TABLE OF CONTENTS
PREAMBLE..................................................................................................................................................v
SUMMARY OF THE PROJECT CONTENT.................................................................................................vi
TABLE OF CONTENTS..............................................................................................................................vii
LIST OF FIGURES.......................................................................................................................................x
CHAPTER I: OVERVIEW OF SUSPENSION SYSTEMS AND DESIGN OPTIONS ..................................1
1.1 Background and motivation....................................................................................................................1
1.2 Overview of the suspension system.......................................................................................................2
1.2.1 Function...............................................................................................................................................2
1.2.2 Requirements......................................................................................................................................2
1.2.3 Classification.......................................................................................................................................2
1.2.4 Classification by Guiding-link Structure..............................................................................................2
1.2.5 Classification by Elastic Element Type...............................................................................................5
1.2.6 Classification by Vibration-damping Method.......................................................................................5
1.3 Main Components of the Suspension System......................................................................................5
1.3.1 Elastic Elements.................................................................................................................................5
1.3.2 Guiding Components..........................................................................................................................7
1.3.3 Shock Absorbers (Dampers)...............................................................................................................8
1.3.4 Rubber Bump Stops (Bump Rubbers).................................................................................................9
1.4 Hino 300 XZU 730L Truck.....................................................................................................................10
1.4.1 Technical Drawing of the Hino 300 XZU 730L Truck..........................................................................10
1.4.2 Analysis of the Rear Suspension System for the Truck......................................................................12
1.4.3 Front suspension system....................................................................................................................13
1.5 Active Suspension..................................................................................................................................14
1.5.1 General Overview of Active Suspension Systems..............................................................................14
1.5.2 Classification of Active Suspension Systems......................................................................................15
1.6 Selection of design options.....................................................................................................................17
1.6.1. Analysis and Selection of Suspension System Type..........................................................................17
1.6.2 Analysis and Selection of Active Suspension Type..............................................................................18
1.7Analysis & Selection of Suspension Design Options...............................................................................19
1.7.1 Analysis and Selection of the Elastic Element......................................................................................19
1.7.2 Analysis and Selection of the Damper..................................................................................................19
1.8 Selection of Design Parameters for the Vehicle.......................................................................................20
CHAPTER II: CALCULATION AND DESIGN OF THE FRONT SUSPENSION SYSTEM............................22
2.1 Elastic Characteristic................................................................................................................................22
2.2 Leaf Spring Load Determination & Design...............................................................................................22
2.2.1 Determination of the Forces Acting on the Leaf Springs.......................................................................22
2.2.2 When the vehicle is fully loaded............................................................................................................23
2.2.3 When the vehicle is unladen.................................................................................................................23
2.3 Design of the front leaf spring..................................................................................................................23
2.3.1 Suspension stiffness C..........................................................................................................................23
2.3.2 Preliminary Selection of Leaf Spring Dimensions.................................................................................24
2.3.3 Calculate the stiffness, static deflection, and verify the oscillation frequency of the leaf spring............26
2.3.4 Strength Calculation of the Leaf Spring and Related Components.......................................................27
2.3.5 Strength Calculation of the Spring Eye..................................................................................................30
2.3.6 Leaf Spring Pin Structural Evaluation....................................................................................................30
2.4 Shock Absorber Design.............................................................................................................................31
2.4.1 Front Shock Absorber Design................................................................................................................31
2.4.2 Determination of the Front Shock Absorber Dimensions.......................................................................33
CHAPTER III: CALCULATION AND DESIGN OF THE REAR SUSPENSION SYSTEM.............................39
3.1 Elastic characteristics...............................................................................................................................39
3.2 Leaf Spring Load Determination & Design...............................................................................................39
3.2.1 Determination of the Forces Acting on the Leaf Springs.......................................................................40
3.2.2 When the vehicle is fully loaded............................................................................................................40
3.2.3 When the vehicle is unladen.................................................................................................................40
3.3Design of the Main Rear Leaf Spring and the Auxiliary Rear Leaf Spring................................................40
3.3.1 Main Rear Leaf Spring..........................................................................................................................41
3.3.2 Auxiliary Rear Leaf Spring....................................................................................................................43
3.3.3 Static Deflection of the Main Rear and Auxiliary Rear Leaf Springs.....................................................44
3.3.4 Strength Calculation of the Main and Auxiliary Rear Leaf Springs.......................................................48
3.3.5 Calculation for the Auxiliary Rear Leaf Spring......................................................................................48
3.3.6 Calculation for the Main Rear Leaf Spring............................................................................................50
3.3.7 Strength Calculation of the Spring Eye.................................................................................................53
3.3.8 Verification Calculation of the Leaf Spring Pin......................................................................................54
3.4 Rear Shock Absorber Design..................................................................................................................54
3.4.1Determination of the Shock Absorber Damping Coefficient KG.............................................................54
3.4.2 Determination of the Rear Shock Absorber Dimensions......................................................................56
CHAPTER IV. MAINTENANCE AND REPAIR OF THE SUSPENSION SYSTEM.......................................61
4.1 Phenomena and Causes of Suspension System Failures......................................................................62
4.1.1 Suspension System Noise....................................................................................................................62
4.1.2 Vehicle Vibration, Jerk, and Harsh Impacts......................................................................................... 65
4.1.3 Inspection and Maintenance Methods.................................................................................................62
4.1.4 Suspension System Maintenance........................................................................................................62
4.2 Maintenance and Repair of the Suspension System..............................................................................62
4.2.1 Disassembly Procedure.......................................................................................................................63
4.2.2 Assembly Procedure............................................................................................................................64
4.3 Suspension System Maintenance...........................................................................................................65
4.4 Repair of the Dependent Suspension System........................................................................................66
4.4.1 Spring Pins, Bushings, and Spring Seats........................................................................................... 69
4.4.2 Leaf-Spring .........................................................................................................................................66
CONCLUSION..............................................................................................................................................67
REFERENCES.............................................................................................................................................69
PREAMBLE
The graduation project titled “Design of the Suspension System for a 5.5-Ton Truck” results from our persistent efforts and the dedicated support of the faculty from the Department of Dynamic Mechanics, School of Mechanical Engineering.
