A Bibliographic Survey of Automobile and Aircraft Wheel Shimmy

Dengler, Max; Goland, Martin; Herrman, Georg

doi:10.21236/ada076003

Cited by 9 publications

(10 citation statements)

References 2 publications

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“…First of all, φ may differ quite substantially between aircraft types, in the range between zero to 10 degrees; by contrast, the relative ranges of most other parameters in Table 1 are much smaller. Secondly, the geometric effects of a nonzero rake angle have been incorporated fully into (2)- (4), so that such a study becomes feasible.…”

Section: Dependence On the Rake Anglementioning

confidence: 99%

“…Another milestone for shimmy research was the seminal work of von Schlippe and Dietrich [17] on tyre mechanics and its influence on shimmy. Shimmy has been studied in general wheeled vehicles, including cars, pulled trailers, motorcycles and aircraft; see, for example, the overview papers by Dengler et al [4], Smiley [13] and Pritchard [12] as an entry point to the literature.…”

Section: Introductionmentioning

confidence: 99%

“…See the overview paper by Dengler et al [4] for a discussion of the early literature on how the vertical mode may interact either with the torsional or with the lateral mode. By contrast, the vertical mode of a commercial aircraft is generally sufficiently damped so that it does not get excited on today's smooth runways or taxiways.…”

Section: Introductionmentioning

confidence: 99%

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Interaction of torsion and lateral bending in aircraft nose landing gear shimmy

2008

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In this paper we consider the onset of shimmy oscillations of an aircraft nose landing gear. To this end we develop and study a mathematical model with torsional and lateral bending modes that are coupled through a wheel-mounted elastic tyre. The geometric effects of a positive rake angle are fully incorporated into the resulting five-dimensional ordinary differential equation model. A bifurcation analysis in terms of the forward velocity and the vertical force on the gear reveals routes to different types of shimmy oscillations. In particular, we find regions of stable torsional and stable lateral shimmy oscillations, as well as transient quasiperiodic shimmy where both modes are excited.

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Section: Dependence On the Rake Anglementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Interaction of torsion and lateral bending in aircraft nose landing gear shimmy

2008

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“…As entry points to the literature see, for example, the surveys by Dengler et al [7], Smiley [8], and Pritchard [9], who discuss theoretical as well as experimental studies, stressing both tire theories and structural aspects of shimmy oscillations. Broulhiet's [10] seminal work on the effect of side slip of an elastic tire on shimmy oscillations forms the basis for many modern shimmy studies.…”

mentioning

confidence: 99%

Bifurcation Analysis of Nose-Landing-Gear Shimmy with Lateral and Longitudinal Bending

Thota

Krauskopf

Lowenberg

2010

Journal of Aircraft

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This work develops and studies a model of an aircraft nose landing gear with torsional, lateral, and longitudinal degrees of freedom. The corresponding three modes are coupled in a nonlinear fashion via the geometry of the landing gear in the presence of a nonzero rake angle, as well as via the nonlinear tire forces. Their interplay may lead to different types of shimmy oscillations as a function of the forward velocity and the vertical force on the landing gear. Methods from nonlinear dynamics, especially numerical continuation of equilibria and periodic solutions, are used to asses how the three modes contribute to different types of shimmy dynamics. In conclusion, the longitudinal mode does not actively participate in the nose-landing-gear dynamics over the entire range of forward velocity and vertical force. Nomenclature c = longitudinal bending damping of strut c = lateral bending damping of strut c = damping coefficient of elastic tire c = torsional damping of strut e = caster length e eff = effective caster length F K = lateral tire force or cornering force F z = vertical load on the gear h = contact patch length of elastic tire I x = moment of inertia of strut with regard to x axis I y = moment of inertia of strut with regard to y axis I z = moment of inertia of strut with regard to z axis k = self-aligning coefficient of elastic tire k = longitudinal bending stiffness of strut k = lateral bending stiffness of strut k = restoring coefficient of elastic tire k = torsional stiffness of strut L = relaxation length l g = gear height M D = moment due to tire lateral damping M D = moment due to damping in the longitudinal mode M D = moment due to damping in the lateral bending mode M D = moment due to damping in the torsional mode M K = self-aligning moment due to tire force M K = moment due to stiffness in the longitudinal mode M K = moment due to stiffness in the lateral bending mode M K = moment due to stiffness in the torsional mode M = coupling moment between the tire deformation and longitudinal mode M = coupling moment between the tire deformation and lateral mode R = radius of nose wheel V = forward velocity of the aircraft m = self-aligning moment limit = longitudinal bending angle = wheel tilt or camber angle = lateral bending angle = swivel angle = rake angle = torsion angle

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“…Due to their implications for passenger comfort, safety and maintainance costs, shimmy oscillations are an unwanted type of dynamics. They may occur in any wheeled vehicle, including cars, pulled trailers, motorcycles and indeed aircraft; see the overview papers [1,4,5].…”

Section: Introductionmentioning

confidence: 99%

Geometric Nonlinearities of Aircraft Systems

Krauskopf

Thota

Lowenberg

2010

Progress in Industrial Mathematics at ECMI 2008

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Summary. Nonlinearities due to geometric effects, in particular, via angular variables that are not small, are important for aircraft operation. Geometric nonlinearities have a strong effect on the dynamics of the aircraft system under consideration, and they are especially pronounced in aircraft ground operations. As a concrete example we consider here the effect of a non-zero rake angle on the dynamics of a nose landing gear. More specifically, we use tools from bifurcation theory to investigate the stability of the straight-rolling motion during a take-off run.

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A Bibliographic Survey of Automobile and Aircraft Wheel Shimmy

Cited by 9 publications

References 2 publications

Interaction of torsion and lateral bending in aircraft nose landing gear shimmy

Interaction of torsion and lateral bending in aircraft nose landing gear shimmy

Bifurcation Analysis of Nose-Landing-Gear Shimmy with Lateral and Longitudinal Bending

Geometric Nonlinearities of Aircraft Systems

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