Deflections and Strains in Cracked Shafts due to Rotating Loads: A Numerical and Experimental Analysis

In this article the deflections of a circular cross-section beam presenting a transverse crack of varying depths caused by various loads (bending, torsion, shear, and axial loads) are analyzed with the aid of a rather refined three-dimensional model that takes into account the nonlinear contact forces in the cracked area. The bending and shear loads are applied in several different angular positions in order to simulate a rotating load on a fixed beam or, by changing the reference system, a fixed load on a rotating beam. Torsion and axial loads are fixed with respect to the beam.Results obtained for the rotating beam can then be used for the analysis of cracked horizontal-axis heavy rotors in which the torsion is combined with the bending load. The effect of friction is also considered in the cracked area. The characteristic "breathing" behavior of the cracked area was analyzed and compared to that obtained with a rather simple one-dimensional model. The differences in results with respect to those based on fracture mechanics are emphasized. In order to highlight the effect of the presence of the crack, the deflections of the uncracked beam loaded with the same loads were subtracted from the deflections of the cracked beam.Finally, a cracked specimen was extensively analyzed by means of several strain gauges to study the strain distribution on the outer surface around the crack in various loading conditions. Consistent pre-stresses were found, and they influence the breathing behavior. The experimental results were compared with those obtained using the onedimensional linear model

Light and short arc rubs in rotating machines: Experimental tests and modelling

Rotor-to-stator rub is a non-linear phenomenon which has been analyzed many times in rotordynamics literature, but very often these studies are devoted simply to highlight non-linearities, using very simple rotors, rather than to present reliable models. However, rotor-to-stator rub is actually one of the most common faults during the operation of rotating machinery. The frequency of its occurrence is increasing due to the trend of reducing the radial clearance between the seal and the rotor in modern turbine units, pumps and compressors in order to increase efficiency. Often the rub occurs between rotor and seals and the analysis of the phenomenon cannot set aside the consideration of the different relative stiffness. This paper presents some experimental results obtained by means of a test rig in which rub conditions of real machines are reproduced. In particular shortarcrubs are considered and the shaft is stiffer than the obstacle. Then a model, suitable to be employed for real rotating machinery, is presented and the simulations obtained are compared with the experimental results. The model is able to reproduce the behaviour of the test rig

A sensitivity analysis of vibrations in cracked turbogenerator units versus crack position and depth

The dynamic behaviour of heavy, horizontal axis, turbogeneratorunits affected by transverse cracks can be analysed in the frequency domain by means of a quasi linear approach, using a simplified breathing crack model applied to a traditional finite element model of the shaft-line. This allows to perform a series of analyses with affordable computational efforts. Modal analysis combined to a simplified approach for simulating the dynamical behaviour allows to predict the severity of the crack-excited vibrations, resolving the old-age question on how deep a crack must be to be detected by means of vibration measurements of the machine during normal operating conditions. The model of a 320 MW turbogeneratorunit has been used to perform a numerical sensitivity analysis, in which the vibrations of the shaft-line, and more in detail the vibrations of the shaft in correspondence to the bearings, have been calculated for all possible positions of the crack along the shaft-line, and for several different values of the depth of the crack

Diagnostic Significance of Orbit Shape Analysis and its Application to Improve Machine Faults Detection

The full spectrum analysis of rotating machine vibrations is a diagnostic tool that enables the symptoms of some special types of fault to be clearly detected. The Shape and Directivity Index (SDI) of journal filtered orbits is an additional diagnostic parameter whose evaluation can be combined with the full spectrum analysis. The ellipticity of the filtered orbit, as well as the amplitude and the inclination angle of the major axis of the orbit, are parameters whose analysis can provide important diagnostic information. In order to validate the proposed approach, the vibrations of a large turbine-generator unit that was subjected to rotor-to-stator rubs have been analyzed in this paper. The results of this investigation have been used to update the model of the rotor-system that has been used to identify the location and the severity of the fault. In the paper, the improvements in the accuracy of the fault identification provided by the model updating enabled by the SDI analysis are shown

Cracked Rotors, A Survey on Static and Dynamic Behaviour Including Modelling and Diagnosis

