Differential Control Strategy Research of Wheeled Electric Drive

ADT Mining Truck

Huilai Sun

1, 2, a

, Pengbo Liu

2, b, *

, Yong Wang

1, c

, Yuanyuan Song

2, d

, Zeying Li

2, e

and Guoming Yao

2, f

Institute of Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250101, China.

College of Mechanical and Automotive Engineering, Qilu University of Technology(Shandong Academy of Sciences),Jinan

250353,China

Corresponding author: pengbosdu@163.com

wyong0101@qq.com

songyuanyuan1028@126.com

18364195056@163.com

2776716601@qq.com

Keywords: Articulated mining truck, wheeled electric drive, electric differential, control strategy, slip rate.

Abstract: Aiming at the special structure and steering characteristic of wheeled electric-driven articulated

underground mining truck, a differential control strategy which takes the equal slip rate as control target was

given. The kinematic and dynamic model of electric-driven mining ADT was established and the movement

relationship and stress condition of the driving wheels were analyzed during steering. Acceleration sensors

in the sample ADT were used to test the actual speed of the vehicle. Results show that the filtered signal has

small delay and fast response and can be directly used to estimate the speed. Equal slip rate control strategy

is superior to equal torque control strategy because it can make full use of the ground adhesion coefficient

and reach reasonable distribution of drive power. Two sides wheel slip rate can be stable -0.08 and sliping

situation is avoided in experimental turning. This control strategy has practical effect for reducing tire wear

and improving driving power utilization.

1 NTRODUCTION

The operating condition of articulated underground

mining trucks is complex, such as narrow road,more

corners, wet and slippery ground, and the vehicle

body load quality is large. In order to adapt to the

narrow underground environment, articulated

steering of front and rear body is used, and full

wheel drive is used to increase traction force. The

35t wheeled electric-driven articulated underground

mining truck is newly developed by University of

Science and Technology Beijing,which is the only

one using diesel-electric power at home and abroad,

wheel drive, and independent control of each drive

wheel torque and speed.

Unlike mechanical transmission, there is no

differential mechanism on the wheeled electric-

driven vehicle. In order to ensure that there is no

sliping between the drive wheels during steering, the

vehicle loses ground traction and excessive tire wear

(Liu Weixin, 2001; M Canale, L Fagiano, M

Milanese, et al, 2007; YU Houyu, Huang Miaohua,

2011; Wang Junnian, Wang Qingnian, Song

Chuanxue, et al, 2010) It is necessary to adopt

accurate model and effective strategy for differential

control. Differential control is one of the key

technologies for the design of wheeled electric-

driven vehicle.

There are many researches on electronic

differential control in passenger cars (Li Bin ,Yu Fan,

2008; A G Nalecz, A C Bindemann, 2003; Y H Ge,

C S Li, G Z Ni, 2003) ,they established kinematics

relationship of each drive wheel mainly through the

Ackerman model to control the wheeled electric

motor and developed differential control strategy

(Fredriksson, Andreasson, Laine, 2004; Umesh

Kumar Rout, et.al, 2013; Zhang Daisheng, Li Wei,

2002; Wang Renguang, Liu Zhaodu, Qi Zhiquan,et

al, 2007). At present, the rear wheel drive is used for

wheeled electric-driven underground mining truck at

home and abroad, and the steering differential

adopts the equal-torque control strategy. The equal-

Sun, H., Liu, P., Wang, Y., Song, Y., Li, Z. and Yao, G.

Differential Control Strategy Research of Wheeled Electric Drive ADT Mining Truck.

DOI: 10.5220/0008868300700077

In Proceedings of 5th International Conference on Vehicle, Mechanical and Electrical Engineering (ICVMEE 2019), pages 70-77

ISBN: 978-989-758-412-1

torque control strategy can not meet the

requirements of the vehicle's passing ability on a

complex roads, and it is prone to inconsistent

operation between the wheels, which consumes

additional power and wears the tires, resulting in

deterioration of steering and handling performance.

