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Research Papers

Linear Stability Analysis and Dynamic Response of Shimmy Dampers for Main Landing Gears

[+] Author and Article Information
Carlos Arreaza

Mechanical and Industrial Engineering,
University of Toronto,
5 King's College Road,
Toronto, ON M5S 3G8, Canada
e-mail: arreaza.c@gmail.com

Kamran Behdinan

Mem. ASME
Mechanical and Industrial Engineering,
University of Toronto,
5 King's College Road,
Toronto, ON M5S 3G8, Canada
e-mail: behdinan@mie.utoronto.ca

Jean W. Zu

Mem. ASME
Mechanical and Industrial Engineering,
University of Toronto,
5 King's College Road,
Toronto, ON M5S 3G8, Canada
e-mail: zu@mie.utoronto.ca

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received September 10, 2015; final manuscript received April 19, 2016; published online May 20, 2016. Assoc. Editor: Alexander F. Vakakis.

J. Appl. Mech 83(8), 081002 (May 20, 2016) (10 pages) Paper No: JAM-15-1491; doi: 10.1115/1.4033482 History: Received September 10, 2015; Revised April 19, 2016

This paper presents the analysis and study of common shimmy dampers used today for main landing gears with the use of analytical and numerical tools. The shimmy phenomenon is studied by using the tire stretched string theory model and by developing linear approximations of the dynamics of a single tire landing gear. The dynamics of commonly used shimmy dampers are then incorporated into the model. The objectives of this paper are to study already developed shimmy damper designs and to develop tools to design a new innovative and better shimmy damper for main landing gears, those which have nonsteerable wheels. Two shimmy damper designs are studied in this paper, one developed by Boeing and another by UTC Aerospace Systems (UTAS). A linear approximation of the dynamics of these dampers is obtained, omitting the freeplay, saturation, and nonlinear dynamics. Stability plots are then created by changing the system's parameters, such as the velocity, caster length, and the shimmy damper stiffness and damping coefficients. These plots show the comparison of using a UTC two-arm design against the Boeing damper, for which the former spans larger zones of stability but requires higher damping coefficients due to the UTC damper's geometry which is very impractical. In addition, a multibody model is developed in MSC adams (from MSC Software Corporation) to study the dynamic response of these systems and to create a modeling tool that can be used to design a new and improved shimmy damper for main landing gears. The simulation results from the model show the disadvantages of using the UTC two-arm damper, which include an asymmetrical vibration response. Further recommendations are given to design an improved shimmy damper.

Copyright © 2016 by ASME
Topics: Stability , Dampers , Gears , Tires
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References

Figures

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Fig. 1

Elastic string model

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Fig. 2

Simple trailing wheel system

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Fig. 3

Boeing damper with upper and lower torque links: (a) side view, (b) front view, and (c) iso view

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Fig. 4

UTAS shimmy damper with remaining lower torque link: (a) side view, (b) front view, and (c) iso view

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Fig. 5

Bending arm and compression/extension of UTAS damper

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Fig. 6

Stability plot of a single tire landing gear with a Boeingdamper in an e–V plane, when L = 0.6 m, γ = 31 deg, cλ = 1000 N s m−1, and kλ = 3800 N m−1

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Fig. 7

Stability plot of a single tire landing gear with a Boeing damper in a cλ−kλ plane changing the velocity (m s−1) when L = 0.6 m and γ = 31 deg

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Fig. 8

Stability plot of a single tire landing gear with a Boeing damper in a cλ−kλ plane changing the length of the torque links L (m)

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Fig. 9

Stability plot of a single tire landing gear with a Boeing damper in a cλ−kλ plane changing the torque link angle γ (deg)

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Fig. 10

Stability plot of a single tire landing gear with a UTAS damper in an e–V plane when L = 0.6 m, γ = 31 deg, b = 0.2 m, cλ = 1000 N s m−1, and Iarm = 5 × 10−5 m4

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Fig. 11

Stability plot of a single tire landing gear with a UTAS damper in a cλ−Iarm plane changing the velocity (m s−1) when L = 0.6 m, γ = 31 deg, and b = 0.2 m

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Fig. 12

Stability plot of a single tire landing gear with a UTAS damper in a cλ−Iarm plane changing the side length b (m) when L = 0.6 m, γ = 31 deg, and V = 100 m s−1

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Fig. 13

Stability plot of a single tire landing gear with a UTAS damper in a cλ−Iarm plane changing Young's modulus of the bending arm when L = 0.6 m, V = 40 m s−1, b = 0.2 m, and γ = 31 deg

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Fig. 14

Multibody landing gear model: rigid bodies

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Fig. 15

Bottom section landing gear multibody model: forces and moments

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Fig. 16

Multibody simulation result using the Boeing damper for a velocity of 160 m s−1, L = 0.6 m, and γ = 31 deg, for different cλ and kλ values (shown in the graph)

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Fig. 17

Multibody simulation result using the UTAS damper for a velocity of 40 m s−1, b = 0.15 m, and Iarm = 5 × 10−6 m4, for different cλ values (shown in the graph)

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