RESEARCH ON DISTRIBUTED TRACTION POWER CONTROL FOR WHEELS ON THE DRIVE AXLE OF VEHICLES USING ABS

UNIVERSITY OF TRANSPORT AND COMMUNICATIONSPHAN TAN TAI RESEARCH ON DISTRIBUTED TRACTION POWER CONTROL FOR WHEELS ON THE DRIVE AXLE OF VEHICLES USING ABS Major: Power Mechanical Engineeri

UNIVERSITY OF TRANSPORT AND COMMUNICATIONS

PHAN TAN TAI

RESEARCH ON DISTRIBUTED TRACTION POWER CONTROL FOR WHEELS ON THE DRIVE AXLE OF VEHICLES USING ABS

Major: Power Mechanical Engineering

Code No: 9520116

THESIS SUMMARY

Hanoi, 2025

Department of Automotive Engineering - Faculty of Mechanical

EngineeringUNIVERSITY OF TRANSPORT AND COMMUNICATIONS

Scientific supervisors:

1) Assoc Prof TRAN VAN NHU

2) Assoc Prof DAO MANH HUNG

The dissertation was defended before the University dissertation juryat:

UNIVERSITY OF TRANSPORT AND COMMUNICATIONS

At on ,

The dissertation can be accessed at the library of UNIVERSITY OFTRANSPORT AND COMMUNICATIONS and the National Library ofVietnam

Research Urgency

The differential distributes power to wheels based on traction tions between both wheels, allocating more power to the wheel with lesstraction, resulting in power loss While various solutions have been imple-mented, traction power distribution control using ABS plays a crucial roleand has become increasingly urgent

Research Subject

Study of the rear-wheel drive powertrain system on the 2003 Ford erick 2.0L equipped with hydraulic ABS actuators for drum brake mecha-nisms

Mav-Research Scope

Investigation of straight-line vehicle motion on level surfaces with ferent traction coefficients between wheels, testing traction power distri-bution control on HIL model

Practical Significance

ABS-based traction power distribution control has practical tions Research on design and quality improvement has practical signif-icance in technology mastery The traction power distribution controllercan be further developed for real vehicle implementation Results can serve

applica-as reference materials for studying and researching vehicle dynamics andcontrol

CHAPTER 1 LITERATURE REVIEW OF

RESEARCH PROBLEM 1.1 Overview of Traction Control in Automobiles

The differential, integrated within drive axles and transfer cases, tributes power to wheels and drive axles while ensuring that wheels anddrive axles can rotate at different speeds, preventing power circulationphenomena However, when a wheel experiences lower traction or losesground contact, the differential allocates more power to this wheel, result-ing in complete wheel slip, vehicle immobilization, and engine power loss.Consequently, in specific circumstances, it becomes necessary to controlpower distribution to drive wheels and axles to ensure vehicle mobilityand enhance traction capability

dis-1.2 Solutions for Enhancing Vehicle Traction ity

Capabil-Figure 1.1: Solutions forEnhancing Vehicle Traction

The solutions are illustrated in

the Figure 1.1, notably, the trend

of combining wheel and engine

con-trol is receiving significant

atten-tion and development

1.2.1 Limited Slip

Differen-tial Implementation

Figure 1.2 demonstrates the

static force analysis of a drive axle

utilizing a limited slip differential

when one wheel is on a low-friction

surface (φmin) and the other on a high-friction surface (φmax)

Figure 1.2: Force Analysis on Drive Axle

When wheel speeds

differ between sides,

internal friction torque

F6= M4

rbx =

M12rbx+

Mms

rbx

(1.2)

When F5 < Fφmin, the left wheel can fully utilize force F5 When

F5 = Fφmin, the left wheel experiences complete slip From Expression(1.2), traction force F6 is determined by F5:

of Kδ = 1 (or Mms = 0.5M1) must be used to ensure complete torquetransmission

1.2.2 Independent Wheel Braking Implementation

Figure 1.3: Dynamic analysis ofsymmetric differential on drive axle

Independent braking on the

low-traction wheel Static force

analysis is shown in Figure 1.3)

Assuming left wheel has low

trac-tion, then Mp1 ̸= 0, Mp2 = 0, the

torque on left/right axle shafts:

