Rotordynamics

The rotor critical speeds are the speeds accompanied by a great dynamic load, and maximum vibration. The critical speeds of rotation coincide with the natural frequencies of transverse vibration of the non-rotating shaft disc system. These speeds should be determined carefully. In this paper, the critical speeds of a shaft-discs system are calculated using several methods. Firstly, Raleigh's method, and transfer matrix method are used to calculate the first and the second critical speeds using MATLAB software. Secondly, the critical speeds are calculated by finite element method using ANSYS package. Finally, an experimental investigation is done to determine the values of critical speeds. The experimental results are presented in comparison with the calculated values.

This paper investigates the supervised classification of an injection fault of an internal combustion Diesel engine using vibration measurement. The S-transform is used to produce a time-frequency representation of the vibration signal. The matrix representation of the time frequency image is then reduced to a lower size matrix using a two-dimensional non-negative matrix factorization. Four algorithms are tested for feature selection from this reduced size matrix and the features are sorted according to their ability in fault classification. A Neural Network classifier is then trained and applied to classify test data. The performances of the four considered selection methods are then evaluated by comparing their percentage of correct classification and the computer execution time. It has been found that the performance of the classifier is enhanced when the number of retained feature is increased for the four investigated selection methods.

In this paper, nonlinear dynamics of an unbalanced composite spinning shaft are studied. Extensional–flexural–flexural–torsional equations of motion are derived via utilizing the three-dimensional constitutive relations of the material and Hamilton’s principle. The gyroscopic effects, rotary inertia and coupling due to material anisotropy are included, while the shear deformation is neglected. To analyze the rotor dynamic behavior, the full form of the equations without any simplification assumption (e.g., stretching or shortening assumption) is used. The method of multiple scales is applied to the discretized equations. An analytical expression as a function of the system parameters describing the forced vibration of a spinning composite shaft in the neighborhood of the primary resonance is obtained. The discretization is done with both one and two modes, and the results are compared. It is shown that although the excitation is tuned in the neighborhood of the first mode, one-mode ...

This material gives a basic aerodynamics related to rotor craft systems. This is a basic theory behind the helicopter blades. How the relative wing is affecting during hover, transnational flight, vertical flight. The theory also gives idea about the ground effect on rotor blades at different conditions.

Abstract—This work shows a method to quantify rotor eccentricities in synchronous machines by exploiting the unbalance caused in the split-phase currents. The paper first develops a machine model comprehensive of eccentricities and parallel circuits in the stator, by using symmetrical components. Then, the model is used for formal calculation of the unbalanced currents. Finally, the equations are reversed to obtain eccentricity degrees from current measurements. Practical formulas are given for fault assessment, only requiring machine line voltage and synchronous reactance. The method can be applied on load. This paper provides full details of the theory underlying the method. The theory also clarifies some aspects about split-phase currents, not deepened before. It is proven that the air gap flux modulation due to eccentricities, acting through additional 2(p±1)-pole flux waves in 2p-pole machines, stimulates additional currents which circulate in the stator and turn into 2(p±1)-pole rotating space-vectors in the complex domain. Vector trajectories have shape and amplitude dictated by eccentricity type and degree, respectively. This study is limited to 2p-pole machines with p≥2. The theory is corroborated by simulations of a practical 1950kVA generator in this Part I. Experimental proofs and simulations of a laboratory 17kVA machine are provided in Part II of the paper.

A strategy for adaptive control and energetic optimization of aerobic fermentors was implemented, with both air flow and agitation speed as manipulated variables. This strategy is separable in its components: control, optimization, estimation. We optimized parameter’s estimation (from the usual KLa correlation) using sinusoidal excitation of air flow and agitation speed. We have implemented parameter’s estimation trough recursive least squares algorithm with forgetting factor. We carried separate essays on control, optimization and estimation algorithms. We carried our essays using an original computational simulation environment, with noise and delay generating facilities for data sampling and filtering.

Our results show the convergence and robustness of the estimation algorithm used, improved with use of both forgetting factor and KLa dead-band facilities. Control algorithm used in our work compares favorably with PID using the integrated area criteria for deviation between oxygen molarity and critical molarity (set point). Optimization algorithm clearly reduces energetic consumption, respecting critical molarity. Integration of control, optimization and adaptive algorithms was implemented, but future work is needed for stability. Methods were defined and implemented for stability improvement. We have implemented data acquisition and computer manipulation of air flow and agitation speed for actual fermentors.

