Active tilting-pad journal bearings supporting flexible rotors: Part II–The model-based feedback-controlled lubrication

Abstract

This is part II of a twofold paper series dealing with the design and implementation of model-based controllers meant for assisting the hybrid and developing the feedback-controlled lubrication regimes in active tilting pad journal bearings (active TPJBs). In both papers theoretical and experimental analyses are presented with focus on the reduction of rotor lateral vibration. This part is devoted to synthesising model-based LQG optimal controllers (LQR regulator + Kalman Filter) for the feedback-controlled lubrication and is based upon the mathematical model of the rotor-bearing system derived in part I. Results show further suppression of resonant vibrations when using the feedback-controlled or active lubrication, overweighting the reduction already achieved with hybrid lubrication, thus improving the whole machine dynamic performance.

Controllable Sliding Bearings and Controllable Lubrication Principles—An Overview

“…The LQG control gains are calculated aided by a multi-physical mathematical model, which links solid mechanics, fluid dynamics, material science and control theory. In order words, the lateral dynamics of flexible rotating shaft and disc is described by an FE model [43]. The nonlinear fluid film forces are obtained by solving the modified Reynolds equations and energy equation via finite difference method [44,45].…”

“…Aided by the linearized mathematical model, written in its statespace form, classical control theory is used and optimal model-based LQG controllers are designed. The synthetization/design of the controllers is thoroughly discussed in [43,46]. FRFs of the rotorbearing system under hydrodynamic (passive, conventional) and hybrid lubrications are also included for comparison.…”

“…Such a procedure of adapting/changing the controller parameters is also adopted when dealing with active magnetic bearings and it is standard (and necessary) when designing control systems. Horizontal and vertical lateral dynamics of the rotor-bearing system measured at the end of the shaft and excited by the electromagnetic shaker when four cases are investigated: hydrodynamic (conventional); hybrid using 100 bar; active using a LQG model-based controller; and active using an empirically-tuned PID controller [43]. Copyright from Elsevier.…”

“…The main idea and novelty of the experimental technique is based on: (i) perturbing the fluid film via controllable lubrication (actuation system); (ii) measuring the lateral vibration movements of the rotor (sensing systems); (iii) generating a huge amount of data, which need to be stored; and finally, (iv) treating computationally the data aided by output-only modal analysis (OMA) techniques to obtain modal parameters, among them the important damping ratio. The novel experimental Horizontal and vertical lateral dynamics of the rotor-bearing system measured at the end of the shaft and excited by the electromagnetic shaker when four cases are investigated: hydrodynamic (conventional); hybrid using 100 bar; active using a LQG model-based controller; and active using an empirically-tuned PID controller [43]. Copyright from Elsevier.…”

Component level study of an actively lubricated LEG Tilting Pad Bearing: Theory and experiment

“…A multiphysics theoretical model for this bearing design has been refined over the years [11,12,13], including a ETHD tilting pad bearing model coupled with the effect of the radial oil injection and dynamics of the hydraulic supply system. The theoretical model has been applied to synthetize model-based controllers to alter the dynamics of a flexible rotor setup in [14]. The feasibility of using this active bearing as an excitation source for carrying out operational modal analysis testing in rotating machinery was experimentally studied in [15].…”