# Simulation Analysis and Experiment Research on Hydro-Pneumatic ISD Suspension

Authors: Xiao-Liang Zhang; Juchao Liu; Jiamei Nie; Hao Wei; Long Chen
Journal: Shock and Vibration
 (2021)

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## Abstract

To address the problems of mechanical two-stage inerter-spring-damper (ISD) suspension such as excessive suspension elements, complex structure, and problematic engineering implementation, a hydro-pneumatic two-stage ISD suspension, which integrates hydro-pneumatic spring and inerter, is proposed. The full vehicle model of hydro-pneumatic ISD suspension is established based on the AMESim. Simulation analysis is performed to demonstrate the effectiveness and performances of the proposed suspension. The hydro-pneumatic ISD suspension prototype is developed and tested on four-poster tire-coupled road simulator. The results suggest that, compared with single-chamber hydro-pneumatic suspension, the hydro-pneumatic ISD one can significantly reduce the vibrations of the vehicle body and wheels, but at the expense of an excessive increase of suspension working space (SWS). In contrast, although proposed suspension is also a type of dual-chamber hydro-pneumatic one, it can not only reduce these vibrations but also downsize the SWS, which means it is the best choice for a more comfortable and safer ride.


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## Body

## 1. Introduction

Traditional passive suspension is mainly composed of spring and damper, and it has little room for improvement [1–3]. In 2001, Smith developed an ideal analogy theory between mechanical and electrical systems based on the conventional analogy theory and proposed the inerter concept [4]. Vehicle suspension was first considered by Smith as a vibration isolation system employing inerters, and a few suspensions with inerter were therefore developed by Smith with different combined configurations, which have been shown to offer performance advantages over conventional passive suspensions [5–9]. Some previous researches on these suspensions highlighted that inerter can add fixed virtual mass to the sprung mass to reduce sprung mass natural frequency and improve ride comfort of vehicles [10–14]. The inerter-spring-damper (ISD) suspension proposed by Smith is a breakthrough in further improving the performance of the spring-damper suspension, which is based on the classical vibration isolation theory [4, 15–20].Zhang proposed a two-stage ISD suspension to realize the skyhook damper configuration passively and verified the effectiveness of the implementation scheme through simulation and bench test [21, 22]. The simulation and experiments in [23] proved that the mechanical two-stage ISD suspension has good performance in reducing vibration and it has potential for broad application, but the problems such as excessive suspension components and complex structure still exist.To address the abovementioned problems, we use fusion design method to organically integrate the hydraulic inerter and the hydro-pneumatic spring to propose a two-stage ISD suspension with single structure, which is a type of dual-chamber hydro-pneumatic suspension. The proposed suspension utilizes a helical channel to connect the two chambers of dual-chamber hydro-pneumatic suspension and obtains inertance with high-speed flowing fluid between two chambers. Based on the AMESim, the full vehicle model of the hydro-pneumatic ISD suspension is established in this paper. The prototype of hydro-pneumatic ISD suspension is developed and tested on four-poster tire-coupled road simulator to verify if the proposed ISD suspension outperforms the dual-chamber hydro-pneumatic one.


## 2. Hydro-Pneumatic Suspension Model

### 2.1. Structure of Hydro-Pneumatic ISD Suspension

The structure of the hydro-pneumatic ISD suspension based on fusion design is presented in this paper (Figure1), and it is equipped with a damping valve at the entrance of the accumulator to suppress vibration. The piston divides hydraulic cylinder into upper and lower chambers, with the upper chamber being connected with the accumulator I and hinged with the sprung mass. The lower end of the piston rod is articulated with the unsprung mass, and the accumulator I and accumulator II are connected by a helical channel. A schematic diagram of single- and dual-chamber hydro-pneumatic suspension is provided for reference in Figure 2.Figure 1
Schematic of hydro-pneumatic ISD suspension.Figure 2
Schematic of (a) single-chamber and (b) dual-chamber hydro-pneumatic suspension.
(a)(b)For hydro-pneumatic ISD suspension, the helical channel serves as the inertial channel where the fluid stores a large amount of kinetic energy in high-speed rotation. The difference in effective circulation areas between the helical channel and the hydraulic cylinder has an amplifying effect on fluid inertance. The nitrogen in the accumulator serves as an elastic medium and its compression can store elastic potential energy, which replaces the traditional spring. Besides, in the accumulator attachment, the damper is replaced by a throttling hole. Eventually, the hydro-pneumatic ISD suspension effectively integrates the inerter, spring, and damper organically through the medium of fluid.


