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Research on multi-body dynamic model of automatic discrete system for protection bearing without cage

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Abstract

Rolling bodies in cageless ball bearings without cage control will always hit each other. This causes the rolling bodies to wear out faster and decreases the bearing's performance. But most of the available references only look at how well the bearing works when the cage is in place. They do not look at how the inner ring's dynamic response changes when the cage is removed and the rolling elements' motion changes. On the basis of this, a nonlinear rolling-body dynamics model with six degrees of freedom and contact between rolling bodies is suggested. The dynamics model of an automatic discrete system is built on the motion coupling and functional slot discrete theories. The power hardware re-turn method is used to figure out how to solve the dynamics model. The results show that after the rotor falls into the inner ring, the rolling bodies will cause cumulative collision for a short time. Then, because of the function slot, the occasional collision between the rolling bodies would not cause cumulative collision again, and the inner ring motion will be more stable. When the speed of the rotor's fall goes up, the rolling bodies hit each other more often. This makes the inner ring move more steadily, but there is a limit. To make sure that the theoretical analysis and the results of the theoretical solution are right, a high-speed camera was used. To make sure that the theoretical analysis and the results of the theoretical solution are right, we built a bearing test platform to take pictures of the rolling body of the bearing as it moved. The image processing program is used to figure out the rolling body's angular speed, compare the test results to the theoretical study and make sure that the theoretical study is right. The theoretical study is compared to the test results to see if the theoretical study is right.

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Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Abbreviations

D w :

Rolling body diameter

d i :

Diameter of the bottom of the inner channel groove

d o :

Diameter of the bottom of the outer trench channel

d m :

Section circle diameter

E :

Material modulus of elasticity

F ij :

Rolling body and inner raceway contact force

F oj :

Rolling body and outer raceway contact force

F n ( j , j −1) :

Collision force between the rolling body and the previous rolling body

F n ( j , j + 1) :

Collision force between the rolling body and the following rolling body

F r :

Radial load

F c :

Rolling body centrifugal force

J n :

Moment of inertia of the rolling body with respect to the center of mass

K b :

Contact stiffness between rolling bodies

K ij :

Contact stiffness of rolling body and inner raceway

K oj :

Contact stiffness of rolling body and outer raceway

m b :

Rolling body mass

m i :

Inner ring quality

n :

Inner ring speed

r bj :

Rolling body radial displacement

r i :

Radial displacement of inner ring center

S ij :

Slip-roll ratio of rolling body to inner raceway

S oj :

Slip-roll ratio of rolling body to outer raceway

T p :

Friction between rolling bodies

T ij :

Rolling body and inner raceway drag force

T oj :

Rolling body and outer raceway drag force

Z :

Number of rolling bodies

δ :

Collision contact deformation between rolling bodies

δ ij :

Rolling body and inner raceway contact elastic deformation

δ oj :

Rolling body and outer raceway contact elastic deformation

δ in :

Rolling body and inner ring relative displacement

δ out :

Rolling body and outer ring relative displacement

θ x :

Circumferential span angle

θ oz :

Axial span angle

θ j :

Rolling body self-turning angle position

μ ij :

Rolling body and inner raceway drag coefficient

μ oj :

Rolling body and outer raceway drag coefficient

ρ :

Material Density

υ :

Material Poisson's ratio

φ j :

Rolling body angle position

ω bj :

Rolling body rotation angular velocity

ω cj :

Angular velocity of rolling body rotation

References

  1. Gu, L., Guenat, E., Schiffmann, J.: A review of grooved dynamic gas bearings. J. Appl. Mech. Rev. 72(1), 15 (2020)

    Article  Google Scholar 

  2. Breńkacz, Ł, Żywica, G., Drosińska-Komor, M.: The experimental determination of bearings dynamic coefficients in a wide range of rotational speeds, taking into account the resonance and hydrodynamic instability. Dyn. Syst. Appl. Łódź 14, 11–14 (2017)

    Google Scholar 

  3. Schmied J.: Behavior of a one ton rotor being dropped into auxiliary bearings. Proceedings, 3rd Int. Symp. Magnetic Bearings, Alexandria, VA, USA, 145–156 (1992)

  4. Xu, L., Li, Y.: Modeling of a deep-groove ball bearing with waviness defects in planar multibody system. J. Multibody Syst. Dyn. 33, 229–258 (2015)

    Article  MathSciNet  Google Scholar 

  5. Jain S.: Skidding and fault detection in the bearings of wind-turbine gearboxes. University of Cambridge, 37–40 (2013)