We present an analytical analysis of a continuous rotor shaft subjected to universal temperature gradients. To this end, an analytical model is derived to investigate the generic thermal vibrations of rotor structures. The analytical solutions are obtained in a rotating frame and include parameters related with both the thermal environment and the rotor dynamic structures. This provides an insight into the mechanisms for the rotor thermal vibration. Furthermore, numerical results based on the analytical solutions are given. An index denoting the temperature gradients is proposed for the occasions with
nonlinear cross-sectional temperature distributions. Finally, the factors influencing the thermal vibrations are analyzed. The results show that the thermal vibration is affected by
many factors including the shaft size, rotational speeds, heating locations, critical speed, etc. Moreover, it is investigated how the convection coefficient and the heat conductivity influence the thermal vibrations in order to provide an insight into the management of thermal vibrations from the perspective of thermal aspects.

An improved rotor-blade dynamic model is developed based on our previous works (Ma et al. in J Sound Vib, 337:301–320, 2015; J Sound Vib 357:168– 194, 2015). In the proposed model, the shaft is dis-cretized using a finite element method and the effects of the swing of the rigid disk and stagger angles of the blades are considered. Furthermore, the mode shapes of rotor-blade systems can be obtained based on the proposed model. The proposed model is more accurate than our previous model, and it is also verified by comparing the natural frequencies obtained from the proposed model with those from the finite element model and published literature. By simplifying the casing as a two degrees of freedom model, the single-and four-blade rubbings are studied using numerical simulation and experiment. Results show that for both the single-and four-blade rubbings, amplitude amplification phenomena can be observed when the multiple frequencies of the rotational frequency (f r) coincide with the conical and torsional natural frequencies of the rotor-blade system, natural frequencies of the casing and the bending natural frequencies of the blades. In addition, for the four-blade rubbing, the blade passing frequency (BPF, 4 f r) and its multiple frequency components also have larger amplitudes, especially, when they coincide with the natural frequencies of the rotor-blade system or casing; the four-blade rubbing levels are related to the rotor whirl, and the most severe rubbing happens on the blade located at the right end of the whirl orbit.

Abstract. In the recent years, the clearance between the rotor blades and stator/casing had been
getting smaller and smaller prior improving the aerodynamic efficiency of the turbomachines as
demand in the engineering field. Due to the clearance reduction between the blade tip and the
rotor casing and between rotor blades and stator blades, axial and radial blade rubbing could be
occurred, especially at high speed resulting into complex nonlinear vibrations. The primary aim
of this study is to address the blade axial rubbing phenomenon using numerical analysis of rotor
system. A comparison between rubbing caused impacts of axial and radial blade rubbing and
rubbing forces are also aims of this study. Tow rotor models (rotor-stator and rotor casing
models) has been designed and sketched using SOILDSWORKS software. ANSYS software has
been used for the simulation and the numerical analysis. The rubbing conditions were simulated
at speed range of 1000rpm, 1500rpm and 2000rpm. Analysis results for axial blade rubbing
showed the appearance of blade passing frequency and its multiple frequencies (1x, 2x 3x etc.)
and these frequencies will more excited with increasing the rotational speed. Also, it has been
observed that when the rotating speed increased, the rubbing force and the harmonics frequencies
in x, y and z-direction become higher and severe. The comparison study showed that axial blade
rub is more dangerous and would generate a higher vibration impacts and higher blade rubbing
force than radial blade rub.