### 2.2. Full Vehicle Model of Hydro-Pneumatic ISD Suspension

In this section, a full vehicle model equipped with a hydro-pneumatic ISD suspension model is established based on the AMESim (Figure3), and its equivalent simplified model is shown in Figure 4, the following models are included, namely, chassis, hydro-pneumatic ISD suspension system, road, tire, simplified brake, models for steering, and transmission. The road and tire models are formulated in Figure 5, and the hydro-pneumatic ISD suspension system model is visualized in Figure 6. The tire model imported by the AMESim is also linear, and we will set a threshold during the simulation and test to ensure that the tire does not lift off the ground. As for the modeling of single-chamber and dual-chamber hydro-pneumatic suspensions, it can be seen from Figure 2 that a short connection between a hydraulic cylinder and the accumulator I is selected in the hydro-pneumatic ISD model, or a helical channel is replaced with a connecting channel to realize the single-chamber and dual-chamber hydro-pneumatic suspension models, respectively, and the corresponding modules in AMESim are also used to connect them to realize the simulation model. The main parameters of vehicle model and hydro-pneumatic ISD suspension are presented in Tables 1 and 2 [24–28].Figure 3
Vehicle dynamics model based on AMESim.Figure 4
Equivalent simplified vehicle model.Figure 5
Road and tire model.Figure 6
Hydro-pneumatic ISD suspension model.Table 1
Main parameters of vehicle.
Main parametersValuesSprung mass1724kgUnsprung mass of front wheel43.5kgUnsprung mass of rear wheel46.5kgPitch moment of inertia2444kg⋅m2Roll moment of inertia380kg⋅m2Wheelbase2800mmFront track1600mmRear track1600mmDistance from front axle to centroid1250mmDistance from rear axle to centroid1550mmTire vertical stiffness192000N⋅m−1Tire damping200N⋅s⋅m−1Table 2
Hydro-pneumatic ISD suspension parameters.
Structural parametersValuesNumber of helical channel turns20Hydraulic cylinder diameter36mmLength of helical channel12.68mLength of high-pressure tubing1.5mDiameter of damper valve I4mmDiameter of damper valve II7.6mmInner diameter of helical channel6.6mmInner diameter of helical channel device200mmInitial volume of front suspension accumulator I0.385LInitial volume of rear suspension accumulator II0.385LPrecharge pressure of front suspension accumulator I42barPrecharge pressure of rear suspension accumulator I32barPrecharge pressure of front suspension accumulator II35barPrecharge pressure of rear suspension accumulator II25.7bar


## 2.1. Structure of Hydro-Pneumatic ISD Suspension

The structure of the hydro-pneumatic ISD suspension based on fusion design is presented in this paper (Figure1), and it is equipped with a damping valve at the entrance of the accumulator to suppress vibration. The piston divides hydraulic cylinder into upper and lower chambers, with the upper chamber being connected with the accumulator I and hinged with the sprung mass. The lower end of the piston rod is articulated with the unsprung mass, and the accumulator I and accumulator II are connected by a helical channel. A schematic diagram of single- and dual-chamber hydro-pneumatic suspension is provided for reference in Figure 2.Figure 1
Schematic of hydro-pneumatic ISD suspension.Figure 2
Schematic of (a) single-chamber and (b) dual-chamber hydro-pneumatic suspension.
(a)(b)For hydro-pneumatic ISD suspension, the helical channel serves as the inertial channel where the fluid stores a large amount of kinetic energy in high-speed rotation. The difference in effective circulation areas between the helical channel and the hydraulic cylinder has an amplifying effect on fluid inertance. The nitrogen in the accumulator serves as an elastic medium and its compression can store elastic potential energy, which replaces the traditional spring. Besides, in the accumulator attachment, the damper is replaced by a throttling hole. Eventually, the hydro-pneumatic ISD suspension effectively integrates the inerter, spring, and damper organically through the medium of fluid.


## 2.2. Full Vehicle Model of Hydro-Pneumatic ISD Suspension

In this section, a full vehicle model equipped with a hydro-pneumatic ISD suspension model is established based on the AMESim (Figure3), and its equivalent simplified model is shown in Figure 4, the following models are included, namely, chassis, hydro-pneumatic ISD suspension system, road, tire, simplified brake, models for steering, and transmission. The road and tire models are formulated in Figure 5, and the hydro-pneumatic ISD suspension system model is visualized in Figure 6. The tire model imported by the AMESim is also linear, and we will set a threshold during the simulation and test to ensure that the tire does not lift off the ground. As for the modeling of single-chamber and dual-chamber hydro-pneumatic suspensions, it can be seen from Figure 2 that a short connection between a hydraulic cylinder and the accumulator I is selected in the hydro-pneumatic ISD model, or a helical channel is replaced with a connecting channel to realize the single-chamber and dual-chamber hydro-pneumatic suspension models, respectively, and the corresponding modules in AMESim are also used to connect them to realize the simulation model. The main parameters of vehicle model and hydro-pneumatic ISD suspension are presented in Tables 1 and 2 [24–28].Figure 3
Vehicle dynamics model based on AMESim.Figure 4
Equivalent simplified vehicle model.Figure 5
Road and tire model.Figure 6
Hydro-pneumatic ISD suspension model.Table 1
Main parameters of vehicle.
Main parametersValuesSprung mass1724kgUnsprung mass of front wheel43.5kgUnsprung mass of rear wheel46.5kgPitch moment of inertia2444kg⋅m2Roll moment of inertia380kg⋅m2Wheelbase2800mmFront track1600mmRear track1600mmDistance from front axle to centroid1250mmDistance from rear axle to centroid1550mmTire vertical stiffness192000N⋅m−1Tire damping200N⋅s⋅m−1Table 2
Hydro-pneumatic ISD suspension parameters.
Structural parametersValuesNumber of helical channel turns20Hydraulic cylinder diameter36mmLength of helical channel12.68mLength of high-pressure tubing1.5mDiameter of damper valve I4mmDiameter of damper valve II7.6mmInner diameter of helical channel6.6mmInner diameter of helical channel device200mmInitial volume of front suspension accumulator I0.385LInitial volume of rear suspension accumulator II0.385LPrecharge pressure of front suspension accumulator I42barPrecharge pressure of rear suspension accumulator I32barPrecharge pressure of front suspension accumulator II35barPrecharge pressure of rear suspension accumulator II25.7bar