I want to express my sincere gratitude and respect to my supervisor, Dr., ……………… for his invaluable guidance throughout the completion of this project.
I am also profoundly thankful to all the lecturers at Hanoi University of Science and Technology for providing me with a strong foundation of knowledge and encouraging a spirit of creativity - essential tools as I begin my journey on a long professional path ahead.
Given my limited experience and understanding, there may be certain shortcomings in the project’s content and analysis. I sincerely welcome all feedback and suggestions from the faculty to help me improve and further refine this work.
Thank you very much!
SUMMARY OF THE PROJECT CONTEN
The graduation project, "Design of the Suspension System for a 5.5-Ton Truck,” aims to optimize this medium-duty truck's ride comfort, load-carrying capacity, and operational stability. In commercial vehicles, the suspension system governs how road irregularities are transmitted to the chassis, cargo, and occupants, balancing support and vibration isolation to prevent excessive shocks, component wear, and loss of tire contact.
The methodology starts with a theoretical review of suspension fundamentals, elasticity, damping, and kinematics, and selects a semi-elliptical leaf-spring plus hydraulic-shock absorber layout for heavy-load service. It then proceeds to detailed design: the front suspension is sized via its elastic curve, spring geometry, static/dynamic deflections, natural frequency, and strength checks; the rear suspension covers main and helper leaf-spring design, a two-stage elastic characteristic, and shock absorber sizing.
The project defines clear maintenance and repair protocols, including scheduled inspections for static sag and dynamic deflection, diagnostic checks for spring fatigue and shock absorber leakage, and step-by-step disassembly/reassembly procedures with torque specifications and lubrication points. It also specifies replacement criteria for spring preload loss, bushing wear, and seal failures, enabling technicians to troubleshoot and efficiently maintain suspension performance and safety.
Structure of the Thesis:
- Chapter 1: Overview of suspension systems and design options
- Chapter 2: Calculation and design of the front suspension system
- Chapter 3: Calculation and design of the rear suspension system
- Chapter 4: Maintenance and repair of the suspension system
Hanoi, … / … / 20…
Student
………………….
CHAPTER I: OVERVIEW OF SUSPENSION SYSTEMS AND DESIGN OPTIONS
1.1 Background and motivation
Automobiles have become indispensable in modern society, serving as a primary means of transportation for people and goods across urban, regional, and international routes. Year after year, the global vehicle population rises, driven by economic growth, urbanization, and expanding logistics demands. In this context, medium-duty commercial vehicles such as the Hino 300 series assume a critical role: they bridge the gap between light delivery vans and heavy-duty trucks, offering a balance of payload capacity, maneuverability, and operating economy.
As service and industry sectors expand, end users demand reliable load‐carrying performance, enhanced ride comfort, handling stability, and operational safety. Among the various subsystems of a vehicle, the suspension system directly governs how road irregularities are transmitted to the chassis, cargo, and occupants. Traditional passive suspension setups—leaf springs and hydraulic shock absorbers—compromise load support and ride smoothness. However, under harsh loading variations and diverse speed profiles, passive designs may fail to maintain optimal tire contact and vibration isolation, leading to increased component wear, reduced driver comfort, and potential safety issues.
1.2 Overview of the suspension system
1.2.1 Function
The suspension system is a crucial assembly directly affecting a vehicle’s ride comfort and stability. It elastically links the chassis to the wheels, ensuring smooth motion while transmitting longitudinal and lateral forces and moments between the wheels and the vehicle body. Doing so preserves the correct kinematic relationship between each wheel and the chassis. [2] pg260
1.2.3 Classification
Automotive suspension systems are typically classified based on several key criteria that influence their design and performance:
+ Steering-Link (Guiding) Element Configuration: These components control the movement of the wheels, ensuring proper alignment and handling characteristics.
+ Elastic Element Design: This refers to the type and arrangement of springs or flexible components that provide the necessary support and absorb road irregularities.
1.2.4 Classification by Guiding-link Structure
Dependent Suspension:
A dependent suspension system connects the left and right wheels by a solid beam (solid axle). Therefore, the other wheel also moves when one wheel moves (in the horizontal or vertical plane). The advantage of a dependent suspension is its simple structure, low cost, and ability to provide sufficient ride comfort for vehicles that do not travel at high speeds. In dependent suspensions with leaf springs, the spring also serves as the guiding element.
Independent Suspension:
- An independent suspension system is one in which the left and right wheels are not rigidly connected; thus, the movement of one wheel does not affect the other. It can be classified according to the plane of movement (horizontal, vertical, or both). This suspension type is usually used in vehicles with a separate body structure, providing a high level of comfort, but with a complex design and high cost.
- Nowadays, the following types of independent suspension are commonly used.
Double-wishbone suspension (two A-arms):
The double-wishbone suspension consists of a spring, shock absorber, and a guiding component with two control arms, where the upper arm is shorter. Its advantages include maintaining wheel alignment angles during cornering, minimizing lateral sway, and optimizing handling performance. However, its structure is complex, making it difficult to repair and expensive to maintain.
1.2.6 Classification by Vibration-damping Method
- Damping vibration using hydraulic shock absorbers, including piston-type and cylinder-type shock absorbers.
- Damping vibration using mechanical friction within the elastic element and within guiding elements.
1.3 Main Components of the Suspension System
1.3.1 Elastic Elements
Function:
Function: to act as a flexible link between the wheel and the vehicle body, adjusting the natural frequency of vibration to suit the human body (60–80 oscillations per minute). The elastic element can be arranged differently on the vehicle but allows the wheel to move vertically
Leaf spring:
The leaf spring is made from elastic spring steel plates stacked in decreasing length, with the longest plate called the main leaf. The two ends of the main leaf are bent into eyes for mounting to the chassis. The leaves are fastened together by a bolt and held firmly by the spring clip. When the vehicle is in motion, the leaves slide relative to each other, creating friction to damp vertical oscillations.
The coil spring in the suspension system only provides elasticity in the vertical direction; other components handle other functions. Coil springs are typically used in independent suspension systems and may be located on the guiding component's upper or lower control arm.