The traction force on good traction

surface F6 is determined by

trac-tion force F5:

F6= M4

rbx =

M12rbx =

 M12rbx −Mp1

rbx

+Mp1

rbx = F5+

Mp1

rbx (1.6)When one wheel has no traction, F5 = Fφmin = 0, traction force Fx =

F6= Mp1/rbx Given M3≥ 0, according to expression (1.5) → Mp1max=

0, 5M1, maximum traction torque equals only 0, 5M1 The differential lockcoefficient Kδ is defined by the formula:

1.3 Domestic and International Research Related to the Research Problem

1.3.1 Differential Control Solutions

These structural solutions typically employ differential locks (NguyenNgoc Que et al determined differential lock coefficients in wheeled trac-tors), limited-slip differentials (Gadola M et al utilized LSD to enhancetraction efficiency), or active differentials (Shukul and Hansra implementedmain brake mechanisms with independent actuation to brake faster-rotatingwheels) to help vehicles traverse low-traction surfaces

1.3.2 Wheel Slip Control Solutions

Wheel control aims to maintain wheel slip within permissible limits (LeAnh Vu, Tran Van Thoan), optimal slip control (Pavel V.O et al., Ren H.and Lei Y.) has been applied in anti-slip control and braking systems (HoHuu Hung’s pneumatic ABS control) The relationships between frictioncoefficients and longitudinal wheel slip, or torque transmission throughdifferentials and wheel resistance torques, were demonstrated by Le Anh

Vu et al To evaluate actuator response capabilities, Ferro designed archical controllers for ABS control

hier-1.3.3 Integration of Engine Power and Wheel Control

Even with high wheel friction coefficients, wheels may not fully utilizeengine power, resulting in wheel slip To reduce wheel spin and redistributepower to wheels with better traction, combined engine power reductioncontrol is implemented (Tran Van Thoan, Song and Byun employed enginepower reduction solutions) In cases where both wheels have equal lowtraction, engine power control and/or simultaneous wheel braking can beused to dissipate excess engine power (Hosomi et al implemented combinedengine power and brake control)

1.4 Chapter 1 Conclusions

Vehicle motion on surfaces with uneven friction coefficients betweenwheels results in differential power distribution to both wheels While mul-tiple solutions exist, recent research has focused on automatic control ofinternal friction torque and independent wheel brake torque Based on thisliterature review, the dissertation has clearly defined objectives, content,and methodology for researching traction power distribution control onpassenger vehicle drive axles using ABS

CHAPTER 2 DEVELOPMENT OF VEHICLE

POWERTRAIN DYNAMIC MODEL INCORPORATING DIFFERENTIAL 2.1 Theoretical Basis for Dynamic Model Develop- ment

The vehicle powertrain dynamic model is developed based on D’Alembert’sprinciple and Lagrange’s equations of the second kind

2.2 General Dynamics of Vehicle Powertrain

2.2.1 Model Development Assumptions

- Engine vibration on chassis is neglected;

- Clutch is considered fully engaged without slip;

- System elements are considered dimensionless, with concentrated massmoments of inertia and elastic-viscous damping connections between ele-ments;

Figure 2.1: Dynamic model diagramshowing connections between powertrain

system components

- Elastic-damping

charac-teristics are considered

ear, with damping force

lin-early dependent on relative

At constant engine

power (Ne = N0),

Mefollows Expression

(2.1), and is limited

by the external

char-acteristic curve,

ac-cording to Expression (2.2)

Where: Nemax - maximum engine power; Megh - limiting torque perengine external characteristics; ωeN - engine angular velocity at maximumpower Nemax; a, b, c - Leiderman coefficients

curve (Fx(λ)), dependent on reaction force (Fz) and tire coefficients Theresearcher determined coefficients B, C, D, E and tire parameters for sim-ulation (tire 225/50R17) with values: b1 = 1, 65; b2 = 0; b3 = 0, 96; b4 =0; b5= 0, 2; b6= 0; b7= 0; b8= 0; b9= 0, 82.

