Abstract
It is essential to establish a dynamic model of angular contact ball bearing with clearance for investigating the nonlinear dynamic behavior. In traditional dynamic model, the elastic contact force model is employed to describe the contact-impact process, which ignores the energy loss and causes lower precision analysis. In order to obtain the dynamic behavior of ball bearing more accurately, a novel dynamic model of angular contact ball bearing with clearance is proposed in this work, which considers the elastic deformation and energy dissipation. The effectiveness of proposed model for angular contact ball bearing is demonstrated by experiment test. The simulation results are agree with the experimental data. And, the simulation results also represent that the existence of clearance increases the nonlinear dynamic characteristics of angular contact ball bearing and contact force plays a significant role in the dynamic analysis of angular contact ball bearing. The motion state of ball is mainly characterized by the phases. In addition, the effects of driving speed and external load on the dynamic behavior of angular contact ball bearing are also conducted.
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References
Tu WB, He HB, Luo Y (2019) Dynamic skidding behavior of rolling elements under bearing steady working conditions. J Vib Shock 38(6):94–99
Liu J, Shao YM (2018) An improved analytical model for a lubricated roller bearing including a localized defect with different edge shapes. J Vib Control 24(17):3894–3907
Tian JY, Zhang C, Liang H (2022) Simulation of the load reduction process of high-speed angular contact ball bearing with coupling model of dynamics and thermo-elastohydrodynamic lubrication. Tribol Int 165:107292
Yan K, Wang N, Zhai Q (2015) Theoretical and experimental investigation on the thermal characteristics of double-row tapered roller bearings of high speed locomotive. Int J Heat Mas Tran 84:1119–1130
Flores P, Leine R, Glocker C (2010) Modeling and analysis of planar rigid multibody systems with translational clearance joints based on the non-smooth dynamics approach. Multibody Sys Dyn 23:165–190
Li H, Li H, Liu Y (2020) Dynamic characteristics of ball bearing with flexible cage lintel and wear. Eng Fail Anal 117:104956
Liu J, Xue L, Xu ZD (2021) Vibration characteristics of a high-speed flexible angular contact ball bearing with the manufacturing error. Mech Mach Theory 162:104335
Zheng EL, Zhu R, Zhu SH (2016) A study on dynamics of flexible multi-link mechanism including joints with clearance and lubrication for ultra-precision press. Nonlinear Dyn 83:137–159
Ye ZH, Wang LQ (2015) Effect of external loads on cage stability of high-speed ball bearings. Proc Inst Mech Eng J 229(11):1300–1318
Hao LN, Deng S, Qian DS (2020) Accurate prediction method of initial value of high-speed ball bearing model and gyroscopic torque analysis. J Mech Sci Technol 34(9):3745–3755
Liu J, Shao YM (2017) Dynamic modeling for rigid rotor bearing systems with a localized defect considering additional deformations at the sharp edges. J Sound Vib 398:84–102
Niu L, Cao H, Xiong X (2017) Dynamic modeling and vibration response simulations of angular contact ball bearings with ball defects considering the three-dimensional motion of ball. Tribol Int 109:26–39
Deng SE, Gu JF, Cui YC (2017) Dynamic analysis of a tapered roller bearing. Ind Lubr Tribol 70(1):191–200
Xu LX, Li YG (2015) Modeling of a deep-groove ball bearing with waviness defects in planar multibody system. Multibody Sys Dyn 33:229–258
Qi ZH, Wang G, Zhang ZG (2015) Contact analysis of deep groove ball bearings in multibody systems. Multibody Syst Dyn 33:115–141
Xi H, Wang HY, Han W (2016) Contact trajectory of angular contact ball bearings under dynamic operating condition. Tribo Int 104:247–262
Bover C, Zamponi I (2016) An approach for predicting the internal behavior of ball bearings under high moment load. Mech Mach Theory 101:1–22
