Applied Mathematics and Mechanics >
Study on the influence of internal bearing parameters on the critical speed and vibration behavior of the rotor-bearing coupled system
Received date: 2025-11-03
Revised date: 2025-12-23
Online published: 2026-03-02
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The dual challenges of critical speed prediction inaccuracies and ambiguous vibration behaviors are present in high-speed flexible rotors, particularly in free turbine rotors in turboshaft engine systems. The study begins with an examination of the rotor-bearing bidirectional coupling mechanism, with a primary focus on the nonlinear characteristics of the bearing. An investigation is carried out on the mechanical modeling methodologies for four-point contact ball bearings (FPCBBs) and cylindrical roller bearings (CRBs). To address the issue of excessive computational time in traditional bearing calculation methods, the sled dog optimization (SDO) algorithm is substituted for the conventional Newton-Raphson method. A rotor-bearing coupling dynamics model is developed by the finite element and lumped mass methods, with experimental validation achieved through a simulator test rig. The effects of three internal bearing parameters in FPCBBs (arching width and raceway groove curvature coefficient) and CRBs (initial radial clearance) on the critical speed characteristics and vibrational behavior of rotor-bearing coupled systems are examined. The numerical simulation results show some interesting conclusions.
Fanyu ZHANG , Yulai ZHAO , Qingyu ZHU , Xiangyu MENG , Junzhe LIN , Qingkai HAN . Study on the influence of internal bearing parameters on the critical speed and vibration behavior of the rotor-bearing coupled system[J]. Applied Mathematics and Mechanics, 2026 , 47(3) : 653 -674 . DOI: 10.1007/s10483-026-3357-7
| [1] | SARAVANAMUTTOO, H. I. H., ROGERS, G. F. C., and COHEN, H. Gas Turbine Theory, Pearson Education, London (2001) |
| [2] | GENTA, G. Dynamics of Rotating Systems, Springer Science & Business Media, Berlin (2005) |
| [3] | PANDA, K. C. and DUTT, J. K. Optimum support characteristics for rotor-shaft system with preloaded rolling element bearings. Journal of Sound and Vibration, 260(4), 731–755 (2003) |
| [4] | ZHOU, J. L., LUO, Z., LI, L., MA, T. Y., and LI, H. Y. Numerical and experimental analysis of the influence of elastic supports on bearing-rotor systems. Mechanical Systems and Signal Processing, 224, 112235 (2025) |
| [5] | LIU, K. P., WANG, D. H., LI, W. Y., SHI, X. J., and ZHANG, Q. C. Dynamic characteristics investigation of a dual rotor-casing system considering the comprehensive stiffness of the intermediate bearing. Journal of Sound and Vibration, 578, 118355 (2024) |
| [6] | QIN, Z. Y., HAN, Q. K., and CHU, F. L. Bolt loosening at rotating joint interface and its influence on rotor dynamics. Engineering Failure Analysis, 59, 456–466 (2016) |
| [7] | WANG, P. F., XU, H. Y., YANG, Y., MA, H., HE, D., and ZHAO, X. Dynamic characteristics of ball bearing-coupling-rotor system with angular misalignment fault. Nonlinear Dynamics, 108, 3391–3415 (2022) |
| [8] | MA, X. F., LI, Z. N., XIANG, J. W., SUN, X. W., CHEN, C. Z., and HUANG, F. C. Nonlinear vibration analysis of rotor-bearing system with insufficient interference and bearing tilt. International Journal of Mechanical Sciences, 287, 109966 (2025) |
| [9] | DENG, S., CHEN, S. R., and PU, M. M. Effect of balls’ quantities, preload and raceway diameters on rotation accuracy and vibration of rigid rotor-bearing system based on nonlinear dynamic model. International Journal of Non-Linear Mechanics, 166, 104821 (2024) |
| [10] | ZHAO, Y. L., WANG, H. B., LIN, J. Z., HAN, Q. K., and LIU, Y. Effect of internal excitation induced by non-uniform contact of roller bearings on nonlinear vibration and stability of rotor system under combined loads. Communications in Nonlinear Science and Numerical Simulation, 125, 107381 (2023) |