Torsion bar:
The torsion bar acts similarly to a coiled spring, but in torsion, it provides elasticity when subjected to vertical force; other suspension parts provide other functions.
- The guiding components of the suspension system are also called stabilizer links. As the name suggests, they play a critical role in the operation of the vehicle suspension.
- Their function is to transmit longitudinal and lateral forces and torque from the wheel to the chassis or vehicle body. Their configuration varies depending on whether the suspension is dependent or independent, and on the types of elastic elements (leaf spring, coil spring, or torsion bar).
1.3.4 Rubber Bump Stops (Bump Rubbers)
On passenger cars, bump stops are often incorporated within the shock absorber casing. They both increase stiffness and limit the piston’s travel to stop the wheel’s travel.
- Advantages of rubber bump stops include:
+ Can be molded into various shapes.
+ Operate without noise and require no lubrication.
1.4 Hino 300 XZU 730L Truck
Hino 300 XZU730L represents the pinnacle of Hino Motors Vietnam’s light-duty range, blending proven Japanese engineering with locally tuned assembly processes at its Hoàng Mai, Hà Nội facility. Designed to carry an 8.5-tonne payload, the XZU730L is driven by the N04C-VB Euro 3 diesel engine that delivers 150 PS and 420 Nm of torque, providing both the low-end grunt needed for stop-start urban routes and the smooth power delivery required on longer inter-city hauls. Its 4200 mm whesebase and robust ladder-frame chassis are intentionally modular, allowing rapid fitment of various bodies from standard flatbeds and box vans to refrigerated and tipper configurations while retaining optimal weight distribution.
Comfort and control have been engineered into every detail: the cab-over-engine layout maximizes driver visibility; the Denso air-conditioning system and ergonomically sculpted seats reduce fatigue; and hydraulic power steering with an adjustable-tilt column ensures precise handling. Braking duties are handled by dual-circuit, vacuum-assisted drum brakes, and the standard 100 L fuel tank supports extended run-times between fill-ups.
1.4.1 Technical Drawing of the Hino 300 XZU 730L Truck
The Hino 300 XZU730L is a popular 8.5-ton truck in Vietnam, ideal for transporting goods over short and medium distances—including inner-city and regional routes. Its modular chassis makes it adaptable to various body types, from flatbeds and box vans to refrigerated and tipper configurations. The XZU730L’s robust N04C-VB Euro 3 engine, 4,200 mm wheelbase, and ergonomic cab ensure reliability and driver comfort in demanding urban logistics.
Leaf Spring (Suspension)
Leaf springs are composed of stacked spring steel leaves, with the longest leaf called the main leaf, its ends formed into eyes that connect to the vehicle frame. The leaves are clamped together using a bolt and fixed by a spring clip. The leaves move longitudinally during operation, generating friction that reduces vertical oscillations—the top surface of the spring experiences tensile loads, and the bottom surface experiences compressive loads.
The simplest schematic of a dependent suspension system comprises two semi-elliptical leaf springs. The axle’s movement relative to the frame depends on the spring parameters. Each leaf spring has six joints (three per spring). The vertical force X and reaction moment MY are transmitted to the chassis via the spring.
1.4.3 Front suspension system
The figure shows the structure of a dependent front suspension system with a leaf spring as the elastic element. The front end of the spring is supported by the bracket (1) through the spring pin, while the rear end is supported by a sliding pad inside the rear bracket (6). When subjected to a load, the rear end of the spring assembly easily slides on the self-aligning pad (7), the spring assembly bends upward, and the upper leaf springs slide on the self-aligning pad (Figure b).
The rubber bump stop (3), mounted at the middle point of the spring assembly, limits the spring's deformation. The contact lug (5) mounted on the frame increases the spring assembly's stiffness. When the load increases, the upper leaf springs come into contact with lug (5), shortening the effective load-bearing length, thereby increasing the spring stiffness.
1.5 Active Suspension
1.5.1 General Overview of Active Suspension Systems
The active suspension system, also known as adaptive suspension, controls the vertical motion of the wheels through a microprocessor system, instead of the wheel movements being entirely determined by the road surface. As a result, this system virtually eliminates issues such as body roll, nose diving, or rear squatting in situations like cornering, braking, or accelerating.
The control microprocessor detects the vehicle body’s movements via sensors installed on the vehicle and uses data calculated by control algorithms to control the suspension system's operations.
1.5.2 Classification of Active Suspension Systems
1.5.2.1. Fully Active Suspension System
EAS- Electronic Actuation system
Main components of the EAS suspension system:
+ Air spring shock absorbers
+ Vehicle height sensors
+ Vehicle speed sensors
1.5.1.2. Semi-Active Suspension System
Can only change the viscosity of the shock absorber fluid, without increasing the stiffness of the elastic component.
It is less costly and consumes less energy.
Semi-active suspension actuated by electromagnetic valves
These include a solenoid valve that alters the flow of fluid inside the shock absorber, thus changing the damping characteristics of the suspension system. The solenoid valves are connected to a computer, which sends commands based on control algorithms.
Unlike traditional systems using mechanical valves, this system uses a special fluid that reacts to magnetic fields.
The MR fluid is not magnetized when the excitation coil inside the system is de-energized or in the “off” state. At this point, the particles are randomly distributed within the fluid, allowing it to flow freely and function as a conventional damping fluid.
1.7 Analysis & Selection of Suspension Design Options
1.7.1 Analysis and Selection of the Elastic Element
For the designed vehicle, which is a 5.5-ton truck, we select the elastic element to be a metallic leaf spring, as the leaf spring offers suitable advantages, such as:
- High durability
- Very high load-bearing capacity
- Small longitudinal dimensions (saving space for the cargo compartment)
1.7.2 Analysis and Selection of the shock absorber
For the designed vehicle, as we have selected the leaf spring as the elastic element, the inherent friction between the leaf plates during oscillation also contributes to damping vibrations (mechanical friction). However, to ensure the ride comfort of the suspension system, an additional hydraulic shock absorber must be installed to ensure that the suspension system can quickly suppress vibrations.
