An investigation of the samco primas buss ride comfort by using the quarter car model with linear asymmetric damper

--- DINH DUY LE AN INVESTIGATION OF THE SAMCO PRIMAS BUS’S RIDE COMFORT BY USING THE QUARTER CAR MODEL WITH LINEAR ASYMMETRIC DAMPER Discipline: Vehicle Engineering Major code: 852011

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DINH DUY LE

AN INVESTIGATION OF THE SAMCO PRIMAS BUS’S RIDE COMFORT BY USING THE QUARTER CAR MODEL

WITH LINEAR ASYMMETRIC DAMPER

Discipline: Vehicle Engineering Major code: 8520116

MASTER’S THESIS

HO CHI MINH CITY, July, 2022

UNIVERSITY OF TECHNOLOGY – VNU – HCM CITY

Instructor: Trần Hữu Nhân, Ph.D

Examiner 1: Hồng Đức Thông, Ph.D

Examiner 2: Nguyễn Văn Trạng, Ph.D

Master’s thesis was defended at Ho Chi Minh City University of Technology, VNU-HCM on July 26th, 2022

The board of the Master’s Thesis Defense Council includes:

1 Chairman: Lê Đình Tuân, Assoc.Prof.Ph.D

2 Member: Võ Tấn Châu, Ph.D

3 Secretary: Lê Tất Hiển, Assoc.Prof.Ph.D

4 Reviewer 1: Hồng Đức Thông, Ph.D

5 Reviewer 2: Nguyễn Văn Trạng, Ph.D

Verification of the Chairman of the Master’s Thesis Defense Council and the Dean

of Faculty of Transportation Engineering after the thesis being corrected (If any)

CHAIRMAN DEAN - FACULTY OF

OF THE COUNCIL TRANSPORTATION ENGINEERING

UNIVERSITY OF TECHNOLOGY

THE TASK SHEET OF MASTER’S THESIS

Full name: Lê Đình Duy Studen code: 1870435 Date of Birth: 07/07/1996 Place of birth: Tiền Giang Major: Vehicle Engineering Major code: 8520116

I THESIS TOPIC: An investigation of the samco primas bus’s ride comfort by

using the quarter car model with linear asymmetric damper

ĐỀ TÀI LUẬN VĂN : Phân tích, đánh giá độ êm dịu của xe khách Samco

Primas bằng mô hình động lực học ¼ xe với giảm chấn thay đổi

II TASKS AND CONTENTS:

1 Research on theoretical basis of the dynamic model with the asymmetric damper

2 Calculate for both cases of random road profile and single bump road profile

3 Conduct simulation, analysis accordance with the suspension system's ride comfort and safety standards

4 Get full understanding of the effect of asymmetric damper on the ride comfort, safety and hanlding control of the suspension system

III TASKS STARTING DATE: September 06th, 2021

IV TASKS ENDING DATE: July 14th 2022

VIII INSTRUCTOR: Trần Hữu Nhân, Ph.D

Ho Chi Minh City, July 14

2022

INSTRUCTOR

(Full name & Signature)

HEAD OF DEPARTMENT

(Full name & Signature)

DEAN - FACULTY OF TRANSPORTATION ENGINEERING

(Full name & Signature)

ACKNOWLEDGMENTS

I would like to thank my mentor Dr Huu Nhan TRAN who instructed me throughout my work His motivation, patience, direct involvement in the research topic and, above all, friendly nature helped me to complete this work His vibration expertise in the automotive engineering field helped me at solving a large number of points throughtout this research I appreciate the guidance he offered me attain a higher level of maturity in my research work Futhermore, his valuable suggestions regarding different aspects of life will be helpful, and his insightful advice on several aspects of life will benefit me throughout my career path

Next, I would like to thank all Faculty of Transportation Engineering members for supporting me in procedures and carrying out experiments during my Research-based Master’s Program I am also indebted to my family, without their cooperation and financial support, pursuing a Master’s degree would have been impossible