| [11] | SU, Y., ZHANG, J. Q., and ZHANG, W. Theoretical and experimental approaches for flexible cage dynamic characteristics of four-point contact ball bearing considering multi-point contact behaviors. Mechanical Systems and Signal Processing, 223, 111929 (2025) |
| [12] | GLOECKNER, P., MARTIN, M., and FLOUROS, M. Comparison of power losses and temperatures between an all-steel and a direct outer ring-cooled, hybrid 133-mm-bore ball bearing at very high speeds. Tribology Transactions, 60, 1148–1158 (2017) |
| [13] | LAVRENTYEV, Y. L., PETROV, N. I., and NOZHNITSKY, Y. A. Empirical correlation of heat generation in hybrid ball bearings, depending on the operational conditions in the aero-engine rotor supports. Journal of Physics: Conference Series, 1771(1), 012046 (2021) |
| [14] | WANG, L. Q. and LI, Y. F. Boundary for aviation bearing accelerated life test based on quasi-dynamic analysis. Tribology International, 116, 414–421 (2017) |
| [15] | HAINES, D. J. and EDMONDS, M. J. Fourth paper: a new design of angular contact ball race. Proceedings of the Institution of Mechanical Engineers, 185, 382–393 (1970) |
| [16] | HAMROCK, B. J. and ANDERSON, W. J. Arched-Outer-Race Ball-Bearing Analysis Considering Centrifugal Forces, National Aeronautics and Space Administration, Washington (1972) |
| [17] | HAMROCK, B. J. Ball motion and sliding friction in an arched outer race ball bearing. Journal of Tribology, 97, 202–210 (1975) |
| [18] | AMASORRAIN, J. I., SAGARTZAZU, X., and DAMIAN, J. Load distribution in a four contact-point slewing bearing. Mechanism and Machine Theory, 38, 479–496 (2003) |
| [19] | LEBLANC, A. and NELIAS, D. Ball motion and sliding friction in a four-contact-point ball bearing. Journal of Tribology, 129(4), 801–808 (2007) |
| [20] | RIVERA, G., TONG, V. C., and HONG, S. W. Contact load and stiffness of four-point contact ball bearings under loading. International Journal of Precision Engineering and Manufacturing, 23, 677–687 (2022) |
| [21] | LI, Z. H., WANG, C. Y., HU, X. L., WANG, H. Z., and YANG, L. H. Study on the effect of angular misalignment and axial preload on the mechanical properties of four-point angular contact ball bearings. Mechanism and Machine Theory, 193, 105565 (2024) |
| [22] | HARRIS, T. A. The effect of misalignment on the fatigue life of cylindrical roller bearings having crowned rolling members. Journal of Lubrication Technology, 91, 294–300 (1969) |
| [23] | LIU, J. Y. The effect of misalignment on the life of high speed cylindrical roller bearings. Journal of Tribology, 93(1), 60–68 (1971) |
| [24] | GUPTA, P. K. Dynamics of rolling-element bearings, part I: cylindrical roller bearing analysis. Journal of Tribology, 101, 293–302 (1979) |
| [25] | HONG, S. W. and TONG, V. C. Rolling-element bearing modeling: a review. International Journal of Precision Engineering and Manufacturing, 17, 1729–1749 (2016) |
| [26] | TEUTSCH, R. and SAUER, B. An alternative slicing technique to consider pressure concentrations in non-Hertzian line contacts. Journal of Tribology, 126(3), 436–442 (2004) |
| [27] | QIU, L. W., LIU, S. B., CHEN, X. Y., and WANG, Z. J. Lubrication and loading characteristics of cylindrical roller bearings with misalignment and roller modifications. Tribology International, 165, 107291 (2022) |
| [28] | YAN, K., MA, S. J., FANG, B., CHEN, F., HONG, J., and ZHANG, P. A new dynamic model for cylindrical roller bearings with flexible rollers and bearing sliding investigation. Mechanical Systems and Signal Processing, 224, 112133 (2025) |
| [29] | WANG, Z. J., ZUO, K. C., GUO, D., SU, H., and TIAN, J. Y. Investigation on contact and power loss characteristics of cylindrical roller bearing under bending moment. Mechanical Systems and Signal Processing, 225, 112308 (2025) |
| [30] | GUPTA, K., GUPTA, K. D., and ATHRE, K. Unbalance response of a dual rotor system: theory and experiment. Journal of Vibration and Acoustics, 115, 427–435 (1993) |
