Interference Diagram Research Articles

Forced response in a multi-stage aeroderivative axial compressor with acoustic excitations: Method validation with field data

This paper presents the application of a forced response prediction process to an industrial aeroderivative axial compressor and its validation against experimental data. The forced response process is based on a dedicated strategy to decompose the overall unsteady aerodynamic forcing coming from URANS analyses, and an improved use of the interference diagram to detect additional acoustic forcing in the entire operating range. The identification of potential resonance conditions, or crossings, in the interference diagram is based on the assumptions of a cyclic symmetry tuned structure and a forcing function having an aliased engine order driven only by the airfoil count of the rotor/stator interactions of interest. Despite this, it is not rare that unexpected resonances appear during compressor validation tests, often calling for painful and time-consuming redesigns. This is witnessed by the unsteady analysis of an 11-stage axial compressor in which the spatial content of engine order forcing is influenced also by further rotor/stator interactions by means of Tyler-Sofrin acoustic modes that cause the onset of additional crossing conditions.The theory based on time and space decomposition is validated with full 3D unsteady forced response simulations of the entire multistage compressor. Numerical results, obtained by an in-house modal work approach, are compared with experimental data focusing on two resonances, the first of which can be detected by the classical interference diagram, while the second one is justified only by the improved use that considers the acoustic excitations. In both cases, the predicted blade responses are in good agreement with measurements.The theory associated with the generation mechanism of the additional nodal diameters is further explained using the results of dedicated numerical experiments conducted by changing the relative stator and rotor airfoil count on a reduced compressor domain.

Modulation of Daily Rainfall in Southern Vietnam by the Madden–Julian Oscillation and Convectively Coupled Equatorial Waves

Abstract Rainfall extremes have a large socioeconomic relevance for southern Vietnam. More than 30 million people live in this low-lying, flood-prone region in Southeast Asia. In this study the influence of the Madden–Julian oscillation (MJO) and convectively coupled equatorial waves on the modulation of daily rainfall during the rainy season (May–October) is evaluated and quantified using an extensive station database and the gridded Asian Precipitation–Highly Resolved Observational Data Integration Toward Evaluation of Water Resources (APHRODITE) product for different phases of the equatorial waves. The MJO, Kelvin, and equatorial Rossby (ER) waves significantly modulate daily rainfall in Vietnam south of 16°N. The MJO shows the most coherent signals across the region, followed by ER waves, whose influence is strongest in central Vietnam; Kelvin waves only affect the southern parts of Vietnam. For all waves, the frequency of occurrence of intense daily rainfall larger than 25 mm is significantly enhanced during wet phases, whereas the magnitude of rainfall anomalies is related to the wave’s amplitude only in the MJO and ER cases. A novel wave interference diagram reveals strong positive interferences of dry and wet anomalies when the MJO occurs concurrently with Kelvin and ER waves. In terms of causes of rainfall anomalies, the waves modulate tropospheric moisture convergence over the region, but a strong influence on the depth of the monsoon flow and the vertical wind shear is discernible from radiosonde data only for the MJO. The results suggest new opportunities for submonthly prediction of dry and wet spells in Indochina.

Fatigue Strength Analysis of Compressor Impeller under Non-typical Aerodynamic Load

The frequency characteristics of aerodynamic load and the resonance of compressor impeller are studied for the fatigue failure of compressor impeller.The frequency,amplitude and phase of aerodynamic load are obtained from the unsteady computational fluid dynamics(CFD) results of compressor impeller using fast Fourier transform(FFT).The aerodynamic excitation phase between adjacent blades is analyzed in detail.For typical load with cyclic symmetric distribution of phase difference between adjacent blades,the interference diagram is used to determine the resonance modal.For non-typical load with non-cyclic symmetric distribution of phase difference,the resonance modal is determined by the result of dynamic stress in all nodal diameters under aerodynamic excitation frequency.Fatigue analysis is performed based on the static stress and resonance dynamic stress of impeller,which shows that the predicted fatigue position matches with the actual crack position.The zero nodal diameter resonance excited by non-typical fluid load with non-cyclic symmetric distribution of phase difference is proved to be the main cause of impeller fatigue failure.

