Yoon-kyu Lee1 Shock Observer

8/12/2019 Yoon-kyu Lee1 Shock Observer

http://slidepdf.com/reader/full/yoon-kyu-lee1-shock-observer 1/8

1

15th International Congress on Sound and Vibration

6-10 July 2008, Daejeon, Korea

SHOCK AND VIBRATION ISOLATION PERFORMANCE OF

DOUBLE-STAGE OLEO-PNEUMATIC SHOCK ABSORBER FOR

ROTORCRAFT

Yoon-kyu Lee1, Sang-wook Lee2, * Kwang-joon Kim3

Ph. D. Student1 and Professor

3

1Center for Noise and Vibration Control, Department of Mechanical Engineering, KAIST

Science Town, Daejeon 305-701, Korea

[email protected]

Senior researcher 2

2Korea Aerospace Research Institute, Science Town, Daejeon 305-333, Korea

Abstract

Roles of shock absorber for rotorcraft are complicated due to several different requirements.

In landing, the shock absorber has to absorb efficiently vertical kinetic energy of the rotorcraft

and in taxiing it has to isolate the rotorcraft from excitations by runway of varying quality. The

requirements for both smooth landing and comfortable taxiing do not match well with each

other. To resolve this problem, a shock absorber with double-stage gas chamber and

unsymmetrical damping device is studied. Mechanism of this absorber with nonlinear stiffness

and damping characteristics depending on stroke, velocity and deformation of flapper valve is

investigated to derive a dynamic model. For each of the landing impact and taxiing excitations,

dynamic performances of the double-stage oleo-pneumatic shock absorber will be illustrated

and effects of the inherent nonlinearities will also be discussed.

1. INTRODUCTION

The oleo-pneumatic shock absorber for the wheel type rotorcraft landing gear mainly

developed to have optimal performance in the case of landing. The resulting suspension layoutmay lead to unsatisfactory vibration isolations when the rotorcraft is operating on the ground.

When taxiing, the landing gear has to carry the rotorcraft over taxiways and runways of varying

quality, a requirement that is mirrored by its MIL-A-8863C [1]. Thus the requirements for the

soft landing and for comfortable taxiing lead to a design contradiction. One of the main

problems is that relatively low damping factor for landing is required to make use of the full

stroke. This makes the shock absorber too weak for rolling when taxiing which leads to an

excitation of fuselage mode. Another problem is that the conventional oleo-pneumatic shock

absorber at static equilibrium state has relatively high stiffness due to avoid the ground

resonance instability which is not suitable to isolate the vibration from the road and has very

little of the total stroke available for the higher compressive loads resulting from traversing

bumps.

In order to design oleo pneumatic shock absorber for the purpose of resisting landing impact

and attenuating vibration when the rotorcraft is operating on the ground, the accurate

2784



ICSV15 • 6-10 July 2008 • Daejeon • Korea

2

characterization of the shock absorber is of paramount importance. Indeed, the characterization

makes it possible to define a sufficiently precise mathematical model of oleo-pneumatic shock

absorber for design purposes. In this research work, an approach for model of double-stage

oleo-pneumatic shock absorber is presented. Specifically, a nonlinear mathematical model for

the double-stage oleo-pneumatic shock absorber is developed. Then the shock and vibration

isolation performance of landing gear are observed and the effects of the double-stage

oleo-pneumatic shock absorber nonlinearities will be discussed

2. MECHANISM OF DOUBLE-STAGE OLEO-PNEUMATIC SHOCK

ABSORBER

Figure 1 shows schematic diagram of oleo-pneumatic shock absorbers. It consist of a

chamber(1) filled with gas(mostly dry air or nitrogen) which is compressed during the stroke

and provides the characteristics of a pneumatic spring, and an oil volume which is pressed

through small tube(valve) between main chamber(3) and recoil chamber(5) at compression and

expansion to account for the damping of the stroke motion. The frictions due to tightness of the

seal at main piston and separators also work as a damper.

Figure 1. Schematic diagram for Single-stage type and double-stage type of landing gear

Figure 2 shows load(force)-stroke curve for single-stage type and double-stage type

oleo-pneumatic shock absorber. For a landing load, the curves are plotted from to① ③. The

areas under the total load-stroke curve(①~②) correspond to the energy generated by the

respective forces. The spring force increases with stroke, storing energy. The restricted flow in

orifice (or small tube with valve) and friction forces dissipate energy until the shock absorber

comes to rest at the static equilibrium state point (③).