| [31] | FERRARIS, G., MAISONNEUVE, V., and LALANNE, M. Prediction of the dynamic behavior of non-symmetrical coaxial co- or counter-rotating rotors. Journal of Sound and Vibration, 195, 649–666 (1996) |
| [32] | MA, P. P. Vibration Analysis of the Dual-Rotor System for Aeroengine (in Chinese), Ph. D. dissertation, Dalian University of Technology (2021) |
| [33] | CAO, H. R., LI, B. J., LI, Y. M., KANG, T., and CHEN, X. F. Model-based error motion prediction and fit clearance optimization for machine tool spindles. Mechanical Systems and Signal Processing, 133, 106252 (2019) |
| [34] | CAO, H. R., SHI, F., LI, Y. M., LI, B. J., and CHEN, X. F. Vibration and stability analysis of rotor-bearing-pedestal system due to clearance fit. Mechanical Systems and Signal Processing, 133, 106275 (2019) |
| [35] | JIN, Y. L., LIU, Z. W., YANG, Y., LI, F. S., and CHEN, Y. S. Nonlinear vibrations of a dual-rotor-bearing-coupling misalignment system with blade-casing rubbing. Journal of Sound and Vibration, 497, 115948 (2021) |
| [36] | WANG, P. F., XU, H. Y., MA, H., HAN, H. Z., and YANG, Y. Effects of three types of bearing misalignments on dynamic characteristics of planetary gear set-rotor system. Mechanical Systems and Signal Processing, 169, 108736 (2022) |
| [37] | TANG, H. S., REN, Y., XIANG, J. W., and KUMAR, A. Numerical and experimental analysis of rotor-bearing system for axial piston pump with misalignment–rubbing coupling fault. Journal of Sound and Vibration, 559, 117786 (2023) |
| [38] | GUAN, H., WANG, P. F., XIONG, Q., MA, H., ZHOU, S. N., MU, Q. Q., ZENG, Y., and CHEN, Y. Y. Modeling of misaligned bearing induced by coupling misalignment and assembly errors and vibration analysis in dual-rotor system. Mechanical Systems and Signal Processing, 230, 112656 (2025) |
| [39] | XU, H. Y., WANG, P. F., MA, H., YANG, Y., LI, X. P., LUO, Z., HAN, Q. K., and WEN, B. C. 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, 196, 110334 (2023) |
| [40] | JIANG, Z. Y., HUANG, X. Z., SUN, L. S., WANG, Y. P., and JIANG, F. S. Dynamic modeling and spectrum modulation effect of multi-type bearing-supported rotor systems with combined misalignment faults. Journal of Sound and Vibration, 609, 119118(2025) |
| [41] | HAN, S. Research on Dynamic Characteristics and High-Speed Dynamic Balance Methods of Flexible Outboard Rotor in Aircraft Engines (in Chinese), Ph. D. dissertation, Northeastern University (2024) |
| [42] | MA, S. J., LI, W. C., YAN, K., LI, Y. T., ZHU, Y. S., and HONG, J. A study on the dynamic contact feature of four-contact-point ball bearing. Mechanical Systems and Signal Processing, 174, 109111 (2022) |
| [43] | HARRIS, T. A. and KOTZALAS, M. N. Rolling Bearing Analysis: Essential Concepts of Bearing Technology, CRC Press, New York (2007) |
| [44] | Popov, V. L. Contact Mechanics and Friction, Springer Berlin Heidelberg, Berlin (2010) |
| [45] | JONES, A. B. A general theory for elastically constrained ball and radial roller bearings under arbitrary load and speed conditions. Journal of Basic Engineering, 82(2), 309–320 (1960) |
| [46] | QIAN, W. C. and YE, K. Y. Elastic Mechanics, Science Press, Beijing (1980) |
| [47] | GAO, W. F., LI, G. H., ZHANG, Q. F., LUO, Y. T., and WANG, Z. K. Solving nonlinear equation systems by a two-phase evolutionary algorithm. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 51(9), 5652–5663 (2019) |
| [48] | GU, Q., LI, S. J., and LIAO, Z. W. Solving nonlinear equation systems based on evolutionary multitasking with neighborhood-based speciation differential evolution. Expert Systems with Applications, 238, 122025 (2024) |
| [49] | PAN, L. Q., ZHAO, Y., and LI, L. H. Neighborhood-based particle swarm optimization with discrete crossover for nonlinear equation systems. Swarm and Evolutionary Computation, 69, 101019 (2022) |
| [50] | HU, G., CHENG, M., HOUSSEIN, E. H., HUSSIEN, A. G., and ABUALIGAH, L. SDO: a novel sled dog-inspired optimizer for solving engineering problems. Advanced Engineering Informatics, 62, 102783 (2024) |
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