Abstract
A method is suggested for building mathematical models of dynamics of rotors in magnetic bearings of different types (passive and active). It is based on Lagrange-Maxwell differential equations in a form identical to that of Routh equations in mechanics. The expressions for magnetic energy and forces in active magnetic bearings with account for control laws for introducing them into the mathematical models have been found by adapting the analytical method of analysing magnetic circuits. This method is based on building equivalent circuits and using the loop flux method to account for dissipation fluxes and magnetic resistances of AMB magnetic circuit sections and ensure noncriticality of the mathematical model to emergence of “zero” gaps and currents. Besides, the mathematical models account for such nonlinearities as nonlinear dependence of magnetic forces on gaps in passive and active magnetic bearings and on currents in the coils of electromagnets, nonlinearities linked to coil inductance, a geometric link between electromagnets in one AMB and links between all AMB in one rotor, which results, among other factors, in connectedness of processes in orthogonal directions. The method’s validity has been confirmed experimentally by a laboratory setup being a prototype of a complete combined magnetic-electromagnetic suspension in small-size rotor machinery. The suggested approach has helped detect in the system and investigate different nonlinear rotor dynamics phenomena such as super- and subharmonic vibrations with determination of resonance modes.
Highlights
A magnetic bearing (MB) is one of the variants of elastic-damping bearings
It shows radial and axial active magnetic bearings (AMBs) with electromagnets (Figs. 1, a, b) and a radial passive magnetic bearings (PMBs) with permanent annular magnets (Figs. 1, c, d), and the following notations are introduced: 1 – rotor; 2 – stators; 3 – AMB windings; 4 – AMB position sensors; 5 – comparator in AMB control system; 6 – AMB control device; 7 – amplifiers feeding control voltages to AMB windings, which are formed according to the accepted control algorithm; 8 and 9 – movable and stationary annular permanent magnets
A downside of the approach to modelling dynamics presented in the studies [16, 17] accounts for only nonlinear effects caused by the geometric interrelation of two pairs of electromagnet poles that create forces in mutually perpendicular directions and the dependence of forces on displacements and currents in AMB coils
Summary
A magnetic bearing (MB) is one of the variants of elastic-damping bearings. Its feature is the use of magnetic fields to provide stable rotor levitation. Based on the possibilities of practical implementation of complete magnetic bearings of rotors, this study considers the options of using either radial or axial AMBs for stabilising a rotor over all five degrees of freedom or one AMB jointly with several PMBs in different design versions. G., turbo-expanders, expander-generator, and expander-compressor units [4] They can use two radial PMBs and one axial AMB arranged in the centre or at one end of the shaft. Building refined mathematical models will enable increasing the accuracy of numerical computation of required dynamic parameters of rotors, magnetic bearings and control systems for active magnetic bearings This will dramatically reduce the amount of experimental investigations and increase the effectiveness of research and development efforts
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Eastern-European Journal of Enterprise Technologies
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