Therefore, it is necessary to put forward the driving

control strategy with sliding rate as the control target,

coordinate and control the driving force of each

wheel, and avoid the above situation. The control

strategy with consistent slip rate needs to calculate

the slip of each wheel by monitoring the vehicle

speed and the driving wheels ' rotational velocity,

and then control the torque to adjust the slip rate of

each drive wheel ,so that they tend to be

consistent(Shen Jun,Song Jian,Wang Huiyi, 2007).

And for full-wheel drive articulated electric-driven

vehicles, how to obtain accurate absolute speed is

also a key issue, and now there is no good solution

for such articulated vehicles.

Taking the steering condition of 35t wheeled

electric-driven articulated underground mining truck

as the research object, this paper establishes

kinematics and dynamics model of the vehicle, and

analyzes the relationship between every wheel’s

rotation speed and torque. The longitudinal

acceleration of the prototype is tested with the

acceleration sensor in real time and Kalman filter is

used to obtain the effective absolute speed of the

vehicle. A multi-body dynamics simulation platform

including steering wheel angle input model, wheeled

electric drive model and underground mine vehicle

virtual prototype model were established, and a joint

simulation of vehicle steering differential conditions

was carried out with the sliding rate controller ,

takes the equal slip rate as control target. And the

results of equal torque control strategy are compared

and analyzed.

Figure 1. Vehicle kinematic model.

2 MATHEMATICAL MODEL

ESTABLISHMENT

2.1 Kinematics Model

In order to accurately describe the slide rate of each

wheel, a vehicle kinematics model needs to be

established. As shown in Fig 1, the coordinate

system OXYZis an absolute coordinate system

fixed on the ground. OXYZ and OXYZare the

dynamic coordinate systems whose coordinate origin

is fixed on the center of mass of the front and rear

vehicle bodies respectively. X, X axles coincide

with the longitudinal axes of the front and rear

bodies, and δ denotes the angle between the front

and rear bodies.B denotes the distance between the

front and rear body, Lf denotes the distance between

the front wheel center and the hinged joint, Lr

denotes the distance between the rear wheel center

and the hinged joint, denotes is the distance between

the front body mass center and the hinged joint, and

hr denotes the distance between the rear body mass

center and the hinged joint. u1, v1, r1 denote the the

front car body’s longitudinal velocity, transverse

velocity, and transverse angle velocity around the Z

axis respectively, while u2, v2, r2 denote the the rear

car body’s longitudinal velocity, transverse velocity,

and horizontal angle velocity around the Z axis

respectively. The sum of r1 and r2 denotes the angle

change rate between the front and rear bodies, that is

rr 





(1)

From the motion relationship of each wheel,

regarding the steering angle as a known parameter,

(1 )

2 cot 2 1 cot







(2)

uflu

, ufr, url, urr denote longitudinal velocity of

the center of the left front wheel, right front wheel,

left rear wheel and right rear wheel respectively.

And derive the slip rate expression of the wheels

(1 )

2 cot 2 1 cot

wR u









(3)

Sflu

, Sfr, Srl, Srrs

denote the slip rate of the

left front wheel, right front wheel, left rear wheel

and right rear wheel respectively. w denote the

wheel angular speed to define the speed, and

Differential Control Strategy Research of Wheeled Electric Drive ADT Mining Truck

propose the accurate method of estimationing the

speed .

2.2 Dynamic Model

The dynamic model of wheeled electric-driven

articulated underground mining truck is established

to analyze the force relationship between the vehicle

and the ground, so as to control the torque of the

wheeled traction motor and monitor the speed of the

wheel side. Select 3 degrees of freedom for

longitudinal, lateral, and yaw-moment to establish a

vehicle dynamics model, as shown in Figure 2.

Figure 2 .Vehicle dynamic model.

In Fig 2, a1x and a1y are the acceleration along

the X axis and the Y axis at the center of the front

body; a2x, a2y are the accelerations along the X

axis and the Y axis at the center of the rear body;

Fix, Fiy denote the tangential and lateral forces face

the i wheel respectively(i = 1,2,3,4); To is the

steering internal torque between the front and rear

bodies; Fx and Fy are the forces of the hinged point

along the X axis and the Y axis, respectively.

