Mathematical Model of Double Row Self-Aligning Ball Bearing

Bartłomiej Ambrożkiewicz; Grzegorz Litak; Anthimos Georgiadis; Arkadiusz Syta; Nicolas Meier; Alexander Gassner

doi:10.1007/978-3-031-56496-3_3

Mathematical Model of Double Row Self-Aligning Ball Bearing

Bartłomiej Ambrożkiewicz^*
, Grzegorz Litak
, Anthimos Georgiadis
, Arkadiusz Syta
, Nicolas Meier
, Alexander Gassner

^*Corresponding author for this work

Research output: Contributions to collected editions/works › Article in conference proceedings › Research › peer-review

Abstract

Ball bearings are widely used in variety of rotary mechanisms expecting their maintenance-free operation. One of the main factors influencing bearing life is radial internal clearance (RIC), which can be simply described as relative movement of ball and raceway perpendicular to the bearing axis. Mentioned parameter has a significant impact on dynamic response of applied ball bearing in the system and brings strong nonlinear effects. In the paper nonlinear 2 degrees of freedom (2-DOF) model of double-row self-aligning ball bearing is established. Mentioned type of bearing is very important from operation point of view, because it is used in applications, where strong misalignments are expected coming from assembly of shaft deflection. Model input data are based on characteristics of bearing 2309SK. Results of bearing dynamic response are studied for different values of radial internal clearance. For quantitative and qualitative analysis of nonlinear time series a few recurrence quantificators, providing information on bearing’s behavior regarding RIC’s value. Results can be used in the validation process with acceleration response coming from the real bearing node.

Original language	English
Title of host publication	Perspectives in Dynamical Systems II — Numerical and Analytical Approaches - DSTA 2021
Editors	Jan Awrejcewicz
Number of pages	11
Publisher	Springer Verlag
Publication date	2024
Pages	29-39
ISBN (Print)	978-3-031-56495-6
ISBN (Electronic)	978-3-031-56496-3
DOIs	https://doi.org/10.1007/978-3-031-56496-3_3
Publication status	Published - 2024
Event	16th International Conference on Dynamical Systems Theory and Applications - DSTA 2021 - Lodz, Poland Duration: 06.12.2021 → 09.12.2021 Conference number: 16 https://assets-plus.eu/event/dsta-2021-16th-international-conference-dynamical-systems-theory-and-applications/

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

Research areas and keywords

Diagnostics
Nonlinear mathematical model
Recurrence analysis
Rolling-element bearing modeling
Self-aligning ball bearing
Mathematics
Engineering

Access to Document

10.1007/978-3-031-56496-3_3

Cite this

Ambrożkiewicz, B., Litak, G., Georgiadis, A., Syta, A., Meier, N., & Gassner, A. (2024). Mathematical Model of Double Row Self-Aligning Ball Bearing. In J. Awrejcewicz (Ed.), Perspectives in Dynamical Systems II — Numerical and Analytical Approaches - DSTA 2021 (pp. 29-39). (Springer Proceedings in Mathematics and Statistics; Vol. 454). Springer Verlag. https://doi.org/10.1007/978-3-031-56496-3_3

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title = "Mathematical Model of Double Row Self-Aligning Ball Bearing",

abstract = "Ball bearings are widely used in variety of rotary mechanisms expecting their maintenance-free operation. One of the main factors influencing bearing life is radial internal clearance (RIC), which can be simply described as relative movement of ball and raceway perpendicular to the bearing axis. Mentioned parameter has a significant impact on dynamic response of applied ball bearing in the system and brings strong nonlinear effects. In the paper nonlinear 2 degrees of freedom (2-DOF) model of double-row self-aligning ball bearing is established. Mentioned type of bearing is very important from operation point of view, because it is used in applications, where strong misalignments are expected coming from assembly of shaft deflection. Model input data are based on characteristics of bearing 2309SK. Results of bearing dynamic response are studied for different values of radial internal clearance. For quantitative and qualitative analysis of nonlinear time series a few recurrence quantificators, providing information on bearing{\textquoteright}s behavior regarding RIC{\textquoteright}s value. Results can be used in the validation process with acceleration response coming from the real bearing node.",

keywords = "Diagnostics, Nonlinear mathematical model, Recurrence analysis, Rolling-element bearing modeling, Self-aligning ball bearing, Mathematics, Engineering",

author = "Bart{\l}omiej Ambro{\.z}kiewicz and Grzegorz Litak and Anthimos Georgiadis and Arkadiusz Syta and Nicolas Meier and Alexander Gassner",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.; 16th International Conference on Dynamical Systems Theory and Applications - DSTA 2021, DSTA 2021 ; Conference date: 06-12-2021 Through 09-12-2021",

