Calculation of Contact Force in Ball Bearings Subjected to High-Frequency Impacts in the Framework of Non-Smooth Structural Dynamics
DOI:
https://doi.org/10.70567/mc.v41i11.59Abstract
This paper presents the application of the contact force calculation model proposed by the authors (E. Sánchez et al., Computational Mechanics Vol XL, 823-832, 2023) to ball bearings that experience high-frequency impacts between their components. To solve the equations of motion, the nonsmooth generalized-alpha time integration scheme is used. Additionally, to regularize the contact problem, a dual mixed formulation based on an augmented Lagrangian method is employed. The computational efficiency of the implemented algorithms is evaluated through numerical simulations of a ball bearing that has a clearance between the balls and the races, causing high-frequency impacts in various directions. Then, a crank-rod mechanism composed of rigid and flexible elements is proposed, where the link between the rod and the crank includes a ball-bearing. The numerical results obtained show how the vibrations coming from the ball-bearing affect the operation of the mechanism.
References
Alart P. y Curnier A. A mixed formulation for frictional contact problems prone to newton like solution methods. Comput. Methods Appl. Mech. Eng., 92(3):353-375, 1991. https://doi.org/10.1016/0045-7825(91)90022-X
Cosimo A., Galvez J., Cavalieri F.J., Cardona A., y Brüls O. A robust nonsmooth generalized-scheme for flexible systems with impacts. Multibody System Dyn., 48(2):127-149, 2020. https://doi.org/10.1007/s11044-019-09692-2
Deng S., Chang H., Qian D., Wang F., Hua L., y Jiang S. Nonlinear dynamic model of ball bearings with elastohydrodynamic lubrication and cage whirl motion, influences of structural sizes, and materials of cage. Nonlinear Dynamics, 110(3):2129-2163, 2022. https://doi.org/10.1007/s11071-022-07683-1
Flores P., Machado M., Silva M.T., y Martins J.M. On the continuous contact force models for soft materials in multibody dynamics. Multibody system dynamics, 25:357-375, 2011. https://doi.org/10.1007/s11044-010-9237-4
Galvez J., Cavalieri F.J., Cosimo A., Brüls O., y Cardona A. A nonsmooth frictional contact formulation for multibody system dynamics. Int. J. Numer. Methods Eng., 121(16):3584- 3609, 2020. https://doi.org/10.1002/nme.6371
Gismeros Moreno R., Marques F., Corral Abad E., Meneses Alonso J., Flores P., y Castejon C. Enhanced modelling of planar radial-loaded deep groove ball bearings with smooth-contact formulation. Multibody System Dynamics, 60(1):121-159, 2024. https://doi.org/10.1007/s11044-023-09952-2
Harris T.A. y Kotzalas M.N. Rolling Bearing Analysis-2 Volume Set. Crc Press, 2006. https://doi.org/10.1201/9781482275148
Hertz H. On the contact of elastic solids. Z Reine Angew. Math., 92:156-171, 1881. https://doi.org/10.1515/9783112342404-004
Jones A. A general theory for elastically constrained ball and radial roller bearings under arbitrary load and speed conditions. 1960. https://doi.org/10.1115/1.3662587
Nan G., Jiang S., y Yu D. Dynamic analysis of rolling ball bearing-rotor based on a new improved model. SN Applied Sciences, 4(6):173, 2022. https://doi.org/10.1007/s42452-022-05058-0
Sánchez E.S., Cavalieri F., y Cardona A. Simulación de un rodamiento de bolas inmerso en un mecanismo considerando efectos de fricción e impacto. Mecánica Computacional, 40(22):823-832, 2023.
Seely F.B. y Smith J.O. Curso superior de resistencia de materiales. 1967.
Xu L.x. A general method for impact dynamic analysis of a planar multi-body system with a rolling ball bearing joint. Nonlinear Dynamics, 78(2):857-879, 2014. https://doi.org/10.1007/s11071-014-1482-2
Yao T., Xian L., Wang L., y Liu X. Multibody contact dynamics on mechanisms with deep groove ball bearing joints. J. Sound Vib., 31:4119-4135, 2017. https://doi.org/10.1007/s12206-017-0808-7
Downloads
Published
Issue
Section
License
Copyright (c) 2024 Argentine Association for Computational Mechanics
This work is licensed under a Creative Commons Attribution 4.0 International License.
This publication is open access diamond, with no cost to authors or readers.
Only those papers that have been accepted for publication and have been presented at the AMCA congress will be published.