## 3. Mathematical Model of Hydro-Pneumatic ISD Suspension

### 3.1. Stiffness Properties

The stiffness properties are an important characteristic of the hydro-pneumatic spring, which refer to the relationship between the elastic force of the piston rod and the stroke of the piston relative to the hydraulic cylinder. The accumulator is the rigid element of the hydro-pneumatic suspension. The gas in the accumulator I and II is considered to be an ideal gas. The state equation of gas is as follows:(1)P2⋅V1n=Pg1⋅Vg1n,P4⋅V2n=Pg2⋅Vg2n.Where Pg1, Vg1, Pg2, and Vg2 are respectively the precharge pressure and initial charging volume of accumulator I and II; P2, V1, P4, and V2 are the instantaneous gas pressure and charging volume of accumulator I and II, respectively; P20, V10, P40, and V20 are respectively the gas pressure and volume at the equilibrium position of accumulator I and II. It is assumed that the accumulator is an adiabatic process of ideal gas, and n is the gas polytropic index, which is taken as 1.3. The change of gas volume in the accumulator can be expressed as(2)V1=Vg1+∫Q1dt,V2=Vg2+∫Q2dt.In static balance, the pressures in all parts of the hydraulic cylinder are equal, that is,(3)P10=P20=P30=P40.


### 3.2. Damping Properties

The outlets of accumulator I and II are respectively provided with damping valve I and II, as shown in Figure1. The corresponding pressure change at both ends can be expressed as(4)P1−P2=12ρQ1Cd⋅S01=C1⋅Q1,P3−P4=12ρQ2Cd⋅S02=C2⋅Q2,where P1 and P3 are the pressures at the inlet of damping valve I and II, respectively, P2 and P4 are the pressures in accumulator I and II, respectively, Cd is the flow coefficient, which is related to Reynolds number Re, S01 and S02 are the equivalent areas of damping valve, respectively, and ρ is the oil density.


### 3.3. Inertance Properties

The piston of hydro-pneumatic ISD suspension drives the high-speed fluid to move back and forth in the helical channel, stores a large amount of kinetic energy, and realizes the effect of amplifying the fluid inertance. The essential feature of hydro-pneumatic ISD suspension is that it can store and amplify the fluid inertance. However, nonlinear factors such as compressibility, viscosity, and fluid temperature still need to be considered. Combined with the hydraulic inerter structure studied [17], the inertance properties of hydro-pneumatic ISD suspension can be expressed by the fluid pressure difference at both ends of the helical channel.(5)P1−P3=ρ⋅lA2⋅Q2.+8μ⋅lA2⋅r2⋅Q2+ρ⋅Q224+ρ⋅Q222,=ρ⋅lA2⋅Q2.+ΔPμ+ΔPin+ΔPout,where l is the length of helical channel, A2 is the effective flow area of helical channel, μ is the fluid viscosity, and R is the inner radius of the helical channel.ΔPin and ΔPout are pressure losses of the inlet and outlet caused by the principle of large and small holes. By adjusting the diameter of damping valve I and II, the optimal compensation for pressure loss of the inlet and outlet can be realized. Therefore, the inertance properties can be simplified as(6)P1−P3=ρ⋅lA2⋅Q2.+ΔPμ.


## 3.1. Stiffness Properties

The stiffness properties are an important characteristic of the hydro-pneumatic spring, which refer to the relationship between the elastic force of the piston rod and the stroke of the piston relative to the hydraulic cylinder. The accumulator is the rigid element of the hydro-pneumatic suspension. The gas in the accumulator I and II is considered to be an ideal gas. The state equation of gas is as follows:(1)P2⋅V1n=Pg1⋅Vg1n,P4⋅V2n=Pg2⋅Vg2n.Where Pg1, Vg1, Pg2, and Vg2 are respectively the precharge pressure and initial charging volume of accumulator I and II; P2, V1, P4, and V2 are the instantaneous gas pressure and charging volume of accumulator I and II, respectively; P20, V10, P40, and V20 are respectively the gas pressure and volume at the equilibrium position of accumulator I and II. It is assumed that the accumulator is an adiabatic process of ideal gas, and n is the gas polytropic index, which is taken as 1.3. The change of gas volume in the accumulator can be expressed as(2)V1=Vg1+∫Q1dt,V2=Vg2+∫Q2dt.In static balance, the pressures in all parts of the hydraulic cylinder are equal, that is,(3)P10=P20=P30=P40.


