Model Identification of a Rotor With Magnetic Bearings

2002 ◽  
Vol 125 (1) ◽  
pp. 149-155 ◽  
Author(s):  
J. A. Va´zquez ◽  
E. H. Maslen ◽  
H.-J. Ahn ◽  
D.-C. Han
Keyword(s):  
Frequency Response ◽  
Dynamic Stiffness ◽  
Model Identification ◽  
Magnetic Bearing ◽  
Response Functions ◽  
Flexible Rotor ◽  
Frequency Response Functions ◽  
Rotor Model ◽  
Reconciliation Process ◽  
Piano Wire

The experimental identification of a long flexible rotor with three magnetic bearing journals is presented. Frequency response functions are measured between the magnetic bearing journals and the sensor locations while the rotor is suspended horizontally with piano wire. These frequency response functions are compared with the responses of a rotor model and a reconciliation process is used to reduce the discrepancies between the model and the measured data. In this identification, the wire and the fit of the magnetic bearing journals are identified as the sources of model error. As a result of the reconciliation process, equivalent dynamic stiffness are calculated for the piano wire and the fit of the magnetic bearing journals. Several significant numeral issues that were encountered during the process are discussed and solutions to some of these problems are presented.

Model Identification of a Rotor With Magnetic Bearings

2001 ◽  
Author(s):  
José A. Vázquez ◽  
Eric H. Maslen ◽  
Hyeong-Joon Ahn ◽  
Dong-Chul Han
Keyword(s):  
Dynamic Stiffness ◽  
Model Identification ◽  
Magnetic Bearing ◽  
Measured Data ◽  
Response Functions ◽  
Flexible Rotor ◽  
Experimental Identification ◽  
Rotor Model ◽  
Reconciliation Process ◽  
Piano Wire

The experimental identification of a long flexible rotor with three magnetic bearing journals is presented. Frequency response functions (FRFs) are measured between the magnetic bearing journals and the sensor locations while the rotor is suspended horizontally with piano wire. These FRFs are compared with the responses of a rotor model and a reconciliation process is used to reduce the discrepancies between the model and the measured data. In this identification, the wire and the fit of the magnetic bearing journals are identified as the sources of model error. As a result of the reconciliation process, equivalent dynamic stiffness are calculated for the piano wire and the fit of the magnetic bearing journals. Several significant numeral issues that were encountered during the process are discussed and solutions to some of these problems are presented.

Crack Identification in a Rotating Shaft via the Reverse Directional Frequency Response Functions

2009 ◽  
Vol 131 (1) ◽  
Author(s):  
Yun-Ho Seo ◽  
Chong-Won Lee ◽  
K. C. Park
Keyword(s):  
Frequency Response ◽  
Transverse Crack ◽  
Crack Identification ◽  
Response Functions ◽  
Flexible Rotor ◽  
Rotating Shaft ◽  
Frequency Response Functions ◽  
Rotor Systems ◽  
Crack Location ◽  
Reference Map

A method is proposed for identifying the location of an open transverse crack in flexible rotor systems by modeling the crack as a localized element with rotating asymmetry. It exploits the strong correlations between the modal constants of the reverse directional frequency response functions (r-dFRFs) and the degree and location of asymmetry. A map of the modal constants of the r-dFRFs for all elements is constructed to identify the location of crack by comparing the identified modal constants to those of the reference map. This paper also addresses practical issues associated with measurement noises and limited number of sensors. The proposed crack identification method is finally applied to a flexible rotor system with an open transverse crack in order to demonstrate the identification procedure for detection of the crack location.

Rotordynamic Evaluation of Centrifugal Compressor Using Electromagnetic Exciter

2011 ◽  
Author(s):  
Naohiko Takahashi ◽  
Yohei Magara ◽  
Mitsuhiro Narita ◽  
Haruo Miura
Keyword(s):  
High Pressure ◽  
Frequency Response ◽  
Damping Ratio ◽  
Practical Method ◽  
Magnetic Bearing ◽  
Response Functions ◽  
Mathematical Operation ◽  
Frequency Response Functions ◽  
Calculation Results ◽  
The Stability

Since heavier gases exert larger effects on rotordynamic stability, stability evaluation is important in developing or designing high-pressure compressors. To evaluate the rotor stability during operation, an excitation test using a magnetic bearing is the most practical method. In stability analysis, labyrinth seals can produce significant cross-coupling forces, which particularly reduce the damping ratio of the first forward mode. Therefore, forward modes should be distinguished from backward modes in the excitation test. One method that excites only the forward modes, not the backward modes (and vice versa), is the use of a rotating excitation. In this method, the force is simultaneously applied to two axes to excite the rotor in circular orbits. Two trigonometric functions, i.e., cosine and sine functions, are used to generate this rotation force. Another method is the use of a unidirectional excitation and a mathematical operation to distinguish the forward whirl from the backward whirl. In this method, a directional frequency response function that separates the two modes in the frequency domain is obtained from four frequency response functions by using a complex number expression for the rotor motion. In this study, the latter method was employed to evaluate the rotor stability of a high-pressure compressor. To obtain the frequencies and damping ratios of the eigenvalues, the curve fitting based on system identification methods, such as the prediction error method, was introduced for the derived frequency response functions. Firstly, these methods were applied to a base evaluation under a low-pressure gas operation, in which the stability mainly depends on the bearing property. Using the obtained results, the bearing coefficients were estimated. Next, the same methods were applied to stability evaluations under high-pressure gas operations. The destabilizing forces were also estimated from the test results and compared with the calculation results.