Twin-tube Shock Absorber:
+ Advantages: Twin-tube shock absorbers offer high durability, low cost, reliable performance during both compression and rebound strokes, and are lightweight..
+ Disadvantages: When operating at high frequencies, air can mix with the fluid, reducing the damping effectiveness..
1.8 Selection of Design Parameters for the Vehicle
We refer to the initial parameters of the reference vehicle Hino 300 model XZU730L as follows.
Basic Specifications of the Reference Vehicle Table 1.
CHAPTER II: CALCULATION AND DESIGN OF THE FRONT SUSPENSION SYSTEM
2.1 Elastic Characteristic
The elastic characteristic is the relationship between the vertical reaction force Z acting on the wheel and the deformation f of the suspension system, measured directly at the wheel axle; this is expressed as the function Z = g(f).
The elastic characteristic is constructed under the assumption that friction and the mass of the unsprung part are neglected, so this unsprung mass can be subtracted when calculating the reaction force Z. The characteristic is considered linear, and the characteristic curve must pass through two points A (ft, Zt) and B (fđ, Zđ).
In which: Zt is the static load acting on the wheel causing deformation ft, Zđ is the dynamic load acting on the wheel causing deformation fđ
2.2 Leaf Spring Load Determination & Design
2.2.1 Determination of the Forces Acting on the Leaf Springs
Unsprung mass on the front axle [1]: Qott = 2600 N
2.2.2 When the vehicle is fully loaded
The total vehicle weight at full load is 85,000 N, distributed on the axles as 22,950 N (front).
The load on one side of the leaf spring on each axle is: Ztt = 10175 N
2.3 Design of the front leaf spring
2.3.1 Suspension stiffness C
The suspension system to be designed must ensure that the vehicle achieves ride comfort according to the established criteria. There are various indicators for evaluating ride comfort, such as oscillation frequency, oscillation acceleration, and oscillation velocity.
In this graduation thesis, we select only one indicator: oscillation frequency.
However, when performing calculations for vehicle suspension systems, the parameter commonly used is the number of oscillations per minute n, where n=90÷120 times/min. The ride comfort evaluation criteria are chosen as follows [2]:
Preliminary selection: n=100 times/minute.
- According to the static deflection formula, it is calculated as follows [2]: f = 0,09m
Dynamic deflection fd = 3÷6 (cm) => Choose fd = 6
2.3.2. Preliminary Selection of Leaf Spring Dimensions
- A leaf spring is assembled from multiple thin steel plates (leaves).
The geometric dimensions of the leaf springs will be:
Leaf lengths: L1, L2, Lk..., Ln
Leaf cross-section: b x hk
n: Number of leaves
b: Leaf width
Hk: Thickness of the k-th leaf.
- The total leaf-spring length Lt can be preliminarily chosen as follows:
For trucks [2]:
- Front leaf spring length: L = (0,26 ¸ 0,35)L; (L is wheelbase)
L = (0,26 - 0,35).4200 = 1092 - 1470 (mm) (4.10)
=> Choose L = 1450 (mm)
Based on the vehicle type, payload, chassis structure, and leaf spring dimensions, the following parameters are used [2]:
Number of leaves: n = 11.
Leaf width: b =70 (mm).
Leaf thicknesses: h1 = h = 8 (mm); h =h =….h =8,5 (mm).
The leaf lengths lk are calculated using the following system of equations:
A + B + C = 0
A + B + C = 0
A + + C = 0
A + B + C = 0
A + B + C = 0
A + B + C = 0
A + B + C = 0
A + B + C = 0
A + B = 0
2.3.4 Strength Calculation of the Leaf Spring and Related Components
Based on the above reasoning, we assume the spring is rigidly clamped at its midpoint for the semi-elliptical leaf spring. Thus, in our calculations, we consider only one half of the leaf spring under the following assumptions:
- Consider the leaf spring as a quarter-elliptical arc, with one end rigidly clamped and the other loaded.
- The curvature radius of all the leaves is the same; they contact one another only at their ends, and the load is transmitted solely through these contact points.
- The deflection at the contact point between two adjacent leaves is equal.
- Under these assumptions, the strength-calculation model for the leaf spring is as follows:
- The system of equations is as follows:
A2 P + B2 X2 + C3 X3 = 0
A3 X2 + B3 X3 + C3 X4 = 0 (* *)
. . . . . . . . . . . . .
An Xn-1 + Bn Xn = 0
Front Leaf Spring Calculations Table 4.
Solving the above system (***) yields:
X2 = X3 =X4 =X5 = X6 = X7= X8 = X9= X = 5087.5 (N)
- Moment at Point A [2]:
MA = Xk(lk- lk+1) (4.15)
- Moment at Point B [2]:
MB = Xklk- Xk+1lk+1 (4.16)
Conclusion: After determining the bending moments, we calculate the resulting stresses and compare them to the allowable stress. For leaf springs made of 60C2 steel, the permissible stress is typically [s]t = 600 (N/mm ) = 600MPa
=> We find that all leaf springs satisfy the strength requirements.
2.3.5 Strength Calculation of the Spring Eye
- The strength-calculation diagram for the spring eye is shown in the adjoining figure
Where:
D: Is the inner diameter of the leaf-spring eye, chọn D = 50 ( mm ).
h0: Is the thickness of the main leaf, h0 = 8 ( mm ).
b: Is the width of the leaf spring, b = 70 ( mm)
- The leaf-spring eye is subjected to a tensile force Pₖ or a braking force Pₚ. The magnitude of this force is determined by [3]:
Pkmax= Ppmax=j. Zbx (4.19)
Where:
j: Is the tire-road adhesion coefficient j = 0,7.
Zbx: Is the reaction force from the road acting on the wheel.,
Zbx = 11475 (N). Þ Pkmax= 0,7. 11475 = 8032.5 (N).
- The compressive (or tensile) stress at the spring eye is:
compressive =Pkmax/(2.b.h0 )=8032,5/2.70.8=7,17(N/mm2) (4.22)
- The combined stress at the spring eye is:
scombined = sbending + scompressive= 177,5 + 7,17 = 184,67 (N/mm2)
- Allowable combined stress:
[scombined] =350MN/m2 = 350 N/mm2
=> s combined < [scombined]
Therefore, the spring eye is sufficiently strong.
