Vibration analysis of a gear-rotor-bearing system with outer-ring spalling and misalignment

Abstract

Misalignment and spalling of bearing rings are typical errors and faults that significantly influence the vibration characteristics of a gear-rotor-bearing system. In order to investigate the coupling effects of misalignment and spalling, it is necessary to analyze the vibration characteristics of a gear-rotor-bearing system with misalignment and spalling. Firstly, considering the outer ring misalignment and spalling, the 5-DOF nonlinear bearing restoring force is calculated. Then, based on the loaded tooth contact analysis (LTCA) method, the meshing stiffness is calculated, and the dynamic model of the spur gear pair is established. Furthermore, the equivalent stiffness model of the spline is established based on the slicing method. Finally, by coupling the bearing restoring force model, the dynamic model of the spur gear pair, and the equivalent stiffness model of the spline with the finite element (FE) model of the rotor system, a dynamic model of a gear-rotor-bearing system is developed. The analysis shows that the contact force, contact angle, and system vibration are only affected when the spalling is located in load-bearing areas. The misalignment of the outer ring leads to the increase of the load-bearing area range of the bearing and the influence probability of the spalling on the system.

Keywords

ball bearing / misalignment / spalling / vibration characteristic / gear-rotor-bearing system

References

[1] LiuJ, ZhaoW, LiuW-wei. Frequency and vibration characteristics of high-speed gear-rotor-bearing system with tooth root crack considering compound dynamic backlash. Shock and Vibration, 2019, 2019: 1854263 J]

[2] WangS, ZhuR-peng. Nonlinear dynamic analysis of GTF gearbox under friction excitation with vibration characteristics recognition and control in frequency domain. Mechanical Systems and Signal Processing, 2021, 151107373 J]

[3] WangS, ZhuR-peng. Theoretical investigation of the improved nonlinear dynamic model for star gearing system in GTF gearbox based on dynamic meshing parameters. Mechanism and Machine Theory, 2021, 156104108 J]

[4] HanJ, LiuY, YuS, et al. . Acousticvibration analysis of the gear-bearing-housing coupled system. Applied Acoustics, 2021, 178108024 J]

[5] SongC-s, BaiH, ZhuC-c, et al. . Computational investigation of off-sized bearing rollers on dynamics for hypoid gear-shaft-bearing coupled system. Mechanism and Machine Theory, 2021, 156104177 J]

[6] SunZ, ChenS, HuZ, et al. . Vibration response analysis of a gear-rotor-bearing system considering steady-state temperature. Nonlinear Dynamics, 2022, 107(1): 477-493 J]

[7] WangF, DaiP, WangJ, et al. . Vibration responses of the bearing-rotor-gear system with the misaligned rotor. Machines, 2022, 10(4): 267 J]

[8] XuM-m, HanY, SunX, et al. . Vibration characteristics and condition monitoring of internal radial clearance within a ball bearing in a gear-shaft-bearing system. Mechanical Systems and Signal Processing, 2022, 165108280 J]

[9] KongX-n, DingH, TangJ, et al. . Bearing internal load analysis and fatigue life estimation based on nonlinear dynamic model of a gear system. Journal of Vibration and Control, 2022, 2813–141635-1642 J]

[10] GuiY, HanQ-k, ChuF-lei. A vibration model for fault diagnosis of planetary gearboxes with localized planet bearing defects. Journal of Mechanical Science and Technology, 2016, 30(9): 4109-4119 J]

[11] YuY, ShiJ-j, LuoY, et al. . The coupled vibration response analysis of gearbox with a bearing localized defect. 2022 Prognostics and Health Management Conference (PHM-2022 London), 2022, London, United Kingdom, IEEE: 67-72 C]

[12] ZhouY-f, XiongX, ZhangJ-s, et al. . Vibration characteristics of defected Sun gear bearing in planetary gearbox. 2021 7th International Conference on Condition Monitoring of Machinery in Non-Stationary Operations (CMMNO), 2021, Guangzhou, China, IEEE: 59 C]

[13] WangP-f, YangY, XuH, et al. . Effect of static and dynamic misalignment of rolling bearing on nonlinear vibration characteristics of rotor system. Journal of Central South University, 2023, 30(3): 871-903 J]

[14] WangP-f, YangY, MaH, et al. . Vibration characteristics of rotor-bearing system with angular misalignment and cage fracture: Simulation and experiment. Mechanical Systems and Signal Processing, 2023, 182: 109545 J]

[15] WangP-f, XuH, MaH, et al. . Effects of three types of bearing misalignments on dynamic characteristics of planetary gear set-rotor system. Mechanical Systems and Signal Processing, 2022, 169108736 J]

[16] JonesA B. A general theory for elastically constrained ball and radial roller bearings under arbitrary load and speed conditions. Journal of Basic Engineering, 1960, 82(2): 309-320 J]