Based on the relative relationship between the

front and back of the vehicle body in Fig 2,

considering the parameters such as the quality

characteristics, acceleration, and moment of inertia

of the vehicle, derive the torque balance equation of

the vehicle body around the X, Y, Z, X, Y, and Z

axes.

fyxxffyyzz

FFLhFFTrI 

)())((

1221011



(4)

FTr

I )sincos())(

(

)

(







(5)

xxyx

FFFFvrum

432222

sincos)( 





(6)

yyyx

FFFFurvm

432222

cossin)( 





(7)

From the results of formula, it is known that

adjusting the driving force of each wheel and the

articulated angle of the front and rear body can

control the longitudinal lateral speed of the vehicle

body during the steering and change the sliding rate

of each drive wheel. However, The above

relationship can not accurately describe the quality

characteristics of the vehicle itself under dynamic

conditions, and the calculation of slip rate is not

accurate enough. Subsequent numerical analysis

uses multi-body dynamics software to consider the

impact of the quality characteristics and operating

status of the vehicle on the slip rate.

3 MULTI-BODY DYNAMICS

MODEL ESTABLISHMENT

The articulated truck tire is the only part that

connects the body and the road. Its force,

deformation and motion response have a great

influence on the movement of the vehicle. The

traditional mathematical model is difficult to

describe the characteristics of the vehicle-tire-road

coupling model accurately. On the basis of vehicle

kinematics, this paper uses multi-body dynamics

software to consider the quality characteristics and

operation status of the vehicle. The shading and

rendering model is shown in Fig 3. Combined with

the above analytical dynamics, the force and torque

of the tire in contact with the ground are calculated

using the UA tire model, which accurately reflects

the slide rate and realizes the driving control effect.

The vehicle drive model joint simulation is

performed with the multi-body dynamics model,

including the motor drive model and the steering

wheel input model. The output torque of the motor

drive model drives the wheel, and the actual wheel

speed is fed back to each motor drive model by the

model. The rigid connection between the motor and

the wheel is simulated, and the deceleration and

torsion are carried out through the wheel side

reducer model. The line displacement of the steering

cylinder and the driving torque of the wheel are used

as the vehicle control signals to simulate the steering

wheel angle and throttle pedal input when the driver

drives the vehicle. The output of the model is the

vehicle operating state parameters, including speed,

steering angle, wheel speed, slip rate, etc.

ICVMEE 2019 - 5th International Conference on Vehicle, Mechanical and Electrical Engineering

Figure 3 .Vehicle driving model.

4 CONTROL STRATEGY BASED

ON CONSISTENT SLIP RATE

The former mentioned vehicle driving model is also

a framework for adopting different strategies for

control and analysis. The consistent slip rate control

strategy is to allocate torque and power according to

the slip rate’s changes of each wheel under different

conditions (Chen Dong, Xu Yin, Liang Huajun, 2013;

Wang Renguang, LiuZhaodu, Qi Zhiquan, et al, 2006) .In

this paper, the average slip rate of four wheels of

articulated vehicles is taken as the target slip rate,

the target slip rate and the slip rate of each wheel is

transmitted to the power distribution module in real

time. Power distribution module based on the

deviation of per wheel’s actual slip rate from Target

slip rate. Calculate the power and speed that each

wheel should allocate, adjust the torque and speed of

each wheel through the motor drive module, and

control that the sliding rate of each wheel is within

ideal range and eventually tends to be the same. The

control flow is shown in Fig 4.

