Complex Modal Testing Research Articles

A modified complex modal testing technique for a rotating tire with a flexible ring model

Natural frequencies, mode shapes and modal damping values are the most important parameters to describe the noise and vibration behavior of a mechanical system. For rotating machinery, however, the directivity of the propagation wave of each mode should also be taken into account. For rotating systems, this directivity can be determined by complex modal testing. In this paper, a rolling tire is represented as a flexible ring model. The limitation of application of the complex modal testing which requires two directional measurements at a certain point, which is difficult to measure in practice, has been overcome through a modified complex modal testing which requires only one directional measurements at any two points. The technique is described in detail and applied to both a numerical example and to an experimental data set of a real rotating tire.

Identification of rotating asymmetry in rotating machines by using reverse directional frequency response functions

A quick and easy but comprehensive identification method for rotating asymmetry in rotating machines is proposed, based on the complex modal testing method. In this work it is shown that the reverse directional frequency response function (reverse dFRF), which indicates the degree of asymmetry, can be identified with a simple testing method requiring only a single vibration sensor and a single exciter. To clarify physical realization associated with estimation of the reverse dFRF, its relation to the conventional frequency response functions, which are defined by the real input (excitation) and output (vibration measurement), are discussed extensively.

Complex modal testing of asymmetric rotors using magnetic exciter equipped with hall sensors

The complex modal testing methods developed for asymmetric rotors are briefly discussed and their performances are experimentally evaluated. For the experiments, a laboratory test rotor is excited by using a newly developed, cost effective magnetic exciter equipped with Hall sensors, which measure the excitation forces. It is concluded that the exciter system is characterized by a wide bandwidth and a high resolution for both the excitation and force measurement, and that the one-exciter/two-sensor technique for complex modal testing of asymmetric rotors is superior to the standard two-exciter/two-sensor technique in terms of practicality and realization.

IDENTIFICATION OF ROTOR-BEARING SYSTEMS IN THE FREQUENCY DOMAIN PART II: ESTIMATION OF MODAL PARAMETERS

This paper discusses the parametric identification of multiple-input–multiple-output (MIMO) rotor-bearing systems in the frequency domain on the basis of the maximum likelihood estimator (MLE). An identification procedure, considering noise on both inputs and outputs (errors-in variables model), is developed for real as well as for complex modal testing. Quantitative measures for the uncertainties (covariances) of the estimated parameters were to be obtained. It is shown that the MLE solution of real and complex modal analysis is fully equivalent. It follows that, in case of complex modal testing, reduction of the system is not allowed in general when noise information is taken into account. A comparison between random and broadband periodic (multisine) excitations is made. Measurements on a rotor test rig demonstrated that multisines yield more accurate estimates of the modal parameters (as compared to random excitation).

IDENTIFICATION OF ROTOR-BEARING SYSTEMS IN THE FREQUENCY DOMAIN PART I: ESTIMATION OF FREQUENCY RESPONSE FUNCTIONS

This paper discusses the non-parametric identification if MIMO rotor-bearing systems in the frequency domain for real as well as for complex modal testing. The FRFs are estimated on the basis of the maximum likelihood estimator, considering noise on both inputs and outputs (error-in-variables model). It is demonstrated that multisine excitations with random phases yield improved FRF measurements as compared to random excitations. Moreover, quantitative uncertainties (covariances of the FRFs) are obtained allowing us to quantify the quality of the measurements. The experiments are performed on a rotor test rig and the evaluation is made for both real and complex modal analysis.

Complex Time Series Modeling and Analysis for Rotor Dynamics Identification

A new time series method, directional ARMAX (dARMAX) model-based approach, is proposed for rotor dynamics identification. The dARMAX processes complex-valued signals, utilizing the complex modal testing theory which enables the separation of the backward and forward modes in the two-sided frequency domain and makes effective modal parameter identification possible, to account for the dynamic characteristics inherent in rotating machinery. The dARMAX is superior in nature to the conventional ARMAX particularly in the estimation of the modal parameters for isotropic and weakly anisotropic rotors. Numerical simulations are performed to demonstrate effectiveness of the dARMAX.

AN EFFICIENT COMPLEX MODAL TESTING THEORY FOR ASYMMETRIC ROTOR SYSTEMS: USE OF UNDIRECTIONAL EXCITATION METHOD

A complex modal testing theory is newly developed for asymmetric rotor systems. The theoretical development is made strictly in the stationary co-ordinate system, and this enables a unidirectional excitation technique efficiently to estimate the directional frequency response functions, which greatly lessens the testing efforts and enhances the practicality of the theory.

In-Situ Identification of Active Magnetic Bearing System Using Directional Frequency Response Functions

Complex modal testing is employed to obtain the directional frequency responses of a four-axis active magnetic bearing system. In the test, magnetic bearings are used as exciters while the system is in operation. The directional frequency response estimates are then used to effectively identify the parameters of the active magnetic bearing system. Experimental results show that the directional frequency response function, which is properly defined in the complex domain, is a powerful tool for identification of bearing as well as modal parameters of the system.

Development of the use of directional frequency response functions for the diagnosis of anisotropy and asymmetry in rotating machinery: theory

A diagnostic method for anisotropy and asymmetry in rotor systems is proposed. The method is based on the use of directional FRFs obtained by the complex modal testing method. It also utilises the co-ordinate transform technique which allows discrimination of anisotropy and asymmetry effects in the frequency domain. An illustrative example of a simple rotor system is given to demonstrate analytical developments.

Theory of excitation methods and estimation of frequency response functions in complex modal testing of rotating machinery

Various excitation methods are proposed for the effective use of complex modal testing for rotating machinery. The proposed excitation methods are developed, based on the input/output relationships for complex signals, for the direct or indirect assessment of frequency response and coherence functions between complex inputs and outputs. From the views of practicality, required testing efforts and estimation errors, the advantages and disadvantages of each method are investigated, when the measurement noises and the errors involved with realisation of excitation forces are present. Numerical simulations are also performed to demonstrate the testing procedures and results using the proposed methods.

A complex modal testing theory for rotating machinery

A new modal testing method, termed complex modal testing, is proposed for modal parameter identification of rotating machinery and compared with the classical method. The proposed method is essentially based on the use of complex notation which has been known to be a powerful mathematical tool in the analysis of, particularly isotropic, rotor systems. Complex modal testing not only allows clear physical insight into the backward and forward modes, but also enables the separation of those modes in the frequency domain so that effective modal parameter identification is possible. In addition, it does not require additional testing effort to obtain the adjoint mode shapes of isotropic rotors which are characterised by non-self-adjointness.