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Ambrożkiewicz, B, Litak, G, Georgiadis, A, Syta, A, Meier, N & Gassner, A 2024, Mathematical Model of Double Row Self-Aligning Ball Bearing. in J Awrejcewicz (ed.), Perspectives in Dynamical Systems II — Numerical and Analytical Approaches - DSTA 2021. Springer Proceedings in Mathematics and Statistics, vol. 454, Springer Verlag, pp. 29-39, 16th International Conference on Dynamical Systems Theory and Applications - DSTA 2021, Lodz, Poland, 06.12.21. https://doi.org/10.1007/978-3-031-56496-3_3

Mathematical Model of Double Row Self-Aligning Ball Bearing. / Ambrożkiewicz, Bartłomiej; Litak, Grzegorz; Georgiadis, Anthimos et al.
Perspectives in Dynamical Systems II — Numerical and Analytical Approaches - DSTA 2021. ed. / Jan Awrejcewicz. Springer Verlag, 2024. p. 29-39 (Springer Proceedings in Mathematics and Statistics; Vol. 454).

Research output: Contributions to collected editions/works › Article in conference proceedings › Research › peer-review

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T1 - Mathematical Model of Double Row Self-Aligning Ball Bearing

AU - Ambrożkiewicz, Bartłomiej

AU - Litak, Grzegorz

AU - Georgiadis, Anthimos

AU - Syta, Arkadiusz

AU - Meier, Nicolas

AU - Gassner, Alexander

N1 - Conference code: 16

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N2 - Ball bearings are widely used in variety of rotary mechanisms expecting their maintenance-free operation. One of the main factors influencing bearing life is radial internal clearance (RIC), which can be simply described as relative movement of ball and raceway perpendicular to the bearing axis. Mentioned parameter has a significant impact on dynamic response of applied ball bearing in the system and brings strong nonlinear effects. In the paper nonlinear 2 degrees of freedom (2-DOF) model of double-row self-aligning ball bearing is established. Mentioned type of bearing is very important from operation point of view, because it is used in applications, where strong misalignments are expected coming from assembly of shaft deflection. Model input data are based on characteristics of bearing 2309SK. Results of bearing dynamic response are studied for different values of radial internal clearance. For quantitative and qualitative analysis of nonlinear time series a few recurrence quantificators, providing information on bearing’s behavior regarding RIC’s value. Results can be used in the validation process with acceleration response coming from the real bearing node.

AB - Ball bearings are widely used in variety of rotary mechanisms expecting their maintenance-free operation. One of the main factors influencing bearing life is radial internal clearance (RIC), which can be simply described as relative movement of ball and raceway perpendicular to the bearing axis. Mentioned parameter has a significant impact on dynamic response of applied ball bearing in the system and brings strong nonlinear effects. In the paper nonlinear 2 degrees of freedom (2-DOF) model of double-row self-aligning ball bearing is established. Mentioned type of bearing is very important from operation point of view, because it is used in applications, where strong misalignments are expected coming from assembly of shaft deflection. Model input data are based on characteristics of bearing 2309SK. Results of bearing dynamic response are studied for different values of radial internal clearance. For quantitative and qualitative analysis of nonlinear time series a few recurrence quantificators, providing information on bearing’s behavior regarding RIC’s value. Results can be used in the validation process with acceleration response coming from the real bearing node.

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KW - Nonlinear mathematical model

KW - Recurrence analysis

KW - Rolling-element bearing modeling

KW - Self-aligning ball bearing

KW - Mathematics

KW - Engineering

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DO - 10.1007/978-3-031-56496-3_3

M3 - Article in conference proceedings

AN - SCOPUS:85199516406

SN - 978-3-031-56495-6

T3 - Springer Proceedings in Mathematics and Statistics

SP - 29

EP - 39

BT - Perspectives in Dynamical Systems II — Numerical and Analytical Approaches - DSTA 2021

A2 - Awrejcewicz, Jan

PB - Springer Verlag

T2 - 16th International Conference on Dynamical Systems Theory and Applications - DSTA 2021

Y2 - 6 December 2021 through 9 December 2021

ER -

Mathematical Model of Double Row Self-Aligning Ball Bearing

Abstract

Bibliographical note

Research areas and keywords

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