Ride safety of a tracked vehicle is the key focus of this research. The factors that affect the ride safety of a vehicle are analyzed and evaluation parameters with their criteria are proposed. A multibody cosimulation approach is used to investigate the effects of hydropneumatic parameters on the ride safety and aid with design optimization and tuning of the suspension system. Based on the cosimulation environment, the vehicle multibody dynamics (MBD) model and the road model are developed using RecurDyn, which is linked to the hydropneumatic suspension model developed in Lab AMESim. Test verification of a single suspension unit is accomplished and the suspension parameters are implemented within the hydropneumatic model. Virtual tests on a G class road at different speeds are conducted. Effects of the accumulator charge pressure, damping diameter, and the track tensioning pressure on the ride safety are analyzed and quantified. This research shows that low accumulator charge pressure, improper damping diameter, and insufficient track tensioning pressure will deteriorate the ride safety. The results provide useful references for the optimal design and control of the parameters of a hydropneumatic suspension.
Hydropneumatics is a technology typically used in vehicle suspensions. A hydropneumatic suspension has good properties such as nonlinear stiffness and damping, high power density, convenient tuning, and vertical position locking. Thus, it is widely used in tracked vehicles and improves ride comfort. In practical applications, common failures are the track separating from the road wheel or the sprocket. These failures may result in the vehicle losing control and bring very serious implications in terms of vehicle ride safety.
Previous studies have done some dynamic simulation analysis on the issue of track separating from the road wheel. It has been shown that improper tuning of the suspension parameters is the main reason for such failures [
Determining the dynamic behavior of the track and its interactions with the hydropneumatic suspension system is very difficult to achieve mathematically. This is due to the complex nature of the nonlinear multibody system. Multibody dynamics (MBD) simulation has long been recognized as an excellent method to predict the dynamic response of vehicles [
The introduction of hydropneumatic suspension components that require extensive use of mathematical functions brings challenges for existing software that use the MBD approach and may restrict its use. MBD cosimulation gives a suitable framework for coupling software tools which specialize in different fields of mechanics without sacrificing overall accuracy, particularly if based on different mathematical methods [
The approach adopted here integrates the MBD software (RecurDynV8R3 [
On the basis of these conditions, the detailed mechanical configurations and hydropneumatic elements can be modeled more readily using a cosimulation approach. The enormous and complicated calculations relating to the dynamic behavior of flexible objects such as tracks can be fulfilled. This leads to more accurate relationships between the parameter variations and the output variables. In this paper, the hydraulicmechanical cosimulation on a virtual G road is conducted. Insights into how the hydropneumatic parameters affect the vehicle ride safety are achieved. The results can be readily used in the design, optimal control, and failure detection of a hydropneumatic suspension system.
This paper is organized as follows. A detailed description of the ride safety of tracked vehicles and the numerical model development is presented in Section
For a high mobility tracked vehicle, the suspension design and tuning should improve the ride comfort on the condition that the ride safety is guaranteed. From the point of view of surviving in the battlefield, the ride safety is generally more important than the ride comfort. The ride safety of wheeled vehicles is usually evaluated by the dynamic load of the wheel. In contrast to wheeled vehicles, the special structure of the track and its interactions with the running system brings new problems to the ride safety. The factors that affect ride safety and the evaluation parameters with their criteria are proposed as follows.
(1) Track separating from the road wheel or the sprocket: the failures of the track separating from the road wheel or the sprocket are usually caused by continuous running after the relative position of the track and the road wheel (sprocket) is skewed. The main causes may be (a) the gap between the track and the road wheel which is too large (often over the teeth height) usually caused by variations in the hydropneumatic suspension parameters, (b) the track excessive jumping caused by insufficient track tensioning force [
By comparing the above three causes, it is identified that the first two are more critical than the third. Thus, the trackwheel gap and the quantity of jumping are taken as evaluation parameters for determining whether track separation from the road wheel or sprocket has occurred.
(2) Endstop impact of suspension: at the endstop of the suspension the arm hits into the bumper [
(3) Wheelground adhesion ability: wheelground adhesion is evaluated by the relative dynamic load of the wheel, which is the ratio of the dynamic load and static load of the wheel. If the RMS of the ratio is more than 1/3, the wheel load on the road will be negative and the wheelground adhesion deteriorates [
As the values of the proposed evaluation parameters listed above belong to a Gaussian random distribution, a statistical metric is more meaningful for evaluating the ride safety. Table
Evaluation parameters and criteria of the ride safety.
Parameter  Symbol  Unit  Criteria 

