2024

DIFFERENTIAL

N.H.TAN PHAT – T.CONG NGUYEN – N.T

BAO SON
NIIE – K20
8/6/2024
 ABSTRACT
Dear teachers and students,

First and foremost, we would like to extend our warm greetings to all the esteemed
teachers and students who have taken the time to consult this lecture. This lecture has been
compiled to provide in-depth knowledge and a systematic understanding of differential
gear, a crucial and indispensable field in automotive engineering. During the preparation
process, we have focused on selecting and presenting essential content, combining theory
with practical applications, to help students not only grasp fundamental knowledge but also
apply it in real-world scenarios.

The objective of this lecture is to impart basic and advanced knowledge, helping
students understand the important definitions, functions, and structures of the differential
gear. Furthermore, it aims to develop practical skills, guiding students on how to apply
their knowledge to specific situations, thereby enhancing their problem-solving abilities
and critical thinking skills. Particularly, we encourage self-study and research, providing
opportunities for students to explore further into the specialized and extended aspects of
differential gears.

We hope that this lecture will serve as a useful resource, effectively supporting the
learning and research processes of all students. We eagerly await valuable feedback from
our esteemed teachers and students to further improve and refine this lecture.

Best Regards!

Nguyen Tran Bao Son.

Truong Cong Nguyen.

Nguyen Huynh Tan Phat.

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 TABLE OF CONTENT
THEORY ............................................................................................................................ 1
1. Drive axle .................................................................................................................... 2
1.1. Definition ............................................................................................................. 2
1.2. Function ............................................................................................................... 2
1.3. Requirements ...................................................................................................... 2
1.4. Classification ....................................................................................................... 2
1.5. General structure ................................................................................................ 3
2. Final Drive ...................................................................................................................... 4
2.1. Function ............................................................................................................... 4
2.2. Requirements ...................................................................................................... 4
2.3. Classification ....................................................................................................... 4
2.4. General Structure of Single-Stage Final Drive ................................................ 5
3. Differential ................................................................................................................. 6
3.1. Functions ............................................................................................................. 6
3.2. Requirements ...................................................................................................... 6
3.3. Classification ....................................................................................................... 6
3.4. Analysis of Symmetrical Bevel Gear Differential Structure .......................... 7
4. Axle Shaft ................................................................................................................. 12
4.1. Function ............................................................................................................. 12
4.2. Requirements .................................................................................................... 12
4.3 Classification ...................................................................................................... 12
GUIDE TO USING AN OPEN DIFFERENTIAL MODEL ....................................... 15
1. Introduce ............................................................................................................. 16
2. Structure ............................................................................................................. 16
2.1. The Shelf ............................................................................................................ 17
2.2. Drive Axle .......................................................................................................... 18
3. Instructions for Use ........................................................................................ 19
REVIEW........................................................................................................................... 23
Multiple Choice Question: .......................................................................................... 24

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 Review Questions:........................................................................................................ 29
REFERENCE................................................................................................................... 30

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THEORY

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1. Drive axle
1.1. Definition
The drive axle of a car is a component of the powertrain system. The wheels of the
drive axle receive power from the transmitted engine and generate thrust at the contact
patch with the road surface, allowing the car to move. A car has at least one drive axle.

1.2. Function
₋ Support the weight of the car distributed on it and receive the reaction forces from
the road surface acting on the car through the wheels.
₋ Assume functions such as a gearbox (reducing the speed of rotation transmitted
from the engine) and distributing power to the drive wheels.
₋ Change the direction of rotation from the engine to the wheels at a 90-degree angle
(rear differential).
₋ Combine with the steering system to control the direction of motion of the vehicle
(front differential).

1.3. Requirements
₋ Ensure high rigidity and mechanical durability.
₋ Dimensions must ensure clearance under the vehicle.

1.4. Classification
According to the arrangement of the steering system::
₋ Front Differential (Steering axle).
₋ Rear Differential (Non-steering axle).

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 Front differential Rear differential

Figure 1.4. 1: Two Type Differential (Source: Internet)

1.5. General structure

The general structure of the drive axle assembly includes: the Final Drive, the
Differential Unit, the Axle Shafts, and the Axle Housings. The entire drive axle assembly
can be arranged on the vehicle body with independent suspension systems or linked to the
body through dependent suspension systems.

Figure 1.5. 1: General Structure Of Drive Axle (Source: Internet)

The Final Drive (1), (2) is connected to the powertrain through the Drive Shaft (3),
which usually has a high transmission ratio and significantly affects the ground clearance
of the vehicle. The Differential (4) is compactly arranged within the Ring Gear (2), with

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the axle shafts leading to the drive wheels through the Axle Shafts (6). The entire drive axle
assembly is enclosed in Axle Housings (5).

