Vibration localization for a rotating mistuning bladed disk with the Coriolis effect by a state-space decoupling method

2017 ◽  
Vol 233 (3) ◽  
pp. 1011-1020 ◽  
Author(s):  
Xuanen Kan ◽  
Zili Xu
Keyword(s):  
State Space ◽  
Natural Frequency ◽  
Coriolis Force ◽  
High Speed ◽  
Forced Response ◽  
Coriolis Effect ◽  
Decoupling Method ◽  
Resonant Amplitude ◽  
Bladed Disk ◽  
Localization Factor

Slight deviations of blades due to manufacturing tolerances can cause mistuning of bladed disk leading to localized vibration, which can accelerate fatigue. Moreover, the rotating blades are subjected to the Coriolis effect and the influence of the Coriolis force on the natural frequencies of high-speed rotational bladed disks such as those of an aero-engine become more apparent. In this paper, the effect of Coriolis force on the forced response localization of a mistuned bladed disk are investigated, for conditions where the natural frequency located in the first and second modal families of the bladed disk. Mistuning is introduced by varying the Young’s modulus of each blade. Due to the asymmetric Coriolis matrix, it is not possible to directly decouple the system. A state-space decoupling method is developed to decouple the system to effectively calculate the forced response of bladed disk with the consideration of the Coriolis effect. The results show that response localization factor is increased by 13.09% considering the Coriolis force compared to the system without considering the Coriolis effect, in the case of where the first modal family is considered. In addition, the response localization factor with the consideration of the Coriolis force is decreased by 30.85% compared to the system without considering the Coriolis force, when the second modal family is considered. It indicates that the forced response localization with the consideration of the Coriolis effect will be changed obviously with the rotational speed increasing, when the concerning natural frequency is located in the first and second modal families. Furthermore, the effect of Coriolis force causes changes in the resonant frequencies and resonant amplitude, but does not introduce additional resonant peaks for the case of the mistuned bladed disk.

Study on Vibration Response Characteristics of Mistuned Bladed Disk Expressed by Vibratory Stress

2019 ◽  
Author(s):  
Yasutomu Kaneko ◽  
Toshio Watanabe ◽  
Tatsuya Furukawa ◽  
Saiji Washio
Keyword(s):  
Amplification Factor ◽  
Harmonic Excitation ◽  
Forced Response ◽  
Von Mises Stress ◽  
Bladed Disks ◽  
Resonant Amplitude ◽  
Response Characteristics ◽  
Bladed Disk ◽  
Disk Structure ◽  
Von Mises

Abstract Although bladed disks of turbomachinery are nominally designed to be cyclically symmetric (tuned system), the vibration characteristics of individual blades on a disk differ slightly owing to manufacturing tolerance, deviation of material properties, wear during operation, etc. These small variations break cyclic symmetry and split eigenvalue pairs. Actual bladed disks with small variations are called mistuned systems. Many researchers have studied mistuning and the main conclusion is that while mistuning has an undesirable effect on forced response, it has a beneficial effect on blade flutter. Although mistuning phenomena have been studied since the 1980s, studies on forced response are mostly related to increase in the resonant amplitude due to harmonic excitation force. In addition, because few papers have treated the amplification factor expressed in terms of vibratory stress, the mistuning phenomena of bladed disks expressed in terms of vibratory stress are not fully understood. In this study, the mistuning effect expressed in terms of vibratory stress is examined using the reduced-order model SNM (Subset of Nominal Modes) without any assumptions. By comparing the amplification factor expressed in terms of displacement response with that expressed in terms of vibratory stress response, including synthesized stress (von Mises stress and principal stress), the mistuning phenomena expressed in terms of vibratory stress are clarified. The effect of bladed disk structure on amplification factor is examined in detail as well.

scholarly journals Vibration Characteristics of a Mistuned Bladed Disk considering the Effect of Coriolis Forces

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Xuanen Kan ◽  
Bo Zhao
Keyword(s):  
Coriolis Force ◽  
Rotational Speed ◽  
Natural Frequencies ◽  
Forced Response ◽  
Vibration Characteristics ◽  
Magnification Factor ◽  
Coriolis Forces ◽  
Rotating Speed ◽  
Bladed Disk ◽  
Coriolis Effects

To investigate the influence of Coriolis force on vibration characteristics of mistuned bladed disk, a bladed disk with 22 blades is employed and the effects of different rotational speeds and excitation engine orders on the maximum forced response are discussed considering the effects of Coriolis forces. The results show that if there are frequency veering regions, the largest split of double natural frequencies of each modal family considering the effects of Coriolis forces appears at frequency veering region. In addition, the amplitude magnification factor considering the Coriolis effects is increased by 1.02% compared to the system without considering the Coriolis effects as the rotating speed is 3000 rpm, while the amplitude magnification factor is increased by 2.76% as the rotating speed is 10000 rpm. The results indicate that the amplitude magnification factor may be moderately enhanced with the increasing of rotating speed. Moreover, the position of the maximum forced response of bladed disk may shift from one blade to another with the increasing of the rotational speed, when the effects of Coriolis forces are considered.

