RELIABILITY SENSITIVITY FOR ROTOR-STATOR SYSTEMS WITH RUBBING

On the basis of the dynamic equations of the Jeffcott rotor-stator model with imbalance, the reliability sensitivity of the rotor-stator systems with rubbing is examined. A statistical fourth moment method is developed to determine the first four moments of system response and state function. The distribution function of the system state function is approximately determined by the standard normal distribution functions using the Edgeworth series technique. The reliability and reliability sensitivity are obtained and the effect on reliability and reliability sensitivity of shaft stiffness and damping, stator stiffness and damping, radial clearance and stator radial stiffness is studied. Numerical results are also presented and discussed.     

Comparaisons entre simulations directes et modélisation κ-ε pour les écoulements dans une cavité interdisques en configuration rotor-stator

The structure of turbulent flow within a rotor-stator enclosure is investigated using two different methodologies. The first one consists of integrating the unsteady Navier-Stokes equations to determine its statistical moments. The numerical algorithm integrates the equations in stream function-vorticity formulation using second order space centred approximations and a second order time stepping scheme. This algorithm was implemented on a parallel machine through an algebraic multi domain decomposition technique. The second consists of integrating the Reynolds averaged equations with a κ-ε model accounting for rotation effects. After a brief discussion of the space-time structure of the unsteady solutions, comparisons between the results produced by both methods are performed. We analyze the differences on the turbulence kinetic budgets whose main consequence is an underestimation of the angular velocity in the core region.     

Integrated design of piezoelectric damping system for flexible structure

This paper aims at developing an integrated design method of the active/passive hybrid type of piezoelectric damping system for reducing the dynamic response of the flexible structures due to external dynamic loads. The design method is based on the numerical optimization technique whose objective function is a control effort of the active damping. A vibration suppression performance, which is evaluated by the maximum value of the gain of the frequency response function of the structure, is constrained. In order to demonstrate the structural damping capability of the hybrid type of piezoelectric damping system designed by proposed method, numerical simulation and laboratory experiment will be done using a three-story flexible structure model equipped with 12 surface bonded PZT tiles pairs. Both numerical and experimental results indicate that the optimally designed hybrid piezoelectric damping system can be successfully achieving excellent performance as compared to a conventional purely active piezoelectric damping system.     

Diagnosis of continuous rotor-stator rubbing in large scale turbine units using acoustic emissions

Continuous rubbing between the shaft and surrounding seals or end-glands of electricity generating turbine units can escalate into very severe vibration and costly rotor damage. Therefore such rotor-stator contacts require early diagnosis so as to minimize the financial consequences of any unplanned shutdowns. Acoustic emissions (AEs) or stress wave monitoring at the bearings has been identified as a sensitive non-destructive monitoring technique for such rub conditions [Electr. Eng. Jpn. 110(2) (1990); IEEE Proc. 6 (2000) 79; Hall and Mba, 14th International Congress on Condition Monitoring and Diagnostic Engineering Management (COMADEM’2001), Manchester, UK, 2001, p. 21]. However, experimental results from real turbines have been scarce. This paper presents a diagnosis of continuous rotor-stator rubbing in an operational 500 MW turbine unit via high frequency AE measurement within a 100 KHz-1 MHz ultrasonic band. As detailed by Sato [Electr. Eng. Jpn. 110(2) (1990)] and reported in this paper the onset of a continuous rub contact at a seal/gland was revealed by a sinusoidal modulation within the raw ‘rf’ AE response. By synchronous measurement at adjacent bearings, an estimation of the location of the rub was calculated using the phase delay between the adjacent AE modulations. Importantly, the AE diagnosis was closely corroborated by post-inspection of the turbine rotor.     