2. Final Drive
2.1. Function
₋ Transmit and convert (reduce speed) rotational motion from the gearbox to the drive
wheels.
₋ Increase the transmission ratio to enhance torque, thereby increasing the pulling
force of the drive wheels.
₋ Change the direction of rotation from the engine to the wheels at a 90-degree angle
(rear differential).

2.2. Requirements
₋ Ensure appropriate transmission ratio to match towing quality and dynamic
characteristics of the vehicle.
₋ Ensure fuel economy.
₋ Design to provide necessary ground clearance for the vehicle.
₋ High operational efficiency, minimal noise, and high stiffness.
₋ Suspension components should have minimal weight.

2.3. Classification
₋ According to the transmission ratio: the Final Drive is divided into Single-Stage
Final Drive and Two-Stage Final Drive. Single-stage final drive is commonly used in
modern car models, while two-stage final drive is typically used in off-road vehicles,
military vehicles, or other specialized vehicles (the second stage transmission is often a
gear increase in the gearbox).

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 ₋ According to the type of gear: Spur Gear (straight bevel), Helical Gear (spiral
bevel), hypoid gear, worm gear, and chain. Vehicles with longitudinally-mounted engines
typically use helical gears or hypoid gears. Spur gears are commonly used for vehicles with
transversely-mounted engines.

₋ According to the number of gear pairs: Single-Stage Final Drive and Double-Stage
Final Drive. Single-stage final drive consists of only one pair of meshing gears, typically
used for passenger cars, SUVs, or small trucks. Double-stage final drive consists of two
pairs of gear sets, including two types: center differential final drive and edge gear final
drive. Double-stage primary transmission is commonly used in heavy-duty trucks.

2.4. General Structure of Single-Stage Final Drive

The single-stage Finla Drive consists of a Pinion Gear and a Ring Gear meshing
with each other. The general structure typically includes three types: spur gear, helical gear,
and hypoid gear.

Figure 2.4. 1: Final Drive (Souce: Internet)

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3. Differential
3.1. Functions
₋ The function of the differential in the drivetrain is to ensure that the driving wheels
can rotate at different speeds, transmitting and distributing torque from the primary
transmission to the wheels.
₋ Thanks to the differential, the vehicle can move smoothly around corners. If the two
wheels on the driving axle are rigidly connected, it will create a solid link between the two
wheels.
3.2. Requirements
₋ Distribute torque between wheels or axles in proportion to ensure good traction
under load.
₋ Ensure different rotation speeds when two driving wheels encounter curves or
contact with different surfaces.
₋ The size of the differential must be compact.
₋ High transmission efficiency.
3.3. Classification
₋ According to function: Wheel Differentials, Axle Differentials, Center Differentials.
Wheel differentials are used to distribute torque between wheels on the same axle. Axle
differentials distribute torque between front and rear axles in four-wheel-drive (4WD) or
all-wheel-drive (AWD) vehicles. Center differentials distribute torque between internal
drivetrain components in complex systems or multi-axle vehicles.

₋ According to structure: Spur Gear Differentials, Bevel Gear Differentials, Cam

Differentials, Screw Differentials, Hydraulic Friction Differentials, Variable-Ratio
Differentials.

₋ According to torque distribution characteristics: Symmetrical Bevel Gear

Differentials and Asymmetrical Bevel Gear Differentials. Symmetrical differentials evenly
distribute torque across axles, suitable for normal operating conditions. Asymmetrical
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differentials unevenly distribute torque across axles, often used in applications requiring
higher torque for a specific axle.

3.4. Analysis of Symmetrical Bevel Gear Differential Structure

3.4.1 Symmetrical Bevel Gear Differential

Figure 3.4.1. 1: Symmetrical Bevel Gear Differential (Source: Internet)

The Symmetrical Bevel Gear Differential consists of a Differential Case (1)

connected to the Ring Gear (5) of the final drive, so the Differential Case (1) always
rotates together with the Ring Gear (5). Inside the Differential Case (1), there are Spider
Gears (2) and Side Gear (3). The Spider Gears (2) can range in number from 2 to 4
gears, with two main movements: rotating with the Differential Case (1) and spinning
around their own axis. The Spider Gears (2) always mesh with the Side Gears (3).

Relationship of Symmetrical Differential:

ω1 + ω2 = ω

(ω1, ω2: angular velocity of the left and right half-shafts – ω: angular velocity of the
differential case).