## 3.2. Damping Properties

The outlets of accumulator I and II are respectively provided with damping valve I and II, as shown in Figure1. The corresponding pressure change at both ends can be expressed as(4)P1−P2=12ρQ1Cd⋅S01=C1⋅Q1,P3−P4=12ρQ2Cd⋅S02=C2⋅Q2,where P1 and P3 are the pressures at the inlet of damping valve I and II, respectively, P2 and P4 are the pressures in accumulator I and II, respectively, Cd is the flow coefficient, which is related to Reynolds number Re, S01 and S02 are the equivalent areas of damping valve, respectively, and ρ is the oil density.


## 3.3. Inertance Properties

The piston of hydro-pneumatic ISD suspension drives the high-speed fluid to move back and forth in the helical channel, stores a large amount of kinetic energy, and realizes the effect of amplifying the fluid inertance. The essential feature of hydro-pneumatic ISD suspension is that it can store and amplify the fluid inertance. However, nonlinear factors such as compressibility, viscosity, and fluid temperature still need to be considered. Combined with the hydraulic inerter structure studied [17], the inertance properties of hydro-pneumatic ISD suspension can be expressed by the fluid pressure difference at both ends of the helical channel.(5)P1−P3=ρ⋅lA2⋅Q2.+8μ⋅lA2⋅r2⋅Q2+ρ⋅Q224+ρ⋅Q222,=ρ⋅lA2⋅Q2.+ΔPμ+ΔPin+ΔPout,where l is the length of helical channel, A2 is the effective flow area of helical channel, μ is the fluid viscosity, and R is the inner radius of the helical channel.ΔPin and ΔPout are pressure losses of the inlet and outlet caused by the principle of large and small holes. By adjusting the diameter of damping valve I and II, the optimal compensation for pressure loss of the inlet and outlet can be realized. Therefore, the inertance properties can be simplified as(6)P1−P3=ρ⋅lA2⋅Q2.+ΔPμ.


## 4. Simulation Analysis of Hydro-Pneumatic ISD Suspension System

### 4.1. Analysis for Pulse Response

In order to research the vibration response characteristics of the hydro-pneumatic ISD suspension under pulse input conditions, the response to a pulse excitation simulates a vehicle passing the long waveform bump. Choosing the shape of the bump to be that of a haversine of heightA=0.1 m and length L=5m, and with vehicle speed set at u=30 km/h, this gives rise to the displacement input q=A/21−cos2πu/Lt0≤t≤L/u to the suspension.Figure7 and Table 3 show the time-domain response results of the system, according to which, the peak-to-peak (PTP) (the PTP values are calculated as max xt-min xt, where xt are values of the signal in a period.) values of the left front/rear body acceleration (BA) and dynamic tire load (DTL) of the hydro-pneumatic ISD suspension are 19.6%, 27.0%, 27.0%, and 29.6% lower than those of the single-chamber one, while the PTP values of front/rear SWS are 9.7% and 19.0% higher. While compared with the dual-chamber hydro-pneumatic suspension, the PTP values of left front/rear BA, DTL, and SWS decrease by 17.0%, 9.5%, 8.5%, 6.3%, 15.4%, and 16.5%, respectively. Therefore, the hydro-pneumatic ISD suspension can effectively suppress body vibration and improve ride comfort.Figure 7
Comparison of pulse input response for simulation.
(a)(b)(c)(d)(e)(f)Table 3
PTP values of pulse input response for simulation.
Performance indexSingle-chamberDual-chamberHydro-pneumatic ISDDrop I2 (%)Drop II3 (%)LF BA (m⋅s−2)6.084.894.0619.617.0LR BA (m⋅s−2)6.635.384.8727.09.5LF SWS (mm)41.2549.4945.27−9.78.5LR SWS (mm)28.6636.4034.09−19.06.3LF DTL (kN)2.862.472.0927.015.4LR DTL (kN)3.242.732.2829.616.5Drop I refers to the comparison between hydro-pneumatic ISD and single-chamber and can be calculated asS−H/S×100%, where “S” and “H” respectively represent the values of single-chamber and hydro-pneumatic ISD. Drop II refers to the comparison of hydro-pneumatic ISD and dual-chamber and can be calculated as D−H/D×100%, where “D” represents the values of dual-chamber. Drop I and II in Tables 4–6 are the same as this table.Table 4
RMS values of random input response for simulation.
Suspension typeLFBA (m s−2)LRBA (m s−2)LFSWS (mm)LRSWS (mm)LFDTL (mm)LRDTL (mm)Single-chamber1.451.492.362.285.586.16Dual-chamber1.191.222.562.464.835.39Hydro-pneumatic ISD1.081.112.432.354.314.88Drop I (%)25.525.5−3.0−3.122.820.8Drop II (%)9.29.05.14.510.89.5Table 5
PTP values of pulse input response for test.
Performance indexSingle-chamberDual-chamberHydro-pneumatic ISDDrop I (%)Drop II (%)Centroid acc. (m s−2)6.244.694.0235.614.3LF BA (m s−2)5.114.133.5730.113.6LR BA (m s−2)6.805.024.4334.911.8LF wheel acc. (m s−2)9.928.087.1927.511.0LR wheel acc. (m s−2)11.319.358.2427.111.9LF SWS (m)48.3063.4255.46−14.812.5LR SWS (m)53.8871.9764.86−20.49.9Pitch angle (deg)2.833.032.704.610.9Roll angle (deg)2.311.981.7524.211.6Table 6
RMS values of random input response for test.
VehicleSuspension typeCentroid acc.Speed (km h−1) (m s−2)LFSWS (mm)LRSWS (mm)LFBA (m s−2)LF wheelAcc. (m s−2)LRBA (m s−2)LR wheelAcc. (m s−2)PitchAngle (deg)RollAngle (deg) [0.04em]30Single-chamber1.132.231.971.5842.421.5036.530.160.25Dual-chamber0.942.462.211.2438.361.1732.780.130.21ISD0.852.312.041.0135.430.9730.110.110.18Drop I (%)24.8−3.6−3.636.116.535.317.631.228.0Drop II (%)9.66.17.718.57.617.18.115.414.340Single-chamber1.263.033.781.7044.881.6441.220.210.30Dual-chamber1.083.314.381.3540.461.2837.030.170.25ISD0.953.134.141.1337.291.0634.270.150.22Drop I (%)24.6−3.3−9.533.516.935.416.928.626.7Drop II (%)12.05.45.516.37.417.27.511.812.050Single-chamber1.383.454.551.7745.611.7345.570.260.36Dual-chamber1.203.995.281.4241.231.4141.130.220.31ISD1.063.734.841.1638.101.1837.680.190.27Drop I (%)23.2−8.1−6.434.516.531.817.326.925.0Drop II (%)11.76.58.318.37.616.38.413.612.9