2.5.2 "Brush" Model of Wheel-Road Surface Contact

(2.7)

2.6 Straight-Line Vehicle Dynamics

m¨x = F5+ F6− Fw− Ff (2.8)(

x - vehicle acceleration; Ff - total

rolling resistance force

Dynamic equations for right

and left drive wheels (Equation

F5(λ1) = D1sin (C1arctan (B1λ1− E1(B1λ1− arctan(B1λ1))))

F6(λ2) = D2sin (C2arctan (B2λ2− E2(B2λ2− arctan(B2λ2))))

(2.10)

2.7 Simulation of Differential Effects on Vehicle namic Performance

Dy-2.7.1 Model Parameters and Operating Conditions

System simulation and analysis conducted for different road surfaces:

- Road Type A (MD-A): Very low adhesion, slippery surface, completewheel slip (λ = 100%);

- Road Type B (MD-B): Low adhesion, slippery surface, partial wheelslip (30% < λ < 100%);

- Road Type C (MD-C): Good adhesion, non-slippery surface, very lowwheel slip (λ < 30%)

Analysis parameters include:

a) Kinematic Parameters: Angular velocities of: engine ωe; differentialcase ω1; left wheel ω5 and right wheel ω6; Vehicle velocity Vx= ˙x

b) Power and Traction Efficiency Parameters: Power at: differentialcase N1= M0i0ω1; left axle shaft N3= M3ω5 and right N4= M4ω6; leftwheel N5= F5Vxand right N6= F6Vx Traction efficiency ηk= Nk/Ne=(N5+ N6)/Ne

c) Slip Coefficient and Traction-Adhesion Force Parameters: Dynamicslip coefficients for left wheel λ1and right λ2; Torque on left axle shaft M3and right M4; Traction force of left wheel F5 and right F6

On MĐ-C, power N5 = N6 ηk is maximum and constant (ηk =

96, 21%)

On MĐ-A, ω6= 0, ω5 increases rapidly to limit value and doubles ω1.When both wheels have equal adhesion, ω5 = ω6 Trên MĐ-B, ω5 ̸= ω6,this difference decreases as system approaches stability

Traction forces at right and left wheels are equal in all simulation cases.Moments: Me, M3, M5, M4, M6are equal in RT-A and RT-B cases (Figure2.3)

k k k

(d) Hiệu suất kéo

Figure 2.2: Traction efficiency and power distribution between wheels

2.8 Chapter 2 Conclusions

The vehicle powertrain dynamic model incorporating differential hasbeen developed and simulated Quantitative analysis results align withdifferential power transmission and distribution laws under uneven wheeladhesion conditions

The challenge lies in controlling traction power redistribution to wheelswith low or zero adhesion, ensuring power distribution matches wheel-road surface friction coefficients To address this issue, friction/resistancetorque must be applied to slipping wheels to enable appropriate differen-tial power redistribution between wheels Rather than directly controllingtraction power distribution, the dissertation focuses on controlling angularvelocities of both wheels

CHAPTER 3 TRACTION POWER DISTRIBUTION

CONTROL ON DRIVE AXLE 3.1 Control Problem of Traction Power Distribution

on Drive Axle

3.1.1 Problem Statement

Symmetric differentials with low internal friction maintain equal torque

on axle shafts Power distribution favors wheels with lower adhesion cients, resulting in higher rotational speeds

coeffi-Figure 3.1: Methods of Traction Power

Distribution Control

To address this, the

re-searcher proposes using

in-dependent ABS actuators

to equalize wheel speeds

on both sides This

redis-tributes power appropriately

between wheels, enabling

ve-hicles to traverse difficult

terrain while reducing power

loss and improving traction

Clutch, gearbox, and universal

joint are reduced to the final drive

in-put shaft, with engine power applied

at the final drive shaft Where: J0′

-equivalent mass moment of inertia of

clutch, gearbox, and universal joint

re-duced to final drive input shaft; N0, M0, ω0- power, torque, and velocity

of final drive input shaft

Equation (3.2) describes the simplified system dynamics, where: Mp1, Mp2are brake torques at left and right wheels

F5(λ1) = D1sin (C1arctan (B1λ1− E1(B1λ1− arctan(B1λ1))))

F6(λ2) = D2sin (C2arctan (B2λ2− E2(B2λ2− arctan(B2λ2))))

(3.2)

Figure 3.2: PID ControllerDiagram for Traction PowerDistribution Control

3.2 Traction Power

Distri-bution on Drive Axle Using

PID Control Method

3.2.1 PID Controller Design

Assuming the left wheel runs on

RT-A and the right wheel on RT-C

When speed difference between wheels

occurs (e(t) = |ω5− ω6| > 0), the PID

controller activates, controlling M to

brake the left wheel to maintain ω5 = ω6 Mp1 is determined by the pression (3.3).

