Hysteresis effect in the nonlinear stability of towed wheels

Sándor Beregi; Dénes Takács; David A.W. Barton

doi:10.1115/DETC2017-67722

Hysteresis effect in the nonlinear stability of towed wheels

Sándor Beregi, Dénes Takács, David A.W. Barton

Systems Centre

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

3 Citations (Scopus)

Abstract

In this paper the dynamics of towed elastic wheels are studied with the help of the brush tyre model. To calculate the lateral deformation of the contact patch centre-line distributed time-delay is taken into account for the rolling parts, whereas parabolic limits are used to determine the deformation in case of side-slip. After linear stability analysis of the rectilinear motion the limit cycles of the non-smooth time-delayed system are calculated with the method of numerical collocation. With the help of bifurcation diagrams it is demonstrated how the periodic orbits develop from the linear stability boundary in a structure characteristic of piecewise-smooth systems. Moreover, it is shown that the contact memory effect and the dry friction yield bistable parameter ranges besides the linearly unstable domains. Namely, for one particular towing velocity a stable equilibrium corresponding to straight-line motion and a stable periodic orbit coexist resulting a hysteresis effect in the stability of the straightline motion.

Original language	English
Title of host publication	13th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
Publisher	American Society of Mechanical Engineers (ASME)
ISBN (Electronic)	9780791858202
DOIs	https://doi.org/10.1115/DETC2017-67722
Publication status	Published - 2017
Event	ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2017 - Cleveland, United States Duration: 6 Aug 2017 → 9 Aug 2017

Publication series

Name	Proceedings of the ASME Design Engineering Technical Conference
Volume	6

Conference

Conference	ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2017
Country/Territory	United States
City	Cleveland
Period	6/08/17 → 9/08/17

Bibliographical note

Funding Information:
This research has been partly supported by the ÚNKP-16-13-I. New National Excellence Program of the Ministry of Human Capacities and by the Hungarian National Science Foundation under grant no. OTKA108779.

Publisher Copyright:
© Copyright 2017 ASME.

Research Groups and Themes

Engineering Mathematics Research Group

Access to Document

10.1115/DETC2017-67722

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Persistent link

Cite this

@inproceedings{7b7baf27a5104f2895d3fd6da3f0f9bc,

title = "Hysteresis effect in the nonlinear stability of towed wheels",

abstract = "In this paper the dynamics of towed elastic wheels are studied with the help of the brush tyre model. To calculate the lateral deformation of the contact patch centre-line distributed time-delay is taken into account for the rolling parts, whereas parabolic limits are used to determine the deformation in case of side-slip. After linear stability analysis of the rectilinear motion the limit cycles of the non-smooth time-delayed system are calculated with the method of numerical collocation. With the help of bifurcation diagrams it is demonstrated how the periodic orbits develop from the linear stability boundary in a structure characteristic of piecewise-smooth systems. Moreover, it is shown that the contact memory effect and the dry friction yield bistable parameter ranges besides the linearly unstable domains. Namely, for one particular towing velocity a stable equilibrium corresponding to straight-line motion and a stable periodic orbit coexist resulting a hysteresis effect in the stability of the straightline motion.",

author = "S{\'a}ndor Beregi and D{\'e}nes Tak{\'a}cs and Barton, \{David A.W.\}",

note = "Funding Information: This research has been partly supported by the {\'U}NKP-16-13-I. New National Excellence Program of the Ministry of Human Capacities and by the Hungarian National Science Foundation under grant no. OTKA108779. Publisher Copyright: {\textcopyright} Copyright 2017 ASME.; ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2017 ; Conference date: 06-08-2017 Through 09-08-2017",

year = "2017",

doi = "10.1115/DETC2017-67722",

language = "English",

series = "Proceedings of the ASME Design Engineering Technical Conference",

publisher = "American Society of Mechanical Engineers (ASME)",

booktitle = "13th International Conference on Multibody Systems, Nonlinear Dynamics, and Control",

address = "United States",

}

Beregi, S, Takács, D & Barton, DAW 2017, Hysteresis effect in the nonlinear stability of towed wheels. in 13th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. Proceedings of the ASME Design Engineering Technical Conference, vol. 6, American Society of Mechanical Engineers (ASME), ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2017, Cleveland, United States, 6/08/17. https://doi.org/10.1115/DETC2017-67722

Hysteresis effect in the nonlinear stability of towed wheels. / Beregi, Sándor; Takács, Dénes; Barton, David A.W.
13th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. American Society of Mechanical Engineers (ASME), 2017. (Proceedings of the ASME Design Engineering Technical Conference; Vol. 6).

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

TY - GEN

T1 - Hysteresis effect in the nonlinear stability of towed wheels

AU - Beregi, Sándor

AU - Takács, Dénes

AU - Barton, David A.W.

N1 - Funding Information: This research has been partly supported by the ÚNKP-16-13-I. New National Excellence Program of the Ministry of Human Capacities and by the Hungarian National Science Foundation under grant no. OTKA108779. Publisher Copyright: © Copyright 2017 ASME.

PY - 2017

Y1 - 2017

N2 - In this paper the dynamics of towed elastic wheels are studied with the help of the brush tyre model. To calculate the lateral deformation of the contact patch centre-line distributed time-delay is taken into account for the rolling parts, whereas parabolic limits are used to determine the deformation in case of side-slip. After linear stability analysis of the rectilinear motion the limit cycles of the non-smooth time-delayed system are calculated with the method of numerical collocation. With the help of bifurcation diagrams it is demonstrated how the periodic orbits develop from the linear stability boundary in a structure characteristic of piecewise-smooth systems. Moreover, it is shown that the contact memory effect and the dry friction yield bistable parameter ranges besides the linearly unstable domains. Namely, for one particular towing velocity a stable equilibrium corresponding to straight-line motion and a stable periodic orbit coexist resulting a hysteresis effect in the stability of the straightline motion.

AB - In this paper the dynamics of towed elastic wheels are studied with the help of the brush tyre model. To calculate the lateral deformation of the contact patch centre-line distributed time-delay is taken into account for the rolling parts, whereas parabolic limits are used to determine the deformation in case of side-slip. After linear stability analysis of the rectilinear motion the limit cycles of the non-smooth time-delayed system are calculated with the method of numerical collocation. With the help of bifurcation diagrams it is demonstrated how the periodic orbits develop from the linear stability boundary in a structure characteristic of piecewise-smooth systems. Moreover, it is shown that the contact memory effect and the dry friction yield bistable parameter ranges besides the linearly unstable domains. Namely, for one particular towing velocity a stable equilibrium corresponding to straight-line motion and a stable periodic orbit coexist resulting a hysteresis effect in the stability of the straightline motion.

UR - https://www.scopus.com/pages/publications/85034738146

U2 - 10.1115/DETC2017-67722

DO - 10.1115/DETC2017-67722

M3 - Conference Contribution (Conference Proceeding)

AN - SCOPUS:85034738146

T3 - Proceedings of the ASME Design Engineering Technical Conference

BT - 13th International Conference on Multibody Systems, Nonlinear Dynamics, and Control

PB - American Society of Mechanical Engineers (ASME)

T2 - ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2017

Y2 - 6 August 2017 through 9 August 2017

ER -

Hysteresis effect in the nonlinear stability of towed wheels

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