[17] HarrisT A, KotzalasM NAdvanced concepts of bearing technology: Rolling bearing analysis, 2006FifthBoca Raton, CRC Press M]

[18] NoelD, RitouM, FuretB, et al. . Complete analytical expression of the stiffness matrix of angular contact ball bearings. Journal of Tribology, 2013, 135(4): 041101 J]

[19] ZhangJ, FangB, HongJ, et al. . A general model for preload calculation and stiffness analysis for combined angular contact ball bearings. Journal of Sound and Vibration, 2017, 411435-449 J]

[20] ZhangJ, FangB, HongJ, et al. . Effect of preload on ball-raceway contact state and fatigue life of angular contact ball bearing. Tribology International, 2017, 114365-372 J]

[21] LiX, YuK, MaH, et al. . Analysis of varying contact angles and load distributions in defective angular contact ball bearing. Engineering Failure Analysis, 2018, 91: 449-464 J]

[22] ChengH-c, ZhangY-m, LuW-j, et al. . Research on time-varying stiffness of bearing based on local defect and varying compliance coupling. Measurement, 2019, 143: 155-179 J]

[23] ZhangY-m, ChengH-c, LuW-j, et al. . Effect of inertia forces on contact state of ball bearing with local defect in outer raceway. Journal of Testing and Evaluation, 2021, 49(1): 20190770 J]

[24] ChengH-c, ZhangY-m, LuW-j, et al. . Effect of boundary position and defect shape on the mechanical properties of ball bearings. Mechanics Based Design of Structures and Machines, 2023, 5131645-1665 J]

[25] SawamotoT, KonishiK. Development of machine tool spindles with higher rotational speeds. Tribology International, 1982, 15(4): 199-207 J]

[26] WangW-z, HuL, ZhangS, et al. . Modeling angular contact ball bearing without raceway control hypothesis. Mechanism and Machine Theory, 2014, 82: 154-172 J]

[27] ZhangJ, FangB, ZhuY-s, et al. . A comparative study and stiffness analysis of angular contact ball bearings under different preload mechanisms. Mechanism and Machine Theory, 2017, 115: 1-17 J]

[28] LiuG, HongJ, WuW, et al. . Investigation on the influence of interference fit on the static and dynamic characteristics of spindle system. The International Journal of Advanced Manufacturing Technology, 2018, 99(5): 1953-1966 J]

[29] FengW, LiuB, YaoB, et al. . An integrated prediction model for the dynamics of machine tool spindles. Machining Science and Technology, 2018, 22(6): 968-988 J]

[30] FengW, ZhangK, LiuB, et al. . Dynamic modeling and vibration response analysis of a synchronous motorized spindle with inclined eccentricity. Journal of Vibration and Control, 2022, 28(19–20): 2950-2964 J]

[31] ZhangX-n, HanQ-k, PengZ-k, et al. . A new nonlinear dynamic model of the rotor-bearing system considering preload and varying contact angle of the bearing. Communications in Nonlinear Science and Numerical Simulation, 2015, 22(1–3): 821-841 J]

[32] YangL, SunY, SunR-b, et al. . Analytical modeling and mechanism analysis of time-varying excitation for surface defects in rolling element bearings. Journal of Dynamics, Monitoring and Diagnostics, 2023, 2: 89-101[J]

[33] XuH, WangP-f, MaH, et al. . Dynamic behaviors and contact characteristics of ball bearings in a multi-supported rotor system under the effects of 3D clearance fit. Mechanical Systems and Signal Processing, 2023, 196: 110334 J]

[34] XuH, YangY, MaH, et al. . Vibration characteristics of bearing-rotor systems with inner ring dynamic misalignment. International Journal of Mechanical Sciences, 2022, 230107536 J]

[35] XuH, WangP-f, MaH, et al. . Analysis of axial and overturning ultimate load-bearing capacities of deep groove ball bearings under combined loads and arbitrary rotation speed. Mechanism and Machine Theory, 2022, 169104665 J]

[36] ChenK-k, HuangfuY-f, MaH, et al. . Calculation of mesh stiffness of spur gears considering complex foundation types and crack propagation paths. Mechanical Systems and Signal Processing, 2019, 130273-292 J]

[37] HuangfuY-f, ChenK-k, MaH, et al. . Meshing and dynamic characteristics analysis of spalled gear systems: A theoretical and experimental study. Mechanical Systems and Signal Processing, 2020, 139106640 J]

[38] MarmolR A, SmalleyA J, TeczaJ A. Spline coupling induced nonsynchronous rotor vibrations. Journal of Mechanical Design, 1980, 102(1): 168-176 J]

[39] CornellR W. Compliance and stress sensitivity of spur gear teeth. Journal of Mechanical Design, 1981, 103(2): 447-459 J]