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This is an author produced version of a paper published in Smart Materials and
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White Rose Research Online URL for this paper:
http://eprints.whiterose.ac.uk/8862/
Published paper
Batterbee, D.C., Sims, N.D., Stanway, R. and Wolejsza, Zbigniew (2007)
Magnetorheological landing gear: 1. A design methodology. Smart Materials and
Structures, 16 (6). pp. 2429-2440.
http://dx.doi.org/10.1088/0964-1726/16/6/046
1
MAGNETORHEOLOGICAL LANDING GEAR.
PART 1: A DESIGN METHODOLOGY
D C Batterbee
†
, N D Sims
†*
, R Stanway
†
, and Zbigniew Wolejsza
‡
†
Department of Mechanical Engineering, The University of Sheffield,
Sheffield, S1 3JD, UK.
‡
The Institute of Aviation, Al. Krakowska 110/114, 02-256 Warsaw, Poland.
ABSTRACT
Aircraft landing gears are subjected to a wide range of excitation conditions, which result in
conflicting damping requirements. A novel solution to this problem is to implement semi-
active damping using magnetorheological (MR) fluids. This paper presents a design
methodology that enables an MR landing gear to be optimised, both in terms of its damping
and magnetic circuit performance, whilst adhering to stringent packaging constraints. Such
constraints are vital in landing gear, if MR technology is to be considered as feasible in
commercial applications.
The design approach focuses on the impact or landing phase of an aircraft’s flight, where
large variations in sink speed, angle of attack and aircraft mass makes an MR device
potentially very attractive. In this study, an equivalent MR model of an existing aircraft
landing gear is developed. This includes a dynamic model of an MR shock strut, which
accounts for the effects of fluid compressibility. This is important in impulsive loading
applications such as landing gear, as fluid compression will reduce device controllability.
Using the model, numerical impact simulations are performed to illustrate the performance of
the optimised MR shock strut, and hence the effectiveness of the proposed design
methodology. Part 2 of this contribution focuses on experimental validation.
KEYWORDS: Magnetorheological, aircraft landing gear, semi-active damping, smart
fluids, impacts
*
Corresponding author. Email: n.sims@sheffield.ac.uk; Tel: +44 (0)114 2227724.
2
NOTATION
a
2i
Piston area r Tyre exponent
a
2o
Outer cross-sectional area of inner cylinder R
c
Resistance of coil
b Mean annular circumference of valve Re Reynolds number
B
f
Magnetic flux density in the fluid Re
c
Critical Reynolds number
B
s
Magnetic flux density in the steel t Time
c Tyre constant t
a
Bobbin core radius
d Mean valve diameter t
b
Bobbin flange height
D Piston diameter t
d
Deflection time
F
s
Shock strut force v Fluid volume
F
t
Tyre force v
10
Initial fluid volume in chamber 1
g Acceleration due to gravity (9.81ms
-2
) v
20
Initial fluid volume in chamber 2
h Valve gap height v
a
Gas volume
h
c
Coil height v
a0
Initial gas volume
H
f
Magnetic field strength in the fluid V
s
ink
Aircraft sink velocity
H
s
Magnetic field strength in the valve material w
c
Coil width
I Current z Displacement of SDOF impact system
l Constrained length of valve z
p
Displacement of aircraft or drop mass
l
a
Active valve length z
w
Displacement of wheel and tyre assembly
l
t
Total length of multi-staged valve
d
t
z
&&
Critical acceleration to cause shock strut
deflection
L Lift
α
Dimensionless valve length
m Gas exponent
β
Bulk modulus of the fluid
m
p
Mass of aircraft or drop mass
a
l
P
Δ
Pressure drop across the active valve length
m
w
Mass of wheel and tyre assembly
Δ
P
0
Zero field valve pressure drop
n Stage number
Δ
P
max
Maximum valve pressure drop (Active +
inactive)
p Power
Δ
Q
Net volume flow rate
P Pressure
λ
Control ratio
P
1
Fluid pressure in chamber 1
μ
Viscosity of MR fluid
P
2
Fluid pressure in chamber 1
ρ
Density of MR fluid
P
a
Gas pressure
τ
Time constant
P
a0
Initial gas pressure
τ
y
MR fluid yield stress
Q Volume flow rate
max
y
τ
Maximum MR fluid yield stress
Q
max
Maximum valve flow rate during impact
3
1 INTRODUCTION
Aircraft landing gears are subjected to a wide range of impact conditions due to variations in
sink speed, angle of attack and mass. The landing gear must be able to absorb sufficient
energy in severe impacts or crash landing scenarios in order to minimise structural damage.
To accommodate this requirement, the performance for more common (i.e. less severe)
impacts will be compromised, and this may reduce the structure’s fatigue life and increase
levels of passenger discomfort. Conflicting damping requirements between the landing
impact and taxiing phases results in further performance compromises [1]. In the 1970’s,
NASA researchers began the development of active landing gear concepts in order to
overcome these passive limitations [2]. However, such technologies have not come to
fruition as a result of their large size, weight and power requirements. A more attractive
solution is to implement semi-active energy dissipation using smart fluids. Such fluids allow
the continuous adjustment of damping force through the application of either an electric field
(for electrorheological (ER) fluids) or a magnetic field (for magnetorheological (MR) fluids).
For both fluids, polarisation causes the formation of particle chains and hence the
development of a controllable yield stress within the smart device. In comparison to active
devices, smart dampers are less complex, have lower power requirements, and can be better
packaged within a limited space.
Practical ER fluids were produced over two decades ago [3]. However, their use in the
aerospace industry was ruled out, owing to a reluctance to provide the voltages required to
generate electric fields of up to 4kV/mm [4]. In addition, ER fluids have a narrow working
temperature range [5], making them unsuitable for high altitudes. Consequently, the
application of smart fluids in the aerospace industry, and more specifically in aircraft landing
4
gears, was until recently, largely unexplored. The more recent developments in MR fluids
have led to a renewed interest in this field. In contrast to ER fluids, MR fluids are powered
by a low voltage source and have been shown to be capable of operating between -40°C and
150°C [6]. Consequently they are far better suited to aerospace applications, and will
therefore be the focus of the present study.
The use of smart fluids in landing gear has been considered previously, and various
configurations of device have been considered [7-9]. Lou et al. [7] presented a shear mode
ER landing gear, which used a device to convert translational motion of the piston rod into
rotational motion between shearing disks. Berg and Wellstead [8] developed a shear/squeeze
mode ER device, which was numerically investigated in series with a conventional passive
landing gear. Finally, Choi and Wereley [9] investigated the use of a flow mode ER/MR
landing gear shock strut, and concluded that accelerations can be significantly attenuated
using a sliding mode controller.
Whilst these earlier investigations have helped to demonstrate the benefits of using smart
fluids in landing gear, they have often overlooked packaging requirements/constraints and the
effects of fluid compressibility in numerical models. Adhering to sizing constraints is vital if
the feasibility of a new landing gear concept is to be proven. Furthermore, the consideration
of fluid compressibility is particularly important in impulsive loading applications, as fluid
compression will reduce valve flow and hence controllability. Consequently, the aim of the
present research is to investigate the feasibility of an MR landing gear through direct
consideration of the packaging constraints. This will involve the use of a dynamic landing
gear model that accounts for fluid compressibility thus enabling an accurate prediction of
performance. The study focuses on the impact phase of an aircraft’s landing, where the loads
