Breathing Crack Model Effect on Rotor's Postresonance Backward Whirl

2020 ◽  
Vol 15 (12) ◽  
Author(s):  
Tariq Alzarooni ◽  
Mohammad A. Al-Shudeifat ◽  
Oleg Shiryayev ◽  
C. Nataraj
Keyword(s):  
Linear Time ◽  
Crack Opening ◽  
Equations Of Motion ◽  
Angular Acceleration ◽  
Crack Model ◽  
Fe Model ◽  
Breathing Crack ◽  
Full Spectrum ◽  
Acceleration Rate ◽  
Backward Whirl

Abstract In this work, we investigate the appearance of postresonance backward whirl (Po-BW) using the model of a rotor with a breathing crack. This phenomenon could be employed as an indicator of crack and bearing damage in rotor systems that undergo recurrent passage through critical forward whirl rotational speed during startup and coast down operations. The finite element (FE) model is used to develop the linear-time-varying equations of motion of the considered accelerating cracked rotor. The whirl response is obtained by direct numerical integration. In addition, the effect of bearing anisotropy on Po-BW excitation is investigated. It is found that the appearance of Po-BW zones is significantly affected by the depth of the crack, angular acceleration rate, anisotropy of bearings, and the orientation of the unbalance force vector with respect to the crack opening direction. The full spectrum analysis (FSA) is also employed and found to be an efficient tool for identifying the Po-BW zones of rotational speeds in the whirl response.

Effect of Angular Acceleration and Unbalance Force Orientation on the Backward Whirl in Cracked Rotors

2018 ◽  
Author(s):  
Fatima K. Alhammadi ◽  
Mohammad A. AL-Shudeifat ◽  
Oleg Shiryayev
Keyword(s):  
Experimental Testing ◽  
Crack Opening ◽  
Real Life ◽  
Angular Acceleration ◽  
Sharp Drop ◽  
Rotating Systems ◽  
Start Up ◽  
Backward Whirl ◽  
Unbalance Force ◽  
Vector Orientation

Rotors have wide applications in several aerospace and industrial heavy-duty systems. In most of these applications, the rotating system reaches its steady state operational speed after the passage through at least one of its critical rotational speeds. In real-life applications, the probable appearance of a residual slight unbalance in the system could cause an elevation in vibration amplitudes at the critical rotational speeds. Accordingly, propagation of cracks in rotating shafts usually influences the level of these vibration amplitudes during start-up and cost-down operations. For such rotating systems, the critical whirl speeds are usually associated with forward and backward whirl responses where it has been always assumed that the backward whirl zone should precede the forward whirl zone. Here, two configurations of cracked rotor-disk systems are considered to study the effect of the angular acceleration and the unbalance force vector orientation with respect to the crack opening direction on the whirl response at the backward whirl zone of rotational speeds. The obtained numerical simulation results are verified through a robust experimental testing for system startup operations. The backward whirl zone is found here to appear immediately after the passage through the critical forward whirl rotational speed. The onset of the backward whirl is also found to be associated with a sharp drop in vibration whirl amplitudes. This backward whirl zone is found to be significantly affected by the unbalance force angle vector orientation and the shaft angular acceleration. More importantly, this zone of backward whirl orbits is not found to be preceding the critical forward whirl zone for the considered cracked shaft-disk configurations.

Crack Identification by Jointly Time-Frequency Analysis

2006 ◽  
Vol 324-325 ◽  
pp. 161-164
Author(s):  
Xin Feng ◽  
Jing Zhou
Keyword(s):  
Frequency Analysis ◽  
Crack Opening ◽  
Sampling Frequency ◽  
Dynamic Responses ◽  
Crack Identification ◽  
Crack Model ◽  
Breathing Crack ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Novel Approach

A novel approach for crack identification based on jointly time-frequency analysis is presented in the paper. A bilinear stiffness model for the breathing crack was introduced to represent the nonlinear dynamics of a cracked beam. The nonlinearity of the dynamic responses due to the crack opening-closing is used to identify the occurrence of the crack. The Wigner-Wille distribution technique is applied to analyze the response signals and the instantaneous frequency is extracted as damage-sensitive feature. The numerical simulations of a breathing crack model were carried out to validate the possibility and effectiveness of the proposed approach. The effects of crack severity and sampling frequency on crack identification were also studied in the simulations respectively. The results show that the proposed method can effectively identify the crack with slight severity without any baseline model or data, and the better the identification obtains as the larger the sampling frequency. The study demonstrates that the proposed approach by using of jointly time-frequency analysis is a promising technique for crack identification.

