 3, the validation of the newly established model will be shown; Section 4 illustrates the relationships between the vehicle dynamic performances and four key physical parameters; and finally, Section 5 concludes the main results.

Modeling of Vehicle with DHIS Subsystem
As the DHIS subsystem is working together with the entire spring-damper suspension system in this paper, a 10-DOFs vehicle model is firstly established, for the sake of conducting steering maneuvers and random pavement excitations, simultaneously.e DHIS subsystem, considering the co-actions of the two accumulators in each circuit on oil pressure variations, has been constructed.Consequently, the analytical model of vehicle with DHIS subsystem is presented.

Vehicle with Original Suspension.
As shown in Figure 1, the vehicle model consists of 10-DOFs, including longitudinal, lateral, and vertical displacements at CG, namely, x s , y s , and z s , respectively; roll, pitch, and yaw angles at CG, namely, ϕ, θ, and ψ, respectively; and the vertical displacements z ui (i � 1, 2, 3, 4) and rotating angles ϑ ui of four tyres, where the subscript i � 1, 2, 3, and 4 correspond to the left-front, rightfront, left-rear, and right-rear stations, respectively.e physical parameters of vehicle are listed in Table 1.
In Figure 1, the longitudinal and lateral equations can be obtained with Newton's second law: where m s is the sprung mass; m ui (i � 1, 2, 3, 4) are the unsprung masses (generally speaking, m u1 � m u2 � m uf , m u3 � m u4 � m ur ); x ui , y ui are the longitudinal and lateral displacements of four wheels relative to vehicle coordinate, respectively, which can be obtained through the displacements at CG and the vehicle geometry; z ui are the vertical displacements of four wheels along z-axis; and F xti and F yti are the longitudinal and lateral forces in x and y directions generated by tyre-terrain contact, which can be derived through the following equations: 2 Shock and Vibration where F txi and F tyi are the contact forces in tyre coordinates generated with DUGOFF tyre model [35] and δ ui are tyre steering angles.
Meanwhile, the dynamic equation at z-axis for sprung mass can be derived as where F zsi are the suspension forces imposed on sprung mass along z-axis.F zsi can be derived with suspension de ections and their derivatives as follows: where z si are z-axis displacements of the sprung mass at four suspension stations.z si can be obtained through the state variables of sprung mass and the suspension geometry as where l f and l r are the length from CG to the front and rear axles, respectively, and t f and t r are the half-track width of the front and rear axles, respectively.Similarly, the momentum equations along x-axis and y-axis for sprung mass can be formulated as where I xx and I yy are the rotary inertia along x-axis and y-axis of sprung mass and M xri and M yri are the x-axis and y-axis momentums imposed by unsprung mass onto sprung mass, respectively.e summations of M xri and M yri can be obtained as follows:

Shock and Vibration
3 where h oc is the height from the vehicle body rolling center to the chassis bottom.e momentum equation for vehicle in z-plane can be obtained as follows: where I zz is the rotary inertia of the vehicle along z-axis and M zri is the z-axis momentum imposed by tyre-terrain contact onto vehicle.e summation of M zri can be obtained by the following equation: where M tzi are the self-aligning momentums of tyres.e z-axis force balance equations for unsprung masses can be formulated as follows: where c ti and K ti are the damping and stiffness coefficients of tyres, respectively, and z gi are the road pavement excitations at each tyre.Based on the above analysis, the integrated vehicle model can be formulated as follows: where ), 0 denotes the zero matrix of proper dimensions, and Shock and Vibration