5 TEST ANALYSIS

5.1 Real Vehicle and other Torque

Control Test

In order to evaluate the application effect of the

control strategy, the actual vehicle test and joint

simulation were carried out. In the test,

comprehensive speed estimation and analysis is

carried out, which fully reflects the acceleration,

deceleration and uniform speed. The design test

vehicle is gradually accelerated after 5s start. After

reaching the stable speed, it will travel at a constant

speed along the fixed circumference and keep the

steering wheel angle for two turns. Once again, the

vehicle is slowly and continuously accelerated, and

after the limit safety speed, the vehicle is slowly

braked to reduce the speed until the vehicle stops,

and the test is over. The entire process includes

acceleration, turning, uniform steering and

deceleration. Fig 6 and Table 1 show the test vehicle

and vehicle assembly parameters respectively. Fig 5

shows the obvious trace of the circular car mark on

the cement road.

Figure 4. The slip ratio control flow chart.

Differential Control Strategy Research of Wheeled Electric Drive ADT Mining Truck

Table 1. Assembly parameter.

Assembly

parameter

Numerical value

engine

Rated power (speed)/KW(n·min

-1

)

399(2100)

Traction motor

rated power / KW

Rated torque / Nm

1200

reducer

Reduction ratio

Tire

29.5R29

quality

Load mass /t

Curb quality /t

Figure 5. Testing field of 35 tons electric drive

underground articulated mining truck.

In order to fully evaluate the control strategy

effect and collect signals, the test uses LMS

SCADAS MOBILE SCM05 signal acquisition card,

and the sensor sampling frequency is 2560Hz, which

meets the test requirements. The INS is installed at

the center of the front and rear axles to measure the

acceleration and angular velocity of the three

orthogonal axes of the front and rear bodies. The

rotary encoder is installed under the steering column

of the steering wheel to measure the input angle of

the steering wheel. The angular displacement sensor

is installed at the hinge point to measure the front

and rear vehicles. The articulation angle between the

bodies is shown in Fig 6. The signals such as the

speed and current of the engine, generator and motor

are directly output by the CAN bus, which can be

easily collected by the USBCAN interface.

Figure 6. Sensor installation position.

5.2 Vehicle Speed Estimation Based on

Kalman Filtering

In the slip rate control, the vehicle speed needs to be

specifically estimated, and the wheel speed signal

must be filtered after removing the coarse error and

the measurement error of the system itself, and the

traditional vehicle speed estimation method is not

applicable to the all-wheel drive vehicle: signal

noise. The lower ratio will result in a large error in

the direct integration of the longitudinal acceleration

signal, which is easy to diverge; the method of

obtaining the vehicle speed using the non-driving

wheel speed is not applicable to the all-wheel drive

of the vehicle. In this paper, the longitudinal

acceleration signal and the wheel speed signal are

used as input, and the Kalman filter algorithm is

used to estimate the front and rear body speeds. The

filtering process starts from the known initial value

of the state and the initial value of the state

covariance matrix, and filters and estimates the input

wheel speed. The velocity estimation process of

Kalman filtering algorithm consists of two parts:

prediction and calibration, which includes state

equations and observation equations.

)()()()1( kwkxkAkx 

(8)

)()()()( knkxkBkz 

(9)

Which

()

x(k)









()

Z(k)











Where ae, ve represent the estimated values of

longitudinal acceleration and longitudinal vehicle

speed, respectively, am, ω represent the

experimental values of longitudinal acceleration and

wheel angular velocity, R represents the rolling

radius, Δt represents the time interval, and w1, w2

represent the system noise, na, nv denotes

ICVMEE 2019 - 5th International Conference on Vehicle, Mechanical and Electrical Engineering

measurement noise, system noise and measurement

noise are Gaussian white noise with known

statistical information. The estimated vehicle speed

after Kalman filtering is of great significance to the

specific implementation of the control strategy. To

represent the true value of the rolling radius,

Gaussian white noise can be added based on the

actual fluctuation amount.

Figure 8 is the curve of the longitudinal velocity

estimation and measured value of the front body

after the filtering process. To see the difference

between the two is shown in Fig 9. The analysis

shows that the acceleration phase of 5~25s is large,

the difference between the two is large, the

maximum difference is 0.19m/s; the difference in

the steady steering phase is not large, and the

acceleration speed reaches the maximum value of

4.5m/s and starts to decelerate. The error is large,

0.2m/s. Generally speaking, in the steady-state

steering phase, the difference between the two is

small, and the more uniform the data, the more

consistent the data is.