2.4 Shock Absorber Design
2.4.1 Front Shock Absorber Design
2.4.1.1 Determination of the Shock Absorber Damping Coefficient KG
The damping coefficient K of the suspension system plays an important role in providing vehicle comfort. Similar to the elastic components, it depends on how the shock absorber is mounted on the vehicle. The damping coefficient of the shock absorber K may be equal to or different from the damping coefficient of the suspension system.
2.4.1.2 Suspension System Damping Coefficient
y: The damping ratio, (y = 0, 15¸0, 3). Take y = 0,2.
C: Suspension stiffness, C =95274 (N/m).
M: Sprung mass per wheel, M = 1047,5 (kg).
Ktr: Damping coefficient of the suspension system.
=> The damping coefficient of the suspension system is determined by the formula:
Ktr =2.0,2.√95274.1017,5=3938,35 (Ns/m)
2.4.1.4 Determination of Shock Absorber Damping Force
- Damping force during the compression stroke :
Pn = Kn. Vg (4.28)
Where:
Vg: Piston velocity during compression, Vg = 0,3 (m/s).
Kn: Damping coefficient during compression, Kn= 2378,7 (Ns/m).
Þ Pn = 2378,7.0,3 = 714 (N).
- Damping force during hard compression:
Pnmax = Pn + K’n. (Vgmax-Vg) (4.29)
Where:
Vgmax: Piston velocity during hard compression, Vgmax = 0,6 (m/s).
K’n: Damping coefficient during hard compression, K’n= 0,6Kn
=> Pnmax = 714 + 0,6.2378,7.(0,6-0,3) = 1142 (N).
- Damping force during the rebound stroke:
Ptr = Ktr. Vg (4.30)
Where:
Vg: Piston velocity during the rebound stroke, Vg = 0,3 (m/s).
Ktr: Damping coefficient of the shock absorber during rebound,
Ktr= 6541,45 (Ns/m) Þ Ptr = 6541,45.0,3 = 1962 (N).
- Damping force during hard rebound:
Ptrmax = Ptr + K’tr. (Vgmax-Vg ) (4.31)
Where:
Vgmax: Piston velocity during hard rebound, Vgmax = 0,6 (m/s).
K’tr: Damping coefficient during hard rebound, K’tr= 0,6 (Ktr)
=> Ptrmax = 1962 + 0,6.6541,45.(0,6-0,3) = 3140 (N).
2.4.2 Determination of the Front Shock Absorber Dimensions
2.4.2.1 Determination of piston diameter and stroke.
- The working stress condition is determined at V = 0, 3(m/s).
- The heat dissipation power of a metallic object with heat dissipation area F is calculated as follows:
Nt = 427. a. F. (Tmax - Tmin) (4.32)
Where:
a : Heat transfer coefficient, chosen as a = 0, 13 J/m2
Tmax: Allowable temperature, Tmax=1500; Tmin = 200
- From the thermal balance equation, we have:
401,4 = 427. 0,13. F. (150 - 20)
=> F = 0,0556 m‑2 = 55625 (mm2)
That is: F = pDn.L = 55625 (mm2)
- The preliminary dimensions of the shock absorber include the lengths of its components:
Ld Is the length of the shock absorber head.
Lm Is the length of the sealing component.
LP Is the length of the shock absorber piston.
Lv Is the length of the valve base.
LG Is the maximum working stroke of the shock absorber, (LG must be greater than the wheel displacement between the upper stop and the lower stop points.)
- Therefore:
L = L + L + L + L = 415 (mm) > 354,1 (mm)
= > Satisfies the thermal condition
2.4.2.3 Determination of the compression valve hole size
- The total area of the compression valve holes is determined:
Therefore :
Fvn= (Fp.Vn1)/(μ√((2gPn1)/(Fp.γ)))= 11,58 (mm2)
- Diameter of each compression valve hole: Fvn=(nπ.d^2)/4=11,58 (mm2)
Number of valve holes selected: n = 4 Þ d = 1,9 (mm).
2.4.2.6 Determination of the bypass valve hole size during rebound
- The total area of all valve holes during strong rebound is determined :
Therefore:
Fvt'=(Fp.Vt2)/(μ√((2gPtr2)/(Fp.γ))) =11,04 (mm2)
- Total area of the bypass valve holes during rebound:
Fvm = F’vt –Fvt = 11,04 – 6,98 = 4,06 (mm2)
- Diameter of each bypass valve hole during rebound:
Fnm=(nπ.d^2)/4=4,06 (mm2)
Choose number of holes n = 4 => d = 1,2 (mm).
2.4.2.7 Determination of the Spring Dimensions for the Shock Absorber Valves
- Allowable stress of the spring material, [t] = 500 ¸ 700 (MN/m2).
Choose [t] = 700 (MN/m2).
=> d > 2,1 mm
=> Choose d = 3 (mm).
- The length of the spring when the valve is fully open is calculated as:
Hm = n.d + d.n0 = 5.3 + 0,8.6 = 19,8 (mm)
Where :
d : Distance between coils, d = 0,8 (mm).
n0 : Total number of coils, n0 = n+1 = 5 +1 = 6 (coils).
- Length of the spring when the valve is closed :
Hd = Hm + h = 19,8 + 2 = 21,8 (mm)
- Length of the spring in the free state :
Htd = Hd + l = 21,8 + 3,55= 25,35 (mm)
Where :
l : Deformation of the spring when the valve is open. l = 3,55 mm
- Spring pitch : t = 4,73
CHAPTER III: CALCULATION AND DESIGN OF THE REAR SUSPENSION SYSTEM
3.1 Elastic characteristics
The elastic‐characteristic curve of the selected suspension system consists of two segments: a linear segment OA of constant stiffness, and a non-linear segment AB of variable stiffness. The abscissa OE is the static deflection of the suspension under the static load Ft Point C marks the support of the limiter, so EC is the dynamic deflection fdt. Segment OE represents the behavior of an elastic element with changing stiffness; to obtain this characteristic curve we choose the elastic element as a leaf spring and the limiter support as rubber.