Vibration Analysis of the Flexible Connecting Rod With the Breathing Crack in a Slider-Crank Mechanism

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Yan-Shin Shih ◽  
Chen-Yuan Chung
Keyword(s):  
Governing Equation ◽  
Moving Boundary ◽  
Beam Theory ◽  
Crack Model ◽  
Breathing Crack ◽  
Connecting Rod ◽  
Bernoulli Beam ◽  
The Galerkin Method ◽  
Euler Bernoulli Beam ◽  
Crank Mechanism

This paper investigates the dynamic response of the cracked and flexible connecting rod in a slider-crank mechanism. Using Euler–Bernoulli beam theory to model the connecting rod without a crack, the governing equation and boundary conditions of the rod's transverse vibration are derived through Hamilton's principle. The moving boundary constraint of the joint between the connecting rod and the slider is considered. After transforming variables and applying the Galerkin method, the governing equation without a crack is reduced to a time-dependent differential equation. After this, the stiffness without a crack is replaced by the stiffness with a crack in the equation. Then, the Runge–Kutta numerical method is applied to solve the transient amplitude of the cracked connecting rod. In addition, the breathing crack model is applied to discuss the behavior of vibration. The influence of cracks with different crack depths on natural frequencies and amplitudes is also discussed. The results of the proposed method agree with the experimental and numerical results available in the literature.

A Seismic Effective Method for Double-Layer Reticulated Shell Using Buckling-Restrained Braces

2010 ◽  
Vol 163-167 ◽  
pp. 2852-2856
Author(s):  
Chang Wu ◽  
Xiu Li Wang
Keyword(s):  
Double Layer ◽  
Seismic Performance ◽  
Linear Time ◽  
Ground Motions ◽  
Equations Of Motion ◽  
Time History ◽  
Original Structure ◽  
Loading Test ◽  
Strong Earthquakes ◽  
Buckling Restrained Braces

In this study a kind of buckling-restrained braces (BRBs) as energy dissipation dampers is attempted for seismic performance of large span double-layer reticulated shell and the effectiveness of BRBs to protect structures against strong earthquakes is numerically studied. The hysteretic curve of such members is obtained through the simulation of the cyclic-loading test, and the equations of motion of the system under earthquake excitations are established. BRBs are then placed at certain locations on the example reticulated shell to replace some normal members, and the damping effect of the two installation schemes of BRBs is investigated by non-linear time-history analyses under various ground motions representing major earthquake events. Compared with the seismic behavior of the original structure without BRBs, satisfactory seismic performance is seen in the upgraded models, which clarifies the BRBs can reduce the vibration response of spatial reticulated structure effectively and the new system has wide space to develop double layer reticulated shell.

Vibrations of beams with a breathing crack and large amplitude displacements

2015 ◽  
Vol 230 (1) ◽  
pp. 34-54 ◽  
Author(s):  
Gonçalo Neves Carneiro ◽  
Pedro Ribeiro
Keyword(s):  
Time Domain ◽  
Equations Of Motion ◽  
Shape Functions ◽  
Breathing Crack ◽  
Dimensional Theory ◽  
One Dimensional ◽  
Time Histories ◽  
Linear Effects ◽  
Fourier Spectra ◽  
The Time Domain

The vibrations of beams with a breathing crack are investigated taking into account geometrical non-linear effects. The crack is modeled via a function that reduces the stiffness, as proposed by Christides and Barr (One-dimensional theory of cracked Bernoulli–Euler beams. Int J Mech Sci 1984). The bilinear behavior due to the crack closing and opening is considered. The equations of motion are obtained via a p-version finite element method, with shape functions recently proposed, which are adequate for problems with abrupt localised variations. To analyse the dynamics of cracked beams, the equations of motion are solved in the time domain, via Newmark's method, and the ensuing displacements, velocities and accelerations are examined. For that purpose, time histories, projections of trajectories on phase planes, and Fourier spectra are obtained. It is verified that the breathing crack introduce asymmetries in the response, and that velocities and accelerations can be more affected than displacements by the breathing crack.

On the Modeling of Open and Breathing Cracks of a Cracked Rotor System

2010 ◽  
Author(s):  
Mohammad A. AL-Shudeifat ◽  
Eric A. Butcher
Keyword(s):  
Finite Element ◽  
Crack Detection ◽  
Linear Time ◽  
Harmonic Balance Method ◽  
Rotor System ◽  
Crack Model ◽  
Open Crack ◽  
Cracked Rotor ◽  
Critical Rotational Speed ◽  
Cracked Rotor System

The modeling of a cracked rotor system with an open or breathing transverse crack is addressed here. The cracked rotor with an open crack model behaves as an asymmetric shaft. Hence, the time-varying area moments of inertia of the cracked section are employed in formulating the periodic finite element stiffness matrix for both crack models which yields a linear time-periodic system. The harmonic balance method (HB) is used in solving the finite element (FE) equations of motions for studying the dynamic behavior of the cracked rotor system. The unique behavior of the whirl orbits during the passage through the subcritical rotational speeds and the sensitivity of these orbits to the unbalance force direction can be used for early crack detection of the cracked rotor for both crack models. These whirl orbits were verified experimentally for the open crack model in the neighborhood of 1/2 of the first critical rotational speed where a good match with the theoretical whirl orbits was observed.

