Frequency response functions and modal parameters of a rotating system exhibiting rotating damping

In the analysis of the stability threshold speed caused by rotating damping in rotating machinery, there is a lack of experimental data. This stability threshold speed can be found theoretically by means of a linear speed dependent model. The accuracy of the model depends highly upon the linearity and especially on the damping type that has been chosen. In this paper, the theoretical model and the importance of the stability analysis is discussed together with an experiment to validate the model. A rotating shaft is used to extract frequency response functions at different speeds. The shaft is excited with an automated impact hammer and the response is measured by eddy current probes. From these frequency response functions, the poles are extracted and compared to the poles derived from the model. It is found that the imaginary part of the poles, or the Campbell diagram, agrees quite well. The decay rate plot shows a similar increase as from the model, but there seems to be an extra stabilizing effect that is not accounted for in the model

Instability due to internal damping of rotating shafts

Rotor internal damping has been indicated as one of the main causes of instability in rotating machinery for more than a century. However, the exact characterisation of this damping is still an unsolved research topic. Therefore, in this thesis the consequences of material damping in rotating shafts are examined more in depth. Two main steps are considered. Firstly, a finite element model of the beam, including viscous and hysteretic damping, is constructed. This model allows to calculate the threshold speed of instability and the resonance frequencies of a shaft. Furthermore it allows to vary the damping parameters and to compare the considered models giving an indication of the general relations between instability and damping properties. Secondly, an experimental approach should elucidate which model fits best for the physical damping. In general, the main purpose is to gain new insights into how the damping should really be modelled to have the most accurate and safe prediction of a designed rotor

Sensititity of the stability threshold in linearized rotordynamics

Rotors exposed to lateral vibration can become unstable at a certain speed due to rotor internal damping. This stability threshold speed is unique and it is impossible to rotate above the threshold. In this paper, a rotor is treated as a linear speed dependent system and inertia, stiffness, gyroscopic and damping forces are included. In order to find the stability threshold, the multiple degree of freedom equations of motion are decoupled into a set of scalar equations. Therefore, the quadratic eigenvalue problem has to be solved. Consequently, the stability threshold speed can be calculated as the lowest speed by which one of the roots has a positive real part. The parameters that influence this stability threshold are discussed and verified by numerical results

Experimental validation of modal parameters in rotating machinery

In this paper, instability of rotating machinery systems due to rotating damping is investigated through experimental modal analysis. Generally, advanced methods are needed for these kind of systems because of the asymmetry of the matrices. However, it is shown by means of cyclic energy dissipation that the rotating damping can be handled as damping which changes due to the rotating speed. The use of damping matrix estimation techniques is discussed and a method is proposed to estimate and model the influence of the rotating damping matrix. A dedicated experimental setup, with negligible gyroscopic effect, is presented for validation purposes. It is shown experimentally that the estimation of the rotating damping matrix is able to predict the decay rate of the first forward mode

Online identification of a two-mass system in frequency domain using a Kalman filter

Some of the most widely recognized online parameter estimation techniques used in different servomechanism are the extended Kalman filter (EKF) and recursive least squares (RLS) methods. Without loss of generality, these methods are based on a prior knowledge of the model structure of the system to be identified, and thus, they can be regarded as parametric identification methods. This paper proposes an on-line non-parametric frequency response identification routine that is based on a fixed-coefficient Kalman filter, which is configured to perform like a Fourier transform. The approach exploits the knowledge of the excitation signal by updating the Kalman filter gains with the known time-varying frequency of chirp signal. The experimental results demonstrate the effectiveness of the proposed online identification method to estimate a non-parametric model of the closed loop controlled servomechanism in a selected band of frequencies

Torque ripples in stepping motor driven systems

Stepping motor operation is characterized by torque ripples. In this paper it is shown these torque ripples are caused by both the stepping motor drive algorithms and the toothed construction of rotor and stator of the studied hybrid stepping motors. These torque ripples are analyzed, discussed and measured. The torque ripples are measured in the complete operating range of the motor and depicted in this paper for full- half- and micro-stepping. By doing this, the paper provides insight in the vibrating behavior of a stepping motor driven system and possible solutions to overcome this are placed in the right perspective