Study and simulation stability of the vehicle body with the air suspension

https //iaeme com/Home/journal/IJETR 26 editor@iaeme com International Journal of Engineering and Technology Research (IJETR) Volume 7, Issue 1, January December 2022, pp 26 34, Article ID IJETR 07 01[.]

Available online at https://iaeme.com/Home/issue/IJETR?Volume=7&Issue=1

ISSN Print: 2347-8292 and ISSN Online: 2347-4904

DOI: https://doi.org/10.17605/OSF.IO/BV49A

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STUDY AND SIMULATION STABILITY OF THE VEHICLE BODY WITH THE AIR SUSPENSION

Truong Ho Xuan

Dong Nai Technology University, Vietnam

ABSTRACT

The article mentions to the content of the study simulation stability trunk with air suspension uses Matlab Simulink software, the study effects of air suspension system to stability trunk when the vehicle is moving Since we conduct simulated stability truck control with air suspension based on parameters Mobihome HB120SSL Thaco bus Results thesis has successfully built a simulation model for stability trunk in linear motion on vehicle specifications Thaco Mobihome HB120SSL, survey control changes

in these parameters as the stiffness of the air suspension system helps stability trunk when the vehicle moves The simulation results indicate that, when using the air suspension system can change the parameters of the elastic member stiffness according

to the distribution of the load on the wheels, thereby limiting air suspension get the trunk moving at the wheel, greatly improving the stability of the trunk when Thaco Mobihome HB120SSL bus move

Key words: Air suspension system, stability trunk, vertical stability, horizontal stability Cite this Article: Truong Ho Xuan, Study and Simulation Stability of the Vehicle Body

with the Air Suspension, International Journal of Engineering and Technology

Research (IJETR) 7(1), 2022, pp 26-34

https://iaeme.com/Home/issue/IJETR?Volume=7&Issue=1

1 INTRODUCTION

The stability of the vehicle body will determine the comfort and safety of passengers Therefore, this issue is of great concern to manufacturers [1-3] There are many solutions proposed to improve vehicle stability, but the method of using controlled air suspension to change the stiffness of the elastomer is the most effective method in improving efficiency stable results The air suspension system can independently control the operation of the airbags at each wheel, allowing the suspension to adapt to different loads while keeping the body in balance [3-7] Therefore, the study of the air suspension system on the vehicle models will evaluate the feature of improving the stability of the vehicle using the air suspension [8] On the basis of this research, it is possible to make recommendations to improve the performance of the air suspension system and improve the safety and stability of the automobile [9]

2 THEORETICAL BASIS

2.1 Air Suspension Elastic Characteristics

Figure 1 Pressure change in the air bags

In there:

Fzs: Vertical load acting on the airbag(N)

Fzs(0): Vertical load in static state (N)

pa: Atmospheric pressure (N/cm2)

p0: Air pressure in the airbag in a stationary state (N/cm2)

p: Compressed air pressure in the air bag (N/cm2)

A: Airbag working surface area (cm2)

The load acting on the airbag is determined by the formula [1],[2]: 𝐹𝑧𝑠 = (𝑝 − 𝑝𝑎) 𝐴 [N] (1.1)

When compressed, the piston moves a distance ∆z We have the volume of the compressed air chamber in the instantaneous state:

Pneumatic pressure at variable load is determined:

𝑝 =𝐹𝑧𝑠+𝑝𝑎.𝐴

𝐴 [ 𝑁

In the working state with variable load F = 𝐹𝑧𝑠 placed on the elastic chamber, the stiffness

of the elastic chamber is determined:

𝐶 =𝑛(𝐹𝑧𝑠+𝑝𝑎.𝐴)𝐴

𝑉 =𝑛.𝑝.𝐴2

𝑉 (1.4)

In there:

• n: adiabatic coefficient of the gas

• C: airbag stiffness in working state

2.2 Computational Model of Vehicle Body Stability in Straight Motion with Constant Acceleration

Figure 2 Car model moving in a straight line with constant acceleration

Symbols on the figure:

Vehicle coordinate system (XV, ZV), road coordinate system (X, Z)

h v (0) : Base height (m)

∆ℎ𝑣: Lifting center of gravity of the body (m)

∆ℎ12, ∆ℎ34 : Lift of the front and rear axles (m)

ℎ𝑘𝑖 : Distance from wheel center i to road surface (m)

𝑉 : Body tilt angle (rad)

l, a v , b v : The base dimensions of the car (m)

G v = m v g: Body weight at center of gravity (N)

Vx, dx : Velocity and acceleration in the direction X (km/h), (m/s 2)

