Dynamics of a Jeffcott rotor with slant crack

2007 ◽  
Vol 303 (1-2) ◽  
pp. 1-28 ◽  
Author(s):  
Ashish K. Darpe
Keyword(s):  
Jeffcott Rotor ◽  
Slant Crack

The Analytical Imbalance Response of Jeffcott Rotor During Acceleration

2000 ◽  
Vol 123 (2) ◽  
pp. 299-302 ◽  
Author(s):  
Shiyu Zhou ◽  
Jianjun Shi
Keyword(s):  
Natural Frequency ◽  
Initial Condition ◽  
Constant Acceleration ◽  
Transient Vibration ◽  
Critical Speeds ◽  
Rotor Systems ◽  
Jeffcott Rotor ◽  
Physical Insight

Since many rotor systems normally operate above their critical speeds, the problem of accelerating the machine through its critical speeds without excessive vibration draws increasing attention. This paper provides an analytical imbalance response of the Jeffcott rotor under constant acceleration. The response consists of three parts: transient vibration due to the initial condition of the rotor, “synchronous” vibration, and suddenly occurring vibration at the damped natural frequency. This solution provides physical insight to the vibration of the rotor during acceleration.

Experimental Study on Lateral and Torsional Vibration of Cracked Rotor With Torsional Excitation

2013 ◽  
Author(s):  
Chao Liu ◽  
Dongxiang Jiang
Keyword(s):  
Experimental Study ◽  
Normal Condition ◽  
Torsional Vibration ◽  
Transverse Crack ◽  
Rotating Machinery ◽  
Lateral Vibration ◽  
Cracked Rotor ◽  
Diagnostic Features ◽  
Slant Crack ◽  
Torsional Excitation

Crack failures in rotating machinery can result in catastrophic accidents, and they are are difficult to detect online. Condition monitoring is widely applied in field to detect changes of vibration, and form diagnostic features. However, effective features in vibration of the cracked rotor need more tests, especially validating the features with experiments. This work carried out an experimental study on cracked rotors in laboratory. The experiments are as following: (I) vibration of the rotor in normal condition is firstly tested, where lateral vibration and torsional vibration are measured; (II) torsional excitation is exerted on driven end of rotor system, and vibration characteristics of the rotor are tested; (III) cracked rotors are tested with transverse and slant cracks, respectively. With the measured signals, comparisons of vibrations in normal rotor and cracked rotors are carried out. The results show that, the transverse crack introduces more significant changes in 1X frequency and coupled frequency, while the slant crack employs larger changes in 2X frequency. And variation of phases of 1X frequency is presented. Also, the crack plays an impact on the torsional responses.

Rolling Bearing Parametric Excitation of a Jeffcott Rotor System

2021 ◽  
Author(s):  
GHASEM TEHRANI GHANNAD ◽  
CHIARA GASTALDI ◽  
Teresa Berruti
Keyword(s):  
Parametric Excitation ◽  
Rolling Bearing ◽  
Rotor System ◽  
Jeffcott Rotor

Rolling Bearing Parametric Excitation of a Jeffcott Rotor System

2020 ◽  
Author(s):  
Ghasem Ghannad Tehrani ◽  
Chiara Gastaldi ◽  
Teresa Maria Berruti
Keyword(s):  
Parametric Excitation ◽  
Rotational Speed ◽  
Input Parameter ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Rolling Bearing ◽  
Mean Value ◽  
Hertzian Contact ◽  
Rolling Bearings ◽  
Jeffcott Rotor

