scholarly journals Numerical and Experimental Stability Investigation of a Flexible Rotor on Two Different Tilting Pad Bearing Configurations

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Weimin Wang ◽  
Qihang Li ◽  
Feng He ◽  
Paul Allaire
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Frequency Response Function ◽  
High Performance ◽  
System Stability ◽  
Polynomial Method ◽  
Inlet Temperature ◽  
Centrifugal Compressors ◽  
Rational Polynomial ◽  
Rotor Bearing

Rotordynamic stability is crucial for high performance centrifugal compressors. In this paper, the weighted instrumental variable (WIV) based system identification method for rotating machinery stability is investigated based on a sine sweep forward excitation with an electromagnetic actuator. The traditional multiple input multiple output (MIMO) frequency response function (FRF) is transformed into a directional frequency response function (dFRF). The rational polynomial method (RPM) combined with WIV is developed to identify the rotor’s first forward mode parameters. This new approach is called the COMDYN method. Experimental work using the COMDYN method is carried out under different rotating speeds, oil inlet temperatures, and pressure conditions. Two sets of bearings with preloads 0.1 and 0.3 are investigated. A numerical rotor-bearing model is also built. The numerical results correlate reasonably well with the experimental results. The investigation results indicate that the new method satisfies the desired features of rotating machine stability identification. Furthermore, the system log decrement was improved somewhat with the increase of oil inlet temperature. The increase of oil supply pressure affects the rotor-bearing system stability very slightly. The results of this paper provide new and useful insights for potentially avoiding instability faults in centrifugal compressors.

Forward and Backward Mode Excitation of Flexible Rotor Supported by Tilting Pad Bearings: Numerical and Experimental Investigation

2014 ◽  
Author(s):  
Weimin Wang ◽  
Qihang Li ◽  
Jinji Gao ◽  
Timothy Dimond ◽  
Paul Allaire
Keyword(s):  
Frequency Response ◽  
Number Field ◽  
Response Function ◽  
Frequency Response Function ◽  
Operating Conditions ◽  
Modal Parameters ◽  
Polynomial Method ◽  
Centrifugal Compressors ◽  
Simulation Results ◽  
Sine Sweep

Understanding rotor modal excitations is crucial for high performance centrifugal compressors and other rotating machines. Assuring low vibration levels of such machines at operating conditions before delivery is important both for original equipment manufacturers (OEMs) and end users. In this paper, transient simulations of a full scale test rig rotor subject to sine sweep excitations are performed to investigate the forward and backward rotor whirling response. The applied sine sweep excitations are circular forward, circular backward, and elliptical forward, respectively. The effects of excitation force amplitude are also investigated to determine the minimum force required to accurately identify the rotor system modal parameters. The transient simulation results are then used to investigate a forward and backward mode system identification method for rotating machinery stability based on sine-sweep excitations. Both simulations and experimental testing on a full size rotor with an electromagnetic actuator were performed to verify and validate the method. The traditional Multiple Input Multiple Output (MIMO) Frequency Response Function (FRF) is transformed into a directional Frequency Response Function (dFRF) form. This transformation recasts the real number field into complex number field via a transformation matrix. This transformation separates the MIMO FRFs into forward and backward components, which improves the accuracy of the identified results. This method is used to identify the first forward bending modal parameters to estimate rotor stability. The rational polynomial method is used to fit and identify both the dFRFs. Excellent correlation was obtained between simulation results and the identification experiments. The results of this paper provide new insights for avoidance of rotor instability in centrifugal compressors.

scholarly journals Road Roughness Estimation Based on the Vehicle Frequency Response Function

Actuators ◽  
2021 ◽  
Vol 10 (5) ◽  
pp. 89
Author(s):  
Qingxia Zhang ◽  
Jilin Hou ◽  
Zhongdong Duan ◽  
Łukasz Jankowski ◽  
Xiaoyang Hu
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Frequency Response Function ◽  
Gaussian White Noise ◽  
Estimation Method ◽  
Time Shift ◽  
Ride Quality ◽  
The Road ◽  
Road Roughness ◽  
Measured Response

Road roughness is an important factor in road network maintenance and ride quality. This paper proposes a road-roughness estimation method using the frequency response function (FRF) of a vehicle. First, based on the motion equation of the vehicle and the time shift property of the Fourier transform, the vehicle FRF with respect to the displacements of vehicle–road contact points, which describes the relationship between the measured response and road roughness, is deduced and simplified. The key to road roughness estimation is the vehicle FRF, which can be estimated directly using the measured response and the designed shape of the road based on the least-squares method. To eliminate the singular data in the estimated FRF, the shape function method was employed to improve the local curve of the FRF. Moreover, the road roughness can be estimated online by combining the estimated roughness in the overlapping time periods. Finally, a half-car model was used to numerically validate the proposed methods of road roughness estimation. Driving tests of a vehicle passing over a known-sized hump were designed to estimate the vehicle FRF, and the simulated vehicle accelerations were taken as the measured responses considering a 5% Gaussian white noise. Based on the directly estimated vehicle FRF and updated FRF, the road roughness estimation, which considers the influence of the sensors and quantity of measured data at different vehicle speeds, is discussed and compared. The results show that road roughness can be estimated using the proposed method with acceptable accuracy and robustness.

