The Dynamics of a Rotor System with a Cracked Shaft

1986 ◽  
Vol 108 (2) ◽  
pp. 189-196 ◽  
Author(s):  
H. D. Nelson ◽  
C. Nataraj
Keyword(s):  
Computer Code ◽  
Fourier Series Expansion ◽  
Simulation Studies ◽  
Cracked Rotor ◽  
Rotating Shaft ◽  
Crack Location ◽  
Excited System ◽  
System Equations ◽  
Stiffness Variation ◽  
Cracked Shaft

A theoretical analysis of the dynamics of a rotor-bearing system with a transversely cracked rotor is presented. The rotating assembly is modeled using finite rotating shaft elements and the presence of a crack is taken into account by a rotating stiffness variation. This stiffness variation is a function of the rotor’s bending curvature at the crack location and is represented by a Fourier series expansion. The resulting parametrically excited system is nonlinear and is analyzed using a perturbation method coupled with an iteration procedure. The system equations are written in terms of complex variables and an associated computer code has been developed for simulation studies. Results obtained by this analysis procedure are compared with previous analytical and experimental work presented by Grabowski.

Analysis of the Elastic Wave Behavior in a Cracked Shaft

2007 ◽  
Author(s):  
Kelsen LaBerge ◽  
Maurice Adams
Keyword(s):  
Crack Detection ◽  
Acoustic Velocity ◽  
New Method ◽  
Proof Of Concept ◽  
Test Apparatus ◽  
Rotating Shaft ◽  
One Dimensional ◽  
Crack Location ◽  
The Impact ◽  
Cracked Shaft

A new method currently under development for rotating shaft crack detection is presented. The underlying approach is to utilize the impact inherent in the once-per-revolution closing of a shaft crack. The axially traveling elastic compression wave, which is initiated by this impact, propagates to both ends of the shaft at the governing acoustic velocity. Provided suitable measurement near the shaft ends can detect the wave’s arrival, then extracting both the crack location and size is thereby feasible. Proof-of-concept for this new method for shaft crack detection utilizes one-dimensional wave propagation simulations and a newly designed test apparatus, which are presented.

Stability of a Cracked Rotor Subjected to Parametric Excitation

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Jerzy T. Sawicki ◽  
Zbigniew Kulesza
Keyword(s):  
Parametric Excitation ◽  
Crack Detection ◽  
Averaging Method ◽  
Cracked Rotor ◽  
Parametric Vibrations ◽  
Excited System ◽  
Artificial Damping ◽  
Parametric Resonances ◽  
The Stability ◽  
Cracked Shaft

It is well known that parametric vibrations may appear during the rotation of a rotor with a cracked shaft. The vibrations occur due to periodic stiffness changes being the result of the crack breathing. A parametrically excited system may exhibit parametric resonances and antiresonances affecting the stability of the system. In most cases the destabilizing effect due to parametric resonances is studied. Antiresonant cases seem to be uninteresting. However, the antiresonances have a unique property of introducing additional artificial damping to the system, thus improving its stability and reducing the vibration amplitude. Apart from different control applications, this stabilizing effect may be interesting for its probable ability to indicate the shaft crack. The possible application of the additional damping introduced by parametric excitation for the shaft crack detection is analyzed in the present paper. The approach is demonstrated with a mathematical model of a rotor with a cracked shaft. The stability analysis of the rotor is performed analytically by employing the averaging method. Stability boundaries for different frequencies of the parametric excitation and for different crack depths are derived. The results of this analysis are checked numerically by means of the Floquet's theory. Next, possible applications of the parametric excitation for the shaft crack detection are validated numerically.

