Z. Qian et al. (Eds.): Recent Advances in CSIE 2011, LNEE 126, pp. 301–309. springerlink.com © Springer-Verlag Berlin Heidelberg 2012

Research on Simulation of Aircraft Electric Braking System

Liang Bo1 and Yuren Li

Abstract. More/all electric aircraft (M/A EA) technology is considered to be the future development trend in the aviation industry. However, Aircraft Anti-skid Braking System (ABS) is a key subsystem of M/A EA. With the background of the development of ABS, an aircraft electric braking system is designed to be used in ABS. The paper describes the principles of the work and the features of the air-craft electric braking system, mainly focusing on the motor of the actuating sec-tion used in electric braking system. According to the analysis result, the actuating section—math model of the Electro-Mechanical Actuator (EMA) has been estab-lished and simulated in MATLAB/SIMULINK. Furthermore, based on the fea-tures of the electric braking system, dual-channel model of the whole ABS has been established and studied. The results of the simulation indicates that: the performances of the designed electric braking system gains an advantage over hydraulic braking system obviously; it can reflect the real braking process the aircraft, and the model of the whole system is correct and reasonable.

1 Introduction

As an independent subsystem of the aircraft, aircraft anti-skid braking system sus-tains the static weight of the aircraft, dynamic impact landing and absorbs the ki-netic energy when the aircraft is landing. It also to achieves braking and control as the aircraft taking off, landing, taxing and turning [1]-[3]. The performance of air-craft anti-skid braking system has directly influence on the rapid response, safe return & off and sustained combat capability, and then affects the overall perfor-mance of the aircraft. Aircraft braking system is in constant progress and devel-opment after it first applied. In recent years, with the M/A EA conception proposed, the aircraft braking system is to obtain more significant development. All along, the hydraulic actuator device has been widely used in aircraft braking systems, what the biggest difference between EA and hydraulic brake system lies

Liang Bo . Yuren Li College of Automatic Northwestern Polytechnical University Xi’an, China e-mail: liangbo_219@hotmail.com, liyuren@nwpu.edu.cn

302 L. Bo and Y. Li

in using electric actuator instead of hydraulic actuator. To do this has several ad-vantages, such as: improving security by preventing the risk of hydraulic leak and burning; reducing the weight of aircraft; increasing brake torque control so that significantly improves the anti-skid performance, and extending the life of tires and brakes; system modularizing and real-time detection makes it easier to main-tain and improve the combat survivability; what is more, the operating frequency and efficiency of EA are higher than hydraulic system. Therefore, to study aircraft electric braking system and use it to replace hydraulic braking system becomes a historical necessity.

In the paper, firstly, the mainly components of the aircraft are studied. Then, the constitute and working principle of the core component--Electro-Mechanical Actuator using in EA, which is the most different with hydraulic actuator using in hydraulic braking system, has been studied. To this extent, the drive control algo-rithm of EMA and Electro-mechanical actuator Controller (EMAC) has been de-signed. At last, the dual-channel model of the aircraft electric braking system has been established and simulated in MATLAB/SIMULINK. The result of simulation indicates: the control algorism of the EMA is correct; comparing with hydraulic braking system, the performance of EA is superior to hydraulic braking system, and can be used in aircraft braking system instead of hydraulic braking system.

2 System Components of Aircraft Electric Braking System

The system diagram of all-electric braking system shows in Figure1. The main components are: anti-skid braking system, driving control unit, motor, roller screw and wheel by brake.

Fig. 1 System diagram

2.1 Aircraft Model

To simplify the complexity of the aircraft object, the model can be built under the following assumptions [7]:

a. The aircraft is regarded as a rigid body; b. The landing gear strut is regarded as rigid body, which neglects the verti-

cal, the lateral and the torsion deformation; c. The earth curvature is neglected; d. The earth is regarded as the inertial coordinate system.