### 4.2. Analysis for Random Response

To investigate the vibration response characteristics of hydro-pneumatic ISD suspension under random input conditions, the vehicle drives through a random road with a roughness coefficient of256×10−6m3 at a speed of u=30km/h.The simulation results are shown in Figure8 and Table 4. Compared with the single-chamber hydro-pneumatic suspension, the RMS values of left front/rear BA and DTL of the hydro-pneumatic ISD suspension under the random road input decrease by 25.5%, 25.5%, 22.8%, and 20.8%, respectively, while the RMS values of its front/rear SWS increase by 3.0% and 3.1%, while the RMS values of left front/rear BA, DTL, and SWS decreased by 9.2%, 9.0%, 5.1%, 4.5%, 10.8%, and 9.5% compared with the dual-chamber hydro-pneumatic suspension. These prove that the hydro-pneumatic ISD suspension can effectively suppress vehicle body vibration and improve ride comfort and safety.Figure 8
Comparison of random input response for simulation.
(a)(b)(c)(d)(e)(f)(g)


## 4.1. Analysis for Pulse Response

In order to research the vibration response characteristics of the hydro-pneumatic ISD suspension under pulse input conditions, the response to a pulse excitation simulates a vehicle passing the long waveform bump. Choosing the shape of the bump to be that of a haversine of heightA=0.1 m and length L=5m, and with vehicle speed set at u=30 km/h, this gives rise to the displacement input q=A/21−cos2πu/Lt0≤t≤L/u to the suspension.Figure7 and Table 3 show the time-domain response results of the system, according to which, the peak-to-peak (PTP) (the PTP values are calculated as max xt-min xt, where xt are values of the signal in a period.) values of the left front/rear body acceleration (BA) and dynamic tire load (DTL) of the hydro-pneumatic ISD suspension are 19.6%, 27.0%, 27.0%, and 29.6% lower than those of the single-chamber one, while the PTP values of front/rear SWS are 9.7% and 19.0% higher. While compared with the dual-chamber hydro-pneumatic suspension, the PTP values of left front/rear BA, DTL, and SWS decrease by 17.0%, 9.5%, 8.5%, 6.3%, 15.4%, and 16.5%, respectively. Therefore, the hydro-pneumatic ISD suspension can effectively suppress body vibration and improve ride comfort.Figure 7
Comparison of pulse input response for simulation.
(a)(b)(c)(d)(e)(f)Table 3
PTP values of pulse input response for simulation.
Performance indexSingle-chamberDual-chamberHydro-pneumatic ISDDrop I2 (%)Drop II3 (%)LF BA (m⋅s−2)6.084.894.0619.617.0LR BA (m⋅s−2)6.635.384.8727.09.5LF SWS (mm)41.2549.4945.27−9.78.5LR SWS (mm)28.6636.4034.09−19.06.3LF DTL (kN)2.862.472.0927.015.4LR DTL (kN)3.242.732.2829.616.5Drop I refers to the comparison between hydro-pneumatic ISD and single-chamber and can be calculated asS−H/S×100%, where “S” and “H” respectively represent the values of single-chamber and hydro-pneumatic ISD. Drop II refers to the comparison of hydro-pneumatic ISD and dual-chamber and can be calculated as D−H/D×100%, where “D” represents the values of dual-chamber. Drop I and II in Tables 4–6 are the same as this table.Table 4
RMS values of random input response for simulation.
Suspension typeLFBA (m s−2)LRBA (m s−2)LFSWS (mm)LRSWS (mm)LFDTL (mm)LRDTL (mm)Single-chamber1.451.492.362.285.586.16Dual-chamber1.191.222.562.464.835.39Hydro-pneumatic ISD1.081.112.432.354.314.88Drop I (%)25.525.5−3.0−3.122.820.8Drop II (%)9.29.05.14.510.89.5Table 5
PTP values of pulse input response for test.
Performance indexSingle-chamberDual-chamberHydro-pneumatic ISDDrop I (%)Drop II (%)Centroid acc. (m s−2)6.244.694.0235.614.3LF BA (m s−2)5.114.133.5730.113.6LR BA (m s−2)6.805.024.4334.911.8LF wheel acc. (m s−2)9.928.087.1927.511.0LR wheel acc. (m s−2)11.319.358.2427.111.9LF SWS (m)48.3063.4255.46−14.812.5LR SWS (m)53.8871.9764.86−20.49.9Pitch angle (deg)2.833.032.704.610.9Roll angle (deg)2.311.981.7524.211.6Table 6
RMS values of random input response for test.
VehicleSuspension typeCentroid acc.Speed (km h−1) (m s−2)LFSWS (mm)LRSWS (mm)LFBA (m s−2)LF wheelAcc. (m s−2)LRBA (m s−2)LR wheelAcc. (m s−2)PitchAngle (deg)RollAngle (deg) [0.04em]30Single-chamber1.132.231.971.5842.421.5036.530.160.25Dual-chamber0.942.462.211.2438.361.1732.780.130.21ISD0.852.312.041.0135.430.9730.110.110.18Drop I (%)24.8−3.6−3.636.116.535.317.631.228.0Drop II (%)9.66.17.718.57.617.18.115.414.340Single-chamber1.263.033.781.7044.881.6441.220.210.30Dual-chamber1.083.314.381.3540.461.2837.030.170.25ISD0.953.134.141.1337.291.0634.270.150.22Drop I (%)24.6−3.3−9.533.516.935.416.928.626.7Drop II (%)12.05.45.516.37.417.27.511.812.050Single-chamber1.383.454.551.7745.611.7345.570.260.36Dual-chamber1.203.995.281.4241.231.4141.130.220.31ISD1.063.734.841.1638.101.1837.680.190.27Drop I (%)23.2−8.1−6.434.516.531.817.326.925.0Drop II (%)11.76.58.318.37.616.38.413.612.9