Hilber-Hughes-Taylor-α法在接触约束多体系统动力学中的应用

以柔性梁在重力作用下绕转动铰做大范围定轴转动,并与刚性平面发生碰撞这一动力学过程为例,对Hilber-Hughes-Taylor(HHT-α)法在求解含接触约束的柔性多体系统动力学方程时的数值特性进行了研究.系统运动过程的全局动力学仿真由常微分方程组和微分-代数方程组的数值求解构成.柔性梁在无碰撞阶段系统动力学方程是一组常微分方程组.采用接触约束法模拟接触约束过程,系统的动力学方程为指标3的微分-代数方程组.采用HHT-α法对的该微分-代数方程组进行求解,并与Baumgarte违约修正法进行比较.分析了HHT-α法自由参数和违约修正常数对计算效率、动力学响应和系统机械能的影响,并对数值积分方法对模态截断数的敏感度以及速度约束和加速度约束的违约程度进行了分析.结果表明,违约修正常数对仿真结果影响非常明显,而HHT-α法的自由参数α对动力学响应的影响较小,从而避免了违约修正常数对数值积分结果的影响.HHT-α法的自由参数α可以消除碰撞高频模态的影响.     

Effect of diffusion and fluctuations in the nonequilibrium charge carrier density on the angular distribution of the output intensity for injection lasers based on an InAsSb/InAsSbP heterostructure

We have used numerical modeling to study the effect of diffusion and fluctuations in the nonequilibrium carrier density in the active layer of injection lasers based on an InAsSb/InAsSbP heterostructure on the angular distribution of the output intensity. We show that diffusion smoothes out the nonequilibrium carrier distribution in the active layer, and the fundamental lasing mode is stable over a much broader range of stripe contact widths. At the same time, diffusional processes can lead to formation of local regions with a jump in the density of nonequilibrium charge carriers, fluctuations in which can act as a source of instability for the fundamental lasing mode. Analysis of the numerical modeling results gives qualitative agreement with experimental data on the dependence of the angular distribution of the output radiation for different stripe contact widths.     

The propagation of ultrasound in an austenitic weld

The propagation of ultrasound through an austenitic weld is investigated experimentally as well as in a numerical simulation. The weld is insonified at normal incidence to the fusion line with a longitudinal contact transducer. In order to experimentally trace the ultrasound through the weld, slices of different thicknesses from the original weld have been fabricated. Through-transmission A-scans have then been produced for each weld slice and compared with the corresponding numerical simulation. A comparison of the direction of ultrasound propagation through the weld for the two approaches shows quite good agreement. However, attenuation due to scattering at grain boundaries in the weld is poorly modelled in the simulation. In order to improve this, a better model of the weld is needed.     

A HYBRID FINITE SEGMENT/FINITE ELEMENT MODELLING AND EXPERIMENT ON A FLEXIBLE DEPLOYMENT SYSTEM

This paper focuses on the dynamic responses of a flexible deployment system that has a central rigid body and four articulated flexible beams and undergoes locking impact. A hybrid finite segment/finite element model and an experiment are presented for the deploy-ment system. The flexible beam components in the system are modelled with the finite segments connected by massless beam elements, wherein the finite segments describe the inertia of the large rotation flexible beam and the massless elastic elements describe the elas-ticity of the flexible beam by taking the advantage of small deformation in the relative co-ordinate system. To model the internal impacts in the articulate joints due to clearances, a continuous contact force model of locking joint is also proposed. The governing differential-algebraic equations of the system are established by the Newton-Euler method with Lagrange multipliers and are solved with the method of generalized co-ordinate partitioning. To accelerate the numerical integration, a “longitudinal constraint” is suggested to alleviate the stiff problem of the dynamic equations. In addition, a physical model of the deployment system is constructed. The deployment is released by the compressed springs in the joints. A position measuring system of linear CCD cameras is used to measure the large displacement of the system. Correlations between the mathematical model and the experiments are also presented. Reasonable results are obtained.     

Time-domain prediction of impact noise from wheel flats based on measured profiles

Railway impact noise is caused by discrete rail or wheel irregularities, such as wheel flats, rail joints, switches and crossings. In order to investigate impact noise generation, a time-domain wheel/rail interaction model is needed to take account of nonlinearities in the contact zone. A nonlinear Hertzian contact spring is commonly used for wheel/rail interaction modelling but this is not sufficient to take account of actual surface defects which may include large geometry variations. A time-domain wheel/rail interaction model with a more detailed numerical non-Hertzian contact is developed here and used with surface roughness profiles from field measurements of a test wheel with a flat. The impact vibration response and noise due to the wheel flat are predicted using the numerical model and found to be in good agreement with the measurements. Moreover, compared with the Hertzian theory, a large improvement is found at high frequencies when using the detailed contact model.     