scholarly journals Predicting Dam Flood Discharge Induced Ground Vibration with Modified Frequency Response Function

Water ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 144
Author(s):  
Yan Zhang ◽  
Jijian Lian ◽  
Songhui Li ◽  
Yanbing Zhao ◽  
Guoxin Zhang ◽  
...  
Keyword(s):  
Frequency Response ◽  
Frequency Distribution ◽  
Response Function ◽  
Frequency Response Function ◽  
Ground Vibration ◽  
Vibration Source ◽  
Ground Vibrations ◽  
High Energies ◽  
Flood Discharge ◽  
Opening Method

Ground vibrations induced by large flood discharge from a dam can damage surrounding buildings and impact the quality of life of local residents. If ground vibrations could be predicted during flood discharge, the ground vibration intensity could be mitigated by controlling or tuning the discharge conditions by, for example, changing the flow rate, changing the opening method of the orifice, and changing the upstream or downstream water level, thereby effectively preventing damage. This study proposes a prediction method with a modified frequency response function (FRF) and applies it to the in situ measured data of Xiangjiaba Dam. A multiple averaged power spectrum FRF (MP-FRF) is derived by analyzing four major factors when the FRF is used: noise, system nonlinearity, spectral leakages, and signal latency. The effects of the two types of vibration source as input are quantified. The impact of noise on the predicted amplitude is corrected based on the characteristics of the measured signal. The proposed method involves four steps: signal denoising, MP-FRF estimation, vibration prediction, and noise correction. The results show that when the vibration source and ground vibrations are broadband signals and two or more bands with relative high energies, the frequency distribution of ground vibration can be predicted with MP-FRF by filtering both the input and output. The amplitude prediction loss caused by filtering can be corrected by adding a constructed white noise signal to the prediction result. Compared with using the signal at multiple vibration sources after superimposed as input, using the main source as input improves the accuracy of the predicted frequency distribution. The proposed method can predict the dominant frequency and the frequency bands with relative high energies of the ground vibration downstream of Xiangjiaba Dam. The predicted amplitude error is 9.26%.

Response Prediction and Dynamic Substructuring for Coupled Structures in the Frequency Domain

2020 ◽  
Vol 36 (6) ◽  
pp. 867-879
Author(s):  
X. H. Liao ◽  
W. F. Wu ◽  
H. D. Meng ◽  
J. B. Zhao
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Frequency Response Function ◽  
Dynamic Properties ◽  
Main Idea ◽  
Prediction Method ◽  
Response Prediction ◽  
Synthesis Methods ◽  
Dynamic Substructuring ◽  
Coupled Structures

ABSTRACTTo evaluate the dynamic properties of a coupled structure based on the dynamic properties of its substructures, this paper investigates the dynamic substructuring issue from the perspective of response prediction. The main idea is that the connecting forces at the interface of substructures can be expressed by the unknown coupled structural responses, and the responses can be solved rather easily. Not only rigidly coupled structures but also resiliently coupled structures are investigated. In order to further comprehend and visualize the nature of coupling problems, the Neumann series expansion for a matrix describing the relation between the coupled and uncoupled substructures is also introduced in this paper. Compared with existing response prediction methods, the proposed method does not have to measure any forces, which makes it easier to apply than the others. Clearly, the frequency response function matrix of coupled structures can be derived directly based on the response prediction method. Compared with existing frequency response function synthesis methods, it is more straightforward and comprehensible. Through demonstration of two examples, it is concluded that the proposed method can deal with structural coupling problems very well.

scholarly journals Alongshore Wind Forcing of Coastal Sea Level as a Function of Frequency

2006 ◽  
Vol 36 (11) ◽  
pp. 2173-2184 ◽  
Author(s):  
Holly F. Ryan ◽  
Marlene A. Noble
Keyword(s):  
United States ◽  
Frequency Response ◽  
Sea Level ◽  
Response Function ◽  
Wind Field ◽  
Frequency Response Function ◽  
The United States ◽  
The West ◽  
Coastal Sea ◽  
Alongshore Wind

Abstract The amplitude of the frequency response function between coastal alongshore wind stress and adjusted sea level anomalies along the west coast of the United States increases linearly as a function of the logarithm (log10) of the period for time scales up to at least 60, and possibly 100, days. The amplitude of the frequency response function increases even more rapidly at longer periods out to at least 5 yr. At the shortest periods, the amplitude of the frequency response function is small because sea level is forced only by the local component of the wind field. The regional wind field, which controls the wind-forced response in sea level for periods between 20 and 100 days, not only has much broader spatial scales than the local wind, but also propagates along the coast in the same direction as continental shelf waves. Hence, it has a stronger coupling to and an increased frequency response for sea level. At periods of a year or more, observed coastal sea level fluctuations are not only forced by the regional winds, but also by joint correlations among the larger-scale climatic patterns associated with El Niño. Therefore, the amplitude of the frequency response function is large, despite the fact that the energy in the coastal wind field is relatively small. These data show that the coastal sea level response to wind stress forcing along the west coast of the United States changes in a consistent and predictable pattern over a very broad range of frequencies with time scales from a few days to several years.

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