## 4.2. Analysis for Random Response

To investigate the vibration response characteristics of hydro-pneumatic ISD suspension under random input conditions, the vehicle drives through a random road with a roughness coefficient of256×10−6m3 at a speed of u=30km/h.The simulation results are shown in Figure8 and Table 4. Compared with the single-chamber hydro-pneumatic suspension, the RMS values of left front/rear BA and DTL of the hydro-pneumatic ISD suspension under the random road input decrease by 25.5%, 25.5%, 22.8%, and 20.8%, respectively, while the RMS values of its front/rear SWS increase by 3.0% and 3.1%, while the RMS values of left front/rear BA, DTL, and SWS decreased by 9.2%, 9.0%, 5.1%, 4.5%, 10.8%, and 9.5% compared with the dual-chamber hydro-pneumatic suspension. These prove that the hydro-pneumatic ISD suspension can effectively suppress vehicle body vibration and improve ride comfort and safety.Figure 8
Comparison of random input response for simulation.
(a)(b)(c)(d)(e)(f)(g)


## 5. Bench Test System for Hydro-Pneumatic ISD Suspension

Figure9 shows the vehicle test system for hydro-pneumatic suspensions. The rear end of vehicle is equipped with a hydraulic pump, which is connected with the hydraulic part of the hydro-pneumatic ISD suspension by a high-pressure pipeline. The charging and discharging of the hydraulic pump can adjust the height of the hydro-pneumatic ISD suspension, and the high-pressure pipeline valve can switch the hydro-pneumatic suspension in single-chamber, dual-chamber, and ISD forms. The instruments used in this bench test are shown in Table 7.Figure 9
Vehicle test system for hydro-pneumatic suspensions.Table 7
Test instruments.
InstrumentFactoryModelPrecision/sensitivityRangeNumberAcceleration sensorsPCB33B301%5000 g4DEWE dynamic signal analyzerKistler43A1μs10 v1DEWE dynamic signal analyzerKistlerSIRIUS1μs10 v1CMOS laser displacement sensorKEYENCEIL30030μm290 mm2S-motion speedometerKistlerCSMOTA0.1%4 g1The PCB acceleration sensors used in the bench test are arranged in four positions, namely, the left front/left rear body and the left front/left rear wheel. In this way, the corresponding acceleration signals can be collected. The COMS laser displacement sensors are also installed on the left front/left rear body position, respectively, to capture signals of SWS. The S-motion speedometer is established on the right side of the vehicle body to acquire signals of the pitch and roll.The DEWE 43A and DEWE SIRIUS are used in the data collection instrument, with the former collecting the SWS signals from the laser displacement sensor, and the latter collecting vertical acceleration signals from vehicle body/wheel and the CAN signal of S-motion. The data acquisition process is shown in Figure10.Figure 10
Schematic of data acquisition.