Figure 7. Difference of front car body longitudinal

velocity estimated and measured value.

Similarly, the estimated value of the rear body

speed is shown in Fig 8. The estimated speed of the

front body is greater than the estimated speed of the

rear body, and the over-range is about 5%. In the

subsequent analysis, the average vehicle body speed

can be used as the vehicle speed, and the slip rate of

each wheel can be calculated.

Figure 8. Front and back car body longitudinal velocity

estimated value.

As can be seen from the above comparison, the

Kalman filtering method is applicable to three

situations of acceleration, braking deceleration and

uniform velocity. The filtered signal has a small

delay, a fast response speed and better smoothing

effect, and the effect is obvious at a constant speed

driving stage. The filtered signal can be used to

directly estimate the speed of the vehicle.

5.3 Simulation and Comparison of

Equal Slip Rate Control

The control strategy is simulated jointly by using the

multi-body dynamics simulation platform of the

whole vehicle, while the equal torque control

strategy is adopted in the real vehicle, which needs

to be verified by the multi-body dynamic model

under the equal torque control strategy to

demonstrate the accuracy of the multi-body dynamic

model. Then the simulation of equal slip rate

strategy is carried out. As mentioned earlier, the

hinged vehicle is steadily accelerated to a speed of

15 km / h after starting and steering at a uniform

speed. In the process of acceleration and uniform

steering, the torque and slip rate data of the two

wheels on the same side have little difference. In

order to make the diagram clear, the simulation data

of the left and right rear wheels and the inner wheels

are selected for analysis. The measured slip rate and

simulation slip rate are shown in Fig 9.

Differential Control Strategy Research of Wheeled Electric Drive ADT Mining Truck

Figure 9. Slip rate under equal-torque control strategy.

It can be seen from Fig 10 that the driver

stabilizes the accelerator pedal after 25s under the

constant torque control strategy, but the torque of the

inner and outer wheel motor is basically the same

during the whole process, while the multi-body

dynamics simulation model rapidly enters the stable

state with the measured data, and finally stabilizes at

680N·m. The above data verify the accuracy of the

multi-body dynamics model and can reflect the

motion of the vehicle under different strategies.

After changing the system model into the equal slip

rate control strategy, the slip rate of the outer and

inner wheels is shown in Fig 10.

Figure 10. Slip rate under equal slip rate control.

Under the equal slip rate control strategy, the

automatic distribution torque of the system quickly

enters the steady turning condition, so the result of

the first 30s can be discussed. After the turning

instruction input and the torque adjustment of the

system, the slip rate of the inner and outer side

wheels can be stabilized to -0.08, there is no

slippage, which increases the utilization of adhesive

force.

6 CONCLUSION

This paper takes the steering condition of 35t

wheeled electric-driven articulated underground

mining truck as the research object. The main results

are as follows:

(1) The multi-body dynamic model and

kinematic model are in good agreement with the test

data of the real vehicle, which can effectively reflect

the motion of the vehicle under various working

conditions. The Kalman filter speed estimation result

has the advantages of small error and good real-time

performance, which can accurately reflect the slip

rate and other data under each control strategy.

(2) The differential speed control strategy with

the equal slip rate is superior to the equal torque

control strategy for wheeled electric-driven

articulated underground mining truck, which can

make full use of the adhesion coefficient, avoid type

wear when being dragged and skidded, reduce the

fuel consumption.

ACKNOWLEDGMENTS

Thanks to Li Yanqiang of Institute of Automation,

Shandong Academy of Sciences. This study is based

on joint scientific research projects ‘Research on

Path Planning and Path Following Control Method

of Auto-driving Electric Vehicle Based on

Reinforcement Learning (2018BSHZ0011), and

Research on Key Technologies of Low Cost and

High Precision Unmanned Driving for Intelligent

Electric Vehicles in Specific Areas

(2017GGX50107).

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Differential Control Strategy Research of Wheeled Electric Drive ADT Mining Truck