3.2 Leaf Spring Load Determination & Design
The suspension system is symmetrical on both sides; therefore, in calculations we only need to analyze one side. The load acting on one side of the rear suspension system.
3.2.1 Determination of the Forces Acting on the Leaf Springs
Unsprung mass on the rear axle [1]: Gott = 4200 N
3.2.3 When the vehicle is unladen
The curb weight is 35 050 N, distributed on the axles as 17 500 N (rear).
The sprung mass acting on the rear suspension: M2' = 1330 kg
The load on one side of the leaf spring on each axle is: Z2' = 8750 N
3.3 Design of the Main Rear Leaf Spring and the Auxiliary Rear Leaf Spring
When the vehicle is running unloaded, the angle α is normally selected to be no less than 5°. Under full-load conditions, α can reach values of 40–50°. To simplify the calculations, the effect of force X will be neglected.
Where:
C : Suspension stiffness (N/m).
M : Sprung mass (kg): M = 5785/2 = 2892,5 (kg)
n : Oscillation frequency. n = 100 (lần/phút).
=> C = 3,17.105 N/m
For truck:
+ Rear leaf spring : L = ( 0,35 ¸ 0,45 )
L; (L is the wheelbase of the vehicle).
L1 =(0,35 - 0,45).4200 = 1470 - 1890 (mm)
=> Choose L = 1850 (mm).
Dimensions of the main leaf spring eye :lg = 90 (mm).
3.3.1 Main Rear Leaf Spring
- Based on the vehicle type, payload, chassis structure, and leaf spring dimensions, the following parameters are used [2]:
+ Number of leaves n = 16.
+ Leaf width : b =80 (mm).
+ Leaf thickness h1 = h = 8,5 mm ; h =h =….h = 9 ( mm).
+ The leaf lengths lk are calculated from the following system of equations:
A + B + C = 0
A + B + C = 0
A + + C =0
A + B + C =0
A + B + C = 0
A + B + C = 0
A + B + C = 0
A + B + C = 0
A + B + C = 0
A + B + C = 0
A + B + C = 0
A + B + C = 0
A + B + C = 0
A + B = 0
Solving the above system of equations yields:
Preliminary Dimensions of the Main Rear Leaf Spring Table 7.
3.3.3 Static Deflection of the Main Rear and Auxiliary Rear Leaf Springs
With this load distribution, it must be ensured that under full load the main rear leaf spring remains sufficiently strong. Since there is no direct formula to calculate this deflection, a trial‐and‐error method is used: assume a certain load on the main rear spring, perform the strength check; if it fails, reduce the assumed load, if it passes with margin, increase it. This assumed load can be determined by selecting a percentage of the vehicle’s total load at the moment the auxiliary rear spring begins to engage
Let a% be the percentage of the vehicle’s load at which the auxiliary rear leaf spring starts to engage.
Where: G = Z = 7050 (N)
By substituting the numerical values, we obtain:
Gc = 6650 + 0,2. 28925= 12435 (N)
=> G f = Gt - G c = 28925 – 12435 = 16490(N)
This is the load that both the main and auxiliary rear leaf springs support together.
Stress Calculations for the Auxiliary Rear Leaf Spring Table 9.
After determining the stiffness of the main rear leaf spring and the auxiliary rear leaf spring, the total system stiffness is:
Ct = C1 + C2 (5.12)
Where:
C1 : Stiffness of the auxiliary rear leaf spring.
C2: Stiffness of the main rear leaf spring.
Therefore:
Ct = 219958 + 85835 = 305793 (N/m)
After determining the spring stiffness, we calculate the static deflection of the main and auxiliary rear leaf springs:
ft = 0,0945 (m) = 9,45(cm)
Þ Sprung weight acting on the auxiliary rear leaf spring when the vehicle is fully loaded:
Gf = C .f = 0,0539. 219958 = 11862 (N)
The sprung mass acting on the main rear leaf spring is:
Gc = Gt – Gf = 28925 – 11862= 17063 (N)
3.3.4 Strength Calculation of the Main and Auxiliary Rear Leaf Springs
For a half-elliptical leaf spring, based on the previous reasoning, we assume the spring is rigidly clamped at the center. Using the concentrated load method to calculate the spring strength, suppose the leaf spring system is arranged as follows:
At point B, the deflections of the first and second leaves are equal; similarly, at points S, the deflections of the (k-1)-th and k-th leaves are equal. By formulating the deflection expressions at these points and equating them pairwise, we obtain a system of n-1 equations with n-1 unknowns X2,.....,Xn.
The system of equations is as follows:
A2.P + B2.X2 + C2.X3 = 0
A3.X2+ B3.X3 + C3.X4 = 0
........................................
A2.Xn-1 + Bn.Xn + Cn.Xn+1 = 0
3.3.5 Calculation for the Auxiliary Rear Leaf Spring
- Number of leaf springs: 9 leaves.
- Load applied to one end of the leaf spring:
=> Pt == 5930,5 (N)
We have: Jk = bk.hk3/12 ; J2 = ... J9
- The system of equations becomes:
0,77.5930,5 – 1,59.X2 + 0,81.X3 = 0
1,22.X2 – 2.X3 + 0,78.X4 = 0
1,26.X3 – 2.X4 + 0,74.X5 = 0
1,31.X4 – 2.X5 + 0,69.X6 = 0
1,40.X5 – 2.X6 + 0,60.X = 0
1,57.X6 – 2.X7 + 0,43.X = 0
2.X7 – 2.X8 = 0
After solving the system of equations, we obtain the results in the table:
X2 =X3 =X4 =X5 =X6 =X = X = 5930,5 (N)
With the values of Xk the bending moments at points A and B of each leaf spring are determined as follows:
The stress of the leaf spring is determined as follows:
s = MUAK/WAK (5.14)
Where:
Mu: Bending moment
Wuc : Moment resisting bending of the leaf spring
Comparing the stress values of the leaves in the table: [st]=600 (N/mm )
=> We find that all the leaf springs meet the strength requirements.