Analytical investigation of the SAFE diagram for bladed wheels, numerical and experimental validation

Compressor and turbine bladed wheels interact with the fluid distributed by the stator vanes. They are subject to vibration and fatigue loading, especially when resonance conditions are excited. Avoiding resonance is fundamental when designing bladed wheels. The Campbell diagram approach is too conservative since bladed wheels show many close frequency natural modes, thus it is almost impossible to avoid frequency matching. Singh׳s Advanced Frequency Evaluation (SAFE) diagram, or interference diagram, also introduces shape matching in addition to the frequency, for resonance prediction, therefore many frequency matching cases can be identified as non-critical and thus tolerated. The present paper explains and demonstrates the SAFE diagram by introducing an analytical expression to identify bladed wheel resonance conditions. The mode shape matching with a harmonic component is investigated by means of specific examples. Symmetry properties of the matching distribution of harmonic indices and mode shapes are also introduced and demonstrated. Finally, a bladed wheel analysis is used for validation, both in FE simulations and experiments.

Investigation of blade failure in a gas turbine

A gas turbine abruptly tripped to a stop during its daily morning start-up period. Out of a total of 81 blades in the first row only one blade was broken at its root. Prior to this accident, there were three blade failure accidents in the same plant during the last 10 years. First, the fracture surface of the troubled blade was investigated. Stress analysis of the blade showed that the maximum stress occurred due to the pressure profiles developed during operation. Modal analysis for one blade and the assembly of blades was performed and Campbell diagram and Interference diagram were drawn to check the dynamic characteristics of the blades. The vibration of the turbine was measured using accelerometers during the operation condition. The result shows that the fatigue fracture of the blade was originated during transient events internal to the combustion chamber which was close to the resonance condition of the assembled blades.

증기터빈 저압 L-1단 블레이드-디스크 연성 진동 특성 분석

ABSTRACT This paper studies causes of the L-1 blade damage of a low pressure turbine, which was found during the scheduled maintenance, in 500 MW fossil power plants. Many failures of turbine blades are caused by the coupling of aerodynamic forcing with bladed-disk vibration characteristics. In this study the coupled vibration characteristics of the L-1 turbine bladed-disk in a fossil power plant is shown for the purpose of identifying the root cause of the damage and confirming equipment integrity. First, analytic and experimental modal analysis for the bladed-disk at zero rpm as well as a single blade were performed and analyzed in order to verify the finite element model, and then steady stresses, natural frequencies and corresponding mode shapes, dynamic stresses were calculated for the bladed-disk under operation. Centrifugal force and steady steam force were considered in calculation of steady and dynamic stress. The proximity of modes to sources of excitation was assessed by means of an interference diagram to examine resonances. In addition, fatigue analysis was done for the dangerous modes of operation by a local strain approach. It is expected that these dynamic characteristics will be used effectively to identify the root causes of blade failures and to perform prompt maintenance.

고효율 복합형 진공펌프의 로터다이나믹 해석

A rotordynamic analysis was performed with a dry vacuum pump, which is a major equipment in modern semiconductor and LCD manufacturing processes. The system is composed of screw rotors, lobes picking air, helical gears, driving motor, and support rolling element bearings of rotors and motor. The driving motor-screw rotor system has a rated speed of 6,300 rpm, and was modeled utilizing a rotordynamic FE method for analysis, which was verified through 3-D FE analysis and experimental modal analysis. As loadings on the bearings due to the gear action were significant in the system considered, each resultant bearing load was calculated by considering the generalized forces of the gear action as well as the rotor itself. Each resultant bearing loading was used in calculating each stiffness of rolling element bearings. Design goals are to achieve wide separation margins of lateral and torsional critical speeds, and favorable unbalance responses of the rotor in the operating range. Then, a complex rotordynamic analysis of the system was carried out to evaluate its forward synchronous critical speeds, whirl natural frequencies and mode shapes, unbalance responses under various unbalance locations, and torsional interference diagram. Results show that the entire system is well designed in the operating range. In addition, the procedure of rotordynamic analysis for dry vacuum pump rotor-bearing system was proposed and established.

