A semi-analytic strategy for the system-level modelling of flexibly supported ball bearings
- 276 Downloads
This work presents a semi-analytic approach that allows to efficiently solve the large sliding or rolling contact problems characteristically associated with the dynamic simulation of flexibly supported ball bearings. The approach separates the bulk deformation, represented by a reduced order model, and the analytically described nonlinear local Hertzian deflections at the contact zone. The interacting raceways of the bearing are represented by B-spline surfaces in order to alleviate the issues of non-smoothness. A solution is introduced that allows an efficient redefinition of these deformed interacting surfaces based on the reduced order model, without necessitating iterative procedures or back-projections to the nodal coordinates. Instead, the deformed B-splines are reconstructed by linear combinations of the control points, utilizing the participation factors of the affected mode shapes in the reduced order model. These B-spline surfaces are exploited by a novel ball bearing specific, and spline-based, contact formulation. The numerical results demonstrate the performance and accuracy of the novel technique for various reduction spaces representing the bulk deformation. Moreover, the developed bearing framework offers both accurate stiffness and displacement patterns with respect to the interfaces to the other bodies in the flexible mechanical system. Through a proper selection and adjustments of the mode shapes, even statically and dynamically complete results can be obtained.
KeywordsBearing contact dynamics Flexible multibody dynamics Time-varying contact location Surface smoothing B-splines
The IWT Flanders is gratefully acknowledged for its support within the SCROLL (120489) and OPTIWIND (120029) projects. This work also benefits from the Belgian Programme on Interuniversity Attraction Poles, initiated by the Belgian Federal Science Policy Office (DYSCO), and the Research Fund KU Leuven.
- 7.Craig R (1987) A review of time-domain and frequency-domain component mode synthesis methods. J Modal Anal 2(2):59–72Google Scholar
- 13.Harris T, Kotzalas M (2006) Essential concepts of bearing technology, vol 5. Taylor & Francis Group, New YorkGoogle Scholar
- 14.Jones A (1959) A general theory for elastically constrained ball and radial roller bearings under arbitrary load and speed conditions. J Fluids Eng 82(2):309–320Google Scholar
- 15.Jones A, Harris T (1963) Analysis of a rolling-element idler gear bearing having a deformable outer-race structure. J Fluids Eng 85(2):273–278Google Scholar
- 16.Martinez D, Gregory D (1984) Comparison of free component mode synthesis techniques using MSC/NASTRAN. Technical Report SAND83-0025, Sandia National Laboratories, Albuquerque, NWGoogle Scholar
- 20.Qian W (2013) Dynamic simulation of cylindrical roller bearings. Ph.D. thesis, RWTH Aachen University, Institute for Machine Element and Machine DesignGoogle Scholar
- 21.Schwenkenberg A, Damerau J, Hetzler H, Seemann W (2013) Modeling flexible roller ball bearings in multibody dynamics. In: ECCOMAS conference, University of Zagreb, Zagreb, Croatia, pp 251–256Google Scholar
- 25.Weber C, Banaschek K (1953) Schriftenreihe Antriebstechnik, chap 11. Friedr. Vieweg & sohn, NYGoogle Scholar
- 26.Wensing J (1998) On the dynamics of ball bearings. Ph.D. thesis, University of Twente, Department of Mechanical EngineeringGoogle Scholar