Parameterized reduced order modeling of misaligned stacked disks rotor assemblies

Light and flexible rotating parts of modern turbine engines operating at supercritical speeds necessitate application of more accurate but rather computationally expensive 3D FE modeling techniques. Stacked disks misalignment due to manufacturing variability in the geometry of individual components constitutes a particularly important aspect to be included in the analysis because of its impact on system dynamics. A new parametric model order reduction algorithm is presented to achieve this goal at affordable computational costs. It is shown that the disks misalignment leads to significant changes in nominal system properties that manifest themselves as additional blocks coupling neighboring spatial harmonics in Fourier space. Consequently, the misalignment effects can no longer be accurately modeled as equivalent forces applied to a nominal unperturbed system. The fact that the mode shapes become heavily distorted by extra harmonic content renders the nominal modal projection-based methods inaccurate and thus numerically ineffective in the context of repeated analysis of multiple misalignment realizations. The significant numerical bottleneck is removed by employing an orthogonal projection onto the subspace spanned by first few Fourier harmonic basis vectors. The projected highly sparse systems are shown to accurately approximate the specific misalignment effects, to be inexpensive to solve using direct sparse methods and easy to parameterize with a small set of measurable eccentricity and tilt angle parameters. Selected numerical examples on an industrial scale model are presented to illustrate the accuracy and efficiency of the algorithm implementation.     

Near-field beamforming analysis for acoustic emission source localization

This paper attempts to introduce a near-field acoustic emission (AE) beamforming method to estimate the AE source locations by using a small array of sensors closely placed in a local region. The propagation characteristics of AE signals are investigated based on guided wave theory to discuss the feasibility of using beamforming techniques in AE signal processing. To validate the effectiveness of the AE beamforming method, a series of pencil lead break tests at various regions of a thin steel plate are conducted. The potential of this method for engineering applications are explored through rotor-stator rubbing tests. The experimental results demonstrate that the proposed method can effectively determine the region where rubbing occurs. It is expected that the work of this paper may provide a helpful analysis tool for near-field AE source localization.     

A simplified model to explore the root cause of stick-slip vibrations in drilling systems with drag bits

In this paper a study of the self-excited stick-slip oscillations of a rotary drilling system with a drag bit, using a discrete model that takes into consideration the axial and torsional vibration modes of the system, is described. Coupling between these two vibration modes takes place through a bit-rock interaction law, which accounts for both the frictional contact and the cutting processes. The cutting process introduces a delay in the equations of motion that is responsible for the existence of self-excited vibrations, which can degenerate into stick-slip oscillations and/or bit bouncing under certain conditions. From analysis of this new model it is concluded that the experimentally observed decrease of the reacting torque with the angular velocity is actually an expression of the system response, rather than an intrinsic rate dependence of the interface laws between the rock and the drill bit, as is commonly assumed.     

Dynamic train-track interaction at high vehicle speeds—Modelling of wheelset dynamics and wheel rotation

Vertical dynamic train-track interaction at high vehicle speeds is investigated in a frequency range from about 20 Hz to 2.5 kHz. The inertial effects due to wheel rotation are accounted for in the vehicle model by implementing a structural dynamics model of a rotating wheelset. Calculated wheel-rail contact forces using the flexible, rotating wheelset model are compared with contact forces based on rigid, non-rotating models. For a validation of the train-track interaction model, calculated contact forces are compared with contact forces measured using an instrumented wheelset. When the system is excited at a frequency where two different wheelset mode shapes, due to the wheel rotation, have coinciding resonance frequencies, significant differences are found in the contact forces calculated with the rotating and non-rotating wheelset models. Further, the use of a flexible, rotating wheelset model is recommended for load cases leading to large magnitude contact force components in the high-frequency range (above 1.5 kHz). In particular, the influence of the radial wheel eigenmodes with two or three nodal diameters is significant.     

