Research on Dynamic Model of Rotors with Bearing Misalignment

2014 ◽  
Vol 539 ◽  
pp. 3-8 ◽  
Author(s):  
De Xin Ren ◽  
Jie Hong ◽  
Cun Wang
Keyword(s):  
Dynamic Model ◽  
Rotor System ◽  
Flexible Rotor ◽  
Bending Rigidity ◽  
Lagrange Method ◽  
Motion Equations ◽  
Excitation Force ◽  
Aero Engines ◽  
The Relationship ◽  
Mechanics Characteristics

Based on the structural and mechanics analysis of aero-engines rotor system, the dynamic model of the flexible rotor system with multi-supports are presented in order to solve the bearing misalignment problem of rotor system in aero-engines. The motion equations are derived through Lagrange method. The relationship between structural and mechanics characteristics parameters are built up. Finally, the dynamic influence of bearing misalignment on rotor system is divided into three kinds: additional rotor bending rigidity, additional bearing misalignment excitation force and additional imbalance. The equations suggest that additional imbalance excitation force activates the nonlinearity on rotor system and an additional 2× excitation force might appear.

Modelling of Misaligned Rotor Systems in Aero-Engines

2012 ◽  
Author(s):  
Jun Li ◽  
Jie Hong ◽  
Yanhong Ma ◽  
Dayi Zhang
Keyword(s):  
Dynamic Model ◽  
Rotor System ◽  
Flexible Rotor ◽  
Lagrange Equations ◽  
Rotor Systems ◽  
Nonlinear Properties ◽  
Aero Engine ◽  
Series Of Experiments ◽  
Aero Engines ◽  
Good Agreement

Based on the analysis of structural and dynamic characteristics, a dynamic model of flexible rotor system under misalignment and unbalance excitation in aero-engine was developed through Lagrange equations. The model describes the mechanism and influencing factors of nonlinear properties of misaligned rotors. Then some numerical simulations were performed in order to get the vibration response in time and frequency domain. The results suggest that the rotor system and its coupling may behave in a complex and nonlinear way with the excitation of misalignment and unbalance. The response of the system contains 1× and 2× harmonics, and the spectrum signature closely relate to the misalignment magnitude and the distribution of unbalance mass. A series of experiments were also designed to verify the dynamic model. Their characteristics of response are in good agreement.

Robust Control of the Elastodynamic Vibrations of a Flexible Rotor System With Discontinuous Friction

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Mansour Karkoub
Keyword(s):  
Dynamic Model ◽  
Design Process ◽  
Nonlinear Models ◽  
Control Design ◽  
Rotor System ◽  
Control Technique ◽  
Flexible Rotor ◽  
Highly Nonlinear ◽  
Modeling Errors ◽  
The Difference

The work presented here deals with the control of a flexible rotor system using the μ-synthesis control technique. This technique allows for the inclusion of modeling errors in the control design process in terms of uncertainty weights. The dynamic model of the rotor system, which includes discontinuous friction, is highly nonlinear and has to be linearized around an operating point in order to use μ-synthesis. The difference between the linear and nonlinear models is characterized in terms of uncertainty weights and included in the control design process. The designed controller is robust to uncertainty in the dynamic model, spillover, actuator uncertainty, and noise. The theoretical findings of the μ-synthesis control design are validated through simulations and the results are presented and discussed here.

Modelling of Misaligned Rotor System in Aero-Engines and Interval Method Investigation

2013 ◽  
Author(s):  
Guihua Wang ◽  
Yanhong Ma ◽  
Tianrang Li ◽  
Jun Li ◽  
Jie Hong
Keyword(s):  
Dynamic Response ◽  
Rotor System ◽  
Mechanical Parameters ◽  
Lagrange Method ◽  
Interval Method ◽  
Aero Engine ◽  
Mechanical Factors ◽  
Aero Engines ◽  
Rotor Model ◽  
Engine Rotor

Based on the structural and dynamic characteristics of aero-engine rotor system, we used Lagrange method to develop a two-bearing and a multi-bearing rotor model with misalignment. An equation of motion was derived with features of response examined. Due to the uncertainty of mechanical parameters, interval method was adopted to investigate the dynamic response of rotor system with misalignment. Dynamic response and influence of the key mechanical parameters will be obtained in further research. The two times harmonic was found as a distinctive feature of misalignment and the magnitude of it in spectrum is closely related to some key mechanical factors. We also found interval method outstandingly performed in investigating dynamic response when some key parameters are uncertain.

scholarly journals Estimation of the Dynamic Parameters of the Bearings in a Flexible Rotor System Utilizing Electromagnetic Excitation by a Built-In Motor