Forced Response Analysis of Mistuned Turbine Bladings

2010 ◽  
Author(s):  
Christian Siewert ◽  
Heinrich Stu¨er
Keyword(s):  
Natural Frequency ◽  
Stiffness Matrix ◽  
Natural Frequencies ◽  
Forced Response ◽  
Response Analysis ◽  
Vibrational Behavior ◽  
Bladed Disk ◽  
Fundamental Model ◽  
Mechanical Models ◽  
Number Of Publications

It is well-known that the vibrational behavior of a mistuned bladed disk differs strongly from that of a tuned bladed disk. A large number of publications dealing with the dynamics of a mis-tuned bladed disk is available in the literature. Nearly all published mechanical models for a mistuned bladed disk consider the mistuning in terms of a perturbation of the mass and/or the stiffness matrix or in terms of a perturbation of the tuned system natural frequencies. Therefore, the possible effect of a damping mistuning is neglected in these models. In this paper, a model of a mistuned bladed disk with a combined damping and natural frequency mistuning is presented. This model is based on the well-known Fundamental Model of Mistuning with a novel extension to include the damping mistuning in a straight-forward way.

Effect of coriolis force on forced response magnification of intentionally mistuned bladed disk

2017 ◽  
Vol 399 ◽  
pp. 124-136 ◽  
Author(s):  
Xuanen Kan ◽  
Zili Xu ◽  
Bo Zhao ◽  
Jize Zhong
Keyword(s):  
Coriolis Force ◽  
Forced Response ◽  
Bladed Disk

scholarly journals Design and Fabrication of a High-Speed Atomic Force Microscope Scan-Head

Sensors ◽  
2021 ◽  
Vol 21 (2) ◽  
pp. 362
Author(s):  
Luke Oduor Otieno ◽  
Bernard Ouma Alunda ◽  
Jaehyun Kim ◽  
Yong Joong Lee
Keyword(s):  
Atomic Force Microscope ◽  
Natural Frequency ◽  
High Speed ◽  
Contact Mode ◽  
Ongoing Process ◽  
Atomic Force ◽  
Constant Height ◽  
Mode Tracking

A high-speed atomic force microscope (HS-AFM) requires a specialized set of hardware and software and therefore improving video-rate HS-AFMs for general applications is an ongoing process. To improve the imaging rate of an AFM, all components have to be carefully redesigned since the slowest component determines the overall bandwidth of the instrument. In this work, we present a design of a compact HS-AFM scan-head featuring minimal loading on the Z-scanner. Using a custom-programmed controller and a high-speed lateral scanner, we demonstrate its working by obtaining topographic images of Blu-ray disk data tracks in contact- and tapping-modes. Images acquired using a contact-mode cantilever with a natural frequency of 60 kHz in constant deflection mode show good tracking of topography at 400 Hz. In constant height mode, tracking of topography is demonstrated at rates up to 1.9 kHz for the scan size of 1μm×1μm with 100×100 pixels.

A Method for Use of Cyclic Symmetry Properties in Analysis of Nonlinear Multiharmonic Vibrations of Bladed Disks

2004 ◽  
Vol 126 (1) ◽  
pp. 175-183 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
High Efficiency ◽  
Equations Of Motion ◽  
Linear Part ◽  
Forced Response ◽  
Mode Shapes ◽  
Solution Technique ◽  
Disk Model ◽  
Sector Model ◽  
Bladed Disk ◽  
Symmetry Properties

An effective method for analysis of periodic forced response of nonlinear cyclically symmetric structures has been developed. The method allows multiharmonic forced response to be calculated for a whole bladed disk using a periodic sector model without any loss of accuracy in calculations and modeling. A rigorous proof of the validity of the reduction of the whole nonlinear structure to a sector is provided. Types of bladed disk forcing for which the method may be applied are formulated. A multiharmonic formulation and a solution technique for equations of motion have been derived for two cases of description for a linear part of the bladed disk model: (i) using sector finite element matrices and (ii) using sector mode shapes and frequencies. Calculations validating the developed method and a numerical investigation of a realistic high-pressure turbine bladed disk with shrouds have demonstrated the high efficiency of the method.