Fabrication of durable hydrophobic surfaces through surface texturing

Low surface energy polymer thin-films can be applied to surfaces to increase hydrophobicity and reduce friction for a variety of applications. However, wear of these thin films, resulting from repetitive rubbing against another surface, is of great concern. In this study, we show that highly hydrophobic surfaces with persistent abrasion resistance can be fabricated by depositing fluorinated carbon thin films on sandblasted glass surfaces. In our study, fluorinated carbon thin films were deposited on sandblasted and as-received smooth glass using deep reactive ion etching equipment by only activating the passivation step. The surfaces of the samples were then rubbed with FibrMet abrasive papers in a reciprocating motion using an automatic friction abrasion analyzer. During the rubbing, the static and kinetic friction forces were also measured. The surface wetting properties were then characterized using a video-based contact angle measuring system to determine the changes in water contact angle as a result of rubbing. Assessment of the wear properties of the thin films was based on the changes in the water contact angles of the coated surfaces after repetitive rubbing. It was found that, for sandblasted glass coated with fluorinated carbon film, the water contact angle remained constant throughout the entire rubbing process, contrary to the smooth glass coated with fluorinated carbon film which showed a drastic decrease in water contact angle with the increasing number of rubbing cycles. In addition, the static and kinetic friction coefficients of the sandblasted glass were also much lower than those of the smooth glass.     

Dynamics of a laminated composite beam with delamination and inclusions

In this work numerical and experimental study of the dynamic behaviour of a composite laminated beam having delamination is presented. The model of delamination takes into account a contact interaction between sublaminates including normal forces, shear forces and additional damping. In order to verify the model special samples of multilayered beams have been manufactured. Small parts of adjacent layers have been cut and replaced by inclusions from different materials modelling delamination. The mechanical properties of the inclusions have been considered during the numerical calculations. The beams were subjected to a short pulse loading and then their response was registered. The results from the numerical simulation were in a good agreement with the experimental results. The significance of the additional damping due to delamination on the response of the beam was confirmed numerically and experimentally.     

Flexural wave dispersion in orthotropic plates with heavy fluid loading

Orthotropic plates support flexural waves with wavenumbers that depend on their angle of propagation. The present work investigates the effect of fluid loading on this angular dependence, and finds that the effect is relatively small for typical composite plate materials in contact with water. This finding results from an analytical model of the fluid-loaded plate, in which the plate is modeled by classical laminated plate theory and the fluid is modeled as an ideal acoustic fluid. The resulting dispersion relation is a tenth-order polynomial in the flexural wavenumber. Direct numerical solution, as well as analysis at frequencies below coincidence, reveals that the angular dependence of wavenumber is magnified but not significantly distorted by the addition of fluid loading.     

Vibrations of a rolling tyre

We investigate vibrations of an unloaded and loaded tyre rolling at constant speed without slipping in the contact area. A previously proposed analytical model of a reinforced tyre is considered. The surface of the tyre is represented by flexible tread, combined with parts of two tori (sidewalls of the tyre). The contact between the wheel and the ground plane occurs by the part of the tread. The natural frequencies (NF) and mode shapes (MS) are determined analytically for unloaded tyre and numerically for loaded tyre. The results were compared with experiments for the non-rotating tyre. In the case of loaded rotating tyre, the increasing of the angular velocity of rotation implies that NF decrease. Moreover, a phenomenon of frequency loci veering is visible here: NF as functions of angular velocity approach each other and then veer away instead of crossing. The MS interact in veering region and, as a result, interchange.     

The global responses characteristics of a rotor/stator rubbing system with dry friction effects

Rotor/stator rubbing systems may undertake a number of quite different responses. Recent experiments on rotor/stator rubbing have revealed that two or three different responses may coexist. In this paper the global response characteristics of a general rotor/stator rubbing system, which takes into account the dominant factors in the process of rotor/stator rubbing, especially, the dry friction effect that is mostly neglected in the previous works and is the main factor for the self-excited dry friction backward whirl, are studied. The different solutions of the piecewise nonlinear system are derived and their stability are analyzed to get the existence boundaries of the different responses. An overall picture of the global response characteristics of this model is then obtained by drawing the existence boundaries in a same parameter space. The present results provide good understanding on the coexistence of different rubbing responses observed in tests. Moreover, deeper insight into the types of coexistence of different rubbing responses and their relationship with the system parameters is gained.