  6. Tu Wenbing.: Rolling bearing slippage dynamics model and vibration noise characteristics. Chongqing University, 39–42 (2012)

  7. Qinkai, H., Zheng, Li., Fulei, C.: Slip dynamics model of angular contact ball bearing based on Euler equation. J. Bear. 428(07), 1–7 (2015)

    Google Scholar 

  8. Li, F., Deng, S.I.I., Zhang, W.H.: Study of ball bearing slippage characteristics under frequent oscillation conditions. J. Mech. Eng. 57(01), 168–178 (2021)

    Article  Google Scholar 

  9. Yao, T.Q., Wang, L.H., Liu, H.P.: Dynamics analysis of ball bearing-mechanism system considering cage gap collision. J. Aerodyn. 31(07), 1725–1735 (2016)

    Google Scholar 

  10. Qinkai, H., Fulei, C.: Prediction model of angular contact rolling bearing slippage. J. Vibrat. Eng. 30(03), 357–366 (2017)

    Google Scholar 

  11. Tu, W.-B., Liang, J., Yang, J.-W.: Analysis of collision contact dynamics of rolling bearing cages under variable operating conditions. J. Vibrat. Shock 41(04), 278–286 (2022)

    Google Scholar 

  12. Qianqian, Y., Yongsheng, Z., Jinhua, Z.: Dynamic characteristics of precision bearing cage considering lubrication collision. J. Xi’an Jiaotong Univ. 55(01), 110–117 (2021)

    Google Scholar 

  13. Ma, S., Zhang, X., Yan, K., Zhu, Y., Hong, J.: A study on bearing dynamic features under the condition of multiball-cage collision. J. Lubricants 10(1), 9 (2022)

    Article  Google Scholar 

  14. Zhang Yanlong.: Dynamics of collisional vibration systems with dynamic friction and their engineering applications. Lanzhou Jiaotong University, 121–123 (2019)

  15. Xuening, Z., Qinkai, H., Fulei, C.: Response characteristics of rotor-bearing system with dual-frequency time-varying rolling bearing stiffness. J. Vibrat. Shock 36(13), 116–121 (2017)

    Google Scholar 

  16. Deng, S., Chang, H., Qian, D., Wang, F., Hua, L., Jiang, S.: Nonlinear dynamic model of ball bearings with elastohydrodynamic lubrication and cage whirl motion, influences of structural sizes, and materials of cage. J. Nonlinear Dyn. 110, 2129–2163 (2022)

    Article  Google Scholar 

  17. Deng, S., Chang, H., Zhu, X., Qian, D., Hua, L., Jiang, S.: Sensitivity of different types of structural size combinations to dynamic stability and vibration of angular contact ball bearings based on nonlinear dynamic model. J. Tribol. Int. 181, 108309 (2023)

    Article  Google Scholar 

  18. Patil, M.S., Mathew, J., Rajendrakumar, P.K.: A theoretical model to predict the effect of localized defect on vibrations associated with ball bearing. J. Int. J. Mech. Sci. 52(9), 1193–1201 (2010)

    Article  Google Scholar 

  19. Shah, D.S., Patel, V.N.: A dynamic model for vibration studies of dry and lubricated deep groove ball bearings considering local defects on races. J. Measurement 137, 535–555 (2019)

    Article  Google Scholar 

  20. Behzad M, Bastami A R, Mba D. New model for estimating vibrations generated in the defective rolling element bearings. J. Vibrat. Acoust. 133(4), (2011)

  21. Singh, S., Köpke, U.G., Howard, C.Q.: Analyses of contact forces and vibration response for a defective rolling element bearing using an explicit dynamics finite element model. J. Sound Vibrat. 333(21), 5356–5377 (2014)

    Article  Google Scholar 

  22. Zhenzhen, G., Haiqi, Z., Yanguang, W.: Dynamics modeling and simulation of localized damage failure in rolling bearings. J. Vibrat. Test. Diagn. 32(6), 950–955 (2012)

    Google Scholar 

  23. Xiang, L., Hu, A., Hou, L., et al.: Nonlinear coupled dynamics of an asymmetric double-disc rotor-bearing system under rub-impact and oil-film forces. J. Appl. Math. Model. 40(7–8), 4505–4523 (2016)

    Article  Google Scholar 

  24. He-Chang-Feng, Y.-H., Wang-Xin.: Dynamics modeling of local defects on the surface of deep groove ball bearings under point contact elastofluid lubrication. J. Vib. Shock 35(14), 61–70 (2016)