This paper aims at the blade-casing rubbing in a shaft–disk–blade (SDB) system including shaft, disk, blade and bearing, and focuses the effects of stagger angles of blades, rotational speeds and casing stiffness on the rubbing-induced vibration responses of the SDB system and casing. Firstly, a finite element (FE) model of an SDB system is developed, and the rubbing between the blade-tip and casing is simulated using contact dynamics theory. In the proposed model, Timoshenko beam elements are adopted to simulate the shaft and the blade, and shell elements to simulate the disk, and spring-damping elements to simulate the ball bearings. A point–point contact element is adopted to simulate the blade-casing rubbing. Moreover, the augmented Lagrangian method is utilized to deal with contact constraint conditions, and the Coulomb friction model is used to simulate the friction between the blade and casing. The proposed model is also validated by comparing the natural frequencies with those obtained from the published literature. The results indicate that (1) amplitude amplification phenomena can be observed when the multiple frequency components coincide with the torsional natural frequency of the SDB system and the bending natural frequencies of the blades under rotational state; (2) the torsional vibration features of the SDB system with blade-tip rubbing are more significant than the lateral vibration features of the shaft; (3) the torsional vibration of the SDB system increases, and the blade bending vibration reduces with the increase of the stagger angle of the blade; (4) period-2 motion may appear under the large casing stiffness and high rotational speeds, and the torsional vibration of the SDB system and blade bending vibration tend to increase with the increasing casing stiffness. Blade-casing rubbing has been regarded as a significant contributor to excessive maintenance and in general to engine failure. The rubbing may result in complicated vibration of the overall unit, and may reduce the system performance and the lives of the blade and the casing. Blade-casing rubbing is essentially nonlinear, which involves contacts, large displacements and deformations of the blade. Moreover, the rubbing may be characterized by significant interactions between the global dynamics of the shaft– disk–blade (SDB) system and local vibration of the blade [1]. Many researchers studied the blade-casing rubbing mechanisms and rubbing induced complicated nonlinear dynamic behaviors using cantilever beams to simulate the blades [2–6]. Padovan and choy [2] deduced the relationship between the normal contact force and the blade radial deformation by simplifying the blade as a cantilever beam. Considering the effect of the centrifugal force of the blade, Jiang et al. [3] derived the normal blade-casing rubbing force based on Padovan's model. Based on Jiang's model [3], Ma et al. [4] developed a revised model of the rubbing between the blade and flexible casing, and verified the revised model using experimental results. Sinha [5] presented many mathematical expressions about the impulse loading, such as half-sine wave, rectangular pulse or sawtooth pulse, and analyzed the vibration responses of the rotating Timoshenko beam under the impulse loading of the half-sine wave. Simplifying the blade and casing as the straight beam and curved beam respectively, Batailly et al. [6] analyzed the rubbing between the blade tip and the casing by adopting a combination of component mode synthesis methods with a contact algorithm based on the Lagrange multiplier technique. Because cantilever beam models are difficult to describe the blade torsional vibration, many researchers adopted cantilever plate models to simulate blade-casing rubbing [7,8]. Kou and Yuan [7] simplified two types of functions (sine wave and sine pulse

Los altos costos energéticos asociados a la operación de los compresores centrífugos, aunados a la necesidad de optimizar la relación costo-beneficio de los procesos productivos donde estos se encuentran involucrados, justifican la incorporación de pruebas aerotérmicas rutinarias en los programas de mantenimiento predictivo, como una herramienta clave para el monitoreo y control de la pérdida de eficiencia de los compresores. Este control sobre los costos energéticos tiene mayor relevancia cuando se toma en cuenta que uno de los modos de falla más común en los compresores centrífugos es la pérdida o deterioro de la eficiencia.
Tradicionalmente las curvas aerotérmicas referenciales, usadas para establecer la “mejor condición” del compresor, provienen de simulaciones teóricas suministradas por el fabricante, y en algunas ocasiones, de pruebas de aceptación en fábrica, pero rara vez provienen de las pruebas de aceptación en campo, que son las más idóneas.
Este artículo cubre el marco teórico sobre el cual se basan los cálculos aerotérmicos, menciona los requerimientos de instrumentación, equipos y personal involucrados, explica el efecto de la propagación de errores de las mediciones sobre la incertidumbre de las variables calculadas, y establece los procedimientos necesarios para garantizar la ejecución exitosa de las pruebas de aceptación de campo. Se incluyen finalmente algunos casos reales donde se ha aplicado la técnica.

