The Vibrational Behavior of a Multi-Shaft, Multi-Bearing System in the Presence of a Propagating Transverse Crack

1984 ◽  
Vol 106 (1) ◽  
pp. 146-153 ◽  
Author(s):  
W. G. R. Davies ◽  
I. W. Mayes
Keyword(s):  
Transverse Crack ◽  
Crack Opening ◽  
Crack Depth ◽  
Bending Moment ◽  
Theoretical Treatment ◽  
Dynamic Stresses ◽  
Vibrational Behavior ◽  
Dynamic Bending ◽  
Opening And Closing ◽  
Bearing System

The effects of a transverse crack on the dynamics of a multi-rotor, multi-bearing system have been studied experimentally using a spin rig. It is concluded that except for very large cracks, the vibrational behavior is similar to that of a slotted shaft with additional excitation due to the crack opening and closing. It confirms the theory, described elsewhere, that it is possible to calculate the behavior of a cracked and/or slotted rotor for a realistic turbogenerator model for crack depths sufficient to give a measurable vibration vector change. The dynamic stresses in the cracked shaft were also measured. The results show how the dynamic bending moment at the crack tip depends on the speed of rotation of the shaft and the crack depth. The results are compared with a theoretical treatment previously reported and good agreement obtained. It is concluded that for crack depths in excess of one third the way through, the shaft the dynamic bending moment must be used for fracture mechanics calculations.

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.

Bending Stiffness Analysis of Elastic Shafts with Three Types of Transverse Cracks

2011 ◽  
Vol 356-360 ◽  
pp. 2197-2204
Author(s):  
Zhong Yi Cai ◽  
He Len Wu ◽  
Xiao Li Zhao ◽  
Jian Ping Zhang
Keyword(s):  
Transverse Crack ◽  
Crack Opening ◽  
Bending Stiffness ◽  
Transverse Cracks ◽  
Stiffness Analysis ◽  
Three Point Bending ◽  
Stiffness Variation ◽  
Opening And Closing ◽  
Published Research ◽  
Breathing Mechanism

The breathing mechanism of a transverse crack in an elastic shaft has been extensively researched. Although many different crack models have been presented, little published research has explored experimentally how the shaft crack breathing mechanism interacts with the change of stiffness during each revolution. This study addressed static analysis of the stiffness of elastic shafts with experimentally-induced fatigue, welding or wire cut transverse cracks. Bending stiffness was measured from different angles under a three point bending fixture, to efficiently define the correct periodical stiffness variation for different crack types. The opening and closing of each crack (breathing effect) were investigated for their association with shaft stiffness. It was found that width of the crack opening gap is a crucial factor which influences the crack breathing behaviour. Experimental results are expected to assist with crack diagnosis.

Theoretical Analysis and Experimental Model Study on Stability of a Crack Rotor System

2013 ◽  
Vol 328 ◽  
pp. 651-656 ◽  
Author(s):  
Feng Lan Wang
Keyword(s):  
Theoretical Analysis ◽  
Experimental Model ◽  
Critical Speed ◽  
Transverse Crack ◽  
Crack Depth ◽  
Rotor System ◽  
Model Study ◽  
Single Disk ◽  
The Stability ◽  
Opening And Closing

In this paper, the single disk rotor system with a transverse open and close crack has been taken as an example; square wave function has been adopted to express opening and closing characteristics of a transverse crack. The stability on the system has been discussed by theoretical analysis and experimental model study. The conclusions have shown that the unstable vibrations are found in the regions near the rotational speed at 2/3, 2/5and 2/7 of the critical speed in the large crack and the small damping case. The influence of some factors such as the crack depth and the damping on stability of the system is qualitatively discussed.

Estimation of the severity of damage produced by a transverse crack

2020 ◽  
Vol 65 (1) ◽  
pp. 137-144
Author(s):  
Marius-Vasile Pop
Keyword(s):  
Transverse Crack ◽  
Bending Moment ◽  
Cantilever Beams ◽  
Trend Line ◽  
The Real ◽  
Symmetrical Deformation ◽  
Frequency Drop ◽  
Equidistant Points ◽  
Fixed End ◽  
Crack Position

This paper presents a method to find the severity of a crack for cantilever beams that can be used to estimate the frequency drop due to the crack. The severity is found for the crack located at the location where the biggest curvature (or bending moment) is achieved. Because the fixing condition does not permit a symmetrical deformation around the crack, the apparent severity is smaller as the real one. The latter is found by the estimated value of the trend-line at the fixed end, it being constructed on points that consider the crack position (equidistant points in the proximity of the fixed end) and the resulted deflections.

Elastic-Plastic Analysis of an Elbow With Axial Part-Through Internal Crack at Crown Under In-Plane Bending

2008 ◽  
Author(s):  
K. M. Prabhakaran ◽  
S. R. Bhate ◽  
V. Bhasin ◽  
A. K. Ghosh
Keyword(s):  
Finite Element ◽  
Crack Depth ◽  
Bending Moment ◽  
Internal Crack ◽  
J Integral ◽  
Finite Element Analyses ◽  
Integrity Assessment ◽  
Elastic Plastic ◽  
Axial Part ◽  
Plane Bending

Piping elbows under bending moment are vulnerable to cracking at crown. The structural integrity assessment requires evaluation of J-integral. The J-integral values for elbows with axial part-through internal crack at crown under in-plane bending moment are limited in open literature. This paper presents the J-integral results of a thick and thin, 90-degree, long radius elbow subjected to in-plane opening bending moment based on number of finite element analyses covering different crack configurations. The non-linear elastic-plastic finite element analyses were performed using WARP3D software. Both geometrical and material nonlinearity were considered in the study. The geometry considered were for Rm/t = 5, and 12 with ratio of crack depth to wall thickness, a/t = 0.15, 0.25, 0.5 and 0.75 and ratio of crack length to crack depth, 2c/a = 6, 8, 10 and 12.