    Google Scholar 

  25. Linkai, N., Hongrui, C., Zhengjia, H.: Dynamics modeling of local surface damage in rolling ball bearings considering three-dimensional motion and relative sliding. J. Mech. Eng. 51(19), 53–59 (2015)

    Article  Google Scholar 

  26. Niu, L., Cao, H., He, Z.: An investigation on the occurrence of stable cage whirl motions in ball bearings based on dynamic simulations. J. Tribol. Int. 103, 12–24 (2016)

    Article  Google Scholar 

  27. Niu, L., Cao, H., He, Z.: A systematic study of ball passing frequencies based on dynamic modeling of rolling ball bearings with localized surface defects. J. Sound Vib. 357, 207–232 (2015)

    Article  Google Scholar 

  28. Townsend D P, Allen C W, Zaretsky E V.: Friction losses in a lubricated thrust-loaded cageless angular-contract bearing. (1973)

  29. Kingsbury, E.: Ball-ball load carrying capacity in retainless angular-contact bearings. J. Lubricat. Technol. 104, 327–329 (1982)

    Article  Google Scholar 

  30. Jones W R,:Shogrin B A, Kingsbury E. Long term performance of a retainerless bearing cartridge with an oozing flow lubricator for spacecraft applications. NASA TM-107492(1997)

  31. Zhilnikov, E.P., Balyakin, V.B., Lavrin, A.V.: A method for calculating the frictional moment in cageless bearings. J. Frict. Wear 39, 400–404 (2018)

    Article  Google Scholar 

  32. Cole, M.O.T., Keogh, P.S., Burrows, C.R.: The dynamic behavior of a rolling element auxiliary bearing following rotor impact. J. Tribol. 124(2), 406–413 (2002)

    Article  Google Scholar 

  33. Kärkkäinen, A., Sopanen, J., Mikkola.: Dynamic simulation of a flexible rotor during drop on retainer bearings. J. Sound Vib. 306(3–5), 601–617 (2007)

    Article  Google Scholar 

  34. Jarroux, C., Mahfoud, J., Dufour, R.: Investigations on the dynamic behaviour of an on-board rotor-AMB system with touch-down bearing contacts: modelling and experimentation. J. Mech. Syst. Signal Process. 159, 107787 (2021)

    Article  Google Scholar 

  35. Zhao, Y., Zhang, J., Zhou, E.: Automatic discrete failure study of cage free ball bearings based on variable diameter contact. J. Mech. Sci. Technol. 35, 4943–4952 (2021)

    Article  Google Scholar 

  36. Sun, G., Palazzolo, A.B., Provenza, A.: Detailed ball bearing model for magnetic suspension auxiliary service. J. Sound Vib. 269(3–5), 933–963 (2004)

    Google Scholar 

  37. Neisi N, Sikanen E, Heikkinen J E.: Stress analysis of a touchdown bearing having an artificial crack. International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Cleveland, Ohio, USA, V008T12A034 (2017)

  38. Halminen, O., Karkkainen, A., Sopanen, J.: Active magnetic bearing-supported rotor with misaligned cageless backup bearings: a dropdown event simulation model. J. Mech. Syst. Signal Process. 50, 692–705 (2015)

    Article  Google Scholar 

  39. Halminen, O., Aceituno, J.F., Escalona, J.L.: Models for dynamic analysis of backup ball bearings of an AMB-system. J. Mech. Syst. Signal Process. 95(10), 324–344 (2017)

    Article  Google Scholar 

  40. Aonan, N., Yingchun, L., Weihua, X.: Study on the collision characteristics of protected bearings in active magnetic levitation bearing systems. J. Bearing 6, 30–37 (2022)

    Google Scholar 

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Acknowledgements

The author thanks the National Natural Science Foundation of China for its support for the project. This work was supported by the National Natural Science Foundation of China (Grant No. 51375125).

Funding

Professor Yuan Zhang has National Natural Science Foundation of China (51375125).

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Authors and Affiliations

  1. Key Laboratory of Advanced Manufacturing Intelligent Technology Ministry of Education, Harbin University of Science and Technology, Harbin, 150080, Heilongjiang, People’s Republic of China

    Jingwei Zhang, Yuan Zhang, Enwen Zhou, Yibing Wang, Ziqi Liu & Yanling Zhao

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  1. Jingwei Zhang
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Correspondence to Yuan Zhang.

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Zhang, J., Zhang, Y., Zhou, E. et al. Research on multi-body dynamic model of automatic discrete system for protection bearing without cage. Nonlinear Dyn 111, 20869–20897 (2023). https://doi.org/10.1007/s11071-023-08904-x

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