Apart from these people, I am grateful to other departments at Ho Chi Minh City University of Technology for helping me with some computational problem that I faced in my research

Finally, I acknowledge Ho Chi Minh City University of Technology (HCMUT), VNU-HCM for supporting this study I thank them all

Ho Chi Minh City, July, 2022

Researcher,

Lê Đình Duy

In conclusion, the obtained results show that the linear symmetric damper performs the same as that of the linear asymmetric one in terms of comprehensive performance when the vehicle is subjected to a random road profile The ride comfort, the working space have been significantly improved in specific range of velocity in case of the linear asymmetric damper However, in general, slightly better performance has been obtained in case of the linear symmetric damper case

và bán bình phương hàm sin

Tóm lại, các kết quả thu được cho thấy rằng giảm chấn đối xứng cho khả năng vận hành tương tự như giảm chấn bất đối xứng trên mặt đường ngẫu Độ êm dịu, không gian làm việc được cải thiện một cách đáng kể ở một số vùng vận tốc cụ thể trong trường hợp sử dụng giảm chấn bất đối xứng Tuy nhiên, nhìn chung, giảm chấn đối xứng đem lại khả năng vận hành tốt hơn

ASSURANCE

I am Dinh Duy LE, Master’s student of Department of Vehicle Engineering, Faculty

of Transportation, class 2018, at Ho Chi Minh City University of Technology

I guarantee that the information below is accurate:

(i) I conducted all of the work for this research study by myself

(ii) This thesis uses actual, reliable, and highly precise sources for its

references and citations

(iii) The information and findings of this study were produced independently

by me and honesty

Ho Chi Minh City, 07th July, 2022

Researcher,

Lê Đình Duy

TABLE OF CONTENTS

ACKNOWLEDGMENTS i

ABSTRACT ii

TÓM TẮT LUẬN VĂN THẠC SĨ iii

ASSURANCE iv

LIST OF FIGURES vii

LIST OF TABLES ix

LIST OF ABBREVIATIONS x

CHAPTER 1: OUTLINE 1

1.1 Introduction 1

1.2 Literature Review 2

1.3 Scope 3

1.4 Research methodology 4

1.5 Research findings and contributions 4

CHAPTER 2: THEORY AND SIMULATION MODEL 4

2.1 Damper Configuration 4

2.2 Characteristics of linear asymmetric damper 8

2.3 Linear asymmetric damper model 13

2.4 Quarter car model 15

2.5 Random road profiles 17

2.6 ISO 2631-1:1997 24

2.6.1 Vibration evaluation 24

2.6.2 Frequency weighting 26

2.7 IIR filter design 27

2.8 Evaluation indexes 30

2.9 Runge-Kutta Method 31

2.10 Calculation flowchart 32

2.11 MATLAB Program 33

CHAPTER 3: CALCULATED RESULTS AND DISCUSSION 35

3.1 Analysis of evaluation indexes 40

3.2 Extended results with a transient road profile 43

CHAPTER 4: CONCLUSION 50

DANH MỤC CÁC CÔNG TRÌNH KHOA HỌC 52

REFERENCES 55

APPENDIX 59

❖ INPUT.m 59

❖ fn2k.m 59

❖ RANDOM_road_generate.m 60

❖ RANDOM_Road_Profile.m 61

❖ Main.m 63

PLAGIARISM CHECK 70

CURRICULUM VITAE 73

LÝ LỊCH TRÍCH NGANG 74

LIST OF FIGURES

Fig 1 1 An intercity bus Samco Primas 2

Fig 2 1 A rebound phase of a shock absorber [11] 5

Fig 2 2 Types of shock absorbers and basic structures [5] 6

Fig 2 3 Paramerers of Twin tube shock absorber [5] 7

Fig 2 4 Working principle of Mono-tube shock absorber [12] 8

Fig 2 5 The actual damping characteristic curve [12] 9

Fig 2 6 An experimental model to find the characteristics of shock absorbers [13] 10