## 6. Test Results and Performance Analysis

### 6.1. Test for Natural Frequency

The test adopts drop method to determine the natural frequency of ISD suspension. Throughout the test, the front and rear wheels of the test vehicle are ensured to be in the center of four excitation platforms of the MTS320 tire-coupled road simulator, with the height of excitation platform being set to balance position. Then, the excitation platform is controlled to unload abruptly and descend to the position of −60mm. Finally, the vehicle is dropped and kept free of vibration. Frequency analysis method is adopted to convert the time-domain response data into the system frequency-domain ones.Figure11 shows the frequency-domain response test curves of the suspension, according to which, the natural frequencies of front and rear body for the single- and dual-chamber hydro-pneumatic suspensions are 1.59 and 1.53 Hz and 1.34 and 1.36 Hz, respectively. The corresponding natural frequencies for hydro-pneumatic ISD suspension are 1.32 Hz and 1.37 Hz. Compared with the single-chamber hydro-pneumatic suspension, frequencies of the hydro-pneumatic ISD suspension have been reduced by 17.0% and 10.5%, respectively, and the peak power spectral density at the corresponding natural frequencies have been dropped by 65.4% and 61.2%, respectively. Compared with the dual-chamber hydro-pneumatic suspension, the front and rear body natural frequencies of the hydro-pneumatic ISD suspension have little change, with the peak values of the power spectral density at the corresponding natural frequency decreased by 35.5% and 31.4%, respectively. Therefore, the hydro-pneumatic ISD suspension is more beneficial in reducing the peak of the natural frequency, improving the low-frequency response and enhancing the vibration isolation performance.Figure 11
Comparison of natural frequency test results.
(a)(b)


### 6.2. Test for Pulse Input

The same pulse excitation as simulation in Section4.1 is taken as road input for this test. The test records for the time-domain response of each signal under pulse excitation are evaluated and analyzed by calculating the peak-to-peak (PTP) value. The test results for the vehicle at the speed of u = 30 km/h are shown in Figure 12, and the PTP values of test are presented in Table 5.Figure 12
Comparison of pulse input test results.
(a)(b)(c)(d)(e)(f)(g)(h)(i)These results show that compared with the single-chamber hydro-pneumatic suspension, the PTP values of pitch/roll angle and of vertical acceleration for the left front/rear wheel, the left front/rear body, and the centroid of the hydro-pneumatic ISD suspension are significantly dropped by 4.6%, 24.2%, 27.5%, 27.1%, 30.1%, and 34.9%, respectively; but the PTP values of front/rear SWS increased. Compared with the dual-chamber hydro-pneumatic suspension, the corresponding PTP values of the hydro-pneumatic ISD suspension are improved by 10.9%, 11.6%, 11.0%, 11.9%, 13.6%, 11.8%, 14.3%, 12.5%, and 9.9%, respectively. Apparently, the hydro-pneumatic ISD suspension can effectively decrease the vertical vibration of the vehicle body and wheel, and it can also enhance the SWS and the overall performance of the vehicle compared with the dual-chamber hydro-pneumatic suspension.


### 6.3. Test for Random Input

In this test, the responses to random excitation simulate a vehicle traveling on a stone block pavement at the speed of 30, 40, and 50 km/h. The test results are shown in Table6 and Figure 13.Figure 13
Comparison of random input test results.
(a)(b)(c)(d)(e)(f)(g)(h)(i)It can be seen from Table6 and Figure 13 that, compared with single-chamber hydro-pneumatic suspension, the RMS values of acceleration for the centroid, left front/left rear body, body pitch, and body roll of the hydro-pneumatic ISD suspension at the speed 30, 40, and 50 km/h are all reduced to different degrees with the maximum reduction reaching 35.3%, 35.4%, and 34.5%, respectively; only the RMS values of the left front/left rear SWS have a slight increase. These prove that hydro-pneumatic ISD suspension can effectively suppress vertical, pitch, and roll vibration of the body compared with single-chamber one. Moreover, the hydro-pneumatic ISD suspension can decrease vibration of the wheel, which can reflect road holding of a vehicle [29]; however, the SWS gets worse.Observe from Table6 and Figure 13 that compared with the dual-chamber hydro-pneumatic suspension, the RMS values of the hydro-pneumatic ISD suspension at the speed 30, 40, and 50 km/h are decreased by different degrees, with the maximum drop of 18.5%, 17.2%, and 18.3%, respectively. It turns out the hydro-pneumatic ISD suspension can effectively suppress vertical, pitch, and roll vibration of the body and also decrease the SWS to improve ride comfort and safety of the vehicle.


