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Stability analysis and dynamic behaviour of a flexible asymmetric rotor supported by active magnetic bearings

Attia Hili M., Bouaziz S., Haddar M.

Journal of Theoretical and Applied Mechanics

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2017

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Vol. 55 nr 3

751--763

EN

The objective of this work is to show the influence of dynamic characteristics of Active Magnetic Bearings (AMBs) on the stability and dynamic response of an asymmetric and unbalanced rotor. Indeed, AMBs have been successfully applied in several industrial machinery facilities. Their main advantages are the contactless working principle, frictionless suspension and operation in very high speeds. Firstly, the AMBs dynamic support parameters have been obtained through electromagnetic theory. Then, a generalized system equations of motion have been derived using the finite element method. The motion of a rotor the shaft cross-section of which is asymmetric is generally governed by ordinary differential equations with periodic coefficients. Floquet’s theory is used to investigate the stability of this system of equations. Finally, numerical simulation results are presented and discussed.

2

Cutting parameters and vibrations analysis of magnetic bearing spindle in milling process

Bouaziz A., Barkallah M., Bouaziz S., Choley J. Y., Haddar M.

Journal of Theoretical and Applied Mechanics

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2016

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Vol. 54 nr 3

691--703

EN

In modern production, milling is considered the widespread cutting process in the formatting field. It remains important to study this manufacturing process as it can be subject to some parasitic phenomena that can degrade surface roughness of the machined part, increase tool wear and reduce spindle life span. In fact, the best quality work piece is obtained with a suitable choice of parameters and cutting conditions. In another hand, the study of tool vibrations and the cutting force attitude is related to the study of bearings as they present an essential part in the spindle system. In this work, a modeling of a High Speed Milling (HSM) spindle supported by two pair of Active Magnetic Bearings (AMB) is presented. The spindle is modeled by Timoshenko beam finite elements where six degrees of freedom are taken into account. The rigid displacements are also introduced in the modeling. Gyroscopic and centrifugal terms are included in the general equation. The bearings reaction forces are modeled as linear functions of journal displacement and velocity in the bearing clearance. A cutting force model for peripheral milling is proposed to estimate the tool-tip dynamic responses as well as dynamic cutting forces which are also numerically investigated. The time history of response, orbit, FFT diagram at the tool-tip center and the bearings dynamic coefficients are plotted to analyze dynamic behavior of the spindle.

3

Derivation of nonlinear coefficients in multi lobe journal bearings

Rao T. V. V. L. N., Biswas S., Athre K.

Applied Mechanics and Engineering

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1999

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Vol. 4, no spec.

57-66

EN

The equivalent stiffness and damping coefficients calculated successively along the journal center locus with reference to the equilibrium position are obtained (in the case of stable journal orbit) using Taylor series expansion. To validate the accuracy of the derived coefficients, the journal orbit is compared with the transient simulation under similar operating conditions. The equivalent dynamic coefficients are further evaluated according to the modified journal position using linear interpolation procedure. The average value of the equivalent stiffness and damping coefficients are calculated at various perturbation amplitudes from equilibrium position along the transient orbit. The influence of journal center position and velocities is observed. With nonlinear coefficients close to actual simulation under stable conditions this methodology provides the bearing designer variation of dynamic coefficients in the bearings.