Actuators ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 1
Author(s):  
Yinsi Chen ◽  
Ren Yang ◽  
Naohiro Sugita ◽  
Jianpeng Zhong ◽  
Junhong Mao ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Rotor System ◽  
Radial Excitation ◽  
Maximum Relative Error ◽  
Fe Model ◽  
Dynamic Parameters ◽  
Flexible Rotor ◽  
Electromagnetic Excitation ◽  
Excitation Force ◽  
Good Agreement

Estimation of the dynamic parameters of bearings is essential in order to be able to interpret the performance of rotating machinery. In this paper, we propose a method to estimate the dynamic parameters of the bearings in a flexible rotor system. By utilizing the electromagnetic excitation generated by a built-in PM motor and finite element (FE) modeling of the rotor, safe, low-cost, and real-time monitoring of the bearing dynamics can be achieved. The radial excitation force is generated by injecting an alternating d-axis current into the motor windings. The FE model of the rotor and the measured frequency responses at the motor and bearing locations are used to estimate the dynamic parameters of the bearings. To evaluate the feasibility of the proposed method, numerical simulation and experiments were carried out on a flexible rotor system combined with a bearingless motor (BELM) having both motor windings and suspension windings. The numerical simulation results show that the proposed algorithm can accurately estimate the dynamic parameters of the bearings. In the experiment, the estimates made when utilizing the excitation force generated by the motor windings are compared with the estimates made when utilizing the excitation force generated by the suspension windings. The results show that most of the stiffness and damping coefficients for the two experiments are in good agreement, within a maximum error of 8.92%. The errors for some coefficients are large because the base values of these coefficients are small in our test rig, so these coefficients are sensitive to deviations. The natural frequencies calculated from the dynamic parameters estimated from the two experiments are also in good agreement, within a maximum relative error of 3.04%. The proposed method is effective and feasible for turbomachines directly connected to motors, which is highly significant for field tests.

Multi-harmonic motions of bearing cage affected by rotor unbalance

2017 ◽  
Vol 232 (15) ◽  
pp. 2610-2625
Author(s):  
Baogang Wen ◽  
Meiling Wang ◽  
Xianwen Zhou ◽  
Hongjun Ren ◽  
Qingkai Han
Keyword(s):  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Rotor System ◽  
Test Rig ◽  
Theoretical Predictions ◽  
Reaction Forces ◽  
Harmonic Components ◽  
Aero Engines ◽  
Insight Into ◽  
Combination Frequencies

The motion of bearing cage in the rotor system displays very complicated behavior affected by rotor unbalance. In order to gain an insight into the complex cage motions due to rotor unbalance, a scaled rotor test rig is designed and developed that is made to be dynamically similar to the actual rotor system in aero-engines. Eddy transducers are used to measure the cage motions and monitor the rotor vibrations. Based on the test rig, a dynamic model of its rotor system with four degrees-of-freedom is developed to determine the reaction forces due to rotor unbalance, which are introduced as boundary conditions for the bearing dynamic analysis. And then, a three degrees-of-freedom dynamic model of bearing cage taking the obtained reaction forces into account is also proposed. Finally, the experiment and simulation of the cage motions are carried out and compared at different rotating speeds and rotor unbalances. The experimental results of the cage motions agree with the theoretical predictions and reveal that the cage motions generally contain the multiple harmonic components, such as the cage rotating frequency and its multi-frequency, the inner ring rotating frequency, and also some combination frequencies due to rotor unbalance. The amplitudes of the inner ring rotating frequency and combination frequencies of the cage motions increase with the increment of the rotor unbalance values. Besides, the trajectories of cage are affected by the rotor unbalances.

scholarly journals Dynamic Characteristics of Magnetic Suspended Dual-Rotor System by Riccati Transfer Matrix Method

2019 ◽  
Vol 2019 ◽  
pp. 1-22
Author(s):  
Dongxiong Wang ◽  
Nianxian Wang ◽  
Kuisheng Chen ◽  
Chun Ye
Keyword(s):  
Dynamic Model ◽  
Transfer Matrix ◽  
Dynamic Characteristics ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Weight Ratio ◽  
Rotor System ◽  
Mode Shapes ◽  
Outer Rotor ◽  
The Relationship

The magnetic suspended dual-rotor system (MSDS) can effectively increase the thrust weight ratio of aeroengines. However, the MSDS dynamic characteristics have rarely been investigated. In this research, a MSDS with the outer rotor supported by two active magnetic bearings (AMBs) is designed, and the PID control is employed. The Riccati transfer matrix method using complex variables is adopted to establish the MSDS dynamic model. Subsequently, the influences of AMBs’ control parameters on the MSDS dynamic characteristics are explored. According to the analysis, two rigid mode shapes remain unchanged with the variation of the relationship between their corresponding damped critical speeds (DCSs). Moreover, the rigid DCSs disappear with large derivative coefficient. Eventually, the validity of the dynamic model and the appearance of rigid DCSs are verified.