Abstract Rolling bearings are still widely used in aeroengines. Whenever rotors are modeled, rolling bearing components are typically modeled using springs. In simpler models, this spring is considered to have a constant mean value. However, the rolling bearing stiffness changes with time due to the positions of the balls with respect to the load on the bearing, thus giving rise to an internal excitation known as Parametric Excitation. Due to this parametric excitation, the rotor-bearings system may become unstable for specific combinations of boundary conditions (e.g. rotational speed) and system characteristics (rotor flexibility etc.). Being able to identify these instability regions at a glance is an important tool for the designer, as it allows to discard since the early design stages those configurations which may lead to catastrophic failures. In this paper, a Jeffcott rotor supported and excited by such rolling bearings is used as a demonstrator. In the first step, the expression for the time–varying stiffness of the bearings is analytically derived by applying the Hertzian Contact Theory. Then, the equations of motion of the complete system are provided. In this study, the Harmonic Balance Method (HBM) is used to as an approximate procedure to draw a stability map, thus dividing the input parameter space, i.e. rotational speed and rotor physical characteristics, into stable and unstable regions.

Stability-Optimized Clearance Configuration of Fluid-Film Bearings

2006 ◽  
Vol 129 (1) ◽  
pp. 106-111 ◽  
Author(s):  
Koichi Matsuda ◽  
Shinya Kijimoto ◽  
Yoichi Kanemitsu
Keyword(s):  
Fourier Series ◽  
Load Capacity ◽  
Fluid Film ◽  
Eccentricity Ratio ◽  
Rotating Speed ◽  
Fluid Film Bearings ◽  
Wide Range ◽  
Jeffcott Rotor ◽  
The Stability ◽  
Frequency Ratios

The whirl instability occurs at higher rotating speeds for a full circular fluid-film journal bearing, and many types of clearance configuration have been proposed to solve this instability problem. A clearance configuration of fluid-film journal bearings is optimized in a sense of enhancing the stability of the full circular bearing at high rotational speeds. A performance index is chosen as the sum of the squared whirl-frequency ratios over a wide range of eccentricity ratios, and a Fourier series is used to represent an arbitrary clearance configuration of fluid-film bearings. An optimization problem is then formulated to find the Fourier coefficients to minimize the index. The designed bearing has a clearance configuration similar to that of an offset two-lobe bearing for smaller length-to-diameter ratios. It is shown that the designed bearing cannot destabilize the Jeffcott rotor at any high rotating speed for a wide range of eccentricity ratio. The load capacity of the designed bearings is nearly in the same magnitude as that of the full circular bearing for smaller length-to-diameter ratios. The whirl-frequency ratios of the designed bearing are very sensitive to truncating higher terms of the Fourier series for some eccentricity ratio. The designed bearings successfully enhance the stability of a full circular bearing and are free from the whirl instability.

Some Observations of Chaotic Vibration Phenomena in High-Speed Rotordynamics

1991 ◽  
Vol 113 (1) ◽  
pp. 50-57 ◽  
Author(s):  
F. F. Ehrich
Keyword(s):  
Numerical Model ◽  
High Speed ◽  
Chaotic Behavior ◽  
Narrow Region ◽  
System A ◽  
Vibratory Response ◽  
Local Contact ◽  
Jeffcott Rotor ◽  
Subharmonic Response ◽  
Static Part

Subharmonic response in rotordynamics may be encountered when a rotor is operated with its rotational centerline eccentric to that of a close clearance static part, so that local contact can take place during each orbit when the rotor is excited by residual unbalance. The rotor will tend to bounce at or near its fundamental frequency when the rotor is operated at or near a speed which is a whole number [n] times that frequency. Using a simple numerical model of a Jeffcott rotor mounted on a nonlinear spring, it is found that the vibratory response in the transition zone midway between adjacent zones of subharmonic response has all the characteristics of chaotic behavior. The transition from subharmonic to chaotic response has a complex substructure which involves a sequence of bifurcations of the orbit with variations in speed. This class of rotordynamic behavior was confirmed and illustrated by experimental observations of the vibratory response of a high-speed turbomachine, operating at a speed between 8 and 9 times its fundamental rotor frequency when in local contact across a clearance in the support system. A narrow region between zones of 8th order and 9th order subharmonic response was identified where the response had all the characteristics of the chaotic motion identified in the numerical model.

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