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 ₋ When the vehicle is moving straight: the rolling resistance on both driving wheels is
equal, at this point, the spider gears will not rotate around their axis, the spider gears mesh
with the side gears so the two wheels will rotate at the same speed.
ω1 = ω2 = ω

Figure 3.4.1. 2: Go Straight Ahead (Source: Internet)

₋ When the vehicle is turning: the inner axle experiences a greater rolling resistance
than the outer axle, requiring the wheel speed on the inside to slow down, reducing the
angular velocity of the wheel. At this point, the spider gears begin to rotate around their
axis. Consequently, the torque on the left and right wheels M1; M2 and the angular
velocities ω1; ω2 are not equal: M1 ≠ M2 và ω1 ≠ ω2.
ω1 = ω - ω2

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 ω2 = ω - ω1

Figure 3.4.1. 3: Turning (Source: Internet)

₋ When one wheel is sliding: the inner axle experiences a force large enough to prevent
it from rotating, then the torque and angular velocity from the main transmission will be
transmitted entirely to the remaining axle. The difference in rotational speed between the
two wheels helps reduce pressure and maintain vehicle stability while sliding.
ω2 = ω (ω1 = 0)

ω1 = ω (ω2 = 0)

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 Figure 3.4.1. 4: Siding (Source: Internet)

3.4.2. Advantages and disadvantages of various types of Differentials

Differential
Advantages Disadvantages
Type

 Simple construction, easy to  Low torque load capacity, not

manufacture and maintain. suitable for heavy-duty trucks.
Symmetrical  Compact size, saving space.  Low durability, prone to
Bevel Gear  Lightweight, reducing vehicle damage under harsh operating
Differential weight. conditions.
 High transmission efficiency,  High noise level.
saving energy.
 Better traction, especially on  Energy wastage, resulting in
Friction limited
slippery terrain. higher fuel consumption.
slip differential

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  Improved stability, reducing  Increased tire wear.
the risk of wheel slippage.  Increased load capacity,
 Easier to control when turning reducing the lifespan of the
or braking abruptly. transmission system.
 High precision, ensuring  Complex construction,
synchronization among difficult to manufacture and
wheels. maintain.

Spur Gear  High transmission efficiency,  Large size and weight.

reducing energy loss.  High cost.
 Durable, capable of bearing
heavy loads.
 High transmission ratio, slow  Low transmission efficiency,
movement, high pulling force. high fuel consumption.
 Smooth operation, low noise,  High friction, quick wear.
minimal vibration.  High cost.
Screw Shaft -  High self-locking ability,

Gear Rack capable of moving on steep

terrain without braking.
 Compact, space-saving.
 Simple construction, easy to
manufacture, maintain.
 High load-bearing capacity,  Noisy, low transmission
durable. efficiency, high friction,
 Simple construction, cost- requires frequent lubrication.

Chain effective, compact size.

 Suitable for heavy-duty
trucks, operates in noisy
environments.

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4. Axle Shaft
4.1. Function
₋ Used to transmit torque from the differential to the drive wheels.
₋ Eliminates the uneven speed between the axle shaft and the drive shaft, regardless
of the coupling.

4.2. Requirements
₋ Must transmit torque to the drive wheels.
₋ Must withstand high torque in long working conditions.
₋ The axle shaft must be well balanced.
₋ Must have high mechanical fatigue strength.

4.3 Classification
₋ According to the structural characteristics of the axle shaft: Integral Axle Shaft and
Split Axle Shaft. The integral axle shaft is used in driven axles with dependent suspension
systems. The split axle shaft is used in driven axles with independent suspension systems.
₋ According to load-bearing characteristics: Non-Floating Axle Shaft, ½ Floating
Axle Shaft, ¾ Floating Axle Shaft, and Fully Floating Axle Shaft.

Figure 4.3. 1: Non-Floating Axle

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 ₋ Non - Floating Axle: both inner and outer bearings are directly mounted on the axle
shaft. In this case, the axle shaft bears all forces, including the reaction forces from the road
and the ring gear's circumferential forces, and thus is no longer used.

Figure 4.3. 2: 1/2 Floating Axle

₋ Semi Floating Axle (1/2 Floating Axle): the inner bearing is mounted on the
differential housing, and the outer bearing is directly mounted on the axle shaft.

Figure 4.3. 3: 3/4 Floating Axle

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 ₋ ¾ Floating Axle: the inner bearing is mounted on the differential housing, and the
outer bearing is mounted outside the axle housing and wheel hub, with the outer bearing
not in contact with the axle shaft.

