On the dynamic response of rolling tires according to thin shell approximations

Soedel, W.

doi:10.1016/s0022-460x(75)80099-x

Cited by 52 publications

(37 citation statements)

References 3 publications

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“…Similar phase changes also occur for the secondary mode families. These results are consistent with the well-known fact that for axisymmetric systems the phase difference between the radial and tangential displacements of the eigenmodes is ±90 degrees [9,30].…”

Section: Natural Frequencies and Modessupporting

confidence: 92%

“…A rotational frequency for the cylinder to study the effect of the centrifugal force on the modes is computed following the physical interpretation given by Soedel for the tire standing wave phenomenon [9]. In the case of our model, in dynamic rolling contact analyses the contact forces act as a disturbance traveling around the cylinder with a rotational speed ω.…”

Section: Eigenmode Analysismentioning

confidence: 99%

“…Moreover, according to Kennedy and Padovan [15], if friction is included into a tire contact model, it causes very localized shear distributions in the contact area, but hardly affects the global dynamic response of the system. Often simple point loads have been used to generate the tire standing wave effects, for example, see [9,17]. The role of the loading is mainly to act as a supply of energy required to propagate and sustain a wave.…”

Section: Contact Modelingmentioning

confidence: 99%

“…A few years later, studies giving solid resonance-based physical interpretations on the phenomenon were made by Soedel [9] and Padovan [10,11]. Modern treatises on viscoelastic structures in rolling contact using the finite element method and, also discussing tire standing waves, were first given by Oden and Lin [12], and Padovan et al [13][14][15].…”

Section: Introductionmentioning

confidence: 99%

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A numerical study of traveling waves in a viscoelastic cylinder cover under rolling contact

Karttunen

Hertzen

2013

International Journal of Mechanical Sciences

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Polymer-covered cylinders are widely used in high-speed industrial rolling contact machines. In this paper, traveling waves which appear at high speeds in the viscoelastic polymer cover of a cylinder due to rolling contact are studied using a 2D finite element (FE) model for a two-cylinder system. Through eigenmode analysis of the polymer cover, it is found that an infinite number of natural mode families exist for the cylinder cover due to its finite thickness. A critical speed below which the traveling waves do not appear can be calculated on the basis of a resonance condition using the modal information. In dynamic analyses, traveling waves in the cover are identified as modified quasi-elastic Rayleigh waves composed of the eigenmodes of the polymer cover. The symbiosis of the eigenmode and wave propagation aspects allows the formation of a coherent overall picture of the traveling wave phenomenon. The critical speed according to the resonance condition is also the minimum phase velocity of the waves propagating in the cover. At the critical speed and above, there is a spectrum of resonant speeds due to wave dispersion. It is found that the traveling wave phenomenon is best described as a Rayleigh wave resonance in which contact-induced modified quasi-elastic Rayleigh waves arising at critical and supercritical speeds superpose to form a strong traveling shock wave.

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Section: Natural Frequencies and Modessupporting

confidence: 92%

Section: Eigenmode Analysismentioning

confidence: 99%

Section: Contact Modelingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A numerical study of traveling waves in a viscoelastic cylinder cover under rolling contact

Karttunen

Hertzen

2013

International Journal of Mechanical Sciences

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“…Standing waves appear in the tire when the rotation speed reaches the critical values. These critical values for each mode are reached when the rotation speed coincides with one of the natural frequencies of the tire divided by the number of circumferential wavelengths of the mode n [7],…”

Section: Resultsmentioning

confidence: 99%

Simple Models for the Dynamic Modeling of Rotating Tires

Delamotte

Nascimento

Arruda

2008

Shock and Vibration

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Abstract. Large Finite Element (FE) models of tires are currently used to predict low frequency behavior and to obtain dynamic model coefficients used in multi-body models for riding and comfort. However, to predict higher frequency behavior, which may explain irregular wear, critical rotating speeds and noise radiation, FE models are not practical. Detailed FE models are not adequate for optimization and uncertainty predictions either, as in such applications the dynamic solution must be computed a number of times. Therefore, there is a need for simpler models that can capture the physics of the tire and be used to compute the dynamic response with a low computational cost. In this paper, the spectral (or continuous) element approach is used to derive such a model. A circular beam spectral element that takes into account the string effect is derived, and a method to simulate the response to a rotating force is implemented in the frequency domain. The behavior of a circular ring under different internal pressures is investigated using modal and frequency/wavenumber representations. Experimental results obtained with a real untreaded truck tire are presented and qualitatively compared with the simple model predictions with good agreement. No attempt is made to obtain equivalent parameters for the simple model from the real tire results. On the other hand, the simple model fails to represent the correct variation of the quotient of the natural frequency by the number of circumferential wavelengths with the mode count. Nevertheless, some important features of the real tire dynamic behavior, such as the generation of standing waves and part of the frequency/wavenumber behavior, can be investigated using the proposed simplified model.

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