Piecewise Analytical Solution for Rub Interactions Between a Rotor and an Asymmetrically Supported Stator

Heba El-Mongy; Tamer El-Sayed; Vahid Vaziri; Marian Wiercigroch

doi:10.1007/978-3-031-15758-5_54

Piecewise Analytical Solution for Rub Interactions Between a Rotor and an Asymmetrically Supported Stator

Heba El-Mongy, Tamer El-Sayed^* (Corresponding Author), Vahid Vaziri, Marian Wiercigroch

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Published conference contribution

Abstract

Rotor-stator rubbing phenomenon is a very common fault in various engineering applications. Usually, the stator supports are assumed to be symmetric, however, in some conditions, the stator support stiffness is anisotropic in nature. In this paper, an approximate analytical solution for the rub interactions between a Jeffcott rotor and an asymmetrically supported stator is introduced. The present problem is a good example of piecewise nonlinear dynamics in which contact causes the system to switch between linear and nonlinear dynamic behavior. To evaluate an analytical solution to the contact equations, Taylor’s expansion is used to linearize the contact forces. Then, an analytical solution is introduced based on this approximation. To investigate the validity of the present model, the proposed approximate analytical solution is compared with the numerical solution obtained using direct numerical integration for the same problem. The results show that the proposed piecewise analytical solution is efficient in evaluating the system response for both periodic and chaotic responses.

Original language	English
Title of host publication	Recent Trends in Wave Mechanics and Vibrations. WMVC 2022. Mechanisms and Machine Science
Editors	Z. Dimitrovová, P. Biswas, R. Gonçalves, T. Silva
Publisher	Springer
Pages	532-539
Number of pages	8
Volume	125
ISBN (Electronic)	978-3-031-15758-5
ISBN (Print)	978-3-031-15757-8
DOIs	https://doi.org/10.1007/978-3-031-15758-5_54
Publication status	Published - 7 Oct 2022
Event	WMVC 2022: 10th International Conference on Wave Mechanics and Vibrations - Lisbon, Portugal Duration: 4 Jul 2022 → 6 Jul 2022 Conference number: 10th https://easychair.org/cfp/wmvc2022

Publication series

Name	Mechanisms and Machine Science
Publisher	Springer
ISSN (Print)	2211-0984
ISSN (Electronic)	2211-0992

Conference

Conference	WMVC 2022
Abbreviated title	WMVC 2022
Country/Territory	Portugal
City	Lisbon
Period	4/07/22 → 6/07/22
Internet address	https://easychair.org/cfp/wmvc2022

Keywords

Rotordynamics
Asymmetric stator
Jeffcott rotor
Analytical solution
Periodic
Piecewise nonlinear system

Access to Document

10.1007/978-3-031-15758-5_54Licence: Unspecified

Embargoed Document

EL-Mongy_etal_WMVC_Piecewise_Analytical_Solution_AAM
Accepted author manuscript, 0.99 MB
Licence: Unspecified
Embargo ends: 7/10/24

Cite this

El-Mongy, H., El-Sayed, T., Vaziri, V., & Wiercigroch, M. (2022). Piecewise Analytical Solution for Rub Interactions Between a Rotor and an Asymmetrically Supported Stator. In Z. Dimitrovová, P. Biswas, R. Gonçalves, & T. Silva (Eds.), Recent Trends in Wave Mechanics and Vibrations. WMVC 2022. Mechanisms and Machine Science (Vol. 125, pp. 532-539). (Mechanisms and Machine Science). Springer . https://doi.org/10.1007/978-3-031-15758-5_54

Piecewise Analytical Solution for Rub Interactions Between a Rotor and an Asymmetrically Supported Stator. / El-Mongy, Heba; El-Sayed, Tamer (Corresponding Author); Vaziri, Vahid et al.
Recent Trends in Wave Mechanics and Vibrations. WMVC 2022. Mechanisms and Machine Science. ed. / Z. Dimitrovová; P. Biswas; R. Gonçalves; T. Silva. Vol. 125 Springer , 2022. p. 532-539 (Mechanisms and Machine Science).

Research output: Chapter in Book/Report/Conference proceeding › Published conference contribution

El-Mongy, H, El-Sayed, T, Vaziri, V & Wiercigroch, M 2022, Piecewise Analytical Solution for Rub Interactions Between a Rotor and an Asymmetrically Supported Stator. in Z Dimitrovová, P Biswas, R Gonçalves & T Silva (eds), Recent Trends in Wave Mechanics and Vibrations. WMVC 2022. Mechanisms and Machine Science. vol. 125, Mechanisms and Machine Science, Springer , pp. 532-539, WMVC 2022, Lisbon, Portugal, 4/07/22. https://doi.org/10.1007/978-3-031-15758-5_54

El-Mongy H, El-Sayed T, Vaziri V , Wiercigroch M. Piecewise Analytical Solution for Rub Interactions Between a Rotor and an Asymmetrically Supported Stator. In Dimitrovová Z, Biswas P, Gonçalves R, Silva T, editors, Recent Trends in Wave Mechanics and Vibrations. WMVC 2022. Mechanisms and Machine Science. Vol. 125. Springer . 2022. p. 532-539. (Mechanisms and Machine Science). Epub 2022 Oct 7. doi: 10.1007/978-3-031-15758-5_54

El-Mongy, Heba ; El-Sayed, Tamer ; Vaziri, Vahid et al. / Piecewise Analytical Solution for Rub Interactions Between a Rotor and an Asymmetrically Supported Stator. Recent Trends in Wave Mechanics and Vibrations. WMVC 2022. Mechanisms and Machine Science. editor / Z. Dimitrovová ; P. Biswas ; R. Gonçalves ; T. Silva. Vol. 125 Springer , 2022. pp. 532-539 (Mechanisms and Machine Science).

