Abstract
Nonconforming contact study is fundamental to model the behavior of mechanical equipment such as bearings and gears. In order to predict lifetime of rolling element bearings, film thickness and pressure distribution can describe the lubrication condition, allowing the analysis of the contact response to load, rotation speed, oil parameters and geometry. The EHD elliptical contact can be approximate to an equivalent line contact when taken the central line at the major ellipsis axis, since the maximum Hertzian pressure, lubrication oil, rotation speed and radius of curvature are identical. A comparison between the stiffness reduced order model of elliptical contact and an equivalent line contact, based on an explicit load-distribution relation, is accomplished. Moes load and lubrication dimensionless parameters describe the contacts along with the elliptical contact ellipticity. The influence of speed and ellipticity were verified on the oil film and pressure in a range of load conditions, as well as EHD stiffness reduced order model parameters. The ellipticity range evaluates the similarity between both kinds of contact and verifies its equivalence.
The present work analyses the contact reduced order model and its main parameter influence, the EHD stiffness. As the contact properties, film thickness and pressure distribution, directly affect the lifetime estimation of rolling element bearings, the study can bring useful insights during project stage. Moreover, an improved EHD nominal model can promisingly be applied in fault identification in rotating systems and other mechanisms.
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References
Wijnant, Y.H.: Contact dynamics in the field of elastohydrodynamic lubrication. Ph.D. thesis, University of Twente (1998)
Wensing, J.A.: On the dynamics of ball bearings. Ph.D. thesis, University of Twente (1998)
Tsuha, N.A.H., Nonato, F., Cavalca, K.L.: Formulation of a reduced order model for the stiffness on elastohydrodynamic line contacts applied to cam-follower mechanism. Mech. Mach. Theory 113, 22–39 (2017)
Bizarre, L., Nonato, F., Cavalca, K.L.: Formulation of five degrees of freedom ball bearing model accounting for the nonlinear stiffness and damping of elastohydrodynamic point contacts. Mech. Mach. Theory 124, 179–196 (2018)
Liu, J., Shao, Y.: An improved analytical model for a lubricated roller bearing including a localized defect with different edge shapes. J. Vib. Control 1–14 (2017)
Reynolds, O.: On the theory of lubrication and its application to M. Beauchamps tower’s experiments, including an experimental determination of the viscosity of olive oil. Phil. Trans. Roy. Soc. 177, 157–234 (1886)
Venner, C.H., Lubrecht, A.A.: Multilevel Methods in Lubrication, vol. 37, 400 p. Elsevier, Amsterdam (2001)
Roelands, C.J.A.: Correlational aspects of the viscosity-temperature-pressure relationship of lubricating oils. Ph.D. Thesis, Technical University Delft (1966)
Dowson, D., Higginson, G.R.: Elasto-Hydrodynamic Lubrication – SI Edition, 1st edn. Pergamon Press, Great Britain (1977)
Moes, H.: Optimum similarity analysis with applications to elastohydrodynamic lubrication. Wear I59, 56–66 (1992)
Canzi, A., Venner, C.H., Lubrecht, A.A.: Film thickness prediction in elastohydrodynamically lubricated elliptical contacts. Proc. Inst. Mech. Eng. Part J: J. Eng. Tribol. 224, 917–923 (2010)
Nijenbanning, G., Venner, C.H., Moes, H.: Film thickness in elastohydrodynamically lubricated elliptic contacts. Wear 176, 217–229 (1994)
Nonato, F., Cavalca, K.L.: On the non-linear dynamic behavior of elastohydrodynamic lubricated point contact. J. Sound Vib. 329, 4656–4671 (2010)
Nonato, F., Cavalca, K.L.: An approach for including the stiffness and damping of elastohydrodynamic point contacts in deep groove ball bearing equilibrium models. J. Sound Vib. 333, 6960–6978 (2014)
Marquardt, D.W.: An algorithm for least-squares estimation of nonlinear parameters. J. Soc. Ind. Appl. Math. 11, 431–441 (1963)
Bizarre, L., Nonato, F., Cavalca, K.L.: EHD modeling of angular contact ball element bearings. In: 9th IFToMM International Conference on Rotor Dynamics, Milan, vol. 1, pp. 1–10 (2014)
Bizarre, L., Nonato, F., Cavalca, K.L.: Investigation on the convergence of EHD lubrication in angular contact ball bearing. In: 11th International Conference on Vibrations in Rotating Machinery, Proceedings of the Institution of Mechanical Engineers, London (2016)
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Bizarre, L., Tsuha, N.A.H., Cavalca, K.L. (2019). Study of Stiffness Reduced Order Model Applied to Line and Elliptical Contact Under EHD Lubrication. In: Cavalca, K., Weber, H. (eds) Proceedings of the 10th International Conference on Rotor Dynamics – IFToMM. IFToMM 2018. Mechanisms and Machine Science, vol 60. Springer, Cham. https://doi.org/10.1007/978-3-319-99262-4_3
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DOI: https://doi.org/10.1007/978-3-319-99262-4_3
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