For the landing impact load, the curve of double-stage oleo-pneumatic shock absorber is

plotted from to① ③ in figure 2(b): from fully extended state to static equilibrium state via fully

compressed state. The break-over point in figure 2(B) is an arbitrary position at which thesecondary chamber becomes active and cause the sudden change in the load-stroke curve. Then,

compared with single stage one, the static equilibrium state position of double-stage type is

2785




3

closer to middle of stroke. With the sudden load occurring at static equilibrium state point, the

optimum increments of stroke are available for traversing either bump or hollows.

(a) Single-stage type (b) Double-stage type

Figure 2. Load-stroke curve of oleo-pneumatic shock absorber

To be free from ground resonance, the landing gear stiffness at static equilibrium point has to

be rather stiff value. This hard stiffness is also necessary because rotorcraft weight variations

during the boarding of passengers or while loading freight and arms should not result in

substantial landing gear stroke. Thus, the break-over point for double-stage oleo-pneumatic

shock absorber should be selected at about 1.2 times of the static equilibrium point.

For the dynamic load occurring at static equilibrium state, the dynamic stiffness of the shock

absorber is shown as a blue dotted line in figure 2 which depend on excitation amplitude.

Compare to single-stage oleo-pneumatic shock absorber, the double-stage oleo-pneumatic

shock absorber has soft dynamic stiffness for large amplitude excitation. From this reason, the

landing gear with double-stage oleo-pneumatic shock absorber has good vibration isolation

capability for the rough field ground excitation and it will be shown in chapter 4.

3. MATHEMATICAL MODELING OF DOUBLE- STAGE OLEO

-PNEUMATIC SHOCK ABSORBER

Consider a double-stage oleo-pneumatic shock absorber model shown in figure 3 to derive a

mathematical model for landing gear.

Figure 3 (a) shows the forces acting on the cylinder. Balancing forces on the cylinder gives

the following equation:

(1)

The term on the left hand side of Eq. (1) is the inertial motion term, g is the gravitational

acceleration, f friction is the friction present in the gear, and all other terms are as described in

figure 3. This equation assumes that the fluid pressure in the upper cylinder is identical to the pneumatic pressure.

a b c a b d C

① ①

② ②

③ ③

Excitation amplitude

Break-over point

U u U 1 P fritionM x M g PA P (A A ) f

2786




4

Figure 3(b) shows the forces acting on the piston. Summing the forces on the lower

mass(piston and wheel) the force balance equation is:

L t L 1 P t t t t fritionM x M g PA P (A A ) k x c x f ±

(2)

The pressure terms in Eq. (1) and (2) are as yet unknown and need to be related to the

positional variables xu and xt or their derivatives. The double-stage pneumatic springs due to

compressed gas(nitrogen or air) in two gas chamber can be approximated as a polytropic

process the following pressure-volume relationship governs for a closed system:

n

2u double 0 u t

2 P

Li) P P P P , x x x

L x(A / A)

⎛ ⎞≤ = = −⎜ ⎟

−⎝ ⎠

n

2

u double 0 b2 b P

L

ii) P P P P , x Break over pointL x (A / A)

⎛ ⎞

= = =⎜ ⎟−⎝ ⎠ (3)n

1 bu double u

1 P

L xiii) P P P P

L x(A / A)

⎛ ⎞−> = ⎜ ⎟

−⎝ ⎠

As the piston is forced to move with respect to the cylinder, a pressure differential is

developed across the piston causing the fluid to flow through orifice and valve in piston. At the

compression stroke the same amount of oil which is the insertion volume of the piston rod is

pressed and flows through the piston valve which is described in figure 3(c-ii) and at the

extension stroke the fluid flows through the piston valve which is described in figure 3(c-iii).

The mass flow rate Qc and Qe are different from each other because the orifice valve of the

piston have different number of orifice in compression and extension. In compression it

generates relatively small damping forces which prevent greatly increased flow velocities and

reduce the maximum peak force. It means that the shock isolation performance for the landing

OIL

MUa

A

PU

ffriction

P1,(A-AP)

Ps = pressure in primary gas chamber at static position

Pzero = pressure in primary gas chamber at full extension

PU = pre-charge pressure in secondary gas chamberPc = pressure in primary gas chamber at full compression

A = inner area of cylinder Ap = piston area

i) Static equilibrium

iii) Extension

ii) Compression

Qe

Qc

Ao : Orifice area

AP

MLg

t t t tk X c X

ffriction

P1,(A-AP)

(a) (b) (c)

Figure 3. Schematic diagram of double-stage oleo-pneumatic shock absorber

2787




5

and bump impact depends on the compression damping force. While, in extension, the small

number of orifice generates optimal damping force which is enough to attenuate the vibration

when taxiing and rebounding impact force.