Dynamics of Large Power Rotating Machine with Cracked Shaft

2005 ◽  
Vol 293-294 ◽  
pp. 337-346
Author(s):  
Slawomir Banaszek
Keyword(s):  
Crack Detection ◽  
Crack Depth ◽  
Computer Code ◽  
Crack Model ◽  
Simulation Research ◽  
Large Power ◽  
Crack Location ◽  
Rotating Machine ◽  
Diagnostic Indicator ◽  
Cracked Shaft

The paper presents the course and results of crack propagation simulation research. The object taken into account is a large power turbo-set rotor. The computer code system NLDW is presented. It uses a non-linear model of journal bearings, and well known crack model. Crack depth is marked by a crack coefficient. It is shown the crack generates a coupled forms of lateral, axial and torsional vibrations in multi-support rotor. Their intensity depends on the axial and circumferential crack location on the shaft. The attempt at pointing a proper diagnostic indicator for crack detection in large rotating machine is made according to obtained results.

Dynamics Equations of Robots Mounted on Moving Bases

1991 ◽  
Author(s):  
R. W. Toogood
Keyword(s):  
Angular Velocity ◽  
Control Systems ◽  
Linear Acceleration ◽  
Computer Code ◽  
Dynamics Simulation ◽  
Simulation Studies ◽  
Flexible Link ◽  
Paper Briefly ◽  
Simulation Results ◽  
Simplification Techniques

Abstract A number of programs have been developed for the automatic symbolic generation of efficient computer code for the dynamic analysis of serial rigid and flexible link manipulators. Code for both the inverse and the direct dynamics computations can be generated. The symbolic generators allow the robot base to be given an arbitrary linear acceleration anchor angular velocity and acceleration. The efficiency of the generated code is an important consideration for simulation studies and/or implementation in control systems. This paper briefly describes the symbolic generation and simplification techniques. The added computational load due to including the base motion is discussed. Some dynamics simulation results are presented for a 3R rigid link manipulator mounted on an oscillating base, which graphically illustrates the effect of the base movement on the dynamics.

scholarly journals Dynamic Response of a Cracked Rotor With Some Comments on Crack Detection

1994 ◽  
Author(s):  
G. Meng ◽  
Eric J. Hahn
Keyword(s):  
Dynamic Response ◽  
Crack Detection ◽  
Harmonic Component ◽  
Major Axis ◽  
Vertical Axis ◽  
Crack Size ◽  
Cracked Rotor ◽  
Response Component ◽  
Crack Location ◽  
Backward Whirl

By considering time dependent terms as external excitation forces, the approximate dynamic response of a cracked horizontal rotor is analysed theoretically and numerically. The solution is good for small cracks and small vibrations in the stable operating range. For each steady state harmonic component the forward and backward whirl amplitudes, the shape and orientation of the elliptic orbit and the amplitude and phase of the response signals arc analysed, taking into account the effect of crack size, crack location, rotor speed and unbalance. It is found that the crack causes backward whirl, the amplitude of which increases with the crack. For a cracked rotor, the response orbit for each harmonic component is an ellipse, the shape and orientation of which depends on the crack size. The influence of the crack on the synchronous response of the system can be regarded as an additional unbalance whereupon, depending on the speed and the crack location, the response amplitude differs from that of the uncracked rotor. The nonsynchronous response provides evidence of crack in the sub-critical range, but is too small to be detected in the supercritical range. Possibilities for crack detection over the full speed range include the additional average (the constant) response component, the backward whirl of the response, the ellipticity of the orbit, the angle between the major axis and the vertical axis and the phase angle difference between vertical and horizontal vibration signals.