Fig 2 7 Displacement of harmonic excitation (u = 10 (mm), f = 0.05 (Hz)) [13] 100 Fig 2 8 Velocity of harmonic excitation (u = 10 (mm), f = 0.05 (Hz)) [13] 110 Fig 2 9 A relationship between F v and different velocity values [13] 11 D( ) Fig 2 10 The damping characteristic curve obtained from the experiment [12] 12

Fig 2 11 The force-velocity characteristics 13

Fig 2 12 Quarter car models [16] 15

Fig 2 13 Quarter car model and force diagram 16

Fig 2 14 Classification of roads, classes A to H [9] 19

Fig 2 15 A typical example of C-Class random road at velocity of 60 (km/h) 20

Fig 2 16 Relationship between health and duration of acceleration value [10] 25

Fig 2 17 Frequency weighting curves [10] 27

Fig 2 18 ARMA Model 28

Fig 2 19 Calculation flowchart 33

Fig 2 20 Organization of MATLAB program files 33

Fig 3 1 The sprung mass displacement in time domain at the vehicle’s velocity of 60 (km/h) 36

Fig 3 2 The unsprung mass displacement in time domain at the vehicle’s velocity of 60 (km/h) 36

Fig 3 3 The suspension dynamic deflection in time domain at the vehicle’s velocity

Fig 3 4 The sprung mass velocity in time domain at the vehicle’s velocity of 60

(km/h) 37

Fig 3 5 The sprung mass acceleration in time domain at the vehicle’s velocity of 60 (km/h) 38

Fig 3 6 BVA versus class of road profiles at velocities of 10 and 60 (km/h) 38

Fig 3 7 BVA in case of linear symmetric damper versus velocity 39

Fig 3 8 BVA versus velocity with two types of dampers 40

Fig 3 9 TDL versus velocity with two types of dampers 41

Fig 3 10 SDD versus velocity with two types of dampers 41

Fig 3 11 A physical model of triangular bump 43

Fig 3 12 A physical model of sine-squared bump 44

Fig 3 13 MBVA versus velocity with two types of dampers under GB/T excitation 45 Fig 3 14 MBVA versus velocity with two types of dampers under IRC excitation 45

Fig 3 15 MTDL versus velocity with two types of dampers under GB/T excitation 46 Fig 3 16 MTDL versus velocity with two types of dampers under IRC excitation 46

Fig 3 17 MSDD versus velocity with two types of dampers under GB/T excitation 47 Fig 3 18 MSDD versus velocity with two types of dampers under IRC excitation 47

LIST OF TABLES

Table 2 1 Road roughness values categorized by ISO 8608 [17] 17

Table 2 2 Road roughness in terms of spatial frequency [17] 18

Table 2 3 Comfort reactions to vibration environments [10] 25

Table 2 4 Parameters of the conversion function of frequency weighting [10] 27

Table 2 5 IIR coefficients for weighting filter [25] 29

Table 2 6 User-defined functions 34

Table 3 1 The bus’s technical parameters 35

Table 3 2 Evaluation indexes values in velocity domain with random road profile 42 Table 3 3 Evaluation indexes values in velocity domain with a transient excitation 48

LIST OF ABBREVIATIONS

QCM: Quarter Car Model

RMS: Root-mean-square

BVA: Body’s Vibration Acceleration

TDL: Tire Dynamic Load

SDD: Suspension Dynamic Deflection

MBVA: Maximum Body’s Vibration Acceleration

MTDL: Maximum Tire Dynamic Load

MSDD: Maximum Suspension Dynamic Deflection

CHAPTER 1: OUTLINE

1.1 Introduction

When a vehicle is in motion, the suspension system is the most important part This component is critical in ensuring the movement of the vehicle's structure and keeping the vehicle's connection to the road surface Also, the vibrations sent from the road surface to the vehicle are absorbed thanks to the damper, so it plays a essential role in defining the passenger’s driving experience and comfort