Figure 4.3. 4: Full Floating Axle

₋ Fully Floating Axle: the inner bearing is mounted on the differential housing, and
two outer bearings are used, both positioned as in the ¾ load reducing axle shaft
configuration .

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 GUIDE TO USING AN OPEN
DIFFERENTIAL MODEL

*Note:
 The model has some details reduced compared to reality.
 Handle with care during disassembly as the model is made of plastic and can break
easily.
 Follow the instructions carefully to ensure product quality and durability.

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1. Introduce

Figure 1. 1: 3D “Open Differential” Model Design

This is an overview of the model with an overall size of 750mm x 300mm x 290mm.
The product is designed to serve educational purposes, supporting instructors and students
during theoretical lessons, helping students gain a better understanding of the structure and
operating principles of the Open Differential before moving on to practical sessions.

Figure 1. 2: Realistic “Open Differential” Model

2. Structure
The product consists of two main parts: the Shelf and the Drive Axle.

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 Figure 2. 2: The Shelf

Figure 2. 1: Drive Axle

2.1. The Shelf

The Shelf is constructed from 20mm x 200mm extruded aluminum, a common type
of aluminum used in 3D printer assemblies. The use of this material allows for easy
disassembly and replacement by users. Additionally, its low cost and lightweight properties
help reduce both product expenses and weight.

Aside from its primary function of supporting the model, the Shelf also integrates a
system for altering the operating conditions of the Open Differential, including a rubber
base that is screwed onto the threaded rod.

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 Figure 2. 3: Threaded Rod & Rubber Base

2.2. Drive Axle

Figure 2. 4: Engineering Design Model

Table: Summary of Components on the Model

Number, Detail, Material, Quantity
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 ITEM
PART NUMBER QTY.
NO.
1 Differential Carrier Housing 1
2 Differential Carrier Case 1
3 Flange Face 1
4 Rear Axle Housing (a) 1
5 Rear Axle Housing (b) 1
6 Rear Axle Housing (c) 1
7 Rear Axle Housing (d) 1
8 Rear Axle Housing (e) 2
9 Rod Bearing Cap 2
10 PP Union (a) 2
11 PP Union (b) 2
12 PP Union (c) 2
13 Cross Shaft 1
14 Hand Crank (a) 1
15 Hand Crank (b) 1
16 Opinion Gear 2
17 Ring Gear 2
18 Side Gear 2
19 Side Gear Washer 2
20 Spider Gear 2
21 Spider Gear Washer 2
22 Axle Shaft 3
23 Wheel 2
24 Wheel Washer 2
25 Ball Bearing – 6805 (No. 26 - 29) 4
30 Ball Bearing – 6806 (No. 31 - 34) 2
35 M5 (a) 4
36 M6 x 60 4
37 Nut Square M5 8
38 M5 (b) 30
39 ISO 4762 M5 x 16 - 16N 30
40 M8-20mm 2
41 Split Pin 2

3. Instructions for Use

3.1. Operating Principles
The model simulates the operation of the Open Differential in three scenarios:

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  Go straight ahead.
 Turning.
 Slipping one wheel.

When you manually rotate hand crank, the pinion gear engages with the ring gear,
causing the differential to rotate. Depending on the adjustment of the preload system,
different operating scenarios will be produced.

*Note:
 Rotate the hand crank countterclockwise to simulate the vehicle moving forward.
 When simulating turning and slipping scenarios, adjust the preload system on the
left-hand side (when facing the input shaft of the model).
 Use two 10mm wrenches or two pliers for better control when adjusting the preload
system.

a) Scenario 1: Simulating Going Straight

Step 1: Do not tighten the roller

press system.

Step 2: Turn the orange hand crank.

Result: The two wheels will rotate

at the same speed.

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 b) Scenario 2: Simulating Turning

Step 1: Tighten the roller press

system (left side) to press on the
roller with a moderate force, the
roller can still rotate under heavy
load.

Step 2: Turn the orange hand crank.

Result: The left wheel (roller

pressed) will rotate slower than the
other wheel.

c) Scenario 3: Simulating Slipping One Wheel

Step 1: Tighten the roller press

system (on the left side) to apply a
strong force, preventing the roller
from rotating further.

Step 2: Turn the orange hand crank.

Result: The left wheel will remain

stationary compared to the other
side.

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3.2. Instructions for Assembly and Disassembly
₋ Instructional videos at link:
https://drive.google.com/drive/folders/1PEK9F6Pdw6cX926iVg-
ZGQC9qSb6tDrv?usp=sharing

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REVIEW

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 Multiple Choice Question:
Question 1: The differential ensures that the two driving wheels rotate at different speeds
when:
A. the vehicle is turning.
B. the vehicle is ascending a slope.
C. the vehicle is descending a slope.
D. the vehicle is moving straight ahead.

