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 ...

Most recently proposed techniques for inverse rotordynamic problems seek to identify the unbalance on a rotor using a known structural model and measurements from externally mounted sensors only. Such non-intrusive techniques are important for balancing rotors that cannot be accessed under operational conditions because of temperature or space restrictions. The presence of nonlinear bearings, like squeeze-film damper (SFD) bearings used in aero-engines, complicates the solution process of the inverse rotordynamic problem. In certain practical aero-engine configurations, the solution process requires a substitute for internal instrumentation to quantify the SFD journal vibration. This can be provided by an inverse model of the SFD bearing which outputs the time history of the relative vibration of the SFD journal relative to its housing, for a given input time history of the SFD force. This paper focuses on the inverse model of the SFD and presents an improved methodology for its identification via a Recurrent Neural Network (RNN) trained using experimental data from a purposely designed rig. The novel application of chirp excitation via two orthogonal shakers considerably improves both the quality of the training data and the efficiency of its generation, relative to an earlier preliminary work. Validation test results show that the RNNs can predict the journal displacement time history with reasonable accuracy. It is therefore expected that such an inverse SFD model would serve as a reliable component in the solution of the wider inverse problem of a rotordynamic system.

Recently, there has been a focus on the use of inverse problem techniques in order to monitor rotor unbalance, and obtain a balancing solution, from vibration measurements on the casing and prior knowledge of the rotor-casing structure. In certain practical configurations that use nonlinear bearings like the squeeze-film damper (SFD) bearing, an inverse model of the bearing is an important part of the unbalance identification process. The inverse bearing model is used to estimate the journal vibration from casing vibration measurements, thus acting as a substitute for internal instrumentation in applications where the rotor is not accessible under operational conditions. Previous research has shown that an inverse bearing model can be identified using a trained Recurrent Neural Network (RNN) from experimental input/output data. However, the RNN was both trained and validated under simulated rotational conditions, wherein the motion was driven by two orthogonally-phased perpendicular shakers. In this paper, a RNN of an inverse bearing model that is identified from experimental data generated under simulated rotational conditions is validated under actual rotational (i.e. unbalance-driven) vibration conditions. The necessary modifications to the test rig are presented, together with the identification/training procedure. The results of the validation tests show that the RNN is capable of predicting the frequency spectrum of the dynamic nonlinear response of the journal with reasonable accuracy. This inverse SFD bearing model can be thus used in a future work to identify rotor unbalance.

Modern aero-engine structures typically have at least two nested rotors mounted within a flexible casing via squeezefilm damper (SFD) bearings. The inaccessibility of the HP rotor under operational conditions motivates the use of a noninvasive inverse problem procedure for identifying the unbalance. Such an inverse problem requires prior knowledge of the structure and measurements of the vibrations at the casing. Recent work by the authors reported a non-invasive inverse method for the balancing of rotordynamic systems with nonlinear squeeze-film damper (SFD) bearings, which overcomes several limitations of earlier works. However, it was not applied to a common practical configuration wherein the HP rotor is mounted on the casing via just one weak linear connection (retainer spring), with the other connections being highly nonlinear SFDs. The analysis of the present paper considers such a system. It explores the influence of the condition number and how it is affected as the number of sensors and/or measurement speeds is increased. The results show that increasing the number of measurement speeds has a far more significant impact on the conditioning of the problem than increasing the number of sensors. The balancing effectiveness is reasonably good under practical noise level conditions, but significantly lower than obtained for the previously considered simpler configurations.

Squeeze Film Damper (SFD) bearings play a vital role in attenuating large amplitudes of vibration due to their relatively simple assembly in aero engine designs. The modern aero-engine structures, typically, have at least two nested rotors mounted within a flexible casing via squeeze-film damper (SFD) bearings. There is a growing body of research into identification techniques for bearing models for use in rotor-bearing analysis to improve reliability and/or efficiency of implementation. The authors’ previous work has shown that, for cases where there is no adequate linear connection between the rotor and casing, the identification of the unbalance from externally mounted sensors requires a virtual instrument that can determine the vibration of the rotor relative to the casing, as a substitute for internal instrumentation. The present study is devoted to determining the effectiveness of the inverse SFD model (under different unbalance state conditions), when it is applied to a rotor-casing system, wherein the rotor runs on two unsprung SFD bearings. The validation of the inverse SFD model enables its use in a future study of the identification of unbalance in such complex systems.