In Vietnam's economic development progress, the automobile is the best kind of transportation in many aspects compared to other types of transport due to its mobility In fact, people's travel need comes mainly from the intercity bus because

of their economy and speed In the past, passengers mainly needed to go to their desired destination without caring about the quality of the vehicle, but now with socio-economic development, improving service quality is mandatory for every travel company, if they want to score points with customers In particular, vehicle comfort is a key factor because many passengers easily get motion sickness when the bus runs on a bad road, especially children and the elderly

All types of traffic participants are affected by vibration, especially users of vehicles (both drivers and passengers) on all means of transportation In general, drivers of public transport are considered to be in dangerous working condition, which could threaten their health [1] When compared to passenger vehicle drivers, long-distance bus drivers are impacted by higher intensity vibrations during their 8-hour working shifts [2] As a consequence, vibration leads to a large number of serious effects (physiological and psychological illnesses), which are more noticeable, when it influences someone for a long period of time Because of this harmingful reasons, automotive manufacturers should pay a lot of attention to reducing these kinds of discomfort Due to fast economic and social growth, modern vehicles have to bring a satisfactory level of comfort for passengers by

minimizing the movements as well as the vertical accelerations imposed, and perceived by passengers

Fig 1 1 An intercity bus Samco Primas

In the past, passenger cars were primarily manufactured abroad Completely Built-Up) and then imported to Vietnam Many joint-ventures companies have successfully localized these passenger cars, and a large number of domestic manufacturing enterprises could develop buses in Vietnam based on imported chassis and engines with increasingly enhanced quality and standards such

(CBU-as SAMCO, THACO, HYUNDAI THANH CONG,… Because intercity bus mainly comes from the truck chassis, there are still many problems in designing progress that need to be studied and solved, such as the layout of the powertrain, distribution

of loads on the axles, and especially the ride comfort when a vehicle is moving on the road

1.2 Literature Review

In recent years, several research programs have been focused on enhancing the ride comfort of vehicles that is ranging from simulation to getting signals from realistic models for analysis and evaluation, as then individuals may increase the suspension system's quality Typical examples are the actual signal measurement, analysis, and evaluation based on standards For example, Hassan Nahvi (2009) evaluates the influence of vibrations on the comfort of passengers sitting on the bus

in the frequency domain Based on the signal obtained from the vehicle-mounted sensor, the assessments were conducted [3] Another example is that Hong Zhao

and colleagues (2016) received a signal from passengers' smartphones via Wi-Fi and transmitted it to the server After the signal is processed and evaluated by ISO 2631-1997, the results will be displayed on LCD screens along the bus, and the system will alarm if the value exceeds the allowable threshold [4]

One of the most crucial systems in a vehicle that is responsible for achieving comfort, stability, and safety characteristics is the suspension system The primary goal of this component is to improve the comfort level for vehicle’s occupants, maintain tire-to-road surface contact, and decrease dynamic forces pressing on the vehicle's structure Due to the nonlinear characteristics, it is evident that the damper

is one of the most complicated suspension's components that it influences braking, steering, cornering control, and overall stability Asymmetric dampers with a larger rebound damping coefficient than compression [5], are commonly equipped in almost all vehicle suspensions Many researchers have sought to determine appropriate damper values to achieve better trade-offs between characteristics like

as ride comfort, suspension deflection, and road-holding stability [6-9] Despite the fact that these investigations have offered sufficient insight into suspension’s damper design, the majority of the conclusions were based on limited performance metrics, while asymmetric aspects were mostly disregarded

1.3 Scope

This study seeks to elucidate the different reactions of linear symmetric and linear asymmetric dampers of Samco Primas bus subjected to a random road excitation in range of the common working velocity, and also the single bump road profile cases with triangular and sine-squared bumps The input parameters are determined based on the Samco Primas bus, which is relatively popular in Vietnam The quarter car model with 2 DOFs is employed to investigate the dynamic behaviors Various researchers have different opinions on vehicle comfort evaluation, and there are a large number of arguments but all essentially adhere to International Standard ISO 2631-1:1997 This guideline employs root mean square

