Analysis of Dynamic Response of a Two Degrees of Freedom (2-DOF) Ball Bearing Nonlinear Model
Often the input values used in mathematical models for rolling bearings are in a wide range, i.e., very small values of deformation and damping are confronted with big values of stiffness in the governing equations, which leads to miscalculations. This paper presents a two degrees of freedom (2-DOF)...
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MDPI AG
2021-01-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/11/2/787 |
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| author | Bartłomiej Ambrożkiewicz Grzegorz Litak Anthimos Georgiadis Nicolas Meier Alexander Gassner |
| author_facet | Bartłomiej Ambrożkiewicz Grzegorz Litak Anthimos Georgiadis Nicolas Meier Alexander Gassner |
| author_sort | Bartłomiej Ambrożkiewicz |
| collection | DOAJ |
| description | Often the input values used in mathematical models for rolling bearings are in a wide range, i.e., very small values of deformation and damping are confronted with big values of stiffness in the governing equations, which leads to miscalculations. This paper presents a two degrees of freedom (2-DOF) dimensionless mathematical model for ball bearings describing a procedure, which helps to scale the problem and reveal the relationships between dimensionless terms and their influence on the system’s response. The derived mathematical model considers nonlinear features as stiffness, damping, and radial internal clearance referring to the Hertzian contact theory. Further, important features are also taken into account including an external load, the eccentricity of the shaft-bearing system, and shape errors on the raceway investigating variable dynamics of the ball bearing. Analysis of obtained responses with Fast Fourier Transform, phase plots, orbit plots, and recurrences provide a rich source of information about the dynamics of the system and it helped to find the transition between the periodic and chaotic response and how it affects the topology of RPs and recurrence quantificators. |
| first_indexed | 2024-03-09T04:39:56Z |
| format | Article |
| id | doaj.art-4d9c2211986c4a6087e6ad90710e9656 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-09T04:39:56Z |
| publishDate | 2021-01-01 |
| publisher | MDPI AG |
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| series | Applied Sciences |
| spelling | doaj.art-4d9c2211986c4a6087e6ad90710e96562023-12-03T13:21:45ZengMDPI AGApplied Sciences2076-34172021-01-0111278710.3390/app11020787Analysis of Dynamic Response of a Two Degrees of Freedom (2-DOF) Ball Bearing Nonlinear ModelBartłomiej Ambrożkiewicz0Grzegorz Litak1Anthimos Georgiadis2Nicolas Meier3Alexander Gassner4Department of Automation, Faculty of Mechanical Engineering, Lublin University of Technology, Nadbystrzycka 36, 20-618 Lublin, PolandDepartment of Automation, Faculty of Mechanical Engineering, Lublin University of Technology, Nadbystrzycka 36, 20-618 Lublin, PolandInstitute of Product and Process Innovation (PPI), Leuphana University of Lüneburg, Universitätsallee 1, 21335 Lüneburg, GermanyInstitute of Product and Process Innovation (PPI), Leuphana University of Lüneburg, Universitätsallee 1, 21335 Lüneburg, GermanyInstitute of Product and Process Innovation (PPI), Leuphana University of Lüneburg, Universitätsallee 1, 21335 Lüneburg, GermanyOften the input values used in mathematical models for rolling bearings are in a wide range, i.e., very small values of deformation and damping are confronted with big values of stiffness in the governing equations, which leads to miscalculations. This paper presents a two degrees of freedom (2-DOF) dimensionless mathematical model for ball bearings describing a procedure, which helps to scale the problem and reveal the relationships between dimensionless terms and their influence on the system’s response. The derived mathematical model considers nonlinear features as stiffness, damping, and radial internal clearance referring to the Hertzian contact theory. Further, important features are also taken into account including an external load, the eccentricity of the shaft-bearing system, and shape errors on the raceway investigating variable dynamics of the ball bearing. Analysis of obtained responses with Fast Fourier Transform, phase plots, orbit plots, and recurrences provide a rich source of information about the dynamics of the system and it helped to find the transition between the periodic and chaotic response and how it affects the topology of RPs and recurrence quantificators.https://www.mdpi.com/2076-3417/11/2/787ball bearingsnonlinear mathematical modelshape errorsradial internal clearancediagnosticsrecurrence analysis |
| spellingShingle | Bartłomiej Ambrożkiewicz Grzegorz Litak Anthimos Georgiadis Nicolas Meier Alexander Gassner Analysis of Dynamic Response of a Two Degrees of Freedom (2-DOF) Ball Bearing Nonlinear Model Applied Sciences ball bearings nonlinear mathematical model shape errors radial internal clearance diagnostics recurrence analysis |
| title | Analysis of Dynamic Response of a Two Degrees of Freedom (2-DOF) Ball Bearing Nonlinear Model |
| title_full | Analysis of Dynamic Response of a Two Degrees of Freedom (2-DOF) Ball Bearing Nonlinear Model |
| title_fullStr | Analysis of Dynamic Response of a Two Degrees of Freedom (2-DOF) Ball Bearing Nonlinear Model |
| title_full_unstemmed | Analysis of Dynamic Response of a Two Degrees of Freedom (2-DOF) Ball Bearing Nonlinear Model |
| title_short | Analysis of Dynamic Response of a Two Degrees of Freedom (2-DOF) Ball Bearing Nonlinear Model |
| title_sort | analysis of dynamic response of a two degrees of freedom 2 dof ball bearing nonlinear model |
| topic | ball bearings nonlinear mathematical model shape errors radial internal clearance diagnostics recurrence analysis |
| url | https://www.mdpi.com/2076-3417/11/2/787 |
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