Inverse Problem Methodology for the Balancing of Rotating Machinery Running on Nonlinear Bearings Using Artificial Neural Networks

  • Ghaith Al-Ghazal

Student thesis: Phd


Reducing aeroengine vibration is a key challenge for enhancing passenger comfort in aeroplanes. Economic considerations require aeroengines to be lightweight and flexible structures that have little inherent damping, thus being highly sensitive to the vibration excitation arising from the rotors. A cost-effective means of introducing damping into the system is achieved by surrounding the outer race of the rolling-element bearings by a film of oil ("squeeze-film damper" (SFD)). The resulting SFD bearings are nonlinear elements that complicate the identification of unbalance in aeroengines, which is necessary to balance their shafts and thus, minimise vibration. Typical aeroengine assemblies have at least two nested rotors mounted within a casing through SFD bearings. Since at least one of the rotors is inaccessible, the unbalance identification involves the solution of an inverse problem, in which the rotor unbalance is identified using vibration measurements from externally mounted sensors (on the casing/bearing housings) as well as a model of the rotor and casing. In the thesis, inverse solution techniques are presented for the nonlinear rotordynamic inverse problem, which involves the use of the recurrent neural network (RNN) for the inverse model identification of the SFD bearing. That is, it is held that the RNN inverse SFD model is a reliable substitute for internal instrumentation, being used along with accelerometers on the casing or bearing housings to solve the nonlinear inverse problem. Four experimental and computational investigations under hitherto unconsidered conditions have been applied to test the robustness of the inverse solution techniques. An entirely novel technique has been conducted towards the non-parametric identification of inverse dynamic models of the nonlinear SFD bearings based on the RNN. The RNN models are trained to reproduce the Cartesian displacements of the journal relative to the bearing housing when presented with given input time histories of the Cartesian SFD bearing forces. The technique saves laboratory time and reduces the size of the training data, thus reducing the training time. It delivers very good performance regarding the network's prediction of the SFD vibration response. The experimental validation of the novel techniques has been performed for a nonlinear inverse solution of the rotor-bearing problem, where the relationship between the rotor unbalance and casing vibration is fully/quasi implicit through the oil films of the SFDs i.e. there is a weak linear connection, or none at all, between the rotor and casing/bearing housing. The inverse operators are developed using the Receptance Harmonic Balance Method (RHBM) as the underpinning theory to generate the backwards operator for the inverse solution. A least-squares solution provides the equivalent unbalance distribution at the planes of interest of the shaft, which is then used for the balancing. An iteration procedure is performed to enhance the implicit inverse solution. The inverse methods are successfully validated experimentally on two purposely designed rotating rig configurations with one SFD bearing ("System A2" and "System B"). These methods use the RNN model of the inverse dynamics of the SFD bearing, which is trained from a non-rotating rig configuration excited by electromagnetic shakers. Computational validation is also performed on a more complex rotor-casing system with two SFD bearings and cylindrical casing structure. The results show that the identified RNN models have the potential to serve as reliable virtual instruments for estimating the journal displacement as part of the solution of the inverse problem to identify rotor unbalance using a non-intrusive approach i.e. using external (casing/housing) vibration readings and no trial masses. Moreover, the validation studies show for the first time that the RNN models trained using the proposed approach under shaker-driven conditions are transferable to d
Date of Award31 Dec 2019
Original languageEnglish
Awarding Institution
  • The University of Manchester
SupervisorPhilip Bonello (Supervisor)


  • Recurrent neural networks
  • Rotor balancing
  • Squeeze-film damper bearings
  • Nonlinear vibration
  • Inverse problem

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