A Flexible Rotor on Flexible Bearing Supports: Stability and Unbalance Response

2000 ◽  
Vol 123 (2) ◽  
pp. 137-144 ◽  
Author(s):  
Jose´ A. Va´zquez ◽  
Lloyd E. Barrett ◽  
Ronald D. Flack
Keyword(s):  
Experimental Data ◽  
Frequency Response ◽  
Transfer Functions ◽  
Structure Stability ◽  
Response Functions ◽  
Flexible Rotor ◽  
Support Structure ◽  
Frequency Response Functions ◽  
Critical Speeds ◽  
Unbalance Response

An experimental study of the effects of bearing support flexibility on rotor stability and unbalance response is presented. A flexible rotor supported by fluid film bearings on flexible supports was used with fifteen support configurations. The horizontal support stiffness was varied systematically while the vertical stiffness was kept constant. The support characteristics were determined experimentally by measuring the frequency response functions of the support structure at the bearing locations. These frequency response functions were used to calculate polynomial transfer functions that represented the support structure. Stability predictions were compared with measured stability thresholds. The predicted stability thresholds agree with the experimental data within a confidence bound for the logarithmic decrement of ±0.01. For unbalance response, the second critical speed of the rotor varied from 3690 rpm to 5200 rpm, depending on the support configuration. The predicted first critical speeds agree with the experimental data within −1.7 percent. The predicted second critical speeds agree with the experimental data within 3.4 percent. Predictions for the rotor on rigid supports are included for comparison.

Rotordynamic Evaluation of Centrifugal Compressor Using Electromagnetic Exciter

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Naohiko Takahashi ◽  
Yohei Magara ◽  
Mitsuhiro Narita ◽  
Haruo Miura
Keyword(s):  
High Pressure ◽  
Frequency Response ◽  
Damping Ratio ◽  
Practical Method ◽  
Magnetic Bearing ◽  
Response Functions ◽  
Mathematical Operation ◽  
Frequency Response Functions ◽  
Calculation Results ◽  
The Stability

Since heavier gases exert larger effects on rotordynamic stability, stability evaluation is important in developing or designing high-pressure compressors. To evaluate the rotor stability during operation, an excitation test using a magnetic bearing is the most practical method. In stability analysis, labyrinth seals can produce significant cross coupling forces, which particularly reduce the damping ratio of the first forward mode. Therefore, forward modes should be distinguished from backward modes in the excitation test. One method that excites only the forward modes, not the backward modes (and vice versa), is the use of a rotating excitation. In this method, the force is simultaneously applied to two axes to excite the rotor in circular orbits. Two trigonometric functions, i.e., cosine and sine functions, are used to generate this rotation force. Another method is the use of a unidirectional excitation and a mathematical operation to distinguish the forward whirl from the backward whirl. In this method, a directional frequency response function that separates the two modes in the frequency domain is obtained from four frequency response functions by using a complex number expression for the rotor motion. In this study, the latter method was employed to evaluate the rotor stability of a high-pressure compressor. To obtain the frequencies and damping ratios of the eigenvalues, the curve fitting based on system identification methods, such as the prediction error method, was introduced for the derived frequency response functions. Firstly, these methods were applied to a base evaluation under a low-pressure gas operation, in which the stability mainly depends on the bearing property. Using the obtained results, the bearing coefficients were estimated. Next, the same methods were applied to stability evaluations under high-pressure gas operations. The destabilizing forces were also estimated from the test results and compared with the calculation results.

A Flexible Rotor on Flexible Bearing Supports: Part II — Unbalance Response

1999 ◽  
Author(s):  
José A. Vázquez ◽  
Lloyd E. Barrett ◽  
Ronald D. Flack
Keyword(s):  
Experimental Data ◽  
Frequency Response ◽  
Transfer Functions ◽  
Response Functions ◽  
Flexible Rotor ◽  
Support Structure ◽  
Frequency Response Functions ◽  
Critical Speeds ◽  
Vertical Stiffness ◽  
Unbalance Response

Abstract An experimental study of the effects of bearing support flexibility on rotor unbalance response is presented. A flexible rotor supported by fluid film bearings on flexible supports was used with fifteen support configurations. The horizontal support stiffness was varied systematically while the vertical stiffness was kept constant. The support characteristics were determined experimentally by measuring the frequency response functions of the support structure at the bearing locations. These frequency response functions were used to calculate polynomial transfer functions that represented the support structure. The second critical speed of the rotor varied from 3690 rpm to 5200 rpm, depending on the support configuration. The predicted first critical speeds agree with the experimental data within −1.7%. The predicted second critical speeds agree with the experimental data within 3.4%. Predictions for the rotor on rigid supports are included for comparison.

scholarly journals Identification of relevant acoustic transfer paths for WT drivetrains with an operational transfer path analysis

2021 ◽  
Author(s):  
W. Schünemann ◽  
R. Schelenz ◽  
G. Jacobs ◽  
W. Vocaet
Keyword(s):  
Path Analysis ◽  
Wind Turbine ◽  
Frequency Response ◽  
Mechanical System ◽  
Reference Point ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Transfer Path ◽  
Transfer Path Analysis ◽  
Turbine Model

AbstractThe aim of a transfer path analysis (TPA) is to view the transmission of vibrations in a mechanical system from the point of excitation over interface points to a reference point. For that matter, the Frequency Response Functions (FRF) of a system or the Transmissibility Matrix is determined and examined in conjunction with the interface forces at the transfer path. This paper will cover the application of an operational TPA for a wind turbine model. In doing so the path contribution of relevant transfer paths are made visible and can be optimized individually.

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