DHIS Subsystem.
e DHIS subsystem is designed in the roll plane, as shown in Figure 2, and its physical parameters are listed in Table 2.When the vehicle performs steering maneuvers, without loss of generality, the fact that the cylinders and pistons are moving relatively can be equivalent to the process that only the pistons are traveling in the comprehensive movements while the cylinders are xed, as the red dashed arrows shown in the gure.Consequently, the uid in the chambers is owing in and out as depicted with red solid arrows in the gure, where the line thickness represents the ow quantity relatively.It can be seen clearly from these arrows that a large quantity of uid ows into the accumulators in Circuit A, but contrary for Circuit B. Eventually, oil pressure in A rises while that in B goes down, which means, the oil pressures in each chamber are changed.Consequently, the DHIS subsystem generates a roll-resistant torque to retard further roll motion.
In DHIS subsystem, the upper chambers of cylinders are connected with vehicle body, and lower chambers are connected with unsprung masses, as shown in Figure 2.
erefore, the displacements z si (i 1, 2, 3, 4) of upper cylinders are the same as those in the joints on vehicle body.en, the oil volume variations in upper chambers ΔV Hti and lower chambers ΔV Hbi can be obtained as follows: e oil pressure loss through the damper valves can be expressed as where the uid quantity at the valves adjacent to the upper and lower inlets/outlets of hydraulic cylinders can be expressed as Take Circuit A, for instance, de ne ΔV A as the total oil volume owing into the two accumulators G 1 and G 3 , and de ne ΔV A1 and ΔV A3 as the oil volumes owing into accumulators G 1 and G 3 , respectively.
en, the following equations can be obtained through the properties of accumulators and uid: ΔV Hbj , where Δ _ V A3 is the derivative of ΔV A3 relative to time t; R gj (j 1, 2, 3, 4) are damping coe cients of the valves adjacent to the accumulators G j ; Δp gj are the pressure loss at valve R gj ; p 0 is the precharged oil pressure in DHIS subsystem; V 10 and V 20 are the precharged gas volumes at G 1 /G 2 and G 3 /G 4 , respectively; and p gi (i 1, 2, 3, 4) are the oil pressures at G i , respectively.
e status in Circuit B can be derived similarly with (16).en with (15) and ( 16), the oil pressure at each chamber in DHIS subsystem can be obtained as follows: Damping coe cient of valves adjacent to the accumulators where T F←P is the state transfer matrix from oil pressures to acting forces, namely, Considering the vehicle geometry and the vertical forces (18), forces acting on vehicle system can be expressed as follows: In (20), the rst three lines of F H (s) are momentums acting on z s , ϕ, θ, respectively, and the last four lines are forces acting on z ui (i 1, 2, 3, 4), respectively.

Vehicle Coupled with DHIS Subsystem.
Applying the forces in (20) onto the corresponding vehicle model in (12), the integrated mechanical-hydraulic coupled vehicle model incorporating DHIS subsystem can be rebuilt as follows:

Validation of the Vehicle Model with DHIS Subsystem
e vehicle model with DHIS subsystem will conduct a maneuver, such as sine-wave steering, to verify its e ectiveness through result comparisons between MATLAB and CarSim in this section.
In the ensuing simulations, at initial time t 0 s, the vehicle with DHIS subsystem is in static equilibrium with the precharged oil pressure p 0 2.0 MPa and the precharged gas volumes in G 1 /G 2 V 10 0.35 L together with that in G 3 /G 4 V 20 0.10 L. At the next instant, the wheel steering input is implemented to the vehicle model, so the dynamic states of mechanical and hydraulic subsystems are determined by ( 3), ( 6), ( 7), (11), and (20).A fourth-order Runge-Kutta numerical integration method is utilized to solve the dynamic equations.
e vehicle model is subject to a sine-wave maneuver.Figure 3 shows the wheel steering angle input as a function of time.
e vehicle velocity is set to v 50 km/h.Two vehicle output variables, including roll angle and vertical tyre force in left-front station, are used as the indicators to evaluate vehicle handling performance.
Comparisons of the results from MATLAB and CarSim are shown in Figure 4.It can be seen from the plots that the roll angle and tyre force acquired from MATLAB are slightly larger than the results from CarSim.e main reason for this phenomenon is that some parameters in the two simulation platforms, such as the locations of suspension joints, can hardly be adjusted the same.However, generally speaking, the results from the MATLAB simulations are tting well enough with those acquired from CarSim.
erefore, the vehicle model with DHIS subsystem established in 2 can be e ectively utilized for further analyses.

