Robust estimate of excitations in mechanical systems using M-estimators - Theoretical background and numerical applications

This second part of the study presents some experimental applications to mechanicalsystems in which the results of excitation estimation, obtained using traditional least squares and M-estimate, are compared. The first case presented is a single input–multiple outputs system: a simple test-rig for the study of the vibrations of a two-degrees of freedom system is employed to identify the constraint displacement that causes the measured mass vibrations in presence of heavy noise. The second case is a multiple inputs–multiple outputs system: a rotor test-rig is used to identify the positions, the amplitudes and the phases of two unbalances using the vibrations measured in the bearings. In this case, also an additional theoretical part is introduced about the basics of model-based identification in the frequency domain applied to rotor dynamics. The last case is again a single input–multiple outputs system, but in an industrial application: experimental vibrations of a 320 MW steam turbo-generator are used to identify position and amount of a known balancing mass in an on-field real case. Moreover, whilst in the numerical examples presented in the first part the knowledge of the system was perfect, in these cases some uncertainties are present also in the system model. Finally, the paper introduces the use of the M-estimate technique to evaluate the adequacy the model of the system, by means of the analysis of the weights attributed to the measures as a function of the frequency of the excitation

Robust estimation of excitations in mechanical systems using M-estimators –Experimental applications

This second part of the study presents some experimentalapplications to mechanicalsystems in which the results of excitationestimation, obtained using traditional least squares and M-estimate, are compared. The first case presented is a single input–multiple outputs system: a simple test-rig for the study of the vibrations of a two-degrees of freedom system is employed to identify the constraint displacement that causes the measured mass vibrations in presence of heavy noise. The second case is a multiple inputs–multiple outputs system: a rotor test-rig is used to identify the positions, the amplitudes and the phases of two unbalances using the vibrations measured in the bearings. In this case, also an additional theoretical part is introduced about the basics of model-based identification in the frequency domain applied to rotor dynamics. The last case is again a single input–multiple outputs system, but in an industrial application: experimental vibrations of a 320 MW steam turbo-generator are used to identify position and amount of a known balancing mass in an on-field real case. Moreover, whilst in the numerical examples presented in the first part the knowledge of the system was perfect, in these cases some uncertainties are present also in the system model. Finally, the paper introduces the use of the M-estimate technique to evaluate the adequacy the model of the system, by means of the analysis of the weights attributed to the measures as a function of the frequency of the excitation

Analytical Model of a Particular Type of Positive Displacement Blower

Many papers exist in literature which deal with the twin screw compressor; this usually has two different rotors, a male and a female, and is commonly used to produce compressed gas for industrial uses. However, a different type of positive displacement rotary compressor with two screws is sometimes used; one of its typical applications is in car engine supercharging. Present paper deals with the latter type, which is defined as a two screw blower. This blower has two identical helical rotors, each with three lobes. The kinematics and the geometry of the rotors are analysed here, and a complete mathematical model for the rotor is defined. Moreover different possible shapes of the rotors, depending on the design parameters, are analysed and the limitations in the choice of the design parameters are presented. Finally an analysis of the theoretical specific slipping of the rotors is presented, showing which zones of the profile are the most stressed. This model will be useful for further studies on rotor pressure loads and blower dynamics

Diagnostics of gear faults based on EMD and automatic selection of intrinsic mode functions

Signal processing is an important tool for diagnostics of mechanical systems. Many different techniques are available to process experimental signals, among others: FFT, wavelet transform, cepstrum, demodulation analysis, second order ciclostationarity analysis, etc. However, often hypothesis about data and computational efforts restrict the application of some techniques. In order to overcome these limitations, the empirical mode decomposition has been proposed. The outputs of this adaptive approach are the intrinsic mode functions that are treated with the Hilbert transform in order to obtain the Hilbert–Huang spectrum. Anyhow, the selection of the intrinsic mode functions used for the calculation of Hilbert–Huang spectrum is normally done on the basis of user’s experience. On the contrary, in the paper a merit index is introduced that allows the automatic selection of the intrinsic mode functions that should be used. The effectiveness of the improvement is proven by the result of the experimental tests presented and performed on a test-rig equipped with a spiral bevel gearbox, whose high contact ratio made difficult to diagnose also serious damages of the gears. This kind of gearbox is normally never employed for benchmarking diagnostics techniques. By using the merit index, the defective gearbox is always univocally identified, also considering transient operating conditions