(RMS) of weighted acceleration as an indication of vibration comfort [10], and the obtained results are mostly evaluated based on these criteria

1.4 Research methodology

The research includes theory, and simulation method using “M-files” in Matlab

as a compiler

1.5 Research findings and contributions

The thesis is organized as follows: Chapter 2 introduces background theory includes both the models of linear symmetric and linear asymmetric dampers employed for the simulations The quarter car model is also demonstated that the dynamic equation of system is expressed as a matrix form In the section 2.5, the method for creating random time-domain road profiles, useful for computation and analysis, is provided Next, the ISO 2631-1:1997 and the calculation flowchart are also demonstrated The model’s performance is then analyzed by using a large number of recommended evaluation indexes These details are employed in chapter

3 to examine the dynamic responses of linear symmetric and linear asymmetric dampers based on the data obtained Additionally, an extended result with a transient road input are investigated for deeper understanding in the section 3.2 Finally, the work’s highlights are summarized in the last chapter

In summary, this work is a helpful resource for enhancing ride comfort, safety, and handling control on a random road impact excitation as well as a transient road

in some specific cases

CHAPTER 2: THEORY AND SIMULATION MODEL

2.1 Damper Configuration

A shock absorber is an integral part of any suspension system ranging from simple to complex It is responsible for controlling the vibration of the body and wheels thanks to the force generated by the friction of the hydraulic oil in the shock absorber In fact, this force is nonlinear in the operating range of the shock absorber

A standard damper must include the following specifications:

- Overal size: Piston journey, overal length (L)…

- Other factors affecting the operation: limited working temperature, power dissipation, cooling requirements…

Fig 2 1 A rebound phase of a shock absorber [11]

The most critical parameter of the shock absorber is the damping ratio, which is a scalar quantity that indicates the damper's ability to absorb vibration For passenger cars, the damping ratio is usually in the range of 0.2-0.4, which will give the best performance In addition, the characteristic curve is quite crucial when it comes to damping, which will be mentioned in the following section

In fact, there are three most common types of shock absorbers: Twin tube, Monotube và Monotube with compression piston

Fig 2 2 Types of shock absorbers and basic structures [5]

The essential components of shock absorbers, and their functions are as follows [5]:

- Main piston: contains primary valving to allow oil to flow through

- Compression piston: generates compression force depending on the displacement of the compression piston's rod

- Gas separator piston: keeps the oil and gas separate

- Main piston tube: this tube contains the main piston's workings

- Reservoir tube/Outer tube: generates a space for additional oil and gas pressure

The shock absorber's working principle is dependent on the pressure difference

of hydraulic oil when it passes through the valves on the piston In the case of Twin tube, we have the following dynamic calculation expressions:

Compression rod Compression rod

P : Compression piston pressure

Fig 2 3 Paramerers of Twin tube shock absorber [5]

Due to this structure, the damping force generated during compression and rebound is not equal Moreover, the damping force will also be different at working velocity ranges

In fact, the damping force during compression will be smaller than during expansion, which can be answered for by two key factors:

- The compression damping force controls the unsprung mass’s vibration while the rebound damping force controls the sprung mass, Obviously, the sprung mass is heavier by approximately from 5 to 10 times than the unsprung mass, so the force generated during rebound will be larger than the force generated during compression

- In addition, the damping force and the elastic force have the same direction during compression, so less damping force is needed to prevent the object from moving up when a car goes through the bumpy road Conversely, in the rebound phase, the elastic force and the damping force will be in opposite directions, so more damping force is needed

2.2 Characteristics of linear asymmetric damper

A typical model showing the working principle of a shock absorber is shown below:

Fig 2 4 Working principle of Mono-tube shock absorber [12]

The difference in hydraulic oil pressure between the Rebound Chamber and the Compression Chamber leads to the internal friction between the liquid molecules

when moving through the valves in the shock absorber, which is the primary reason for creating damping force