Cracks can develop in rotating shafts and can propagate to relevant depths without affecting consistently the normal operating conditions of the shaft. In order to avoid catastrophic failures, accurate vibration analyses have to be performed for crack detection. The identification of the crack location and depth is possible by means of a model based diagnostic approach, provided that the model of the crack and the model of the cracked shaft dynamical behavior are accurate and reliable. This monograph shows the typical dynamical behavior of cracked shafts and presents tests for detecting cracks. The book describes how to model cracks, how to simulate the dynamical behavior of cracked shaft, and compares the corresponding numerical with experimental results. All effects of cracks on the vibrations of rotating shafts are analyzed, and some results of a numerical sensitivity analysis of the vibrations to the presence and severity of the crack are shown. Finally the book describes some crack identification procedures and shows some results in model based crack identification in position and depth. The book is useful for higher university courses in mechanical and energetic engineering, but also for skilled technical people employed in power generation industries

Steam whirl analysis in a high pressure cylinder of a turbo generator

In this paper steam-whirl instability occurrence and modelling is described. Some weak points in usual modelling and in standard stability criteria are discussed. The motivation of the present study is the case history of asteam turbine that experienced heavy steam-whirl instability though the calculated stability margin was sufficiently high in design conditions. During the electrical load rise of a power plant, the 425 MW steamturbogenerator showed an unstable vibrational behaviour as soon as maximum output power was approached. The combined effect of steam excitation (in bladed rows and in the steam glands) and of low damping in some of the oil film bearings was most likely the main cause of the observed malfunction. A model of the turbogenerator has been set up, the steam-whirl exciting force coefficients and the oil film bearing coefficients have been applied and eigenfrequencies and damping factors have been calculated. In order to check the accuracy of this calculation also another method based on energy balance has been used but very similar values have been obtained, confirming the results of the standard stability evaluation approach. The calculation showed that the machine should have been stable, with a sufficient margin of stability, in design conditions. Therefore the steam-whirl excitation models have been analysed for identifying possible weak points which could justify the discrepancies between experimental behaviour and calculated results

Bivariate Analysis of Complex Vibration Data: an Application to Condition Monitoring of Rotating Machinery

The problem of the robust definition of the acceptance regions in conditionmonitoring of the vibrations of rotatingmachinery is related to the more wide field of the analysis of bivariate data. Traditional parametric techniques and innovative nonparametric methods based on the statistical concept of the data depth are presented and critically examined in the paper. The performances with respect to the robustness in the estimation of the acceptance regions are analysed by means of experimental cases of real rotatingmachinery of a power plant

A model based identification method of transverse cracks in rotating shafts suitable for industrial machines

This paper presents a model-based transverse crack identification method suitable for industrial machines. The method is validated by experimental results obtained on a large test rig, which was expressly designed for investigating the dynamical behaviour of cracked horizontal rotors. The identification method and the relative theory is briefly presented, while three different types of cracks are considered: the first is a slot, therefore not actually a crack since it has not the typical breathing behaviour, the second a small crack (14% of the diameter) and the third a deep crack (47% of the diameter). The excellent accuracy obtained in identifying position and depth of different cracks proves the effectiveness and reliability of the proposed method

The use of orbitals and full spectra to identify misalignment

In this paper, a SpectraQuest demonstrator is used to introduce misalignment in a rotating set-up. The vibrations caused by misalignment is measured with both accelerometers on the bearings and eddy current probes on the shaft itself. A comparison is made between the classical spectral analysis, orbitals and full spectra. Orbitals are used to explain the physical interpretation of the vibration caused by misalignment. Full spectra allow to distinguish unbalance from misalignment by looking at the forward and reversed phenomena. This analysis is done for different kinds of misalignment, couplings, excitation forces and combined machinery faults

Diagnostic significance of orbit shape analysis and its application to improve machine fault detection

The full spectrum analysis of rotating machine vibrations is a diagnostic tool that enables the symptoms of some special types of fault to be clearly detected. The Shape and Directivity Index (SDI) of journal filtered orbits is an additional diagnostic parameter whose evaluation can be combined with the full spectrum analysis. The ellipticity of the filtered orbit, as well as the amplitude and the inclination angle of the major axis of the orbit, are parameters whose analysis can provide important diagnostic information. In order to validate the proposed approach, the vibrations of a large turbine-generator unit that was subjected to rotor-to-stator rubs have been analyzed in this paper. The results of this investigation have been used to update the model of the rotor-system that has been used to identify the location and the severity of the fault. In the paper, the improvements in the accuracy of the fault identification provided by the model updating enabled by the SDI analysis are shown