## 6.1. Test for Natural Frequency

The test adopts drop method to determine the natural frequency of ISD suspension. Throughout the test, the front and rear wheels of the test vehicle are ensured to be in the center of four excitation platforms of the MTS320 tire-coupled road simulator, with the height of excitation platform being set to balance position. Then, the excitation platform is controlled to unload abruptly and descend to the position of −60mm. Finally, the vehicle is dropped and kept free of vibration. Frequency analysis method is adopted to convert the time-domain response data into the system frequency-domain ones.Figure11 shows the frequency-domain response test curves of the suspension, according to which, the natural frequencies of front and rear body for the single- and dual-chamber hydro-pneumatic suspensions are 1.59 and 1.53 Hz and 1.34 and 1.36 Hz, respectively. The corresponding natural frequencies for hydro-pneumatic ISD suspension are 1.32 Hz and 1.37 Hz. Compared with the single-chamber hydro-pneumatic suspension, frequencies of the hydro-pneumatic ISD suspension have been reduced by 17.0% and 10.5%, respectively, and the peak power spectral density at the corresponding natural frequencies have been dropped by 65.4% and 61.2%, respectively. Compared with the dual-chamber hydro-pneumatic suspension, the front and rear body natural frequencies of the hydro-pneumatic ISD suspension have little change, with the peak values of the power spectral density at the corresponding natural frequency decreased by 35.5% and 31.4%, respectively. Therefore, the hydro-pneumatic ISD suspension is more beneficial in reducing the peak of the natural frequency, improving the low-frequency response and enhancing the vibration isolation performance.Figure 11
Comparison of natural frequency test results.
(a)(b)


## 6.2. Test for Pulse Input

The same pulse excitation as simulation in Section4.1 is taken as road input for this test. The test records for the time-domain response of each signal under pulse excitation are evaluated and analyzed by calculating the peak-to-peak (PTP) value. The test results for the vehicle at the speed of u = 30 km/h are shown in Figure 12, and the PTP values of test are presented in Table 5.Figure 12
Comparison of pulse input test results.
(a)(b)(c)(d)(e)(f)(g)(h)(i)These results show that compared with the single-chamber hydro-pneumatic suspension, the PTP values of pitch/roll angle and of vertical acceleration for the left front/rear wheel, the left front/rear body, and the centroid of the hydro-pneumatic ISD suspension are significantly dropped by 4.6%, 24.2%, 27.5%, 27.1%, 30.1%, and 34.9%, respectively; but the PTP values of front/rear SWS increased. Compared with the dual-chamber hydro-pneumatic suspension, the corresponding PTP values of the hydro-pneumatic ISD suspension are improved by 10.9%, 11.6%, 11.0%, 11.9%, 13.6%, 11.8%, 14.3%, 12.5%, and 9.9%, respectively. Apparently, the hydro-pneumatic ISD suspension can effectively decrease the vertical vibration of the vehicle body and wheel, and it can also enhance the SWS and the overall performance of the vehicle compared with the dual-chamber hydro-pneumatic suspension.


## 6.3. Test for Random Input

In this test, the responses to random excitation simulate a vehicle traveling on a stone block pavement at the speed of 30, 40, and 50 km/h. The test results are shown in Table6 and Figure 13.Figure 13
Comparison of random input test results.
(a)(b)(c)(d)(e)(f)(g)(h)(i)It can be seen from Table6 and Figure 13 that, compared with single-chamber hydro-pneumatic suspension, the RMS values of acceleration for the centroid, left front/left rear body, body pitch, and body roll of the hydro-pneumatic ISD suspension at the speed 30, 40, and 50 km/h are all reduced to different degrees with the maximum reduction reaching 35.3%, 35.4%, and 34.5%, respectively; only the RMS values of the left front/left rear SWS have a slight increase. These prove that hydro-pneumatic ISD suspension can effectively suppress vertical, pitch, and roll vibration of the body compared with single-chamber one. Moreover, the hydro-pneumatic ISD suspension can decrease vibration of the wheel, which can reflect road holding of a vehicle [29]; however, the SWS gets worse.Observe from Table6 and Figure 13 that compared with the dual-chamber hydro-pneumatic suspension, the RMS values of the hydro-pneumatic ISD suspension at the speed 30, 40, and 50 km/h are decreased by different degrees, with the maximum drop of 18.5%, 17.2%, and 18.3%, respectively. It turns out the hydro-pneumatic ISD suspension can effectively suppress vertical, pitch, and roll vibration of the body and also decrease the SWS to improve ride comfort and safety of the vehicle.


## 7. Conclusions

(1)
The full vehicle model of the hydro-pneumatic ISD suspension is established based on AMESim to investigate the performance differences between the hydro-pneumatic ISD suspension and the single-/dual-chamber hydro-pneumatic suspension. The simulation results suggest that the hydro-pneumatic ISD suspension can effectively decrease the vibration of vehicle body and SWS, thus improving driving comfort and safety compared with dual-chamber hydro-pneumatic suspension.(2)
The hydro-pneumatic ISD suspension test prototype was designed and developed, which is installed on the vehicle bench, and a bench test is carried out on the four-poster tire-coupled road simulator. The results show that, compared with the single-chamber hydro-pneumatic suspension, the hydro-pneumatic ISD one can significantly reduce the vibration of vehicle body and wheels, but it would remarkably increase the working space of suspension. Compared with the dual-chamber hydro-pneumatic suspension, the hydro-pneumatic ISD one can not only decrease the vibration of vehicle body and wheels but also reduce the working space of suspension. Thus, it can make driving much more comfortable and safe, and it has the potential to be used as an alternative technical scheme of dual-chamber hydro-pneumatic suspension. In the next research work, we will conduct road tests on real vehicles to check its comprehensive performance and lay the foundation for future applications in vehicles.



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*Source: 2095350-2021-11-03.xml*