Feature extraction based on the 3D spectrum analysis of acoustic signals to identify rotor malfunction

The acoustic signals of an operating rotor contain plenty of information about its running condition and can be measured by non-contact devices. Therefore, it is necessary to base fault diagnosis on the acoustic signals of a rotor. In this study, the typical malfunctions of unbalance, looseness, rubbing, misalignment, and abrupt unbalance were simulated in experiments. Acoustic signals were received by BSWA microphones and a 16-channal Sony tape recorder, which were analyzed by 3D spectrum. The sequential spectra can be separated by uniform increments of time or speed. When data is acquired by a relatively slow acceleration with uniform increases in speed, one dimension (the ordinate) is equivalent to the speed of rotation. Thus, the plot demonstrates the frequency versus speed-of-rotation interference diagram. The plot allows the analyst to evaluate the various frequency components of vibration as the machine approaches its operating speed. The abrupt changes in surging sound signals of rotor malfunctions can be detected, and their fault spectrum features are shown in the 3D spectrum. The results demonstrate the potential and feasibility of this approach for the diagnosis of rotor malfunctions.

진동 해석을 통한 300 MW급 저압터빈 블레이드의 손상 원인 규명

The failure of blades frequently happened in the 300 MW LP(low pressure) turbine until now and they are maintaining the blades periodically during outage. So the blade-disk system is analysed by FEM in order to identify the main cause of failure of blade row. It is found that the stress of root's hole is highest in comparison with other parts from the result of the steady stress analysis. Also, the two dangerous frequencies which is related to the resonance condition are found in the interference diagram. One is 1,316 Hz. The other is 2,981 Hz which is related to the 1 nozzle passing frequency. The dynamic stress analysis is performed to identify more accurate root cause for failure of blade row It is confirmed that the dynamic stress of the former is higher than one of the latter From these results, it is concluded that the former has deeply something to do with the failure of blades more than the tatter. Based on versatile investigation and deliberation, the change of blade's grouping is determined to avoid the resonance condition with the operating speed. After the blade grouping is changed, the former frequency vanish completely but the latter is still in existence in the interference diagram. Fortunately, It is confirmed that the dynamic stress of the new blade grouping is lower than one of the old blade grouping. 2 years has passed since modification and the LP turbine is operated well without failure so far.

Two-Handed Assembly Sequencing

This article considers the computational complexity of automat ically determining assembly sequences for mechanical products. Specifically, we address the partitioning problem: given an assembly of rigid parts, identify a proper subassembly that can be removed as a rigid object without disturbing the rest of the assembly. We examine the complexity of the partition ing problem under various types of relative motions allowed for the subassemblies. We show that when arbitrary motions are allowed to separate the two subassemblies, partitioning is NP-complete. We then describe a general framework for reasoning about assembly motions called the interference diagram. In its most general form the interference diagram yields an exponential- time algorithm to partition an assembly. However, two special cases of the interference diagram studied in this article yield polynomial-time sequencing algorithms. The first case occurs when assembly motions are restricted to single translations. The second case considers infinitesimal rigid motions in translation and rotation and yields a superset of all feasible partitionings. These two algorithms have important practical applications in assembly planning.

Reliability Evaluation of Shrouded Blading Using the SAFE Interference Diagram

The SAFE Interference Diagram is shown to be useful in the design reliability evaluation of shrouded blading, including long-arc shrouding construction. This method provides an alternate method to the widely used Campbell diagram and also brings in more information for easier design evaluation. The SAFE diagram uses the natural frequencies of an entire bladed disk rather than individual blade or packet frequencies. In addition, it compares frequencies, mode shapes, and speed to evaluate whether a resonance occurs. Theoretical arguments are provided for the validity of the SAFE Diagram and its usefulness is shown by practical examples. This method provides an easier means to show why long-arc shrouding works and also when it might not.

Oblique-Angle Determination of the Reflection Coefficient R of Flat Sound Absorbers

Methods for determining the reflection coefficient R usually involve the procedure of insonifying the absorbing material at a fixed frequency at the desired angle of incidence. Then, the quantities required for the calculation of R are either measured with a movable receiver probing the interference field in front of the absorber or with a fixed receiver at the proper point to receive specular reflections. (In the latter case, direct rays from the source must be shielded from the receiver.) The method proposed in this paper combines both of the above approaches but is simpler and quicker than either. The receiver is fixed in space and receives both the specular reflections and the direct rays, as the sound source transmits with steadily increasing (or decreasing) frequency. A level recorder connected to the receiver produces a frequency-dependent interference diagram. Keeping the source-receiver configuration unchanged, one generates another such diagram with a perfectly reflecting plane substituted for the sound-absorbing sample. Comparison of the two sets of data yields the quantities necessary for the calculation of R versus frequency. Frequency response and beam pattern of the loudspeaker and microphone used need not be known.