A comprehensive comparative investigation of frictional force models for dynamics of rotor-bearing systems

Abstract

Vibrations of a rotor-bearing system (RBS) can be affected by the frictional forces between the components of the inherent bearings. Thus, an in-depth investigation of the influences of the frictional moments of the bearings on the vibrations of the RBS can be helpful for understanding the vibration mechanisms in the rotating machinery. In this study, an improved dynamic model of a RBS considering different frictional force models is presented. A comparative investigation on the influences of the empirical and analytical frictional force models on the vibration characteristics of the RBS is proposed. The empirical frictional force models include Palmgren’s and SKF’s models. The analytical frictional force model considers the rolling friction caused by the radial elastic material hysteresis, slipping friction between the ball and races, viscosity friction caused by the lubricating oil, and contact friction between the ball and cage. The influences of the external load and rotational speed on the vibrations of the RBS are analyzed. The comparative results show that the analytical frictional force model can give a more reasonable method for formulating the effects of the friction forces in the bearings on the vibrations of the RBS. The results also demonstrate that the friction forces in the bearings can significantly affect the vibrations of the RBSs.

Keywords

friction force / vibrations / rotor-bearing system / dynamic model

References

[1] LiuJ, ShaoY. Overview of dynamic modelling and analysis of rolling element bearings with localized and distributed faults [J]. Nonlinear Dynamics, 2018, 93(4): 1765-1798

[2] LiuJ, TangC, WuH, XuZ, WangL. An analytical calculation method of the load distribution and stiffness of an angular contact ball bearing [J]. Mechanism and Machine Theory, 2019, 142: 103597

[3] PalmgrenABall and roller bearing engineering [M], 19593rd edBurbank, Philadelphia, SKF Industries

[4] DengS R, LiX L, WangJ G, TengH F. Frictional torque characteristic of angular contact ball bearings [J]. Journal of Mechanical Engineering, 2011, 47(5): 114-120

[5] KakutaK. Generating mechanism of friction torque in a ball bearing 2 [J]. Mechanism, 1965, 3645-648

[6] SnareB. Rolling resistance in lightly loaded bearings [J]. The Ball Bearing Journal, 1968, 152: 3-8

[7] SnareB. Rolling resistance in lightly loaded bearings [J]. The Ball Bearing Journal, 1968, 153: 19-24

[8] SnareB. Rolling resistance in lightly loaded bearings [J]. The Ball Bearing Journal, 1968, 154: 3-14

[9] TODD M J, STEVENS K T. Frictional torque of angular contact ball bearings with different conformities [R]. Risley, Technical Report ESA-CR(P)-1221, 1978.

[10] GentleR, PasdariM. Measurement of cage and pocket friction in a ball bearing for use in a simulation program [J]. ASLE Transactions, 1985, 28(4): 536-541

[11] TRIPPETT R. Ball and needle bearing friction correlations under radial load conditions [J]. SAE Tech, 1985, Paper No. 851512. DOI: https://doi.org/10.4271/851512.

[12] CHIU Y, MYERS M. A rotational approach for determining permissible speed for needle roller bearings [J]. SAE Tech, 1998, Paper No. 982030. DOI: https://doi.org/10.4271/982030.

[13] SKFGeneral catalog 4000 [R], 2004, Gothenburg, Sweden: Svenska Kullargerfabriken

[14] IqbalS, BenderF A, CroesJ, PluymersB, DesmetW. Frictional power loss in solid-grease-lubricated needle roller bearing [J]. Lubrication Science, 2013, 25(5): 351-367

[15] LiuJ, YanZ, ShaoY. An investigation for the friction torque of a needle roller bearing with the roundness error [J]. Mechanism and Machine Theory, 2018, 121: 259-272

[16] LiuJ, LiX, DingS, PangR. A time-varying friction moment calculation method of an angular contact ball bearing with the waviness error [J]. Mechanism and Machine Theory, 2020, 148: 103799

[17] TongV C, HongS W. Study on the running torque of angular contact ball bearings subjected to angular misalignment [J]. Journal of Engineering Tribology, 2018, 232(7): 890-909

[18] HanQ, DingZ, QinZ, WangT, XuX, ChuF. A triboelectric rolling ball bearing with self-powering and self-sensing capabilities [J]. Nano Energy, 2020, 67104277

[19] HanQ, DingZ, XuX, WangT, ChuF. Stator current model for detecting rolling bearing faults in induction motors using magnetic equivalent circuits [J]. Mechanical Systems and Signal Processing, 2019, 131554575