Optimization of Nonlinear Unbalanced Flexible Rotating Shaft Passing Through Critical Speeds

2021 ◽  
Author(s):  
Sadegh Amirzadegan ◽  
Mohammad Rokn-Abadi ◽  
R. D. Firouz-Abadi
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Oscillations ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Angular Acceleration ◽  
Beam Theory ◽  
Rotor System ◽  
Rotating Shaft ◽  
Critical Speeds ◽  
Applied Torque

This work studies the nonlinear oscillations of an elastic rotating shaft with acceleration to pass through the critical speeds. A mathematical model incorporating the Von-Karman higher-order deformations in bending is developed to investigate the nonlinear dynamics of rotors. A flexible shaft on flexible bearings with springs and dampers is considered as rotor system for this work. The shaft is modeled as a beam and the Euler–Bernoulli beam theory is applied. The kinetic and strain energies of the rotor system are derived and Lagrange method is then applied to obtain the coupled nonlinear differential equations of motion for 6 degrees of freedom. In order to solve these equations numerically, the finite element method (FEM) is used. Furthermore, for different bearing properties, rotor responses are examined and curves of passing through critical speeds with angular acceleration due to applied torque are plotted. Then the optimal values of bearing stiffness and damping are calculated to achieve the minimum vibration amplitude, which causes to pass easier through critical speeds. It is concluded that the value of damping and stiffness of bearing change the rotor critical speeds and also significantly affect the dynamic behavior of the rotor system. These effects are also presented graphically and discussed.

Visual ratings of “softness/hardness” of rotating fabrics

2019 ◽  
Vol 32 (1) ◽  
pp. 48-62
Author(s):  
Naohito Jimba ◽  
Tomoharu Ishikawa ◽  
Yoshiko Yanagida ◽  
Hiroshi Mori ◽  
Kazuya Sasaki ◽  
...  
Keyword(s):  
Visual Information ◽  
Angular Acceleration ◽  
Rotary Motion ◽  
Physical Factors ◽  
Bending Rigidity ◽  
Visual Evaluation ◽  
Content Type ◽  
Acceleration Rate ◽  
Fabric Drape ◽  
Key Factor

Purpose The purpose of this paper is to find the optimal rotary motion conditions to create drapes in fabric to visually convey tactile “softness/hardness” and identify key physical factors in visual evaluations of fabric “softness/hardness” via videos of fabric draping. Design/methodology/approach Subjects evaluated visually and by touch, the “softness/hardness” of fabrics draped over a cylinder. In the visual evaluation experiment, subjects were presented with 16 videos of the movement of fabric drapes when the cylinder was rotated (four rotation speeds and four angular acceleration rates) and they evaluated the “softness/hardness” of each fabric visually. By examining the “softness/hardness” ratings in the two experiments, the optimal rotary motion condition that conveyed fabric “softness/hardness” was identified. Changes in the shape of fabric drape when moving under optimal rotary motion conditions were analyzed to determine key physical factors that affected visual evaluations of fabric “softness/hardness.” Findings Optimal rotary motion conditions (rotation speed and angular acceleration rate) that expressed each fabric’s “softness/hardness” appropriately were identified. Additionally, the magnitude of change in the angle of fabric drape when rotating under optimal rotary motion conditions was the key factor used in visual evaluation of each fabric’s “softness/hardness.” Originality/value The conditions needed to produce visual images that convey fabric “softness/hardness” only through visual information (i.e. without touching the fabric) were identified, based on the fabric’s bending rigidity. The magnitude of change in the angle of fabric drape enabled accurate visual judgments of fabric “softness/hardness.”

Effect of a Circumferential Arc Crack on the Vibration Characteristics of a Flexible Spinning Disk

2007 ◽  
Author(s):  
Nikhit N. Nair ◽  
Hamid N. Hashemi ◽  
Grant M. Warner
Keyword(s):  
Crack Opening ◽  
Equations Of Motion ◽  
Crack Depth ◽  
Bending Moment ◽  
Rotating Disk ◽  
Vibration Characteristics ◽  
Coupled Systems ◽  
Mode Shapes ◽  
Critical Speeds ◽  
Crack Location

The vibration characteristics of a circumferentially cracked rotating disk are investigated. The disk is assumed to be axisymmetric, flexible and clamped at the center. The crack increases the local flexibility of the disk at the crack location and is modeled as linear and torsional springs, connecting the two segments of the disk. The spring constants are evaluated by considering crack opening displacements due to bending moment and shear force at the crack location. The equations of motion of two segments of the disk, for disk operating in vacuum as well as subjected to shear fluid flow are developed. Using the Finite Difference Technique, the coupled systems of equations are solved and the natural frequencies and mode shapes are obtained. The mode shapes are seen to be comparatively flattened in the inner region of the disk separated by the crack and heightened towards the periphery of the disk. Shear fluid loading reduces the critical speeds and results in a quicker onset of instability. The degree of instability caused by the crack is a function of crack depth and location. Critical speeds increase with increasing crack distance from the central clamp and decrease with increasing crack depth.

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