Results and Discussion
In this section, the vehicle performance, including handling performance in time domain and ride performance in frequency domain, is investigated.e physical parameters of DHIS subsystem play signi cant roles in vehicle dynamic behaviors.Considering the similarity of vehicle responses between front and rear axles, only those parameters in front axle are considered for brevity.Four physical parameters, including the precharged oil pressure p 0 in hydraulic suspension subsystems, the area di erence/ratio of hydraulic chambers in front axle (ΔA f /λ Af , namely, , and the damping coecients of R g1 /R g2 , are chosen as the crucial factors due to their important e ects on suspension characteristics, and their variation ranges are prescribed as shown in Table 3. To observe the di erences among vehicle behaviors in uenced by suspension system, the results of vehicle with an additional DHIS subsystem (denoted as S-III for brevity) are derived compared with those results of vehicles with the other two types of suspension system: the original spring-damper suspension system (denoted as S-I) and the  Shock and Vibration suspension system with both the original suspension and HIS subsystem (denoted as S-II).

In uence of Physical Parameters on Handling
Performance.e maneuver with sine-wave steering (Figure 3) is adopted to evaluate the handling performances of vehicle with the three types of suspension system.For brevity, only the responses, including the roll angle ϕ and tyre force in left-front tyre F tz1 , are chosen to indicate handling performance.Simulations are carried out to investigate the in uence of the four physical parameters on the two responses.
During the simulations, the vehicle runs at a speed of v 50 km/h.e dynamic responses in time domain are depicted in Figure 5.
Figure 5(a) shows that the hydraulic suspension systems (including both DHIS and HIS subsystems) have signi cantly reduced the amplitudes of roll angle, which means the roll sti ness has been e ectively enhanced with hydraulic suspension subsystems.Figure 5(b) shows that the tyre load has been observed signi cant decreases for vehicle with DHIS and HIS subsystems comparing with vehicle with only the original suspension system, which means the tyre-terrain contact situation has been improved.However, comparing with HIS subsystem, DHIS subsystem has a less sti ened roll motion, which is due to e ect of the additional gas accumulators.e DHIS subsystem has provided more gas to soften the suspension sti ness compared with the HIS subsystem.
Analyses above show that the hydraulic suspension subsystems can e ectively a ect the vehicle performances.However, these e ects can be further simpli ed by choosing the appropriate features of responses.It is obvious that the mean values of roll angle ϕ and tyre force F tz1 are constant (ϕ m 0 rad, F tz1m 4282 N, where the subscript "m" denotes the mean value) during the whole simulation processes.However, the amplitudes for the dynamic responses keep varying among the three types of suspension system.erefore, the amplitude of roll angle ϕ a and that of tyre force F tz1a are chosen as the features to indicate the handling performances.

Precharged Oil Pressure.
Figure 6 shows the characteristics of vehicle responses as the precharged oil pressure p 0 changes.In Figure 6(a), the roll angle decreases as p 0 increases.is phenomenon can be explained that when p 0 goes up, the roll sti ness generated by hydraulic suspension subsystems increases, and thus, roll motion of vehicle is retarded.erefore, the load transferred from left side to right side which mainly depends on the sprung mass roll motion is reduced, which means the roll holding ability has been enhanced, as shown in Figure 6(b).Although the lateral acceleration can also contribute to the tyre load transfer, but this value hardly changes as the suspension system alters.It can also be observed from Figures 6(a) and 6(b) that the DHIS subsystem produces larger peak values of roll angle and tyre force than the HIS subsystem.

Area Di erence in Front Hydraulic Cylinders.
Figure 7 shows the characteristics of vehicle responses as the chamber area di erence in front axle ΔA f changes.Figure 7(a) shows that as ΔA f increases, the roll angle decreases, but as ΔA f goes larger, such as from 8 × 10 −4 m 2 to 13 × 10 −4 m 2 , the decrease tendency becomes slow.e reason for the downward trend of roll angle amplitude can be explained: the volumes of uid owing into the accumulators increase together with the ΔA f when vehicle performs roll motion, and then the gas pressure, as well as the oil pressure, goes up.Consequently, the vehicle becomes di cult to perform roll motion.In Figure 7(b), the vertical tyre load F tz1 shows an upward trend as ΔA f increases.It can be observed in Figure 7 that the DHIS subsystem produces larger peak values for roll angle and tyre force, but as ΔA f

Symbol (unit)
Lower limits Upper limits p 0 (MPa) 0.0 4.0 Shock and Vibration 7 increases, the gap between the responses of vehicle with DHIS subsystem and HIS subsystem has been narrowed.