[20] XuT, YangL, WuY. Friction torque study on double-row tapered roller bearing [C]. 2019 IEEE International Instrumentation and Measurement Technology Conference (I2MTC), 2019, Auckland, New Zealand, IEEE, 18974243

[21] KwakW, LeeJ, LeeY B. Theoretical and experimental approach to ball bearing frictional characteristics compared with cryogenic friction model and dry friction model [J]. Mechanical Systems and Signal Processing, 2019, 124424-438

[22] BabuC K, TandonN, PandeyR K. Vibration modeling of a rigid rotor supported on the lubricated angular contact ball bearings considering six degrees of freedom and waviness on balls and races [J]. Journal of Vibration and Acoustics, 2012, 134(1): 011006

[23] BabuC K, TandonN, PandeyR K. Nonlinear vibration analysis of an elastic rotor supported on angular contact ball bearings considering 6 DOF and waviness on balls and races [J]. ASME Journal of Vibration and Acoustics, 2014, 136: 044503

[24] LiuJ, ShaoY M, MingJ Z. The effects of the shape of localized defect in ball bearings on the vibration waveform [J]. Journal of Multi-body Dynamics, 2013, 2273261-274

[25] LiuJ, ShaoY M, ZhuW D. A new model for the relationship between vibration characteristics caused by the time-varying contact stiffness of a deep groove ball bearing and defect sizes [J]. ASME Journal of Tribology, 2015, 137(3): 031101

[26] CaoH, NiuL, XiS, ChenX. Mechanical model development of rolling bearing-rotor systems: A review [J]. Mechanical Systems and Signal Processing, 2018, 10237-58

[27] CaoH, LiY, ChenX. A new dynamic model of ball-bearing rotor systems based on rigid body element [J]. Journal of Manufacturing Science and Engineering, 2016, 138(7): 071007

[28] HalminenO, AceitunoJ F, EscalonaJ L, SopanenJ, MikkolaA. A touchdown bearing with surface waviness: Friction loss analysis [J]. Mechanism and Machine Theory, 2017, 11073-84

[29] LiuJ, ShaoY. Dynamic modeling for rigid rotor bearing systems with a localized defect considering additional deformations at the sharp edges [J]. Journal of Sound and Vibration, 2017, 39884-102

[30] LiuJ. A dynamic modelling method of a rotor-roller bearing-housing system with a localized fault including the additional excitation zone [J]. Journal of Sound and Vibration, 2020, 469: 115144

[31] NeisiN, HeikkinenJ E, SopanenJ. Influence of surface waviness in the heat generation and thermal expansion of the touchdown bearing [J]. European Journal of Mechanics-A/Solids, 2019, 7434-47

[32] XuL X, ChenB K, LiC Y. Dynamic modelling and contact analysis of bearing-cycloid-pinwheel transmission mechanisms used in joint rotate vector reducers [J]. Mechanism and Machine Theory, 2019, 137: 432-458

[33] ZHENG D, CHEN W, XIAO G, ZHENG D. Effect of vibration on power loss of angular contact ball bearings [J]. Industrial Lubrication and Tribology, 2019, DOI: https://doi.org/10.1108/ILT-06-2019-0217.

[34] PopescuA, HoupertL, OlaruD N. Four approaches for calcuting power losses in an angular contact ball bearing [J]. Mechanism and Machine Theory, 2020, 144: 103669

[35] HammamiM, MartinsR, FernandesC, SeabraJ, AbbesM S, HaddarM. Friction torque in rolling bearings lubricated with axle gear oils [J]. Tribology International, 2018, 119419-435

[36] ZhangX, XuH, ChangW, XiH, XingY, PeiS Y, WangF C. Torque variations of ball bearings based on dynamic model with geometrical imperfections and operating conditions [J]. Tribology International, 2019, 133: 193-205

[37] MajdoubF, SaunierL, Sidoroff-CoicaudC, MevelB. Experimental and numerical roller skew in tapered roller bearings [J]. Tribology International, 2020, 145: 106142

[38] HarrisT A, KotzalasM NRolling bearing analysis-essential concepts of bearing technology [M], 20075th edNew York, Taylor and Francis

[39] LynaghN, RahnejatH, EbrahimiM, AiniR. A bearing induced vibration in precision high speed routing spindles [J]. International Journal of Machine Tools and Manufacture, 2000, 40561-577