http://michael.friswell.com/PDF_Files/J157.pdf

Model based Identification of Rotating Machines

In the transportation domain, on-board rotors in bending are subjected not only to rotating mass unbalance but also to several movements of their base. The main objective of this article is to predict the dynamic behavior of a rotor in the presence of base excitations. The proposed on-board rotor model is based on the Timoshenko beam finite element. It takes into account the effects corresponding to rotary inertia, gyroscopic inertia, and shear deformation of shaft as well as the geometric asymmetry of disk and/or shaft and considers six types of deterministic motions (rotations and translations) of the rotor's rigid base. The use of Lagrange's equations associated with the finite element method yields the linear second-order differential equations of vibratory motion of the rotating rotor in bending relative to the moving rigid base which forms a non-inertial frame of reference. The linear equations of motion highlight periodic parametric terms due to the geometric asymmetry of the rotor components and time-varying parametric terms due to the rotational motions of the rotor rigid base. These parametric terms are considered as sources of internal excitation and can lead to lateral dynamic instability. In the presented applications, the rotor is excited by a rotating mass unbalance combined with constant rotation and sinusoidal translation of the base. Quasi-analytical and numerical solutions for two different rotor configurations (symmetric and asymmetric) are analyzed by means of stability charts, Campbell diagrams, steady-state responses as well as orbits of the rotor.

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Steady-state dynamic behavior of an on-board rotor under combined base motions.

Modeling of hydrodynamic bearing wear in rotor-bearing systems

Analytical modeling of asymmetric multi-segment rotor - bearing systems with Timoshenko beam model including gyroscopic moments

Thermal turbulent lubrication analysis of rough surface journal bearing with journal misalignment

An investigation on the influence of the supporting structure on the dynamics of the rotor system

An analytical model of a tilting pad bearing was developed based on the short bearing assumption with the turbulence effect included. In order to determine its influence on the dynamic behavior of the rotor, this model was compared against one without the turbulence effect through a simulation of a Jeffcott/Laval rotor supported by a couple of bearings. Both models were also used to determine the influence of geometric parameters on tilting pad bearing making use of the aforementioned system at different rotor speeds. When analyzing the results, the parameters which presented the largest influence were: pad preload, number of segments, radial clearance, pad position, and pad pivoting angle. As the pad moment of inertia and the pivoting distance have changed the shaft motion only a few microns, their effects can be neglected. The bearing model with turbulent flow effect has generated higher hydrodynamic forces when compared to the one without this effect, which remarks the importance of considering such phenomenon during the analysis of the high speed hydrodynamic bearings.

Rotordynamic analysis of systems with a non-linear model of tilting pad bearings including turbulence effects

Analytical model of a tilting pad bearing including turbulence and fluid inertia effects

This work presents a methodology to analyse the influence of the foundation or supporting structure on the rotor-bearings system. A frequency response analysis of the complete system was accomplished by considering physical co-ordinates for the rotor-bearings system and principal co-ordinates for the foundation. The mathematical procedure applied a modal approach to the supporting structure, using modal parameters of generalised mass, damping ratio and natural frequency, which were calculated from the frequency response functions (FRF) of an actual structure. Convergence of the method was verified and the effect of the flexible foundation on the complete system response was analysed. A new formulation for the Mixed Co-ordinates method was presented to evaluate the influence of the supporting structure on the directional response of a rotor. An analysis of the directional frequency response function (dFRF) of the complete system was accomplished considering directional co-ordinates for the rotor-bearings system and principal co-ordinates for the foundation. These results were compared to the conventional FRF procedure.

Eduardo Paiva Okabe

Papers

An investigation on the influence of the supporting structure on the dynamics of the rotor system

Rotordynamic analysis of systems with a non-linear model of tilting pad bearings including turbulence effects

Analytical model of a tilting pad bearing including turbulence and fluid inertia effects

On the Analysis of Rotor-Bearing-Foundation Systems

Operational modal analysis application to support structure identification under rotating machinery unbalance