A Simple Approach for Including Weld Residual Stresses in the Calculation of Pipe Circumferential Through-Wall Crack Opening Displacements

2016 ◽  
Author(s):  
Richard Olson
Keyword(s):  
Residual Stresses ◽  
Axial Force ◽  
Analytic Solution ◽  
Crack Opening ◽  
Bending Moment ◽  
Generalized Solution ◽  
Finite Element Analyses ◽  
Opening Displacement ◽  
Crack Face ◽  
Basic Equations

Current methodologies for predicting the crack opening displacement (COD) of circumferentially through-wall cracked pipe do not include the effect of weld residual stresses (WRS). Even the most advanced COD prediction methodology only includes the effect of applied axial force, bending moment, and crack face pressure. For some years, it has been known that weld residual stresses do alter the COD, but there has been no convenient way to include them in a COD prediction without doing case-specific finite element analyses. This paper documents a generalized solution for including WRS effects on COD. The model uses a closed-form analytic solution to approximate the crack face rotations that the WRS would induce which, subsequently, can be added to the typical axial force-bending-crack face pressure COD solution. The methodology is described and the basic equations for the solution are presented. Following this, application to cases to evaluate the efficacy of the approach are presented which show a mixture of results ranging from amazingly good to “of questionable value” with respect to the FEA results.

J-Integral Analysis of Surface Cracks in Round Bars under Bending Moments

2011 ◽  
Vol 52-54 ◽  
pp. 43-48 ◽  
Author(s):  
Al Emran Ismail ◽  
Ahmad Kamal Ariffin ◽  
Shahrum Abdullah ◽  
Mariyam Jameelah Ghazali ◽  
Ruslizam Daud
Keyword(s):  
Finite Element ◽  
Crack Depth ◽  
Crack Tip ◽  
Bending Moment ◽  
Limit Load ◽  
Fe Model ◽  
Surface Cracks ◽  
Element Analysis ◽  
Reference Stress ◽  
Proposed Model

This paper presents a non-linear numerical investigation of surface cracks in round bars under bending moment by using ANSYS finite element analysis (FEA). Due to the symmetrical analysis, only quarter finite element (FE) model was constructed and special attention was given at the crack tip of the cracks. The surface cracks were characterized by the dimensionless crack aspect ratio, a/b = 0.6, 0.8, 1.0 and 1.2, while the dimensionless relative crack depth, a/D = 0.1, 0.2 and 0.3. The square-root singularity of stresses and strains was modeled by shifting the mid-point nodes to the quarter-point locations close to the crack tip. The proposed model was validated with the existing model before any further analysis. The elastic-plastic analysis under remotely applied bending moment was assumed to follow the Ramberg-Osgood relation with n = 5 and 10. J values were determined for all positions along the crack front and then, the limit load was predicted using the J values obtained from FEA through the reference stress method.

Effect of Load Angle on Limit Load of Polyethylene Miter Pipe Bends

2010 ◽  
Author(s):  
Tarek M. A. A. EL-Bagory ◽  
Maher Y. A. Younan ◽  
Hossam E. M. Sallam ◽  
Lotfi A. Abdel-Latif
Keyword(s):  
Crack Depth ◽  
Bending Moment ◽  
Limit Load ◽  
Factor H ◽  
Pipe Bend ◽  
Combined Load ◽  
Specific Loading ◽  
Out Of Plane ◽  
Plane Bending ◽  
Load Angle

The aim of this paper is to investigate the effect crack depth a/W = 0 to 0.4 and load angle (30°,45°,and 60°) on the limit load of miter pipe bends (MPB) under out-of-plane bending moment with a crosshead speed 500 mm/min. The geometry of cracked and uncracked multi miter pipe bends are: bend angle, α = 90°, pipe bend factor, h = 0.844, standard dimension ratio, SDR = 11, and three junctions, m = 3. The material of the investigated pipe is a high-density polyethylene (HDPE), which is applied in natural gas piping systems. Butt-fusion welding is used to produce the welds in the miter pipe bends. An artificial crack is produced by a special cracking device. The crack is located at the crown side of the miter pipe bend, such that the crack is collinear with the direction of the applied load. The crack depth ratio, a/W = 0, 0.1, 0.2, 0.3 and 0.4 for out-of-plane bending moment “i.e. loading angle φ = 0°”. For each out-of-plane bending moment and all closing and opening load angles the limit load is obtained by the tangent intersection method (TI) from the load deflection curves produced by the specially designed and constructed testing machine at the laboratory. For each out-of-plane bending moment case, the experimental results reveals that increasing crack depth leads to a decrease in the stiffness and limit load of MPB. In case of combined load (out-of-plane and in-plane opening; mode) higher load angles lead to an increase in the limit load. The highest limit load value appears at a loading angle equal, φ = 60°. In case of combined load (out-of-plane and in-plane closing; mode) the limit load decreases upon increasing the load angle. On the other hand, higher limit load values take place at a specific loading angle equal φ = 30°. For combined load opening case; higher values of limit load are obtained. Contrarily, lower values are obtained in the closing case.

Sign in / Sign up

Export Citation Format

Share Document