The hydraulic damping force of shock absorber is determined by the pressure acting on the

both sides of the piston. Assuming that oil is incompressible, the damping force due to restrict

flow through valve can be calculated in the following equation:

2

2

di

u 1P

2 C

ρΔ = (4)

Where,2

1 p

2

orifice

d uu

Nd = ( N = number of orifice )

The Cd is called the discharge coefficient in equation (4) is determined by equations (5)

which are based on experiments [2].

11 22

d1

o o

1

2

d2

o o

L LC 1.5 13.74 for 0.02

d Re d Re

L LC 2.78 64 for 0.02

d Re d Re

−

−

⎡ ⎤⎛ ⎞⎢ ⎥= + <⎜ ⎟⎢ ⎥⎝ ⎠⎢ ⎥⎣ ⎦

⎡ ⎤⎛ ⎞= + >⎢ ⎥⎜ ⎟

⎢ ⎥⎝ ⎠⎣ ⎦ (5)

The friction force exerted by three piston seals being pressed against the wall of the cylinder

depends on the pressure difference in the oil and gas chamber. It can be described as derivative

of stroke x.

friction f f C sign X= (6)

Where, f f nC F= μ

f

n

: friction coefficient

F : normal force due to tightness between piston and cylinder wall

μ

The value of Cf should be obtained by experiments.

Then, the mathematical model of double-stage type rotorcraft landing gear is obtained by

combining the equations (1) ~ (6):

U u U double n u t

2

P double u t u t2

di o

M x M g P A F sign(x x )

A(A A ) P (x x ) (x x )

2C NA

= μ

⎧ ⎫⎞ ⎪ ⎬⎟

⎝ ⎠ ⎪⎭

L t L double n u t t t t t

2

P double u t u t2

di o

M x M g P A F sign(x x ) K X C x

A(A A ) P (x x ) (x x )2C NA

= μ

⎧ ⎫⎞ ⎪ ⎬⎟⎝ ⎠ ⎪⎭

(7)

2788




6

4. SHOCK AND VIBRATION ISOLATION PERFORMANCE OF DOUBLE-

STAGE OLEO-PNEUMATIC SHOCK ABSORBER

Double-stage type and single-stage type landing gear which have same geometrical valuesof size and same stiffness at static equilibrium state are compared 1 . Shock isolation

performances for the landing are evaluated with the value of maximum transmitted force

multiply maximum stroke of shock absorber as following equation (8):

Dimensionless ratio =U U _ max U _maxM x x

2 Input Energy

(8)

Figure 4. Load(force)-stroke curve for landing impact (3.05 m/s)

A smaller value of dimensionless ratio in eq.(8) is better for shock isolation performance.

Then, the figure 4 shows that the shock isolation ability of double-stage type landing gear is

better than the conventional single-stage one.

Figure 5. Bump input profile (MIL-A-8863C [1])

Figure 5 shows the bump input profile which is defined in MIL-A-8863C. It specifies the

bump in terms of bump amplitude vs. wave length.

1 Stiffness at static equilibrium point is presented in figure 4 as a blue dotted line

Un re ared fields Bum H : 0.1128 m

Paved runwa Bum H : 0.0005 m

Semi-prepared fields Bump H : 0.0532

Length L → 0.6096m (2 feet)H X

Z [1 cos2 ( )]2 L= − π

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.5

1

1.5

2

2.5

3

3.5Load-stroke curve

Relative deflection of shock absorber[x/xmax]

L o a d f a c t o r [ F / F

s t a t i c

]

Spring force

Total force

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.5

1

1.5

2

2.5

3


Relative deflection of shock absorber[x/xmax]


s t a t i c

]

Conventional

single-stage type

U U _ max U _ maxM x x

2 Input Energy

= 0.6363

Double-stage type

U U _ max U _ maxM x x

2 Input Energy

= 0.4685

L

H x

z

2789




7

Figure 6. Load-stroke curve for bump impact (Vtaxiing=3m/s )

Figure 6 shows load-stroke curve of double-stage type and single stage type ofoleo-pneumatic shock absorber for the impact from a bump. For the impact from small bump,

there are no differences in load factor between double-stage type and single-stage type as

shown in figure 6-(a) and (b). But for the bump impact that makes the stroke exceed break-over

point, the double-stage oleo-pneumatic shock absorber has some advantage of the increased

load factor. It is shown in figure 6-(c) and (d).