Area Ratio in Front Hydraulic
Cylinders.Figure 8 shows the characteristics of vehicle responses as the chamber area ratio λ Af changes.Figure 8(a) shows that as λ Af increases, the roll angle decreases.When λ Af becomes larger, the inner diameter of hydraulic cylinders in front axle goes up.Consequently, the volume of uid owing into the accumulators becomes larger than that of the uid that owing from the accumulators to the cylinders in rear axle; thus, the gas pressure as well as the oil pressure increases.erefore, the reason for the decrease of roll angle can be explained.Figure 8(b) shows that the tyre load F tz1 increases when λ Af increases.

Damping Valves.
Figure 9 shows the in uence of the damping coe cients of R g1 /R g2 on vehicle responses.It can be seen from Figures 9(a) and 9(b) that the damping coe cients have barely a ected the peak values of vehicle responses.e reason for this phenomenon is that the uid owing through the damper valves at R g1 /R g2 runs at such low speeds so that the ow quantity can hardly contribute to the damping e ects.
Based on the analyses above, the in uences of physical parameters on vehicle handling performance can be concluded.In order to identify the most crucial factor for hydraulic suspension subsystems, the amplitude variations relative to physical parameters from Figures 6-9 are all summarized in Figure 10, where function g(x) |x max − x min |.It is observed obviously that ΔA f is the factor that a ects the handling performance when compared with the other three  8 Shock and Vibration factors, which means that ΔA f is the most crucial factor in DHIS subsystem for handling performance.

In uence of Physical Parameters on Ride Performance.
According to ISO 2631-1997, responses of vehicle running on random road pavements are utilized to obtain the ride performance.A C-class level road pavement, corresponding to the road roughness coe cient G q (n 0 ) 256 × 10 −6 m 3 , is chosen as the road excitations of the tyres.e vehicle speed is still v 50 km/h.In order to qualify the ride comfort e ectively and thoroughly, three types of excitation methods, including the pure-bounce motion (the excitations on four tyres are of the same value and direction), pure-roll motion (the excitations on left and right tyres are of the same value but of the opposite directions), and pure-pitch motion (the excitations on front and rear tyres are of the same value but the opposite directions), are introduced to derive vehicle responses.Considering the defects of the time domain responses, such as the di culty to obtain a smooth frequency spectrum in spite of road pavement errors [36], the frequency-domain response based on the power spectrum density (PSD) is utilized to evaluate the vehicle performance.
According to ISO 2631-1997, the weighted root mean square (WRMS) of accelerations at CG, denoted as σ aw , is applied to evaluate the ride comfort, that is, where k i (i x, y, z) are the weighting factors in x-, y-, and z-axis; w i (i x, y, z) are the frequency weighting factors along x-, y-, and z-axis; a i (i x, y, z) are the accelerations at , but the former undergoes much worse situations of ride performance than the latter.Figure 11(f ) shows that the indicator σ aw in pure-pitch motion has an optimal point where σ aw is minimized for DHIS and HIS subsystems, respectively.But when ΔA f goes up after that point, the ride comfort is worsened dramatically for both hydraulic suspension subsystems.shows that the ride comfort has been obviously damaged in pure-roll motion when λ Af is larger than 0.6.Figure 12(c) shows that λ Af has a trivial e ect on σ aw .

Damping Valves. Figures 12(d)-12(f )
show the inuence of area ratio λ Af on ride comfort.Figure 12(d) shows that DHIS subsystem has little in uence on ride comfort comparing with HIS subsystem when R g1 /R g2 changes in pure-bounce motion.Figure 12(e) shows that there exists an optimal point for DHIS subsystem to minimize σ aw , while a downward trend of σ aw can be witnessed for HIS subsystems.Figure 12(f ) shows that the R g1 /R g2 has merely a ected the ride comfort in pure-pitch motion.
Based on the analyses above, it is obvious that the four physical parameters play important roles in improving vehicle ride comfort.In order to identify the most crucial factor for the mechanical design of DHIS subsystem, the deviation of σ aw , denoted by g(σ aw ), is applied to evaluate the perturbation of ride comfort when the physical parameters vary in the prescribed ranges.
e results are shown in Figure 13, in which the data are generated with the results in Figures 11 and 12. From Figures 13(a)-13(c), we know that the area di erence ΔA f plays the most crucial role in ride performance of vehicle with hydraulic suspension subsystems, followed by precharged oil pressure λ Af and p 0 .On the other hand, the DHIS subsystem has narrower perturbation ranges on ride comfort than HIS subsystem, which means the DHIS subsystem can be used to provide a more comfortable experience for occupants than HIS subsystem.