Question 2: The side gear is linked to the inner end of the axle shaft by:
A. Splines.
B. Bolts.
C. Tapered connection.
D. Locking pin.

Question 3: Among the types of differentials, which one is the most basic?
A. Open differential
B. Torque-sensing differential
C. Limited-slip differential
D. Active differential

Question 4: The minimum number of differentials in a car is:

A. 1 .
B. 2 .
C. 3 .
D. 4 .

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Question 5: What is the main function of an open differential?
A. Increase vehicle speed
B. Distribute torque from the engine to the wheels
C. Reduce fuel consumption
D. Control the braking system

Question 6: Which mechanism helps the differential operate efficiently when the vehicle
turns?
A. Bevel gears
B. Gearbox
C. Driveshaft
D. Clutch

Question 7: Which type of differential helps control part of the torque to improve
traction?
A. Open differential
B. Limited slip differential (LSD)
C. Locking differential
D. Electronic differential

Question 8: Which sign indicates a problem with the differential?

A. Unusual noise when turning
B. High fuel consumption
C. Sudden decrease in speed
D. Uneven acceleration

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Question 9: When one wheel loses traction, what does an open differential do?
A. Distribute torque evenly to both wheels
B. Transfer all torque to the wheel with better traction
C. Transfer all torque to the wheel that lost traction
D. Disengage the engine connection

Question 10: The component used to transmit torque from the main drivetrain to the
driven wheels is:
A. Differential.
B. Auxiliary gearbox.
C. Axle.
D. Clutch assembly.

Question 11: How does a Limited Slip Differential (LSD) work?

A. Allows wheels to spin freely
B. Locks wheels at a fixed rotation speed
C. Controls and distributes torque between wheels to reduce speed difference
D. Increases the rotation speed of the wheels

Question 12: What are the characteristics of a locking differential?

A. Allows wheels to spin at different speeds
B. Locks the wheels to rotate at the same speed
C. Automatically adjusts torque between wheels
D. Reduces friction between wheels

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Question 13: When the vehicle turns left, the right axle will rotate:
A. Faster than the left axle.
B. Slower than the left axle.
C. At the same speed as the left axle.
D. Faster or slower than the left axle depending on the radius of the turn.

Question 14: What is the main disadvantage of an open differential?

A. Poor traction in slippery conditions
B. High cost
C. Requires frequent maintenance
D. Cannot be used on highways

Question 15: The differential in a rear-wheel drive (RWD) vehicle is located:

A. At the front axle
B. At the rear axle
C. In the middle shaft
D. In the transmission

Question 16: Fully floating axles are used in which type of vehicles:
A. Passenger cars.
B. Light trucks.
C. Heavy-duty trucks.
D. All types of vehicles.

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Question 17: Three-quarter floating axles are used in which type of vehicles:
A. Light trucks.
B. Passenger cars.
C. Heavy-duty trucks.
D. Sports cars.

Question 18: Half floating axles are primarily used in which type of vehicles:
A. Heavy-duty trucks.
B. Light trucks.
C. Passenger cars.
D. Coaches.

Question 19: For vehicles equipped with auxiliary gearbox, the necessary number of
differential gears is:
A. 1 .
B. 2 .
C. 3 .
D. 4 .

Question 20: The open differential is not suitable for driving conditions:
A. Normal city streets
B. Highways
C. bad and slippery road
D. Flat roads

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Answer:
1 2 3 4 5 6 7 8 9 10
A C C A B A B A C C
11 12 13 14 15 16 17 18 19 20
C B B A B D B C C C

Review Questions:

Question 1: What is a drive axle? Classify drive axles.

Question 2: Classify the final drives in automobiles.
Question 3: Purpose and structure of an axle beam.
Question 4: Purpose and classification of half-shafts.
Question 5: Classification of differentials.
Question 6: Advantages and disadvantages of a symmetrical bevel gear.
Question 7: Dismantling the differential process.
Question 8: Installing the differential process
Question 9: Types of Bearing Arrangements?
Question 10: Signs of a Faulty Differential Gear

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 REFERENCE
[1] Nguyễn Khắc trai, Nguyễn Trọng Hoan, Hồ Hữ Hải…2020. Kết cấu Ô tô, NXB
Bách Khoa Hà Nội, 2020.
[2] Nguyễn Ngọc Bích, 2001 Lý thuyết và cấu tạo Ô tô, NXB Tp.HCM, 2001.

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