Hybrid Brush Pocket Damper Seals for Turbomachinery

2000 ◽  
Vol 122 (2) ◽  
pp. 330-336 ◽  
Author(s):  
Hector E. Laos ◽  
John M. Vance ◽  
Steven E. Buchanan
Keyword(s):  
Active Vibration Control ◽  
Design Feature ◽  
Aircraft Engine ◽  
Computer Code ◽  
Labyrinth Seal ◽  
Dual Function ◽  
Rotating Shaft ◽  
Labyrinth Seals ◽  
Low Leakage ◽  
Brush Seal

Pocket damper seals perform a dual function: both sealing the pressurized gas around a rotating shaft and providing large amounts of vibration damping. The annular cavity between the labyrinth seal teeth is subdivided into separate annular cavities around the circumference of the rotor by partitioning walls. Also, the upstream and downstream teeth have different radial clearances to the rotor. These seals have been shown to provide a remarkable amount of direct damping to attenuate vibration in turbomachinery, but they generally leak more than conventional labyrinth seals if both seals have the same minimum clearance. Conversely, brush seals allow less than half the leakage of labyrinth seals, but published test results show no significant amount of damping. They are considered to be a primary choice for the seals in new aircraft engine designs because of their low leakage. This paper will describe a recently invented hybrid brush/pocket damper seal that combines high damping with low leakage. Previous brush seal results were studied and calculations were made to select a brush seal to combine with the pocket damper design. The result is a hybrid seal with high damping and low leakage. A special design feature can also allow active vibration control as a bonus benefit. A computer code written for the original pocket damper seal was modified to include the brush element at the exit blade. Results from the computer code indicate that the hybrid seal can have less leakage than a six bladed (or 6 knives) labyrinth seal along with orders of magnitude more damping. Experimental evaluations of the damping and leakage performance of the hybrid seal are being conducted by the authors. The experimental work reported here tested the damping capability of the new hybrid brush seal by exciting the seal journal through an impedance head. A conventional six-bladed labyrinth seal of the same working dimensions was also tested. The brush hybrid pocket damper seal is found to leak less than the labyrinth seal while producing two to three times more damping than the original pocket damper seal (orders of magnitude more than the conventional labyrinth). [S0742-4795(00)01102-9]

Dynamic Response of a Cracked Rotor With Some Comments on Crack Detection

1997 ◽  
Vol 119 (2) ◽  
pp. 447-455 ◽  
Author(s):  
G. Meng ◽  
E. J. Hahn
Keyword(s):  
Dynamic Response ◽  
Crack Detection ◽  
Harmonic Component ◽  
Major Axis ◽  
Vertical Axis ◽  
Crack Size ◽  
Cracked Rotor ◽  
Response Component ◽  
Crack Location ◽  
Backward Whirl

By considering time-dependent terms as external excitation forces, the approximate dynamic response of a cracked horizontal rotor is analyzed theoretically and numerically. The solution is good for small cracks and small vibrations in the stable operating range. For each steady-state harmonic component, the forward and backward whirl amplitudes, the shape and orientation of the elliptic orbit, and the amplitude and phase of the response signals are analyzed, taking into account the effect of crack size, crack location, rotor speed, and unbalance. It is found that the crack causes backward whirl, the amplitude of which increases with the crack. For a cracked rotor, the response orbit for each harmonic component is an ellipse, the shape and orientation of which depend on the crack size. The influence of the crack on the synchronous response of the system can be regarded as an additional unbalance whereupon, depending on the speed and the crack location, the response amplitude differs from that of the uncracked rotor. The nonsynchronous response provides evidence of crack in the subcritical range, but is too small to be detected in the supercritical range. Possibilities for crack detection over the full-speed range include the additional average (the constant) response component, the backward whirl of the response, the ellipticity of the orbit, the angle between the major axis and the vertical axis, and the phase angle difference between vertical and horizontal vibration signals.

scholarly journals Exploration of NDE Properties of AMB Supported Rotors for Structural Damage Detection

2010 ◽  
Author(s):  
Jerzy T. Sawicki ◽  
Dmitry L. Storozhev ◽  
John D. Lekki
Keyword(s):  
Structural Damage ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Line Detection ◽  
Control Loop ◽  
Structural Damage Detection ◽  
Cracked Rotor ◽  
Rotating Shaft ◽  
On Line ◽  
Combination Frequencies

This paper addresses self-diagnostic properties of AMB (active magnetic bearing) supported rotors for on-line detection of the transverse crack on a rotating shaft. In addition to pure levitation, the rotor supporting bearing also serves as an actuator that transforms current signals additionally injected into the control loop into the superimposed specially selected excitation forces into the suspended rotor. These additional excitations induce combination frequencies in the rotor response, providing unique signatures for the presence of crack. The background of theoretical modeling, experimental and computer simulation results for the AMB supported cracked rotor with self-diagnostic excitation forces are presented and discussed.