RMS value of the trackwheel gap 

mm  <(1/3) height of the track teeth 
RMS value of the wheel dynamic force 

kN  <(1/3) static load of the road wheel 
RMS value of the stroke of the actuation cylinder 

mm  <(1/3) designed stroke length 
RMS value of the jumping quantity of the track 

mm  <(1/3) effective engage length between the track and the sprocket teeth 
As mentioned previously, a conventional calculation method based on the simplified mathematical model (high degree of linearization of the system stiffness and damping) is not suitable for a complicated nonlinear multibody system [
(1) Vehicle model: the vehicle components were first modeled using a CAD toolkit. Then, the model is exported to the RecurDyn, where the mass, joint constraints, and the motions are assigned. The model, which is shown in Figure
Vehicle dynamic model and G road model.
(2) Mechanical model of hydropneumatic suspension: the connection sketch of a single hydropneumatic suspension unit with the hull is shown in Figure
Connection sketch of hydropneumatic suspension.
Based on the configuration of Figure
In (
For the above expressions, the definition of the other variables and their initial values are given in Table
Suspension initial value of the design variables.
Variable  Symbol  Unit  Value 

Length of axle arm 

m  0.40 
Crank radius 

m  0.21 
Road wheel diameter 

m  0.60 
Angle of the axle arm from 

deg  −14.0 
Initial angle of the axle arm from 

deg  −28.0 
Angle of the axle arm from 

deg  30.0 
Designed displacement of the road wheel 

m  0.39 
Designed stroke of the actuation cylinder 

m  0.20 
Section area of the actuation cylinder 

m^{2}  4.4 × 10^{−3} 
Working pressure of the actuation cylinder 

Pa  Variable 
Standard atmosphere pressure 

Pa  1.01 × 10^{5} 
Displacement of the road wheel 

m  Variable 
The 

m  Variable 
Velocity of the actuation cylinder 

m/s  Variable 
Differential pressure of the hydraulic restrictor 

Pa  Variable 
Angle of the axle arm from 

deg  Variable 
Angle of the crank from 

deg  Variable 
The angle between the crank and the actuation cylinder 

deg  Variable 
The gas polytrophic exponent 

—  1.3 
(3) Road model: the road model is derived based on the technique of solid modeling. A road roughness coefficient is an evaluation index which determines the road class. The following formula is used as the fitting expression of the power spectral density function of the international standard road:
In this paper, G class road is used to conduct the virtual simulation. The road file is first written in Matlab and introduced to the RecurDyn as shown in Figure
The hydraulic system of the hydropneumatic suspension and the interface module are modeled using AMESim, as shown in Figure
Hydraulic system model of the hydropneumatic suspension.
(1) Mathematical model of the actuation cylinder: the output force of the actuation cylinder contains the gas spring force
The static friction force and the dynamic friction force are calculated from the following, respectively.
(2) Mathematical model of the damping tube: a long and thin damping tube is arranged between the actuation cylinder and the accumulator. According to the theory of hydraulic fluid dynamics, the pressure loss through the tube can be written as [
(3) Mathematical model of the accumulator: the gas chamber of the accumulator is filled with pressurized nitrogen. The state changing process of the gas can be described by the following equation.
If the accumulator is loaded or unloaded rapidly, the thermodynamic process of the gas state change belongs to an adiabatic process and the value of the polytrophic exponent is
(4) Interface module: the function of the interface module is to carry out the exchange of the simulation data between the two simulation platforms, namely, RecurDyn and AMESim. Here, each program executes its respective simulation simultaneously. At each time step (0.001 sec), both codes update one another with new state values before advancing to the next step. Simulations begin when RecurDyn calculates the stroke and velocity of the actuation cylinder. The hydropneumatic system in AMESim calculates the force of the actuation cylinder and feed it back to the MBD vehicle model.
The interface module has 14 input ports and 28 output ports. The input ports
In order to validate the model, a single hydropneumatic unit is tested using the suspension test rig shown in Figure
Initial value of hydraulic variables.
Hydraulic variables  Symbol  Unit  Value 