Ex-Mp1(t) = Kpe(t) + Ki

Z t 0e(τ )dτ + Kd˙e(t) (3.3)The coefficients Kp, Ki, Kd are software-adjusted with values: Kp= 500;

Ki = 10; Kd= 0, 1 These values yield acceptable simulation results, witherror e(t) diminishing and approaching 0 as t → ∞

3.2.2 Simulation Results of Traction Power Distribution trol Using PID Controller

Con-On MĐ-A, N6 increases significantly, approximately 50% Ne (Figure3.3a), causing ηk to also increase by about 50% (without control 0%)

N5 ≈ 0, despite N3 = 150W This power is dissipated through brakemechanism friction and wheel-road surface friction

(b) Without Control - MĐ-A

Figure 3.3: Power Distribution with PID Controller

On MĐ-B, with control implementation, N3 = N 4 ≈ 50%Ne (Figure3.3c) Although the left wheel has low adhesion coefficient, it can receive

N = 1200W , increasing traction power N thus improving η to 62,23%

Figure 3.4: Traction Efficiency with PID Controller

On MĐ-A, the left wheel experiences complete slip during the firstsecond, after which λ is controlled and rapidly decreases to stability OnRT-B, λ is well-controlled, with good wheel adhesion

With control, ω3= ω4= ω5= ω6in all test cases, demonstrating goodresponse of the designed controller

The behavior of e(t) and Mp1curves shows similar patterns - as e(t)increases, Mp1 increases When power becomes constant (at 4s), ωe de-creases, reducing Ne, causing e(t) to trend downward, consequently de-creasing Mp1 Greater adhesion coefficient differences result in higher Mp1values (Figure 3.5)

Mp1

Mp1

Mp1

(b) Controller Output u(t)

Figure 3.5: PID Controller Input/Output Parameters

Vehicle velocity in all three cases MĐ-A, MĐ-B, MĐ-C, shows Vx ̸=

0 with similar acceleration patterns, with MĐ-C demonstrating optimal

The system’s states of interest

are speed differences between axle

shafts (e1) and wheels (e2) State

equation 3.4, where: A, , B are

sys-tem and control matrices

The LQR controller is designed

to minimize performance function J , where: Q ∈ Rn×n and R ∈ Rm×mare positive definite matrices, with n state variables (n = 2); m controlleroutputs (m = 1) Objective function J includes control signal u(t) withweighting matrices R, Q and vector e(t) To minimize e(t) and u(t) mag-nitudes, R and Q are selected to minimize braking energy dissipation

M2 p1max

(3.6)

Q =

" 1

e 2 1max

0

e 2

#, (3.7)

Signal u(t) is determined by

equation 3.8 and matrix K is

cal-culated as (3.9)

Figure 3.7: Power Distribution with LQR Controller

Compared to PID control, Mp1is smaller but e increases (Figure 3.8b).While Mp1max and emax haven’t reached desired values, they remain ac-ceptable Physically, reducing Mp1max increases emax

e (LQR)

e (PID)

(b) Controller Input e(t)

Figure 3.8: LQR and PID Control Input/Output on MĐ-BOther simulation results: F5, F6, M5, M6, λ, ω5, ω6, Vx, show similar pat-terns and values to PID control

Mp max, pc max -

maxi-mum brake torque and

Distribu-Hierarchical PID Controller for Traction Power Distribution Control:

Figure 3.9: Showing hierarchical PID controller diagram

Investigation Results: Solenoid valve on/off signals respond ately to calculated Mp1 and pcd changes Pressure error ep between cal-culated p and actual p is minimal, demonstrating good ABS actuator