Discussion.
ere still exist some de ciencies in this paper.For the rst, the damping e ect of the DHIS subsystem, including pipe damping and cylinder damping, is embodied into the valve damping e ect.
is simpli cation can e ectively  12 Shock and Vibration reduce the modeling complexity but may introduce some inaccuracies.Secondly, the leakage between chambers separated with rubber seal ring has been neglected, which may also contribute a lot to modal parameters shifting if uid leakage emerges.ough it still presents challenges for modeling, but with the help of high-quality seal rings, these problems can be avoided e ectively.irdly, as the discussions on damper valves R vi are similar to that on R gi , the investigation on R vi is not presented for brevity.Meanwhile, the discussions of the feasible regions for these parameters will need to be further studied.

Conclusions
is paper generally presents a new type of hydraulically interconnected suspension system with dual accumulators at each uid circuit.A 10-DOFs vehicle model coupled with DHIS subsystem is proposed and veri ed with results generated from MATLAB and CarSim software.Four crucial parameters of DHIS subsystem are chosen and assumed to vary in certain ranges.ereafter, vehicle responses in time domain including roll angle and vertical tyre force, as well as responses in frequency domain in three types of road pavement excitations, are obtained for vehicles with three types of suspension subsystem.e main results are listed as follows: (1) e simulation results of the proposed 10-DOFs vehicle model with DHIS subsystem t well enough with those results acquired from CarSim software.It means that the 10-DOFs vehicle model can be used for further analyses.
(2) Four key physical parameters, including precharged oil pressure p 0 , damping coe cients of R g1 /R g2 , chamber area di erence ΔA f , and ratio λ Af in front axle, are taken to investigate their relationships with vehicle responses.Results show that the increases of p 0 , ΔA f , and λ Af can restrain the roll propensity of vehicle body, while p 0 and λ Af can help improve road holding, comparing with ΔA f which could further deteriorate this capacity after a critical value.Meanwhile, the damping coe cients at R g1 /R g2 have negligible e ects on both roll angle and tyre force.On the other hand, the four parameters can e ectively a ect the ride comfort in roll motion but have little e ect on bounce and pitch motions.
(3) Results have shown that ΔA f is the most crucial factor for both handling performance and ride comfort comparing with the other three factors, followed by λ Af and p 0 .
(4) DHIS subsystem can e ectively enhance the rollresistant property of vehicle comparing with the original spring-damper suspension system, and it can also bene t much to ride performance comparing with the conventional HIS subsystem.
Data Availability e data used to support the ndings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that no con icts of interest exist regarding the publication of this paper.

Figure 2 :
Figure 2: e diagram of roll plane DHIS subsystem.

Figure 4 :
Figure 4: Comparisons of simulation results: (a) roll angle; (b) vertical tyre force at left-front station.

Figure 6 :Figure 5 :
Figure 6: In uence of p 0 on amplitudes of vehicle responses: (a) roll angle of sprung mass; (b) vertical tyre force at left-front station.

Figure 8 :Figure 7 :
Figure 8: In uence of λ Af on amplitudes of vehicle responses: (a) roll angle of sprung mass; (b) vertical tyre force at left-front station.

Figure 10 :RFigure 9 :
Figure 10: e in uence of physical parameters on vehicle responses.

Figure 11 :
Figure 11: In uence of p 0 and ΔA f on ride comfort indicator σ aw in three motion modes: (a, d) in pure-bounce motion; (b, e) in pure-roll motion; (c, f ) in pure-pitch motion.

Figure 12 :
Figure 12: In uence of λ Af and R g1 /R g2 on ride comfort indicator σ aw in three motion modes: (a, d) in pure-bounce motion; (b, e) in pureroll motion; (c, f ) in pure-pitch motion.

Figure 13 :
Figure 13: In uence of the physical parameters on the deviations of σ aw in (a) pure-bounce motion; (b) pure-roll motion; (c) pure-pitch motion.

Table 1 :
Physical parameters of vehicle.

Table 2 :
Physical parameters of DHIS subsystem.

Table 3 :
Parameter variation ranges of hydraulic suspension subsystems.