Weakfish sonic muscle: influence of size, temperature and season

2002 ◽  
Vol 205 (15) ◽  
pp. 2183-2188 ◽  
Author(s):  
M. A. Connaughton ◽  
M. L. Fine ◽  
M. H. Taylor
Keyword(s):  
Natural Frequency ◽  
Pulse Duration ◽  
Dominant Frequency ◽  
Forced Response ◽  
Acoustic Energy ◽  
Honest Signal ◽  
Muscle Twitch ◽  
Cross Sectional ◽  
Fish Size ◽  
Sonic Muscle

SUMMARYThe influence of temperature, size and season on the sounds produced by the sonic muscles of the weakfish Cynoscion regalis are categorized and used to formulate a hypothesis about the mechanism of sound generation by the sonic muscle and swimbladder. Sounds produced by male weakfish occur at the time and location of spawning and have been observed in courtship in captivity. Each call includes a series of 6-10 sound pulses, and each pulse expresses a damped, 2-3 cycle acoustic waveform generated by single simultaneous twitches of the bilateral sonic muscles. The sonic muscles triple in mass during the spawning season, and this hypertrophy is initiated by rising testosterone levels that trigger increases in myofibrillar and sarcoplasmic cross-sectional area of sonic muscle fibers. In response to increasing temperature, sound pressure level (SPL), dominant frequency and repetition rate increase, and pulse duration decreases. Likewise, SPL and pulse duration increase and dominant frequency decreases with fish size. Changes in acoustic parameters with fish size suggest the possibility that drumming sounds act as an `honest' signal of male fitness during courtship. These parameters also correlate with seasonally increasing sonic muscle mass. We hypothesize that sonic muscle twitch duration rather than the resonant frequency of the swimbladder determines dominant frequency. The brief (3.5 ms), rapidly decaying acoustic pulses reflect a low-Q, broadly tuned resonator, suggesting that dominant frequency is determined by the forced response of the swimbladder to sonic muscle contractions. The changing dominant frequency with temperature in fish of the same size further suggests that frequency is not determined by the natural frequency of the bladder because temperature is unlikely to affect resonance. Finally, dominant frequency correlates with pulse duration (reflecting muscle twitch duration),and the inverse of the period of the second cycle of acoustic energy approximates the recorded frequency. This paper demonstrates for the first time that the dominant frequency of a fish sound produced by a single muscle twitch is apparently determined by the velocity of the muscle twitch rather than the natural frequency of the swimbladder.

The Effect of Non-Uniform Aerodynamic Loading on the Blade Responses

2007 ◽  
Author(s):  
Abdelgadir M. Mahmoud ◽  
Mohd S. Leong
Keyword(s):  
Turbine Blades ◽  
Forced Response ◽  
Flow Section ◽  
Flow Distortion ◽  
Inlet Flow ◽  
Bladed Disk ◽  
Aerodynamic Loading ◽  
Bladed Disk Assembly ◽  
Flow Generator ◽  
Inlet Flow Distortion

Turbine blades are always subjected to severe aerodynamic loading. The aerodynamic loading is uniform and Of harmonic nature. The harmonic nature depends on the rotor speed and number of nozzles (vanes counts). This harmonic loading is the main sources responsible for blade excitation. In some circumstances, the aerodynamic loading is not uniform and varies circumferentially. This paper discussed the effect of the non-uniform aerodynamic loading on the blade vibrational responses. The work involved the experimental study of forced response amplitude of model blades due to inlet flow distortion in the presence of airflow. This controlled inlet flow distortion therefore represents a nearly realistic environment involving rotating blades in the presence of airflow. A test rig was fabricated consisting of a rotating bladed disk assembly, an inlet flow section (where flow could be controlled or distorted in an incremental manner), flow conditioning module and an aerodynamic flow generator (air suction module with an intake fan) for investigations under laboratory conditions. Tests were undertaken for a combination of different air-flow velocities and blade rotational speeds. The experimental results showed that when the blades were subjected to unsteady aerodynamic loading, the responses of the blades increased and new frequencies were excited. The magnitude of the responses and the responses that corresponding to these new excited frequencies increased with the increase in the airflow velocity. Moreover, as the flow velocity increased the number of the newly excited frequency increased.

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