In many studies, the damping coefficient is considered constant This implies that the damping force depends on velocity The graph is a linear line where the damping force F depends only on the velocity However, the actual characteristic D

curve of the shock absorber is exceptionally complicated depending on the reduction, rebound process, piston position, etc…, as shown in the following figure:

Fig 2 5 The actual damping characteristic curve [12] From the graph, it is easy to see that the shock absorber will quickly compress when the vehicle suddenly hits a bump on the road surface But, on the contrary, the suspension system must promptly generate great force to absorb the vibration during the rebound phase

The actual characteristic curve of the damper is found in the following experimental model:

Fig 2 6 An experimental model to find the characteristics of shock absorbers [13]

Fig 2 7 Displacement of harmonic excitation (u = 10 (mm), f = 0.05 (Hz)) [0 13]

Fig 2 8.Velocity of harmonic excitation (u = 10 (mm), f = 0.05 (Hz)) [0 13]

A computer-controlled hydraulic mechanism will apply a harmonic displacement 0

= sin(2π )

u u ft to the damper By varying the frequency f , we can get different damping forces F u respectively at specific frequency (velocity) values D( )

Fig 2 9 A relationship between F v and different velocity values [ D( ) 13]

A set of damping force F v values describing the actual damping D( )characteristics is obtained by taking the maximum value of the data obtained at times, u=u , corresponding to the velocity 0 v= 2π fu 0

Fig 2 10 The damping characteristic curve obtained from the experiment [12] The characteristic curve from the experiment shows that the rebound phase will generate more resistance force than the compression process

2.3 Linear asymmetric damper model

The suspension damper with linear asymmetric characteristic in the compression and rebound is taken into consideration, as shown in Figure 2.11 [14]

The suspension characteristic curve for the given parameters has the form:

Fig 2 11 The force-velocity characteristics

From Figure 2.11, the bilinear damping coefficient c can be formulated as [ s 13]:

From Eq (2.13), various values of the asymmetric ratio β correspond to

different damping properties

2.4 Quarter car model

The quarter-car model is commonly employed in automotive engineering, as shown in Fig 2.12, because of its simplicity and the qualitatively correct information it convey, at least in the initial design stages [15] In all circumstances, the absolute vertical displacement of the wheel subsystem and the vehicle’s body is represented by the coordinates ( )x and ( u x , respectively s)

a) Linear symmetric model b) Linear asymmetric model

Fig 2 12 Quarter car models [16]

Fig 2.13 shows the equilibrium state and the force diagram of the suspension system

Fig 2 13 Quarter car model and force diagram

Firstly, considering the symmetrical linear model of Fig 2.12(a), the motion equations are simply transposable into matrix form as:

random process As a result, the forcing vector has the form as:

The key difference between the models, which are shown in Fig 2.12(a) and Fig 2.12(b), is the linear asymmetric damping characteristics, where the suspension damping coefficient c fluctuates between two unique values s

2.5 Random road profiles

Roughness features of motorways, secondary roads, and poor roads have been described as zero-mean, and Gaussian distribution in several research According to ISO 8086, the Power Spectral Density (PSD) values provided in Figure 2.14 and Table 2.1 are used for classifying road roughness [17] The PSD function of roads indicates a distinctive decline in magnitude with the wave number, which can be used for constructing the random road profile In particular, it can be determined by:

d

G Ω

(10−6 m2/(rad/m)) where Ω = 0 1 (rad/m)

D 32 64 128

Table 2 2 Road roughness in terms of spatial frequency [17]

0( )

d

G n

(10−6 m2/(cycle/m)) where n =0 0.1 (cycle/m)

Fig 2 14 Classification of roads, classes A to H [9]

: wavelength, m

d d

G Ω G n : displacement power spectral density, m2/(rad/m), m2/(cycle/m)

We employ the sinusoidal approximation technique to study the dynamic response by solving the equations of motion at continuous sample times If the vehicle is anticipated to keep a consistent speed v along a given road section of 0

length L, a random profile of a single track may be estimated by using the accumulationN →  sine waves [( ) 18]

in which N - 1

=

N -1

Ω (rad/s), then the series of Ω are determined thanks i

correspondingly to N equal step intervals of Ω . Additionally, the phase angles

i,i = 1, , N

 are provided as random variables inside the [0, 2 ).