Due to development in fields of materials and power electronics, use of high-speed electrical machines has boosted significantly in recent decades. They are widely used in number of applications, such as electrically assisted turbochargers, flywheel energy storage systems, spindle applications, turbo molecular pumps, micro gas turbines. In applications where high efficiency and high power density are required, the most suitable machine type for high-speed operations is a permanent magnet (PM) machine. In this paper the performance of several different topologies of high-speed PM machines required for use in a micro-gas turbine application are evaluated. Different winding topologies, retaining sleeve materials and magnetization patterns are considered, where the main criterion for the machine performance are eddy current losses in the rotor. Influence of time harmonics in stator currents caused by the inverter Pulse Width Modulation (PWM) is incorporated in the calculation.

Computations of the blade loading and the local flow field around the Model Rotor Experiments In Controlled Conditions (MEXICO) rotor are presented using an actuator line method, implemented within the open source code OpenFOAM. The nacelle and near wake mesh refinement are shown to have little influence on the computed blade loads but a significant impact on the near wake flow field. In addition, the blade loads and near wake flow field calculated with 3 different distributions of the Gaussian smearing parameter ǫ are compared with experimental measurements. Local chord and lift coefficient scaled smearing distributions are shown to yield a significant improvement in the representation of the computed tip vortices and also a small improvement in the blade loading prediction, when compared with a spanwise constant smearing distribution. Despite these improvements in performance prediction, the performance of the rotor is shown to be more strongly influenced by the tip correction fac...

The aim of the article is to propose a robust and reliable engineering method for identifying and characterizing vortical structures within a flow field measured with a classic two-component PIV measurement system. Some of the most popular vortex-detection criteria are briefly presented for comparison purposes. Many of these fail if spurious vectors are present within the flow field due to poor PIV image quality. The proposed method was tested both on synthetic images of ideal vortices, having different spatial resolutions and different noise levels in order to perform a parametric assessment, and on real PIV images of a four-bladed rotor wake.

Computations of the blade loading and local flow field around the Model Rotor Experiments In Controlled Conditions (MEXICO) rotor are presented using an actuator line method, implemented within the open source code OpenFOAM. The nacelle and near wake mesh refinement are shown to have little influence on the computed blade loads but a significant impact on the near wake flow field. In addition, the blade loads and near wake flow field calculated with 3 different distributions of the Gaussian smearing parameter are compared with experimental measurements. Local chord and lift coefficient based smearing distributions are shown to yield a significant improvement in the representation of the computed tip vortices and also a small improvement in the blade loading prediction, when compared with a spanwise constant smearing distribution. Despite these improvements in performance prediction, the performance of the rotor is shown to be more strongly influenced by the tip correction factor, where considerable improvement is still required before actuator line methods can represent real rotors with sufficient accuracy.

A new class of drill strings is investigated whereby strategically designed and placed periodic inserts are utilized to filter out the vibration transmission along the drill strings. Such mechanical filtering capabilities allow the vibrations to propagate along the periodic drill string only within specific frequency bands called the 'pass bands' and completely block it within other frequency bands called the 'stop bands'. The design and the location of the inserts are selected to confine the dominant modes of vibration of the drill string within the stop bands generated by the periodic arrangement of the inserts in order to completely block the propagation of the vibrations. A finite element model (FEM) that simulates the operation of this new class of drill strings is developed to describe the complex nature of the vibration encountered during drilling operations. Experimental prototype of the passive periodic drill string was built and tested to demonstrate the feasibility and effectiveness of the concept of periodic drill string in mitigating undesirable vibrations. The experimental results are used to validate the developed theoretical model and to develop a scalable design tool that can be used to predict the dynamical behavior of this new class of drill strings.

In this paper a new continuous model for flexural vibration of rotors with an open edge crack has been developed. The cracked rotor is considered in the rotating coordinate system attached to it. Therefore, the rotor bending can be decomposed in two perpendicular directions. Two quasi-linear displacement fields are assumed for these two directions and the strain and stress fields are calculated in each direction. Then the final displacement and stress fields are obtained by composing the displacement and stress fields in the two directions. The governing equation of motion for the rotor has been obtained using the Hamilton principle and solved using a modified Galerkin method. The free vibration has been analyzed and the critical speeds have been calculated. Results are compared with the finite element results and an excellent agreement is observed.