@inproceedings{a34abf8d8bb2450da0fbbcaa03310f4e,

title = "Piecewise Analytical Solution for Rub Interactions Between a Rotor and an Asymmetrically Supported Stator",

abstract = "Rotor-stator rubbing phenomenon is a very common fault in various engineering applications. Usually, the stator supports are assumed to be symmetric, however, in some conditions, the stator support stiffness is anisotropic in nature. In this paper, an approximate analytical solution for the rub interactions between a Jeffcott rotor and an asymmetrically supported stator is introduced. The present problem is a good example of piecewise nonlinear dynamics in which contact causes the system to switch between linear and nonlinear dynamic behavior. To evaluate an analytical solution to the contact equations, Taylor{\textquoteright}s expansion is used to linearize the contact forces. Then, an analytical solution is introduced based on this approximation. To investigate the validity of the present model, the proposed approximate analytical solution is compared with the numerical solution obtained using direct numerical integration for the same problem. The results show that the proposed piecewise analytical solution is efficient in evaluating the system response for both periodic and chaotic responses.",

keywords = "Rotordynamics, Asymmetric stator, Jeffcott rotor, Analytical solution, Periodic, Piecewise nonlinear system",

author = "Heba El-Mongy and Tamer El-Sayed and Vahid Vaziri and Marian Wiercigroch",

year = "2022",

month = oct,

day = "7",

doi = "10.1007/978-3-031-15758-5_54",

language = "English",

isbn = "978-3-031-15757-8",

volume = "125",

series = "Mechanisms and Machine Science",

publisher = "Springer ",

pages = "532--539",

editor = "Dimitrovov{\'a}, {Z. } and P. Biswas and R. Gon{\c c}alves and T. Silva",

booktitle = "Recent Trends in Wave Mechanics and Vibrations. WMVC 2022. Mechanisms and Machine Science",

note = "WMVC 2022 : 10th International Conference on Wave Mechanics and Vibrations, WMVC 2022 ; Conference date: 04-07-2022 Through 06-07-2022",

url = "https://easychair.org/cfp/wmvc2022",

}

TY - GEN

T1 - Piecewise Analytical Solution for Rub Interactions Between a Rotor and an Asymmetrically Supported Stator

AU - El-Mongy, Heba

AU - El-Sayed, Tamer

AU - Vaziri, Vahid

AU - Wiercigroch, Marian

N1 - Conference code: 10th

PY - 2022/10/7

Y1 - 2022/10/7

N2 - Rotor-stator rubbing phenomenon is a very common fault in various engineering applications. Usually, the stator supports are assumed to be symmetric, however, in some conditions, the stator support stiffness is anisotropic in nature. In this paper, an approximate analytical solution for the rub interactions between a Jeffcott rotor and an asymmetrically supported stator is introduced. The present problem is a good example of piecewise nonlinear dynamics in which contact causes the system to switch between linear and nonlinear dynamic behavior. To evaluate an analytical solution to the contact equations, Taylor’s expansion is used to linearize the contact forces. Then, an analytical solution is introduced based on this approximation. To investigate the validity of the present model, the proposed approximate analytical solution is compared with the numerical solution obtained using direct numerical integration for the same problem. The results show that the proposed piecewise analytical solution is efficient in evaluating the system response for both periodic and chaotic responses.

AB - Rotor-stator rubbing phenomenon is a very common fault in various engineering applications. Usually, the stator supports are assumed to be symmetric, however, in some conditions, the stator support stiffness is anisotropic in nature. In this paper, an approximate analytical solution for the rub interactions between a Jeffcott rotor and an asymmetrically supported stator is introduced. The present problem is a good example of piecewise nonlinear dynamics in which contact causes the system to switch between linear and nonlinear dynamic behavior. To evaluate an analytical solution to the contact equations, Taylor’s expansion is used to linearize the contact forces. Then, an analytical solution is introduced based on this approximation. To investigate the validity of the present model, the proposed approximate analytical solution is compared with the numerical solution obtained using direct numerical integration for the same problem. The results show that the proposed piecewise analytical solution is efficient in evaluating the system response for both periodic and chaotic responses.

KW - Rotordynamics

KW - Asymmetric stator

KW - Jeffcott rotor

KW - Analytical solution

KW - Periodic

KW - Piecewise nonlinear system

U2 - 10.1007/978-3-031-15758-5_54

DO - 10.1007/978-3-031-15758-5_54

M3 - Published conference contribution

SN - 978-3-031-15757-8

VL - 125

T3 - Mechanisms and Machine Science

SP - 532

EP - 539

BT - Recent Trends in Wave Mechanics and Vibrations. WMVC 2022. Mechanisms and Machine Science

A2 - Dimitrovová, Z.

A2 - Biswas, P.

A2 - Gonçalves, R.

A2 - Silva, T.

PB - Springer

T2 - WMVC 2022

Y2 - 4 July 2022 through 6 July 2022

ER -

Piecewise Analytical Solution for Rub Interactions Between a Rotor and an Asymmetrically Supported Stator

Abstract

Publication series

Conference

Keywords

Access to Document

Embargoed Document

Fingerprint

Cite this