Cui YC, Deng SE, Zhang WH (2017) The impact of roller dynamic unbalance of high-speed cylindrical roller bearing on the cage nonlinear dynamic characteristics. Mech Mach Theory 118:65–83
Yin XX, Gu HG, Feng G (2017) Analysis of non-uniform abrasion evolution for cylindrical roller bearings. Mech Mach Theory 117:148–159
Oktaviana L, Tong VC, Hong SW (2019) Skidding analysis of angular contact ball bearing subjected to radial load and angular misalignment. J Mech Sci Technol 33(2):837–845
Jafari SM, Rohani R, Rahi A (2020) Experimental and numerical study of an angular contact ball bearing vibration response with spall defect on the outer race. Arch Appl Mech 90:2487–2511
Zhang JH, Fang B, Yan K (2020) A novel model for high-speed angular contact ball bearing by considering variable contact angles. J Mech Sci Technol 34(2):809–816
Fang B, Yan K, Hong J (2021) A comprehensive study on the off-diagonal coupling elements in the stiffness matrix of the angular contact ball bearing and their influence on the dynamic characteristics of the rotor system. Mech Mach Theory 158:104251
Gao S, Chatterton S, Naldi L (2021) Ball bearing skidding and over-skidding in large-scale angular contact ball bearings: Nonlinear dynamic model with thermal effects and experimental results. Mech Syst Signal Process 147:107120
Gao S, Chatterton S, Pennacchi P (2021) Behaviour of an angular contact ball bearing with three-dimensional cubic-like defect: a comprehensive non-linear dynamic model for predicting vibration reponse. Mech Mach Theory 163:104376
Bai ZF, Zhao Y (2012) Dynamic behaviour analysis of planar mechanical systems with clearance in revolute joints using a new hybrid contact force model. Int J Mech Sci 54(1):190–205
Zheng EL, Wang TY, Guo J (2019) Dynamic modeling and error analysis of planar flexible multilink mechanism with clearance and spindle-bearing structure. Mech Mach Theory 131:234–260
Xiao MH, Geng GS, Li GH (2017) Analysis on dynamic precision reliability of high-speed precision press based on Monte Carlo method. Nonlinear Dyn 90:2979–2988
Zhao HY, Xu MQ, Wang JD (2015) A parameters optimization method for planar joint clearance model and its application for dynamics simulation of reciprocating compressor. J Sound Vib 344:416–433
Zhao B, Dai XD, Zhang ZN (2016) A new numerical method for piston dynamics and lubrication analysis. Tribol Int 94:395–408
Zhao B, Zhou K, Xie YB (2016) A new numerical method for planar multibody system with mixed lubricated revolute joint. Int J Mech Sci 113:105–119
Xu LX (2017) A method for modelling contact between circular and non-circular shapes with variable radii of curvature and its application in planar mechanical systems. Multibody Syst Dyn 393:153–174
Erkaya S (2019) Investigation of joint clearance effects on actuator power consumption in mechanical systems. Measurement 134:400–411
Erkaya S (2019) Determining power consumption using neural model in multibody systems with clearance and flexible joints. Multibody Sys Dyn 47:165–181
Yao TQ, Xian LG, Wang LH (2017) Multibody contact dynamics on mechanisms with deep groove ball bearing joints. J Mech Sci Technol 31(9):4119–4135
Yao TQ, Wang LH, Liu XB (2020) Multibody dynamics simulation of thin-walled four-point contact ball bearing with interactions of balls, ring raceways and crown-type cage. Multibody Syst Dyn 48:337–372
Chen XL, Jiang S, Deng Y (2018) Dynamic analysis of 2-DOF complex planar mechanical system with joint clearance and flexible links. Nonlinear Dyn 93:1009–1032
Chen XL, Jia Y (2022) Dynamic modeling and responses investigation of spatial parallel robot considering lubricated spherical joint. Eur J Mech A/Solids 92:104458
Wang S, Tian Q, Hu HY (2021) Sensitivity analysis of deployable flexible space structures with a large number of design parameters. Nonlinear Dyn 105:2055–2079