𝐹𝑋𝐸12, 𝐹𝑋𝐸34: Tangential traction force at front and rear wheels (N)

𝐹𝑍12, 𝐹𝑍34: Normal reaction at front and rear wheels (N)

m v dx : axial inertia forceX (N)

R d12 (0) , R d34 (0) : base kinematic radius with dx=0 (m)

G k12 ,G k34 : Weight of front and rear wheels (N)

m k12 ,m k34 : Weight of front and rear wheels (kg)

D k12 ,Dx k34 : Force of inertia at the center of the front and rear wheels (N)

The body tilt angle can be determined from the calculation model:

𝑉 = ∆ℎ34 −∆ℎ 12

ℓ (1.5) Load changes on the elastomers on the front and rear

axles:

{

∆𝐹𝑧12𝑠 = −1

𝑖12[

(𝑚 𝑣 ℎ𝑣(0)+𝑚 𝐾12 ℎ 𝐾12 +𝑚 𝐾34 ℎ 𝐾34 )𝑑𝑥

𝑙

−ℎ𝑋𝑍12 −𝑅 𝑑12

𝑃𝑋𝑍12 𝐹𝑋𝑆12+ℎ𝑋𝑍12 −𝑅 𝑑12

𝑃𝑋𝑍12 𝐵𝐸12

]

∆𝐹𝑧34𝑠 = −1

𝑖 34[ −

(𝑚𝑣.ℎ𝑣(0)+𝑚𝐾12.ℎ𝐾12+𝑚𝐾34.ℎ𝐾34)𝑑𝑥

𝑙

−ℎ𝑋𝑍34 −𝑅𝑑34

𝑃 𝑋𝑍134 𝐹𝑋𝑆34+ℎ𝑋𝑍34 −𝑅𝑑34

𝑃 𝑋𝑍12 𝐵𝐸34

] (1.6)

The equation describing the body displacement at the front and rear wheels is as follows:

{

∆ℎ12 = −∆𝑍𝑉𝑆12= −∆𝐹𝑧12𝑠

2𝑖122 .𝐶 12

∆ℎ34 = −∆𝑍𝑉𝑆34 = −∆𝐹𝑧34𝑠

2𝑖342 .𝐶34 (1.7)

2.3 Body balance Control with Air Suspension in Straight Motion

From the vehicle body stability model in straight motion, we can see that when the vehicle is moving in a straight line with constant acceleration, there are movements of the body at the wheels Through problem analysis, these displacements are mainly due to suspension deformation and are the main cause of vehicle body instability when in motion We already know that the deformation of the suspension is related to the elastic or stiffness characteristics

of the suspension in use In this content, the control equations will be given to change the parameters of the air suspension system to help the body balance

We have the formula to determine the airbag pressure of the front and rear suspension systems:[3]

{

𝑝12=𝐹𝑧12𝑠 +𝑝𝑎.𝐴12

𝐴 12

𝑝34=𝐹𝑧34𝑠 +𝑝 𝑎 𝐴 34

𝐴 34

[ 𝑁

𝑐𝑚 2] (2.1) Gas volume change:

Figure 3 Change of gas mass when the load changes [7]

From the above general formula, we can determine the required air flow in the air bags in the front and rear axles corresponding to the instantaneous pressure 𝑝𝑖 as follows:

{𝑚12=

𝜇.𝑝 12 𝑉 (0)12

𝑅.𝑇

𝑚34 =𝜇.𝑝34.𝑉(0)34

𝑅.𝑇 (2.2)

In there:

𝑚12, 𝑚34: mass of air in the air bags when the vehicle body is in equilibrium (kg)

𝑉(0)12, 𝑉(0)34: volume of air bags in the static state in front and rear axles (l)

𝑝12, 𝑝34: The airbag pressure when the load is applied is 𝐹𝑧𝑠.(atm)

R: ideal gas constant (R = 0.082)

T: absolute temperature (T = 273+27) (K)

𝜇: Molar mass of air (𝜇 ≈ 0.029 kg/mol)

The required stiffness C of the air suspension elastic chambers on the front and rear axles for the body to be balanced is determined by [4], [5]:

{

𝐶12 =𝑛(𝐹𝑧12𝑠 +𝑝 𝑎 𝐴 12 )𝐴 12

𝑉(0)12

𝐶34= 𝑛(𝐹𝑧34𝑠 +𝑝 𝑎 𝐴 34 )𝐴 34

𝑉(0)34

(2.3)

Figure 4 Simulation model of vehicle body stability when moving in a straight line in Matlab