In-Plane Vibration and Crack Detection of a Rotating Shaft-Disk Containing a Transverse Crack

1998 ◽  
Vol 120 (2) ◽  
pp. 551-556 ◽  
Author(s):  
Ming-Chuan Wu ◽  
Shyh-Chin Huang
Keyword(s):  
Crack Detection ◽  
Transverse Crack ◽  
Rotation Speed ◽  
Crack Depth ◽  
Multiple Scale ◽  
Crack Identification ◽  
Response Curves ◽  
Rotating Shaft ◽  
Crack Location ◽  
Depth Rotation

Dynamic response and stability of a rotating shaft-disk containing a transverse crack is investigated. FFT analysis of response amplitudes showed that the 2Ω component (Ω: rotation speed) was excited by crack breathing and could serve as a good index for crack identification. Intensive numerical studies of crack location, crack depth, rotation speed, and sensing position on response amplitudes displayed a feasible technique for the identification of crack depth and crack location. It is achieved by intersecting the two equi-amplitude response curves of two separated sensing probes. Finally, the instability of the system caused by a crack is examined via Floquet theory and the multiple scale method. The stability diagrams, illustrated as functions of crack depth, rotation speed, and damping, are shown and discussed.

Hybrid Brush Pocket Damper Seals for Turbomachinery

1999 ◽  
Author(s):  
Hector E. Laos ◽  
John M. Vance ◽  
Steven E. Buchanan
Keyword(s):  
Active Vibration Control ◽  
Design Feature ◽  
Aircraft Engine ◽  
Computer Code ◽  
Labyrinth Seal ◽  
Dual Function ◽  
Rotating Shaft ◽  
Labyrinth Seals ◽  
Low Leakage ◽  
Brush Seal

Pocket damper seals perform a dual function: both sealing the pressurized gas around a rotating shaft and providing large amounts of vibration damping. The annular cavity between the labyrinth seal teeth is subdivided into separate annular cavities around the circumference of the rotor by partitioning walls. Also, the upstream and downstream teeth have different radial clearances to the rotor. These seals have been shown to provide a remarkable amount of direct damping to attenuate vibration in turbomachinery, but they generally leak more than conventional labyrinth seals if both seals have the same minimum clearance. Conversely, brush seals allow less than half the leakage of labyrinth seals, but published test results show no significant amount of damping. They are considered to be a primary choice for the seals in new aircraft engine designs because of their low leakage. This paper will describe a recently invented hybrid brush/pocket damper seal that combines high damping with low leakage. Previous brush seal results were studied and calculations were made to select a brush seal to combine with the pocket damper design. The result is a hybrid seal with high damping and low leakage. A special design feature can also allow active vibration control as a bonus benefit. A computer code written for the original pocket damper seal was modified to include the brush element at the exit blade. Results from the computer code indicate that the hybrid seal can have less leakage than a six bladed (or 6 knives) labyrinth seal along with orders of magnitude more damping. Experimental evaluations of the damping and leakage performance of the hybrid seal are being conducted by the authors. The experimental work reported here tested the damping capability of the new hybrid brush seal by exciting the seal journal through an impedance head. A conventional six-bladed labyrinth seal of the same working dimensions was also tested. The brush hybrid pocket damper seal is found to leak less than the labyrinth seal while producing two to three times more damping than the original pocket damper seal, (orders of magnitude more than the conventional labyrinth).

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