Initial charge pressure of the accumulator 

Pa  6.8 × 10^{6} 
Volume of the accumulator 

m^{3}  0.85 × 10^{−3} 
Length of the damping tube 

m  1.2 
Flow diameter of the damping tube 

m  6 × 10^{−3} 
Section area of the actuation cylinder 

m^{2}  4.4 × 10^{−3} 
Initial track tensioning pressure 

Pa  6.2 × 10^{6} 
Section area of the track tensioning cylinder 

m^{2}  2.0 × 10^{−3} 
Density of the oil 

kg/m^{3}  0.87 × 10^{3} 
Kinematic viscosity of the oil 

cSt  10 
Test rig of the hydropneumatic suspension.
Modeling and simulation of the vehicle traversing a barrier.
Figure
Test and simulation results of the stroke.
The test and simulation results of the road wheel’s (
Test and simulation results of the road wheel acceleration.
Using the modeling and simulation environment, the virtual tests on the G road are conducted under different conditions such as vehicle speed, flow diameter of the damping tube; accumulator charge pressure, and track tensioning pressure. The influences of the above parameters on the vehicle ride safety are investigated.
The damping of the hydropneumatic suspension is directly set by the flow diameter (
The RMS value of the trackwheel gap versus the flow diameter.
Similar to Figure
The RMS value of the road wheel dynamic force versus the flow diameter for various speeds.
The RMS value of the stroke (
The RMS value of the stroke versus the flow diameter for various speeds.
The accumulator charge pressure determines the basic stiffness of the suspension. Through simulations and analysis of various charge pressures, the effects of the charge pressure on the RMS value of the trackwheel gap, the road wheel dynamic force, and the stroke are obtained.
Figure
The RMS value of the trackwheel gap versus the accumulator charge pressure.
Variations of the RMS value of the road wheel dynamic force (
The RMS value of the road wheel dynamic force versus the accumulator charge pressure for various speeds.
The RMS value of the stroke (
The RMS value of the stroke versus the accumulator charge pressure for various speeds.
The track tensioning force and its fluctuations play an important role in the ride safety of the vehicle. A decline of tensioning force will cause a rise in fluctuations and more frequent track jumping from the sprocket. Thus, the failure of the track separating from the sprocket will occur. In the hydropneumatic suspension system, a pair of hydraulic tensioning cylinders is used to adjust the track. The tensioning force is directly related to the actuating pressure
The RMS value of jumping quantity (
The standard deviation of track tension force and the RMS value of jumping quantity versus the actuating pressure of the track tensioning cylinder.
Factors which influence the ride safety of a tracked vehicle are analyzed. Systematic evaluation parameters of ride safety and their criteria are proposed. Using a cosimulation technique, the vehicle MBD model and the hydropneumatic suspension model are built and verified. Through simulations at various vehicle speeds, accumulator charge pressures, and damping diameters, the effect they have on ride safety are investigated and quantified. The key conclusions are as follows.
Different optimal damping parameters exist for the minimum wheeltrack gap and the wheel dynamic force at different vehicle speeds. The value of the optimal diameter decreases as the vehicle speed increases. If the diameter is not tuned well, the dynamic wheel force at a low speed may be higher than that at a high speed.
As the accumulator charge pressure decreases, the RMS value of the wheeltrack gap and the stroke increases but the RMS value of road wheel dynamic force decreases. For the hydropneumatic suspension studied in this paper, when the pressure drops below about 2 MPa, the probability of the endstop impact of the suspension increases significantly.
As the actuating pressure of the track tensioning cylinder decreases, the track tensioning force decreases. An insufficient tensioning force leads to a looser track, a rise in fluctuations, and more frequent track jumping from the sprocket. Thus, the ride safety deteriorates. In order to improve the ride safety, the track tensioning force should be increased sufficiently.
The authors declare that there are no conflicts of interest regarding the publication of this manuscript.