Simulink [8], [9]

3 SIMULATION RESULTS IN RECTILINEAR MOTION

3.1 The Case when the Car Accelerates dx >0

Figure 4 Graph of the load change on the elastic member

From the resulting graph (Figure 4), we can see that when the vehicle moves faster with constant acceleration, it will increase the load distributed on the front axle and reduce the distributed load on the rear axle If the suspension spring stiffness is constant, then body movements at the wheels begin to occur due to the change in the load on the suspension We have a graph describing the body displacements and load changes on the front and rear airbags after towing

Suspension Airbag Pressure

For the air suspension system, the load acting on the air bags will determine the air pressure inside the air bags So when there is a change in the load ∆𝐹𝑖 acting on the front and rear suspension airbags, the rear axle will change the pressure in the airbag The change of pressure

is described according to the graph of simulation results (Figure 5)

Figure 5: Pressure changes at the air bags of the suspension system

Figure 5 shows: When the vehicle moves with greater acceleration, the air pressure gradually decreases inside the air bags in the front axle and gradually increases in the rear air bags The change in pressure will be proportional to the increase or decrease of the load acting

on the suspension systems

With the airbag volume controlled to the original volume by the control of the air suspension system Meanwhile, the air pressure inside the airbag changes, which will lead to the change in the stiffness 𝐶𝑖 of the air bags (Figure 6) The stiffness of the front air bags will decrease with the decrease of load as the vehicle accelerates, whereas the stiffness of the rear airbag will increase with the increase of the load This will help the air suspension system reduce body movements at the front and rear axles

Figure 6 Changes in the stiffness of the suspension airbag during towing

Comment

From the simulation results of vehicle body stability on Thaco Mobihome HB120SSL passenger car in straight movement when towing, we draw the following general comments:

In order for Thaco Mobihome passenger car to maintain equilibrium when traveling with acceleration (dx = 7 m/s2), the air suspension system needs to control to increase the 𝐶𝑖 stiffness

of the rear airbags to increase by 47.2 % and reduced stiffness in the front air bags by 52% (Figure 6) through changes in air pressure and air mass at the air bags

3.2 The case when the car brakes dx < 0

When the car performs the braking process, it will produce an inertial force in the same direction

as the vehicle's motion Under the influence of external forces, the load will change on the suspension system at the axles (Figure 7)

Figure 7: The change of normal force on the elastic part when braking

From the graph we can see: When the car brakes, the load distributed on the airbags in the front axle increases due to the inertia of the vehicle's mass moving forward and the load on the rear axle will decrease This means that body movements appear on the front and rear axles When the load acting on the air bags changes, the pressure and volume of the air bags in the front and rear axles will change The pressure of the front air bags will increase due to the increased load distributed on the front axle and vice versa, the rear airbag pressure will decrease due to the reduced load distributed on the rear axle (Figure 8) At the same time when braking, the load distributed on the front airbag increases, reducing the volume of the front airbag, the reduced load on the rear axle increases the volume of the rear airbag To return the airbags to their original height, the air suspension system must control the increase in air mass in the front suspension airbags and decrease in the air mass in the rear suspension air bags With the control

of the change in air mass and combined with the change in the pressure in the air bags, the stiffness of the front and rear airbags begins to change (Figure 9)

Figure 8: Graph of airbag pressure change when braking

From the graph of the change in stiffness (Figure 9) of the airbags when the vehicle is

acceleration, this helps to reduce the deformation of front suspension system The stiffness of the rear suspension airbag is somewhat reduced, Which make the rear suspension airbags softer, limiting movement to help the body return to a balanced position

Figure 9: Stiffness of the suspension airbags during braking

Comments

From the simulation results of vehicle body stability on Thaco Mobihome HB120SSL passenger car in straight movement when braking, we have the following general comments:

In order to maintain the body balance for Thaco Mobihome passenger car when braking with acceleration (dx = -7 m/s2), the control air suspension system increases the stiffness of the front airbag to 62.84% (Figure 9) reduces body displacement at the front axle As for the rear suspension airbags, the controlled air suspension reduces the stiffness of the rear airbag by 12.37% to reduce body movement at the rear axle

4 CONCLUSION

The influence of the suspension elastomer stiffness parameter on the balance of the vehicle body during movement is very large It largely determines the magnitude of the body movements at the wheels when the load on the wheels changes, the value of these displacements

is inversely proportional to the stiffness of the suspension

The application of air suspension system on Thaco Mobihome HB120SSL passenger car is completely capable of improving body stability in motion It helps to reduce the body tilt angle, improve safety and comfort for passengers

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