J. Tobin's Monetary Dynamic Model and the Analysis of Russian Economy

2009 ◽  
pp. 70-93
Author(s):  
V. Manevich
Keyword(s):  
Dynamic Model ◽  
Economic Thought ◽  
Financial Policies ◽  
Russian Economy ◽  
Q Theory ◽  
Keynesian Economic ◽  
The Relationship ◽  
Monetary Assets

The paper considers the monetary dynamic model developed by J. Tobin, the leader of Keynesian economic thought in 1970-1990. Particularly, the author examines q-theory of investment proposed by Tobin which allows to expose the relationship between supply of monetary assets and investment in real capital. Application of various tools of monetary and financial policies is also considered in its different forms. The author aspires to use Tobin's model for the analysis of processes existing in the Russian economy and to test theoretical propositions and relationships elaborated by Tobin on Russian statistics.

scholarly journals ESG Disclosures and Stock Price Crash Risk

2021 ◽  
Vol 14 (2) ◽  
pp. 70 ◽  
Author(s):  
Rio Murata ◽  
Shigeyuki Hamori
Keyword(s):  
Dynamic Model ◽  
Stock Price ◽  
The United States ◽  
Crash Risk ◽  
Firm Level ◽  
Market Participants ◽  
Major Market ◽  
Market Index ◽  
Index Components ◽  
The Relationship

In this study, we investigate the relationship between environmental, social, and governance (ESG) disclosures and stock price crash risk. A stock price crash is a dreadful event for market participants. Thus, exploring stock price crash determinants is helpful for investment decisions and risk management. In this study, we use samples of major market index components in Europe, the United States, and Japan to perform regression analyses, after controlling for other potential stock price crash determinants. We estimate static two-way fixed-effect models and dynamic GMM models. We find that coefficients of firm-level ESG disclosures are not statistically significant in the static model. ESG disclosure coefficients in the dynamic model are not statistically significant in the U.S. market sample. On the other hand, coefficients of ESG disclosure scores in the dynamic model are statistically significant and negative in the European and Japanese marker sample. Our findings suggest that ESG disclosures lower future stock price crash risk; however, the effect and predictive power of ESG disclosures differ among regions.

Modeling and validation of crankshaft speed fluctuations of a single-cylinder four-stroke diesel engine

2021 ◽  
pp. 095440702110262
Author(s):  
Mustafa Babagiray ◽  
Hamit Solmaz ◽  
Duygu İpci ◽  
Fatih Aksoy
Keyword(s):  
Diesel Engine ◽  
Dynamic Model ◽  
Moment Of Inertia ◽  
Mass Motion ◽  
Cylinder Pressure ◽  
Motion Equations ◽  
Single Cylinder ◽  
Mass Moment ◽  
Mass Moment Of Inertia ◽  
Speed Fluctuations

In this study, a dynamic model of a single-cylinder four-stroke diesel engine has been created, and the crankshaft speed fluctuations have been simulated and validated. The dynamic model of the engine consists of the motion equations of the piston, conrod, and crankshaft. Conrod motion was modeled by two translational and one angular motion equations, by considering the kinetic energy resulted from the mass moment of inertia and conrod mass. Motion equations involve in-cylinder gas pressure forces, hydrodynamic and dry friction, mass inertia moments of moving parts, starter moment, and external load moment. The In-cylinder pressure profile used in the model was obtained experimentally to increase the accuracy of the model. Pressure profiles were expressed mathematically using the Fourier series. The motion equations were solved by using the Taylor series method. The solution of the mathematical model was performed by coding in the MATLAB interface. Cyclic speed fluctuations obtained from the model were compared with experimental results and found compitable. A validated model was used to analyze the effects of in-cylinder pressure, mass moment of inertia of crankshaft and connecting rod, friction, and piston mass. In experiments for 1500, 1800, 2400, and 2700 rpm engine speeds, crankshaft speed fluctuations were observed as 12.84%, 8.04%, 5.02%, and 4.44%, respectively. In simulations performed for the same speeds, crankshaft speed fluctuations were calculated as 10.45%, 7.56%, 4.49%, and 3.65%. Besides, it was observed that the speed fluctuations decreased as the average crankshaft speed value increased. In the simulation for 157.07, 188.49, 219.91, 251.32, and 282.74 rad/s crankshaft speeds, crankshaft speed fluctuations occurred at rates of 10.45%, 7.56%, 5.84%, 4.49%, and 3.65%, respectively. The effective engine power was achieved as 5.25 kW at an average crankshaft angular speed of 219.91 rad/s. The power of friction loss in the engine was determined as 0.68 kW.

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