We review here three experiments performed (in 2014-2016) at ID18 of ESRF to measure the influence of acceleration on time dilation by measuring the relative shift between the absorption lines of two states of the same rotating absorber with accelerations anti-parallel and parallel to the incident beam. Statistically significant data PREPRINT: Journal of Synchrotron Radiation A Journal of the International Union of Crystallography 2 for rotation frequencies up to 510Hz in both directions of rotation were collected. For each run with high rotation, a stable statistically significant "vibration free" relative shift between the absorption lines of the two states was measured. This may indicate the influence of acceleration on time dilation. However, the measured relative shift was also affected by the use of a slit necessary to focus the beam to the axis of rotation to a focal spot of sub-micron size. The introduction of the slit broke the symmetry in the absorption lines due to the Nuclear Lighthouse Effect and affected the measured relative shift, preventing to claim conclusively the influence of acceleration on time dilation. Assuming that this loss of symmetry is of first order, the zero value of the relative shift, corrected for this loss, falls always within the experimental error limits, as predicted by Einstein's Clock Hypothesis. The requirements and an indispensable plan for a conclusive experiment, once the improved technology will be available, is presented. This will be useful to future exper-imentalists wishing to pursue this experiment or a related rotor experiment involving a Mössbauer absorber and a SMS.

Helicopter blade-vortex interaction noise is one of the most severe noise sources and is very important both in community annoyance and military detection. Research over the decades has substantially improved basic physical understanding of the mechanisms generating rotor blade-vortex interaction noise and also of controlling techniques, particularly using active rotor control technology. This paper reviews active rotor control techniques currently available for rotor blade-vortex interaction noise reduction, including higher harmonic pitch control, individual blade control, and on-blade control technologies. Basic physical mechanisms of each active control technique are reviewed in terms of noise reduction mechanism and controlling aerodynamic or structural parameters of a blade. Active rotor control techniques using smart structures/materials are discussed, including distributed smart actuators to induce local torsional or flapping deformations.

In this work the effects of the electromechanical interaction on rotordynamics and vibration characteristics of cage rotor electrical machines were considered. An eccentric rotor motion distorts the electromagnetic field in the air-gap between the stator and rotor inducing a total force, the unbalanced magnetic pull, exerted on the rotor. In this paper a low-order parametric model for the unbalanced magnetic pull is coupled with a three-dimensional finite element structural model of the electrical machine. The main contribution of the work is to present a computationally efficient electromechanical model for vibration analysis of cage rotor machines. In this model, the interaction between the mechanical and electromagnetic systems is distributed over the air gap of the machine. This enables the inclusion of rotor and stator deflections into the analysis and, thus, yields more realistic prediction for the effects of electromechanical interaction. The model was tested by implementing ...

The aim of the article is to propose a robust and reliable engineering method for identifying and characterizing vortical structures within a flow field measured with a classic two-component PIV measurement system. Some of the most popular vortex-detection criteria are briefly presented for comparison purposes. Many of these fail if spurious vectors are present within the flow field due to poor PIV image quality. The proposed method was tested both on synthetic images of ideal vortices, having different spatial resolutions and different noise levels in order to perform a parametric assessment, and on real PIV images of a four-bladed rotor wake.

The positive benefits of early faults detection in rotating systems have led scientists to develop automated methods. Although unbalancing is the most prevalent defect in rotor systems, this fault normally is accompanied by other defects such as crack. In this article, an effective self-acting procedure is addressed in identifying shallow cracks in rotor systems throughout the steady-state operation. To classify rotor systems suffering cracks with three various depths, firstly, healthy and cracked systems are modeled by employing the finite element method (FEM). In the following, systems' vibration signals are calculated in different situations numerically; for pre-processing stage, the persistence spectrum is implemented. Finally, by using a supervised convolutional neural network (CNN), rotor systems are classified by regarding the crack depths. The result of the testing step revealed that this hybrid method has rational capacity in distinguishing shallow cracks in steady-state operation where many other methods are somehow powerless.

Temporary Rotor Bow occurs with centrifugal compressors during start- up  after a short shutdown and may lead to severe damage to compressor internals .High synchronous (1x) vibration at 1st resonance speed cause a high probability of rubs particularly in rotor mid span area . Detection of rotor bow based on phase amplitude plots and  comparator logic and mitigation are proposed.