3.3.7 Strength Calculation of the Spring Eye
Where:
D: Inner diameter of the spring eye, selected as D = 50 (mm).
h0: Thickness of the main leaf spring, h0 = 8,5 (mm).
b: Width of the leaf spring, b = 80 (mm).
- The spring eye is subjected to tensile force Pk or braking force Pp. The magnitude of this force is determined by the following formula:
Pkmax=Ppmax=j. Zbx (5.16)
Where:
j: Coefficient of friction, taken as j = 0,7.
Zbx: Reaction force from the wheel path Zbx = 8532 (N).
Þ Pkmax= 0,7. 8532 = 5972,4 (N).
- Compressive (or tensile) stress at the spring eye is:
scompressive = 4,4 ( N/mm2)
- Combined stress at the spring eye is:
s combined = sbending + scompressive = 104+ 4,4 = 121 (N/mm2).
- Allowable combined stress is:
[scombined] =350MN/m2 = 350 N/mm2
=> s combined < [scombined]. Therefore, the spring eye is sufficiently strong.
3.4 Rear Shock Absorber Design
3.4.1 Determination of the Shock Absorber Damping Coefficient KG
The damping coefficient K of the suspension system plays an important role in providing vehicle comfort. Similar to the elastic components, it depends on how the shock absorber is mounted on the vehicle. The damping coefficient of the shock absorber K may be equal to or different from the damping coefficient of the suspension system.
3.4.1.1 Suspension System Damping Coefficient
Where:
y : Damping ratio, (y = 0, 15¸0, 3). Lấy y = 0, 2.
C: Suspension stiffness, C = 305793 (N/m).
M : Sprung mass per wheel, M = 2892,5 (kg).
Ktr : Damping coefficient of the suspension system.
=> The damping coefficient of the suspension system is determined by the formula:Ktt = 11896,26 Ns/m
3.4.1.3 Determination of Shock Absorber Damping Force
- Damping force during the compression stroke :
Pn = Kn. Vg
Where:
Vg: Piston velocity during compression, Vg = 0,3 (m/s).
Kn: Damping coefficient during compression, Kn= 7185,18 (Ns/m)
Pn = 7185,18.0,3 = 2155,5 (N).
- Damping force during hard compression:
Pnmax = Pn + K’n.(Vgmax-Vg) (5.20)
Where:
Vgmax: Piston velocity during hard compression, Vgmax = 0,6 (m/s).
K’n: Damping coefficient during hard compression, K’n= 0,6 (Kn)
Þ Pnmax = 2155,55 + 0,6.7185,18.(0,6-0,3) = 3448,8 (N)
- Damping force during the rebound stroke:
Ptr = Ktr. Vg (5.21)
Where:
Vg: Piston velocity during rebound, Vg = 0,3 (m/s).
Ktr: Damping coefficient during rebound, Ktr= 19759,24(Ns/m)
Þ Ptr = 19759,24.0,3 = 5927,7 (N).
- Damping force during hard rebound:
Ptrmax = Ptr + K’tr. (Vgmax-Vg) (5.22)
Where:
Vgmax: Piston velocity during hard rebound, Vgmax = 0,6 (m/s).
K’tr: Damping coefficient during hard rebound, K’tr= 0,6Ktr
=> Ptrmax = 5927,77 + 0,6. 19759,24.(0,6-0,3) = 9484,4 (N)
3.4.2 Determination of the Rear Shock Absorber Dimensions
3.4.2.1 Determination of Piston Diameter and Stroke
- The working stress condition is determined as: V = 0,3 (m/s).
- The heat dissipation power of a metallic object with heat dissipation area FFF is calculated as follows [3]:
Nt = 427. a. F. (Tmax - Tmin)
Where:
a: Heat transfer coefficient, chosen as a = 0,15 (J/m2)
T: Allowable temperature: Tmax=1500, Tmin = 200
- From the thermal balance equation: 1212,5 = 427. 0,15. F. (150-20)
=> F = 145620 (mm2)
Since F = pDn.L = 145619 (mm2).
- Preliminary shock absorber dimensions include the lengths of components:
Ld: Length of the shock absorber head
Lm: Length of the sealing part
LP: Length of the shock absorber piston
Lv: Length of the valve base
LG: Maximum working stroke of the shock absorber (LG must be greater than the wheel displacement between the upper stop and the lower stop)
- Therefore: L= L + L + L + L = 670 (mm) > 662,5 (mm)
=> Satisfies the thermal condition
3.4.2.4 Determination of Rebound Valve Hole Size
- The formula calculates the total area of the rebound valve holes:
Fvt=5,99.10^(-6) (m ) = 5,99 ( mm2)
- Diameter of each rebound valve hole:
FVT=(nπ.d^2)/4=5,99 ( mm )
=> Choose number of holes n = 4 - d = 1,4 (mm)
3.4.2.7 Determination of Shock Absorber Valve Spring Dimensions
- The length of the spring when the valve is fully open is calculated as :
Hm = n.d + d.n0 = 5.3 + 0,8.6 = 19,8 (mm)
Where :
d : Pitch between coils, d = 0,8 (mm).
n0 : Total number of coils, n0 = n+1 = 5 +1 = 6 (coils)
- Length of the spring when the valve is closed :
Hd = Hm + h = 19,8 + 2 = 21,8 (mm).
- Length of the spring in the free state :
Htd = Hd + l = 21,8 + 3,4= 25,2 (mm)
Where :
l Deformation of the spring when the valve is open.
=> l =P1/C=149,54/32970=4,54.10^(-3) m=4,54 (mm)
- Spring pitch: t = 4,13 (mm)
Conclusion:
The completed front leaf-spring suspension design meets all basic requirements for load-carrying capacity, durability, and operational stability. The selected spring rate and material ensure balanced load distribution, reduced vibration, and long service life. Damping performance and vehicle stability under cornering and emergency braking are also addressed. Experimental testing on a prototype or running vehicle is still needed to validate the calculations and fine-tune the design before full-scale production.
CHAPTER IV. MAINTENANCE AND REPAIR OF THE SUSPENSION SYSTEM
4.1 Phenomena and Causes of Suspension System Failures
4.1.1 Suspension System Noise
a) Phenomenon
When the vehicle is in service, abnormal noise can be heard from the suspension assembly, and the noise level increases with speed.
b) Causes
- Leaf springs are excessively worn, cracked, or broken, with reduced elasticity and insufficient lubrication.