Figure 7. Transmissibility curve for landing gear

A transmissibility of landing gear comparison between the single-stage type and

(a)

(a)

(b)

0.65 0.7 0.75 0.8 0.85 0.9-1

-0.5

0

0.5

1

1.5

2Load-stroke curve

Relative deflection of s hock absorber[x/xmax

]

L o a d f a c t o r [ F / F s t a t i c

]

Spring force

Total force

0.15 0.2 0.25 0.3 0.35 0.4-1

-0.5

0

0.5

1

1.5

2Load-stroke curve


]

L o a d f a c t o r [ F / F s t a t i c

]

Spring force

Total force

Bump height of semi prepared runway

H: 0.0532 m

Bump height of semi prepared runway

H: 0.0532 m

F :0.48F :0.72

Break over point

Double-stage type Single-stage type

(d)(c)

10-1

100

101

102

0

0.5

1

1.5

2

2.5

Frequency[Hz]

T r a n s m i s i b i l i t y [ x U p p e r m a s s / x r o a d

]

Transmiss ibility of landing gear

Single-stage type

Double-stage t ype

10-1

100

101

102

0

0.5

1

1.5

2

2.5

Frequency[Hz]

T r a n s m i s i b i l i t y [ x U p p e r m a s s / x r o a d

]

Transmiss ibility of landing gear

Single-stage type

Double-stage t ype

Excitation amplitude : 0.02 m Excitation amplitude : 0.05 m

0.7325 0.733 0.7335 0.734 0.7345 0.735 0.7355 0.7360.98

0.985

0.99

0.995

1

1.005



]


s t a t i c ]

Spring force

Total force

0.2325 0.233 0.2335 0.234 0.2345 0.235 0.2355 0.2360.98

0.985

0.99

0.995

1

1.005



]


s t a t i c ]

Spring force

Total force

Bump height of paved runway

H: 0.0005 m

Bump height of paved runway

H: 0.0005 m

F :0.0045 F :0.0045

Double-stage type Single-stage type

2790




8

double-stage type landing gear by two different amplitude sinusoidal sweep simulation was

used to determine the vibration reduction capability. This process should not be confused with

the typical transmissibility used when dealing with linear system. Merely, the purpose of

simulation was to make a comparison vibration reduction between those two types of landing

gear. As shown in figure 7, double-stage type landing gear reveals improved transmissibility.

Especially, improvement of transmissibility is significant for the large excitation amplitude.

Because the dynamic stiffness of the double-stage oleo-pneumatic shock absorber which

described as blue dotted line in figure 2 is getting softer than the single-stage one as the

excitation amplitude getting bigger.

5. CONLUSIONS

Shock and vibration isolation performances of double-stage oleo-pneumatic shock

absorber were investigated in comparison with single-stage one. The results of analyticalstudy for the landing and taxiing simulation have led to following conclusions.

1. For the landing impact the double-stage oleo-pneumatic shock absorber showed a

good isolation performance compare with conventional single-stage one.

2. For the bump impact and the vibrations due to road excitation, the double-stage

oleo-pneumatic shock absorber performed well significantly even if the single-stage one has

a metering pin. This is because the dynamic stiffness of double-stage oleo-pneumatic shock

absorber is softer than single-stage one when the shock absorber operate in static equilibrium

state.

ACKNOWLEDGMENTS

This study has been supported by the KARI under KHP Dual-Use Component Development

Program funded by the MKE of Korea.

REFERENCES

[1] MIL-A-8863C, “Airplane strength and rigidity ground loads for NAVY acquired

airplanes,”1987

[2] Herbert E. Merritt, “Hydraulic control systems,” John Wiley & Sons, 1967.

[3] J. N. Daniels, “A method for landing gear modeling and simulation with experimental

validation,” NASA LRC, June 1996.

[4] W.W. Williams, G.K. Williams and W.C.J. Garrard, “Soft and Rough Field Landing

Gears,” SAE Paper 650844, Oct.1965.

[5] Hong Su, Rakheja and T.S. Sankar, “Random response analysis of a non-linear vehicle

suspension with tunable shock absorber,” Journal of mechanical systems and signal

processing, 6(4), pp. 363-381, 1992.

[6] J. S. Przemieniecki, “Aircraft landing gear design: Principle and practices,” AIAA

Educational series, 1988.

[7] Wolf Krüger, “Integrated design process for the development of semi-active landing gears

for transport aircraft,” DLR, Institut für Aeroelastik, Oberpfaffenhofen, Jun 1999.

2791

Documents

Yoon-kyu Lee1 Shock Observer