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The identification of nonlinear squeeze-film damper (SFD) bearings, typically used in aero-engines, has so far focused on their forward model (i.e. displacement input/force output). The contributions of this paper are the non-parametric identification of the inverse model of the SFD bearing (force input/displacement output) from empirical data, and its application to a nonlinear inverse rotor-bearing problem. This work is motivated by the need for a reliable substitute for internal instrumentation, to enable the identification of rotor unbalance using vibration data from externally mounted sensors, in applications where the rotor is inaccessible under operating conditions and there is no adequate linear connection between rotor and casing. The identification of the inverse model is fundamentally different from that of the forward model due to the need to account for system memory. A suitably trained Recurrent Neural network (RNN) is shown to be capable of identifying the inverse model of an actual SFD through two validation studies. In the first study, the RNN model satisfactorily predicted the SFD journal’s displacement time histories for given periodic time histories of the Cartesian SFD forces, although it could not predict the user-applied static offset in the SFD since it was not trained to do so. This was no limitation for the second study where, for both centred and non-centred SFD conditions, the RNN proved to be a reliable substitute for actual instrumentation as part of the inverse problem solution process for identifying the amplitudes and phases of the external excitation forces on a simple test rig.

This paper is devoted to the unbalance identification and balancing of an aircraft engine rotor running on Squeeze Film Damper (SFD) bearings that show highly nonlinear features. The high pressure (HP) rotor in a twin-spool assembly cannot be accessed under operational conditions because of the restricted space for instrumentation and temperatures that are beyond the safe operating limits of the sensors. This motivates the use of a non-invasive procedure, requiring prior knowledge of the structure. The only such method for rotating machinery with non-linear bearings reported in the literature is highly limited in its application (e.g. assumes circular centred orbits). The methodology proposed in this paper is aimed at overcoming such limitations. It uses the Receptance Harmonic Balance Method (RHBM) to generate the backward operator using vibration measurements taken from sensors installed on the engine casing. The operator is then inverted using either Least Squares Fit (LSF) or Singular Value Decomposition (SVD). The resulting solution is the equivalent unbalance distribution in prescribed unbalance planes of the HP rotor which are consequently used to balance it. This method is validated using two distinct rotordynamic systems and simulated casing vibration readings corrupted by different noise levels.

A non-invasive inverse problem method for rotor balancing relies on casing vibration readings and prior knowledge of the structure. Such a method is important for rotors that are inaccessible under operating conditions. This paper introduces a method for solving the quasi-implicit inverse problem that arises when identifying the required balancing correction for a rotor with only one weak linear connection to the casing, apart from the nonlinear connections. This is typical of aero-engine designs that use a retainer spring with only one of the nonlinear squeeze-film damper (SFD) bearings that support the rotor within the casing. The SFD journal displacements are estimated from casing vibration readings using identified inverse SFD models based on Recurrent Neural Networks (RNNs). The information from these is then used to enhance the condition of the explicit inverse problem set up in previous research for simpler configurations. The methodology is validated using simulated casing vibration readings. The reliability of the RNN inverse SFD models is first demonstrated. The second part of the validation shows that the novel enhanced explicit inverse problem method is essential for effective balancing of this previously unconsidered system. Repeatability and robustness to noise/model uncertainty are satisfactorily demonstrated and limitations discussed.The identification of the rotor unbalance from vibration measurements at the casing and/or the rotor is referred to as an "inverse" problem [3], in contrast to the "forward" problem, which refers to the prediction of the system vibration in response to a known unbalance distribution. Traditional balancing methods (which include the standard "trim" balancing procedures) [4][5][6][7][8] involve the use of several trial runs and the application of trial masses at fixed balancing planes. Such types of methods are typically based on two representative methods, the influence coefficients balancing method [5] and the modal balancing method [4]. Darlow [6] developed the Unified Balancing Approach (UBA) that combined the advantages of both previous methods. The UBA method involved the calculation of modal trial mass sets, based on the influence coefficient approach of using trial mass data. Foiles et al [7] provided a comprehensive review of the several direct methods for rotor balancing, which were based on the fundamentals of the influence coefficients method and modal method.Chen et al [9] proposed an optimisation technique based on nonlinear programming to determine the balancing corrections to be applied to prescribed planes. This method required a valid mathematical model of the rotor-dynamic system to use within the optimisation scheme. Unlike the methods of [4][5][6][7][8], the method of Chen et al [9] did not require several trial runs and trial masses since the optimisation was based on measurements from the initial (unbalanced) configuration. However, the method was still invasive since it required measurement of the vibration of the rotor. Moreover, the system ...

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