Wang K, Tian Q, Hu HY (2021) Nonsmooth spatial frictional contact dynamics of multibody systems. Multibody Syst Dyn 53:1–27
Li YY, Li M, Liu YF (2022) Parameter optimization for torsion spring of deployable solar array system with multiple clearance joints considering rigid-flexible coupling dynamics. Chin J Aeronaut 35(3):509–524
Li YY, Yang Y, Li M (2022) Dynamics analysis and wear prediction of rigid-flexible coupling deployable solar array system with clearance joints considering solid lubrication. Mech Syst Signal Process 162:108059
Xiao SG, Liu SL, Song MM (2020) Coupling rub-impact dynamics of double translational joints with subsidence for time-varrying load in a planar mechanical system. Multibody Syst Dyn 18:451–486
Liu Y, Liu H (2021) A coupled model of angular-contact ball bearing-elastic rotor system and its dynamic characteristics under asymmetric support. J Vib Eng Technol 9:1175–1192
Liu J, Xu Z, Zhou L (2019) A statistical feature investigation of the spalling propagation assessment for a ball bearing. Mech Mach Theory 131:336–350
Li KY, Tang WC (2021) Load-displacement relationship model and measurement of deep groove ball bearing and 4-point contact ball bearing. J Mech Sci Technol 35(7):3045–3058
Hong SW, Tong VC (2016) Rolling-element bearing modeling: a review. Int J Precis Eng Manuf 17(12):1729–1749
Liu Y (2020) Kinematic investigation and fatigure life analysis of angular contact ball bearing in wide speed range based on raceway friction. Ind Lubr Tribol 72(7):845–850
Zhang WH, Deng SE, Chen GD (2017) Impact of lubricant traction coefficient on cage’s dynamic characteristics in high-speed angular contact ball bearing. Chin J Aeronaut 30(2):827–835
Chen GC, Jia P, He JQ (2013) Effects of geometric parameters on static load capacity of a double-row four-point contact ball bearing. J Mech Sci Tech 27(2):1053–1061
Bai ZF, Sun Y (2016) A study on dynamics of planar multibody mechanical systems with multiple revolute clearance joints. Eur J Mech A/Solid 60:95–111
Kan ZY, Li F, Peng HJ (2021) Sliding cable modeling: a nonlinear complementarity function based framework. Mech Syst Signal Process 146:107021
Chen Y, Wu K, Wu XZ (2021) Kinematic accuracy and nonlinear dynamics of a flexible slider-crank mechanism with multiple clearance joints. Eur J Mech A/Solid 88:104277
Chen XL, Jiang SY (2022) Nonlinear dynamic behavior analysis of multi-linkage mechanism with multiple lubrication clearances. Eur J Mech B/Fluids 91:177–193
Wu XZ, Sun Y, Wang Y (2020) Dynamic analysis of the double crank mechanism with a 3D translational clearance joint employing a variable stiffness contact force model. Nonlinear Dyn 99:1937–1958
Bai ZF, Zhao Y (2013) A hybrid contact force model of revolute joint with clearance for planar. Int J Nonlinear Mech 48:15–36
Flores P, Lankarani HM (2012) Dynamic response of multibody systems with multiple clearance joints. J Comput Nonlinear Dyn 7(3):031003–031013
Zhao CJ, Yu XK, Huang QX (2015) Analysis on the load characteristics and coefficient of friction of angular contact ball bearing at high speed. Tribo Int 87:50–56
Han QK, Li XL, Chu FL (2018) Skidding behavior of cylindrical roller bearings under time-variable load conditions. Int J Mech Sci 135:203–214
Acknowledgements
This work is supported by the “National Natural Science Foundation of China (No. 52005230)”, “Changzhou Science and Technology Planning Project (No. CJ20210067)”, “Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No. 21KJB470003)” and “Outstanding Young Backbone Teacher of Jiangsu Qinglan Project”.
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Chen, Y., Wu, X., Wang, X. et al. Clearance-induced contact trajectory uncertainty of angular contact ball bearing under coupling operating condition. Meccanica 58, 43–66 (2023). https://doi.org/10.1007/s11012-022-01629-y
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DOI: https://doi.org/10.1007/s11012-022-01629-y