- Spring pins and their bushings are worn or lacking grease.
- Cracks or fractures in the spring hanger or spring clip.
4.1.3 Inspection and Maintenance Methods
In-service Inspection
During vehicle operation, listen carefully for any unusual noise from the suspension assembly. If abnormal noise is detected or the vehicle’s stability is compromised, an inspection and prompt repair are necessary.
External Inspection of the Suspension
- Check for broken or loose spring seats, clips, and hangers.
- Use a magnifying glass to examine for cracks, misalignment, or sagging on the exterior of the leaf spring assemblies.
4.1.4 Suspension System Maintenance
- Clean all external suspension components:
+ Disassemble the leaf spring assemblies and thoroughly clean each part.
+ Inspect individual components for damage or wear.
+ Replace wearable parts on a scheduled basis (e.g., shims and spring seats).
+ Apply grease and reassemble all components.
4.2 Maintenance and Repair of the Suspension System
4.2.1 Disassembly Procedure
Sequence of Disassembly and Assembly of the Suspension System Table 16.
4.2.2 Assembly Procedure
The reverse of the disassembly sequence, after repair and replacement of any damaged components
Assembly Notes:
- Jack up and chock the wheels to ensure safety when working under the vehicle.
- Apply grease to all moving parts: spring bushings, pins, and leaf spring surfaces.
- scrutinize each component for cracks and any signs of thread damage.
- Use the correct tools and tighten all fasteners to the specified torque values.
- Pump grease into the spring pins and lubricate the leaf springs before final assembly.
4.3 Suspension System Maintenance
Stage 1 -Preparation
- Tools: Suspension disassembly/assembly hand‐tool set (wrenches, specialty sockets, pullers, presses), magnifying glass, gloves, safety glasses.
- Materials: Lubricating grease, cleaning solvent, clean rags, air compressor.
- Work Area: Ensure a clean, well-lit space with secure jacking points.
Stage 2 - Disassembly
- Jack under the frame rail ahead of the front spring eye; place jack stands under the frame (not the axle).
- Put a second jack under the axle (diff or each perch) to carry axle weight. Remove the wheels.
Stage 5 - Lubrication & Reassembly
- Grease all pin bushings, spring pins, and leaf-spring contact faces.
- Reassemble components in reverse order, torquing bolts to the specified values.
- Replace shock absorber oil and recharge nitrogen (if applicable).
Stage 6 - Final Check & Cleanup
- Install shock absorber: Secure upper and lower mounts, torque to spec.
- Operational check: Perform a bounce test, verify ride height, and conduct a short road test to ensure no abnormal noise or vibration.
- Industrial cleaning: Clean and dry all tools; tidy and organize the work area.
4.4 Repair of the Dependent Suspension System
4.4.1 Spring Pins, Bushings, and Spring Seats
a) Damage & Inspection
- Failure modes: Bushings, spring pins, and seats may develop cracks or wear excessively.
- Inspection methods: Use calipers and a dial indicator to measure bushing and pin wear (allowable wear ≤ 0.5 mm). Employ a magnifying glass to detect hairline cracks.
b) Repair
- Spring pins & pin eyes:
+ If wear exceeds the permissible limit, rebuild by welding and machining back to original dimensions.
+ If cracked, replace with new components.
- Spring seats:
Replace any seats that are cracked or excessively worn.
4.4.2 Leaf-Spring
a) Damage & Inspection
Failure modes:
- Cracked or broken leaf springs
- Surface wear on leaves
- Broken spring clamps, spring clips, or loose locating bolts
Inspection methods:
- Measure leaf thickness with calipers and compare against OEM wear limits.
- Use a magnifying glass to examine the exterior of each leaf and all clamps/clips for cracks.
b) Repair
- Worn or damaged shock absorbers must be replaced with the correct type.
- Shock absorbers that have run dry must be refilled with the proper oil.
CONCLUSION
After many months of focused work, we have completed the graduation project, “Design of the Suspension System for a 5.5-Ton Truck.” The project strengthened our grasp of suspension theory and practice-from load case definition and modeling to analysis, evaluation, and selection of viable design solutions.
Working with realistic loading conditions, we performed detailed calculations and verified the outcomes against widely used performance criteria. The results meet the targeted standards for safety, efficiency, and durability. The project helped us bridge classroom knowledge with real engineering tasks, marking our first substantive step into practical automotive development—especially in heavy-duty suspension design within Vietnam.
Given time and resource limits, I acknowledge that the work still has gaps and does not cover every related aspect. We welcome comments and suggestions from instructors and peers to refine and extend the study in future iterations.
I am deeply grateful to: Dr………………and the Academic Group of Automotive Engineering for their guidance and support throughout this project.
Sincerely!
REFERENCES
[1]. Nguyễn Trọng Hoan, Thiết kế tính toán ô tô, NXB giáo dục Việt Nam, 2019.
[2]. Nguyễn Khắc Trai, Nguyễn Trọng Hoan, Hồ Hữu Hải, Phạm Huy Hường,
Nguyễn Văn Chưởng, Trịnh Minh Hoàng, Kết cấu ô tô, NXB Bách Khoa Hà Nội, Hà Nội 2009.
[3]. Ninh Đức Tốn, Dung sai và lắp ghép, NXB giáo dục Việt Nam, 2000.
[4]. Trịnh Chất, Lê Văn Uyển, Tính toán thiết kế hệ dẫn động cơ khí, NXB giáo dục, 2006.
[5]. Nguyễn Trọng Hiệp, Chi tiết máy, NXB giáo dục, 2011.
[6]. Nguyễn Phùng Quang, Matlab & Simulink, NXB Khoa học và kỹ thuật, 2006.
[7]. Hồ Hữu Hải, Bài giảng Cơ điện tử ô tô cơ bản Hà Nội.
[8]. Hino 700 series, Service manual
"TẢI VỀ ĐỂ XEM ĐẦY ĐỦ ĐỒ ÁN"