Performance Evaluation of a Novel Hydro-Pneumatic Suspension System of a Heavy Truck on Ride Comfort

The purpose of this work is to evaluate the performance of novel hydrfo-pneumatic suspension system (HPSs) in comparison with traditional hydro-pneumatic fsuspension system (HPSs) of a heavy truck in the direction of improving vehicle ride comfort. Firstly, the nonlinear dynamic models of the traditional and novel HPS systems are set up to determine the vertical forces. And then, the vertical forces are connected with a 3-D nonlinear dynamic model of heavy truck with 10 degrees of freedom under random excitation of road surface. The root mean square (RMS) acceleration responses of the vertical cab, pitch and roll angles of the cab (awzcb, awfcb and awtcb) based on the International Standard ISO 2631-1: 1997 are chosen as objective functions. The study results show that the awzcb, awfcb and awtcb values with novel HPSs reduce by 28.27%, 28.32% and 6.89% in comparison with traditional HPSs when vehicle moves on ISO class D road surface at vehicle speed of 50 km/h and full load. Finally, the ride performance of novel HPSs is verified and compared and evaluated with traditional HPSs under different operating conditions and the evaluation results are also indicated that the ride performance of a novel HPSs is better than the traditional HPSs under survey conditions.


Introduction
Hydro-pneumatic suspension systems (HPS) are used more and more widely on heavy truck due to their advantages. Heavy trucks often operate in mine areas where the road surface conditions are not good, so improving the ride comfort of vehicles is always interested in research. Due to the viscous resistance of the fluid and the compressibility of gas the damping and stiffness coefficient of the HPS are adjusted when vehicles operate with different conditions. Research to improve the performance of HPS has been studied many scientists. The nonlinear factors of the HPS were considered to improve the precise determination the height of the HPS in the process control [1]. The effects of hydro-pneumatic parameters on the ride safety and aid with design optimization and tuning of the suspension system were investigated based on the cosimulation environment, the vehicle multi body dynamics (MBD) model and the road model [2]. A multi-cylinder hydro-pneumatic suspension system was proposed and analyzed their design parameters based on an inplane multi-body dynamics (MBD) model and road model [3]. The effect of various suspension parameters on storage stiffness and damping coefficient of a dual-chamber hydro-pneumatic suspension was analyzed using numerical simulation [4]. A Hydro-Pneumatic (HP) suspension system interconnected for load sharing in heavy vehicles was analyzed based on the nonlinear mathematical model of a three-axle heavy vehicle [5]. The parameter optimization of the hydro-pneumatic suspension was found out to obtain the minimum root mean square of vertical accelerations under different driving conditions based on the multi body model of the wheel loader [6]. The damping force property of the hydro-pneumatic suspension system under different fractional orders was proposed and analyzed using a hydropneumatic suspension model based on fractional order [7]. A novel suspension configuration with both hydraulically interconnected suspension and electronic controlled air spring was proposed and controlled through the height of the elastic part using a fuzzy controller based on a 9-degree-of-freedom vehicle multi-body model [8]. The semi-active hydro-pneumatic suspension proposed and controlled by fuzzy controller [12]. This study proposes a novel HPSs which is developed the traditional HPS by connecting a main air chamber and an auxiliary air chamber through the surge pipe which has more the elasticity of gas and nonlinear viscous damper and the friction damper of the air in the surge pipe for controlling the nonlinear stiffness and damping coefficients of the novel HPS when vehicle operates under the different conditions. Firstly, the nonlinear dynamic models of the traditional and novel HPS systems are set up to determine the vertical forces. And then, a 3-D nonlinear dynamic model of heavy truck with 10 degrees of freedom (DOFs) is set up under random road surface roughness according to ISO 8608(1995) [9]. The root mean square (RMS) acceleration responses of the vertical cabin, pitch and roll angles of the cab (a wzcb , a wfcb and a wtcb ) based on the International Standard ISO 2631-1: 1997 [11] are chosen as objective functions. Finally, the ride performance of the novel HPSs is evaluated and compared to the traditional HPSs under different operating conditions.

Model of hydro-pneumatic suspension systems
In the traditional HPSs, the stiffness force of the suspension system is formed by the elasticity of air chamber and the damping force of the suspension system is formed by the viscous of the oil through the orifice of combined piston. In addition to the same characteristics of traditional HPS, in the novel HPS, the stiffness coefficient of the suspension system is formed more by the elasticity of air in surge pipe and reservoir and the damping is created more by the nonlinear viscous damper and the friction damper of the air in the surge pipe. The structural diagrams of the traditional and novel HPS are shown in Where, F k and F c are the elastic and damping force of the traditional HPS The elastic force (F k ) of the traditional HPS is formed by the compressive property of the gas in air chamber which is calculated based on the laws of thermodynamics method.
The pressure in air chamber is defined as an adiabatic process following the laws of thermodynamics Where, p 0 and V 0 are the initial absolute pressure and volume in air chamber, p a and V a are the absolute pressure and volume in air chamber, n is the polytrophic rate (1< n<1.4).
Combination of Eq. (2) and Eq. (4), the elastic force of the gas chamber of the traditional HPS is determined as The damping force (F c ) of the traditional HPS is formed by the viscous of the oil through the orifice of combined piston. It can be calculated as where, A b , A c , and A p are the area of cylinder, rod and floating piston, p b and p c are pressure in the main and ring oil chamber.
The flow rate through the orifice is calculated as where, C d is coefficient of discharge, A is the area of the orifice, cylinder and floating piston and ρ is the density of oil.
On the basic of volume balance, the flow rate is inferred as From Eq. (7) and Eq. (8), the relationship p 1 and p 2 is determined as The differential motion equation of floating piston can be defined as Combination of Eq. (6), Eq. (9) and Eq. (10), the damping force is computed as