Analysis of Rotor-to-Stator Rub in a Large Steam Turbogenerator

Rotor to stator rub is a very common topic in rotor dynamics and several models have been proposed in literature. Anyhow these models are often able to explain only the experimental dynamical behaviour of simple test rigs, which are deliberately reproducing a Jeffcott rotor. On the contrary case histories related to real machines are seldom presented and analyzed. The aim of this paper is to present an actual case history of a large turbo generator unit that was subjected to partial arc rubs. The experimental results are shown and discussed along with the model based diagnostic strategy employed to identify the fault severity and the location of the shaft cross-sections where the heaviest rubs occurred. Comparisons between experimental data and simulated vibrations caused by the identified fault are shown to validate the proposed methodolog

Experimental and Theoretical Application of Fault Identification Measures of Accuracy in Rotating Machine Diagnostics

Model-based diagnostic techniques can be used successfully in the health analysis of rotormachinery. Unfortunately, a poor accuracy of the model of the fully assembled machine, as well as errors in the evaluation of the experimental vibrations caused only by the impending fault, can affect the accuracy of fault identifications. This can make difficult to identify the type of the actual fault as well as to evaluate its severity and its position. This paper shows some methods that have been developed to measure the accuracy of the results obtained with model-based techniques aimed to identify faults in rotating machines. The testing of the capabilities of these methods is carried out using both machine response simulated with mathematical models and experimental data on a real machine. (C) 2003 Elsevier Science Ltd. All rights reserved

Deviations Induced by Tool Sharpening in the Profile of Three Screw Pump Rotors

Three screw pumps represent an important family of positive displacement rotary pumps. They are quite easy to construct, even if the use of a shaped milling cutter for the rotor machining can cause some problems when the tool is not new. In fact the sharpening of the tool modifies the total geometry of the milling cutter by reducing its diameter. The shape of the single cutter does not change, but the cutter radial position is shifted towards the tool center. This causes deviations in the profile cut and the screws consequently need a long breaking in. In this paper the problem is analyzed from a quantitative point of view, using a method that allows us to determine the machining error as a function of the tool geometry variation. Moreover some alternative solutions to this problem are suggested

Effects of the hot alignment of a power unit on oil-whip instability phenomena

This paper shows the results of the analysis of the dynamic behaviour of a power unit, whose shaft-train alignment was significantly influenced by the machine thermal state, that was affected in operating condition by high subsynchronous vibrations caused by oil-whip instability phenomena. The dynamic stiffness coefficients of the oil-film journal bearings of the generator were evaluated considering the critical average journal positions that caused the instability onsets. By including these bearing coefficients in a mathematical model of the fully assembled machine, the real part of the eigenvalue associated with the first balance resonance of the generator rotor became positive. This paper shows the successful results obtained by combining diagnostic techniques based on mathematical models of journal bearings and shaft train with detailed analyses of monitoring data aimed to investigate the effects of the hot alignment of rotating machines on the occurrence of oil-whip instability onsets

Non Undercutting Conditions in Internal Gears

Many contributions regarding internal gear theory exist in literature. They mainly consider the problem of undercutting by means of analytical methods applied to specific and limited cases. The present paper deals with a general method showing the analytical condition for avoiding undercutting by the use of the concept of the limit curve. In particular the analytical determination of the limit curve allows the designer to obtain significant graphical representations of the design limits

Discussion of the dynamic stability of a multi-degree-of-freedom rotor system affected by a transverse crack

The dynamic behaviour of cracked rotors is one of the most discussed topics in the rotordynamic literature due to the wide range of problems that may arise from this fault. Among them, it is a common notion that cracks in horizontal rotating shafts may cause instability of the system because of the periodic opening and closing of the crack, i.e., the breathing mechanism, determines the stiffness variation and the parametric excitation of the rotor system. Simplified models have been used to study this phenomenon using Jeffcott rotors. For the first time in this paper, a model of a real hyperstatic rotor with several degrees of freedom is used, which also considers the bearings and the foundation of the system, and the stability is discussed by means of the Floquet theory. The sensitivity of the obtained results to the system anisotropy and the crack position is also investigated. The results presented are quite different from those obtained by means of the simple Jeffcott rotor but are consistent with real and documented field experiences