In this study, I take the grade C (G  d( 0) = 8 x 10-6 (m2/(rad/m)) as an quality excitation [10] throughout the velocity interval considered (from 5 to 120

average-(km/h)) The nominal parameters of the road are taken to be L=100(m), N=256(waves) The frequency is chosen from 0.5 to 50(Hz) that the road roughness

has the most considerable influence on the oscillatory behavior, then the series of angular spatial frequencies are calculated within this range [19] Then, Figure 2.15 illustrates a typical road profile produced by the approximation method

Fig 2 15 A typical example of C-Class random road at velocity of 60 (km/h)

Proof

Considering the influence of frequency and velocity of the vehicle, the combination of the Inverse Fourier Transform (IFT) and the Power Spectral Density (PSD) has a clear idea and algorithm Hence, it gives more accurate results than other methods [20]

Assuming that the spatial frequency of the RSR has an upper and lower bound of 2

Ω and Ω , respectively The power spectral density is determined according to the 1

frequency: n2 = f2 /v and n1= f1/v For a distance of length L and the number of divided points N , the distance between two points is l or L= N l The distance

between two points in the frequency domain is n= 1 /L

Setting q with m m= 0,1, 2, , N -1 is the series of RSR

Applying the Fourier transform formula:

where q l is RSR at point m in the space domain m( )

Since the random road profile is a Gaussian random process, the signal is symmetric about the vertical axis:

where G n is the discrete PSD value d( k)

Based on the equation (2.25), there is

[21] Since the random road profile's phase adheres to the normal distribution, we obtain:

=| | j k, [0, 2π]

The Inverse Fourier Transform (IFFT) can be used for getting the discrete signal

of the RSR in the space domain:

- The behavior of the vehicle during movement controlled by the driver

- Random road profile (Primary source)

Factors of vibration that affect people's perceptions, including:

- Posture and body part affected

The variation of acceleration is crucial as it determines the vehicle's vibration, but it is important to carefully analyze the natural frequency of the human body According to VDI 2057 standard, the vertical direction is the main vibrational direction appearing on most road vehicles [22]

The root mean square of acceleration is the most used approach for determining the physiological response to vibration levels, which computed using the following equation [10]:

1/2 2

T – Duration time, (s)

The influence of vibration on passengers based on the root mean square of acceleration is shown as below:

Table 2 3 Comfort reactions to vibration environments [10]

Fig 2 16 Relationship between health and duration of acceleration value [10]

After considering many different criteria, the evaluation strategy is primarily concentrated on the root mean square of the acceleration The simulation calculation process will focus on the ISO 2631-1:1997 to investigate the quality of passenger vehicles (Samco Primas)

2.6.2 Frequency weighting

Acceleration data obtained from simulation must be multiplied by frequency weighting to properly assess how vibration influences human health at the bands to which people are most sensitive [23]

The ISO 2631-1:1997 standard examines vibrations with frequencies between 0.4 and 100 Hz [10] Accordingly, accelerometer data from measurement or simulation will be filtered by analog filters:

- High-pass:

2

1 1

2 2

4 3

4 4

+( ) =

6 6

The following table shows the conversion function's specifications:

Table 2 4 Parameters of the conversion function of frequency weighting [10]

2.7 IIR filter design

The first step in using ISO 2631-1:1997 for vibration evaluation is to use analog filters to find the acceleration taking into account the influence of frequency weighting But the acceleration data obtained from the simulation is in the time domain, and using the frequency filter requires complex calculations If these filters are used in the time domain, the computation becomes more straightforward, hence

a digital filter should be designed to carry out this procedure