The vertical dynamic force of the novel HPS
Due to the influence of the nonlinear viscous damper, friction damper and the elasticity of the air in the surge pipe, the elastic and the damping force of the novel HPS is changed in comparison with traditional HPS. The vertical dynamic force of novel HPS (F hn ) could be determined as Where, F kn , F cn are the elastic and damping force of the novel HPS The elasticity of the gas in air chamber, the reservoir and surge pipe create the elastic force of the novel HPS. The elastic force of the novel HPS is defined as where, the static, viscous stiffness constants (K e , K v ) and the mass (M) [14,15] could be calculated as: where, n is the polytropic rate (1 <n< 1.4); p 0 is the initial absolute pressure in air chamber;  a is the air density; V 0 and V r0 are initial volume of air chamber and reservoir.
The model parameter C z is related to the velocity over the damper and not like C s to the velocity in the surge pipe. The vertical viscous force is written as The Eq. (15) can be rewritten as The relationship between the nonlinear damping C z and the damping c s caused by the flow in the surge pipe is defined: Where, C st is total loss coefficient, C fr , C e , C c , C b are the loss coefficient due to friction, enlargement, contraction and bends in the pipe,  is viscous damping parameter.

The motion equation of vehicle model
A structural diagram of a heavy truck is shown Fig.3 which consist of front and rear axles, vehicle body, cab, four hydro-pneumatic suspension struts of vehicle and four isolation systems of cab. A three-dimensional vehicle-road coupled dynamic model of a heavy vehicle (a mining dump truck) with 10 degrees of freedom under random road surface roughness is set up to analyze the effectiveness of HPSs compared to the traditional HPS in the direction of the ride comfort of vehicle, as shown in Fig.3., which consists of the tire stiffness and damping coefficients k ti and c ti , the stiffness and damping coefficients of HPSs k i and c i , the stiffness and damping coefficients of cab isolation system k ci and c ci , the vertical displacements of front axle, rear axle, vehicle body, cab, z a1 , z 1 , z 2 , z b and z c , the angular displacements of axles, vehicle and cab bodies,  a1 ,  a2 ,  b ,  b and  c ,  c , the inertia moments of axle, vehicle and cab masses I ax1 , I ax2 , I bx , I by and I cx , I cy , the distances l j and the road surface excitations q i (i=1÷4, j=1÷10). From the full-vehicle dynamic model of Fig.3, the motion equations of two axle masses, vehicle body mass and cab body mass are written using Newton's second law. The general dynamic differential equation for the 2-axle heavy truck is given by the following matrix form

Random road surface excitation
There are several methods for modeling road surface roughness according to different theories, such as the harmonic superposition method, the filtering white noise and AR method [13][14][15][16][17]. In this study, the random road surface roughness of random white noise is selected as excitation source waveform for vehicle suspension [16], the random road profile is produced by filtering the white noise using the following mathematical model of the road roughness where, G q (n 0 ) is the road roughness coefficient which is defined for typical road classes from A to E according to ISO 8608(1995) [9], n 0 is a reference spatial frequency which is equal to 0.1 m; v is the speed of vehicle; f 0 is a minimal boundary frequency with a value of 0.0628 Hz; n 0 is a reference spatial frequency which is equal to 0.1 m; w(t) is a white noise signal.  Vehicle ride comfort indicator is based on ISO 2631-1 (1997) [11], vibration evaluation based on the basic evaluation method, the RMS acceleration is determined as where, a(t) is the weighted acceleration (translational and rotational) as a function of time, m/s 2 ; T is the duration of the measurements. The percent reduction of the a wzcb , a wfcb and a wtcb values with novel and traditional HPS systems are shown in Table 1 under the different road surface conditions. The calculation results in Table 1 show that vehicle ride comfort with novel HPSs is much better than traditional HPSs under the different road surface conditions.   In this study, a novel HPSs which was developed the traditional HPS by connecting a main air chamber and an auxiliary air chamber through the surge pipe was proposed as well as the mathematical models of traditional and novel HPS are established to determine their vertical forces. The ride performance of the novel HPSs was evaluated and compared to that of traditional HPSs based on a nonlinear dynamic model of heavy truck with 10 degrees of freedom (DOFs) under different operating conditions. Some conclusions could be drawn from the comparison and evaluation results: (1) The a wzcb , a wfcb and a wtcb values with novel HPSs reduced by 28.27%, 28.32% and 6.89% in comparison with the traditional HPSs when vehicle moves on ISO class D road surface at speed of 50 km/h and full load, (2) The a wzcb , a wfcb and a wtcb values with the novel HPSs respectively reduced in comparison with traditional HPSs under the different road surface, and (3) The a wzcb , a wfcb and a wtcb values with the novel HPSs respectively reduced in comparison with traditional HPSs at the different vehicle speeds.