Aircraft landing roll force as shown in Figure 2. In the Figure, the role of the force on the plane there: gravity G , lift

yF ，the remaining engine thrust 0T , air

Research on Simulation of Aircraft Electric Braking System 303

resistance xF ，drag parachute pull

sF ，runway on the main wheel reaction

1N and front reaction 2N ，the role of friction in the main wheel

1xF and in the

front wheel 2xF .where 111 NFx μ= ,

222 NFx μ= .Aircraft on the runway roll motion

can be described as following three equations：

⎪⎩

⎪⎨

⎧

−=−+−++=−−−

=−−−−

)()()(

0

1102112

21

210

LLNhThFFhhFLN

NNFG

MaFFFFT

TcXXTsS

Y

XXSX

(1)

1N 、2N and acceleration of aircraft a can be calculated from (1).

Fig. 2 Aircraft landing roll force ground

θ

Plane body X

direction

FH1FH

the center of gravity

front buffer main buffer

ww1

Hh

a

θhs

2f 1f1N2N

hM G SX FF ,

iniT?0

gY FF ,

2.2 Wheel and Landing Geer Model

When the aircraft taxing on the runway, the ground force to aircraft through the landing gear, so the dynamics and kinematics of the aircraft can be impacted by landing gear. The main function of the landing gear, which is to improve the ver-tical and longitudinal direction force of the aircraft, is to make a sense of prop and buffer. By consulting materials of buffer characteristics, the landing gear can be simplified as follow:

⎪⎩

⎪⎨

⎧

+=

+=•

•

222222

211111

XCXKN

XCXKN (2)

where

1N 、2N the force of the main and former buffer force on the body;

1K、2K stiffness coefficient of main and former buffer;

1C 、2C damping coefficient of main and former buffer;

1X 、2X compression of main and former buffer;

1

•X 、 2

•X compression variation of main and former buffer.

The movement of the wheel shown in Figure 2 can be described as formula 3.

g

ZWSj

R

V

J

MMw +

−=

• (3)

304 L. Bo and Y. Li

gj wRV = (4)

14

1NkRRg σ−= (5)

where w - angular velocity •w - angular acceleration;

ZWV - wheel speed;

jM - friction torque;

SM - brake torque;

J - inertia of single wheel;

jV - line Speed;

gR - rolling radius.

2.3 Brake Apparatus Model

Brake apparatus, which located in the wheel hub, is an important part of the air-craft. As the piston spring preload air travel and the existence of the brakes pro-duces a dead zone, together with the piston friction and other factors lead to static torque characteristics of the brake present a more specific hysteresis（Described by the formulator 6）.In MATLAB, the brake apparatus is established shown in Figure 8, according to the formulator [1].

⎪⎪⎪⎪⎪⎪⎪

⎩

⎪⎪⎪⎪⎪⎪⎪

⎨

⎧

<+−

+≤<

≤<+

+≤<−

≤

=

pK

MpPpK

K

MpppM

ppK

MpM

K

MpppppK

pp

M

n

nnn

nn

n

1001

10

20

20002

0

)(

)(

0

(6)

where

smM : Maximum brake torque;

mp : Maximum brake pressure;

0p : Minimum brake pressure;

xp : Maximum brake pressure lags.

The apparatus model shown in Figure 3 and the simulation result shown in Figure 4.

Research on Simulation of Aircraft Electric Braking System 305

Fig. 3 The apparatus model

Fig. 4 The simulation result of apparatus

2.4 EMA and EMAC Model

The performance of the whole system depends on the EMA, which is the key component of EA. The EMA designed in this paper shown in Figure 5.

The EMA [6] consists of motor, roller screw and reduction gear. In all-electric braking system, the roller screw is driven by the motor through the reduction gear, changes the rotation motion of the motor as linear motion, then presses the brake panel to achieve braking function. The system has a good redundancy because each roller screw driven by the motor was controlled independently.

Due to the inner dynamic characteristics of the motor is not the mainly study point, the motor can be simplified as following assumptions:

a. excellent compensation motor; b. ignore the armature reaction, eddy current effect and hysteresis; c. constant excitation current.

Fig. 5 EMA

The motor math model simplified as formula 5.

dt

dILRIEU d

dddd +=− (5)

According to the lows of rigid body rotation, the motor differential motion equ-ation [4] shows in formula 6.

306 L. Bo and Y. Li

d

emmd U

Cn

dt

dnT

dt

ndTT

Φ=++ 1

2

2 (6)

where

d

dd R

LT = : constant electromagnetic time of the Armature circuit;

me

d

me

dm CC

RGD

CC

JRT

Φ=

Φ=

375

2 : electrical time constant;

n : speed of the motor; 2GD :rotation inertia of electric drive system converted to the motor side.

