The stiffness characteristics analysis of the duplex angular contact ball bearings based on a comprehensive multi-degree-of-freedom mathematical model
•A comprehensive mathematical model scheme is proposed for the duplex angular contact ball bearings with three configurations.•The analytical expression of the stiffness matrix is formulated based on the implicit differential method.•The detailed two layers iterative algorithm based on the Newton-Ra...
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| Vydané v: | Applied Mathematical Modelling Ročník 106; s. 601 - 626 |
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| Hlavní autori: | , , , , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Elsevier Inc
01.06.2022
Elsevier BV |
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| ISSN: | 0307-904X, 1088-8691, 0307-904X |
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| Abstract | •A comprehensive mathematical model scheme is proposed for the duplex angular contact ball bearings with three configurations.•The analytical expression of the stiffness matrix is formulated based on the implicit differential method.•The detailed two layers iterative algorithm based on the Newton-Raphson method is given.•The impacts of angular misalignment on the stiffness characteristics of the bearing are analyzed.
Although the duplex angular contact ball bearings (DACBBs) are widely used in industry, the published mathematical model of DACBBs is sparse. To analyze the stiffness characteristics of DACBBs, this paper proposes a comprehensive multi-degree-of-freedom (multi-DOF) mathematical model for the DACBBs in three traditional configurations. The implicit differential method is adopted to derivate the analytical stiffness matrix formulation of DACBBs. The geometrical constraints and interactions inside the DACBBs are presented based on the vector-and-matrix method. The detailed iterative algorithm with two layers for solving the presented model is given based on the Newton-Raphson method. A systematic study for evaluating the impacts of angular misalignment on the stiffness characteristics of DACBBs has been carried out under three typical load conditions: the pure axial load condition, the pure radial load condition, and the combined-loaded condition. The results indicate that the angular misalignment remarkably affects the stiffness characteristics of DACBBs. Under the pure axial and radial load conditions, the stiffness curves of DACBBs can be divided into two segments according to the value of misalignment angle, and the angular misalignment will be the predominant factor when the angular misalignment is great. Under the combined-loaded condition, the mode (single or combined angular misalignment) and the direction of angular misalignment significantly influence the stiffness characteristics of DACBBs. Also, the angular misalignment effects depend on the radial load. The proposed model can also analyze the mechanical performance of double-row angular contact ball bearings. |
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| AbstractList | Although the duplex angular contact ball bearings (DACBBs) are widely used in industry, the published mathematical model of DACBBs is sparse. To analyze the stiffness characteristics of DACBBs, this paper proposes a comprehensive multi-degree-of-freedom (multi-DOF) mathematical model for the DACBBs in three traditional configurations. The implicit differential method is adopted to derivate the analytical stiffness matrix formulation of DACBBs. The geometrical constraints and interactions inside the DACBBs are presented based on the vector-and-matrix method. The detailed iterative algorithm with two layers for solving the presented model is given based on the Newton-Raphson method. A systematic study for evaluating the impacts of angular misalignment on the stiffness characteristics of DACBBs has been carried out under three typical load conditions: the pure axial load condition, the pure radial load condition, and the combined-loaded condition. The results indicate that the angular misalignment remarkably affects the stiffness characteristics of DACBBs. Under the pure axial and radial load conditions, the stiffness curves of DACBBs can be divided into two segments according to the value of misalignment angle, and the angular misalignment will be the predominant factor when the angular misalignment is great. Under the combined-loaded condition, the mode (single or combined angular misalignment) and the direction of angular misalignment significantly influence the stiffness characteristics of DACBBs. Also, the angular misalignment effects depend on the radial load. The proposed model can also analyze the mechanical performance of double-row angular contact ball bearings. •A comprehensive mathematical model scheme is proposed for the duplex angular contact ball bearings with three configurations.•The analytical expression of the stiffness matrix is formulated based on the implicit differential method.•The detailed two layers iterative algorithm based on the Newton-Raphson method is given.•The impacts of angular misalignment on the stiffness characteristics of the bearing are analyzed. Although the duplex angular contact ball bearings (DACBBs) are widely used in industry, the published mathematical model of DACBBs is sparse. To analyze the stiffness characteristics of DACBBs, this paper proposes a comprehensive multi-degree-of-freedom (multi-DOF) mathematical model for the DACBBs in three traditional configurations. The implicit differential method is adopted to derivate the analytical stiffness matrix formulation of DACBBs. The geometrical constraints and interactions inside the DACBBs are presented based on the vector-and-matrix method. The detailed iterative algorithm with two layers for solving the presented model is given based on the Newton-Raphson method. A systematic study for evaluating the impacts of angular misalignment on the stiffness characteristics of DACBBs has been carried out under three typical load conditions: the pure axial load condition, the pure radial load condition, and the combined-loaded condition. The results indicate that the angular misalignment remarkably affects the stiffness characteristics of DACBBs. Under the pure axial and radial load conditions, the stiffness curves of DACBBs can be divided into two segments according to the value of misalignment angle, and the angular misalignment will be the predominant factor when the angular misalignment is great. Under the combined-loaded condition, the mode (single or combined angular misalignment) and the direction of angular misalignment significantly influence the stiffness characteristics of DACBBs. Also, the angular misalignment effects depend on the radial load. The proposed model can also analyze the mechanical performance of double-row angular contact ball bearings. |
| Author | Xu, Endian Wu, Wei Han, Yaoyu Wang, Kai Xu, Tengfei Yang, Lihua |
| Author_xml | – sequence: 1 givenname: Tengfei surname: Xu fullname: Xu, Tengfei organization: State key Laboratory for Strength and Vibration of Mechanical Structures, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China – sequence: 2 givenname: Lihua surname: Yang fullname: Yang, Lihua email: yanglihua_2@126.com organization: State key Laboratory for Strength and Vibration of Mechanical Structures, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China – sequence: 3 givenname: Wei surname: Wu fullname: Wu, Wei organization: State key Laboratory for Strength and Vibration of Mechanical Structures, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China – sequence: 4 givenname: Yaoyu surname: Han fullname: Han, Yaoyu organization: State key Laboratory for Strength and Vibration of Mechanical Structures, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China – sequence: 5 givenname: Endian surname: Xu fullname: Xu, Endian organization: State key Laboratory for Strength and Vibration of Mechanical Structures, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China – sequence: 6 givenname: Kai surname: Wang fullname: Wang, Kai organization: State key Laboratory for Strength and Vibration of Mechanical Structures, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China |
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| Keywords | Stiffness matrix formulation A multi-degree-of-freedom mathematical model Angular misalignment Duplex angular contact ball bearings |
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| Snippet | •A comprehensive mathematical model scheme is proposed for the duplex angular contact ball bearings with three configurations.•The analytical expression of the... Although the duplex angular contact ball bearings (DACBBs) are widely used in industry, the published mathematical model of DACBBs is sparse. To analyze the... |
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| SubjectTerms | A multi-degree-of-freedom mathematical model Angular misalignment Axial loads Ball bearings Contact angle Degrees of freedom Duplex angular contact ball bearings Iterative algorithms Iterative methods Mathematical analysis Mathematical models Matrix methods Mechanical properties Misalignment Newton-Raphson method Stiffness matrix Stiffness matrix formulation |
| Title | The stiffness characteristics analysis of the duplex angular contact ball bearings based on a comprehensive multi-degree-of-freedom mathematical model |
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