The transfer function between voltage and speed of the motor can be described as:

1

1

)(2 ++

Φ=STSTT

CsW

mdm

ed

(7)

The drive circuit can be equivalent as:

1

)(+

=S

KSW

z

zz τ

(8)

3 Control Algorithm

In recent years, the emergence of new control algorithm in the control field, such as: fuzzy PID, adaptive control, neural network and pre-estimation theory, have greatly enriched the aircraft anti-skid control algorithm. Voltage bias+PID which verification by practice, has been chose in the paper.

In Figure 4, the motor is the core power section in the EMA, the control algo-rithm of which impacts the performance of the whole system. And the response speed and accuracy speed of the motor is a key research in EMA. Permanent mag-net brushless DC motor has been chosen in the paper and the ideal equivalent cir-cuit of the motor shown [5] in Figure 6.

The model of the motor built in MATLAB shown in Figure 7. In the figure, the current-speed dual-loop control method has been chosen.

The current regulatori

iiLT

sKW

ττ 1+= and the parameters are 326.0=ipK ，

4109.2 −×=iiK ;the speed regulator is

aai TK

RTK

∑

∑=β2

and the parameters are

320=psK ，3102.1 −×=siK 。

Research on Simulation of Aircraft Electric Braking System 307

Fig. 6 Ideal equivalent circuit of the motor

L

L

L

ea

eb

ua

ub

uc

i a

i b

i c

UNUdc

V1

V2

V3

V4

V5

V6

D1 D3 D5

D4 D6 D2

ec

R

R

R

Fig. 7 The model of the motor

The motor simulation result illustrated in Figure 8.

Fig. 8 The simulation result 0 2 4 6 8 100

2000

4000

6000

4 System Simulation

The electric braking system model can be got from formula 1 to 8, and the model illustrated in Figure 9.

Fig. 9 The simulation model

The control algorithm of the model is ode4 Runge-Kutta, the simulation step is 002.0 . The simulation parameters of the aircraft model such as: landing speed of the aircraft is sm /72 , the rated speed of the EMA motor is min/5000rad the brake apparatus started action at s5.1 and etc..The results have shown in Figure 10-13.

308 L. Bo and Y. Li

Fig. 10 The aircraft and wheel speed

0 5 10 15 20 25 30

0

20

40

60

80

t(s)

V(m

/s)

plane speed

left wheel speedright wheel speed

Fig. 11 The motor speed of two EMA

0 5 10 15 20 25 30

-2000

0

2000

4000

6000

t(s)

n(ra

d/m

in)

left motor of EMA

right motor of EMA

Fig. 12 The slip ratio

0 5 10 15 20 25 30

0

0.2

0.4

0.6

0.8

1

t(s)

u

left slip ratio

right slip ratio

Fig. 13 Braking distance

0 5 10 15 20 25 30

0

200

400

600

800

1000

t(s)

S(m

)

The results showed above indicates that: the work frequency of EA is higher than hydraulic braking system apparently, and the braking efficiency is higher too.

5 Conclusion

The results shave shown that using EA replace hydraulic braking system has great advantages in corresponding rate and reflect frequency. And the braking efficien-cy is higher than hydraulic braking system.

Research results and practice testing show that built model of EA can reflect the real aircraft braking process, and using EMA instead of hydraulic braking sys-tem approach is reasonable and feasible.

Research on Simulation of Aircraft Electric Braking System 309

References

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Feedback. SAE 961299 (1996) 4. Li, Y.: Researches on Electric Brake of Aircraft Based on Iterative Learning Control,

Doctor degree of NWPU (2006) (in Chinese) 5. Liang, B.: Simulation of Aircraft Electrical Hydrostatic Actuator Anti-skid Braking

Control System. Northwestern Polytechnic University (2009) (in Chinese) 6. Trosen, C.D.W., Cannon, B.J.: Electric Actuation and Control System. IEEE (1996) 7. Yuan, Z., Wang, Y.: A design of airplane’s integrated ground directional system with

fuzzy control. IEEE (2009)