scholarly journals Predicting the Dynamic Response of Dual-Rotor System Subject to Interval Parametric Uncertainties Based on the Non-Intrusive Metamodel

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 736 ◽  
Author(s):  
Chao Fu ◽  
Guojin Feng ◽  
Jiaojiao Ma ◽  
Kuan Lu ◽  
Yongfeng Yang ◽  
...  
Keyword(s):  
Steady State ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Distribution Functions ◽  
Rotor System ◽  
Propagation Mechanism ◽  
Parametric Uncertainties ◽  
Scanning Method ◽  
Rotor Systems ◽  
Interval Uncertainties

In this paper, the non-probabilistic steady-state dynamics of a dual-rotor system with parametric uncertainties under two-frequency excitations are investigated using the non-intrusive simplex form mathematical metamodel. The Lagrangian formulation is employed to derive the equations of motion (EOM) of the system. The simplex form metamodel without the distribution functions of the interval uncertainties is formulated in a non-intrusive way. In the multi-uncertain cases, strategies aimed at reducing the computational cost are incorporated. In numerical simulations for different interval parametric uncertainties, the special propagation mechanism is observed, which cannot be found in single rotor systems. Validations of the metamodel in terms of efficiency and accuracy are also carried out by comparisons with the scanning method. The results will be helpful to understand the dynamic behaviors of dual-rotor systems subject to uncertainties and provide guidance for robust design and analysis.

scholarly journals Numerical Investigation on the Gravity Response of a Two-Pole Generator Rotor System with Interval Uncertainties

2019 ◽  
Vol 9 (15) ◽  
pp. 3036 ◽  
Author(s):  
Zhaoli Zheng ◽  
Yonghui Xie ◽  
Di Zhang
Keyword(s):  
Material Properties ◽  
Equations Of Motion ◽  
Deep Understanding ◽  
Element Model ◽  
Rotor System ◽  
Scanning Method ◽  
Rotor Systems ◽  
Generator Rotor ◽  
Gravity Response ◽  
Asymmetric Rotor

Asymmetric rotor systems widely exist in commercial plants. In the previous studies about asymmetric rotor systems, parameters such as material properties and boundary conditions are deterministic. To obtain a deep understanding of the dynamics of asymmetric rotor systems, a generator rotor system considering uncertain factors is studied in this paper. The equations of motion of the three-dimensional finite element model are solved in the rotating frame. The component mode synthesis is used to reduce the degrees of freedom. By employing the Chebyshev interval method (CIM), the uncertain gravity responses of the generator rotor system are investigated. The influences of the uncertainties in the bearing’s properties and the rotor’s material properties on the gravity response are studied in cases with a single uncertainty and double uncertainties. The accuracy and the efficiency of CIM are validated by comparing with the results of the scanning method. The results show that uncertainties have remarkable influences on the gravity response, and that these influences are different from each other. The proposed method and the results can provide guidance to the design and optimization of the rotary machinery.

Steady-State Characteristics of a Dual-Rotor System With Intershaft Bearing Subjected to Mass Unbalance and Base Motions

2018 ◽  
Author(s):  
Xi Chen ◽  
Mingfu Liao
Keyword(s):  
Steady State ◽  
High Efficiency ◽  
Equations Of Motion ◽  
Axial Rotation ◽  
Rotor System ◽  
Mode Shapes ◽  
Mass Unbalance ◽  
Moving Base ◽  
Lateral Rotation ◽  
Force Vectors

A dual-rotor system with an intershaft bearing subjected to mass unbalance and base motions is established. Using Lagrange’s principle, equations of motion for dual-rotor system relative to moving base are derived. Rotary inertia, gyroscopic inertia, transverse shear deformation, mass unbalance, and six components of deterministic base motions are taken into account. Using state-space vector, steady-state characteristics of dual-rotor system are analyzed through dual-rotor critical speed map, mode shapes, unbalance responses considering base rotations, frequency responses due to base motions, and shaft orbits. The results show that base translations just add external force vectors, while base rotations bring on parametric system matrices and additional force vectors. Base rotations not only change natural frequencies of dual-rotor system, but also break the symmetry of dynamic characteristics in the case of base lateral rotation. Excited by base harmonic translation, resonant frequencies correspond to whirl frequencies. The orbit remains circular under base axial rotation, while it becomes elliptical with a static offset under lateral rotation and then a complicated curve due to harmonic translation. When harmonic frequency of base translation gets close to dual-rotor excitation frequencies, obvious beat vibration appears. Overrall, this flexible approach can ensure calculation accuracy with high efficiency and good expandability.

Transient Characteristics of a Dual-Rotor System With Intershaft Bearing Subjected to Mass Unbalance and Base Motions During Start-Up

2018 ◽  
Author(s):  
Xi Chen ◽  
Mingfu Liao
Keyword(s):  
High Efficiency ◽  
Equations Of Motion ◽  
Axial Rotation ◽  
Rotor System ◽  
Transient Characteristics ◽  
Rotor Systems ◽  
Rotating Speed ◽  
Mass Unbalance ◽  
Start Up ◽  
Lateral Rotation

Using Newmark-Hilber-Hughes-Taylor (Newmark-HHT) integration method, transient characteristics of the dual-rotor system with an intershaft bearing subjected to mass unbalance and base motions during start-up are illustrated. Rotary inertia, gyroscopic moment, shear deformation, mass unbalance and deterministic base motions are considered. Due to variable angular velocities, additional stiffness matrices associated with rotating angular accelerations are also introduced in the equations of motion. The effects of base motion parameters on the dynamic characteristics of the dual-rotor system are discussed, including base axial rotation, lateral rotations, and harmonic translations. The results show that base axial rotation significantly changes the transient critical speeds and resonant amplitudes of the dual-rotor system. In the case of base lateral rotation, the center of the orbit is no longer on the bearing centerline, but with a dynamic offset. When increasing the rotating speeds, the dynamic offset becomes greater. Unlike base lateral rotation, base harmonic translation doesn’t result in dynamic offset, but it amplifies response amplitudes over the entire range of rotating speed. In conclusion, it provides a flexible approach with high efficiency and good expandability to predict transient responses of dual-rotor systems under base motions, and to prevent dual-rotor systems against potential excessive vibration in the design phase.

Negative Effective Stiffness Content in Cracked Rotors

2018 ◽  
Author(s):  
Mohammad A. AL-Shudeifat ◽  
Fatima K. Alhammadi
Keyword(s):  
Equations Of Motion ◽  
Rotor System ◽  
Effective Stiffness ◽  
Cracked Rotor ◽  
Force Vector ◽  
Rotor Systems ◽  
Wide Range ◽  
Unbalance Force ◽  
Time Periodic ◽  
Cracked Rotor System

The appearance of cracks in rotor systems affects the whirl response in the neighborhood of the critical whirl rotational speeds. The combined effect of the crack depth and the unbalance force vector angle orientation with respect to the crack opening direction on the effective stiffness content of the cracked rotor system in the neighborhood of the critical rotational speed is addressed here. The effective stiffness expression of the cracked system can be obtained from the direct integration of the equations of motion of the cracked rotor system. The cracked rotor equations of motion can be expressed by the Jeffcott rotor or the finite element models. The appearance of cracks in rotor systems converts them into parametrically excited dynamical systems with time-periodic stiffness components. The interaction between the time-periodic stiffness and the external periodic forcing function of the unbalance force significantly alters the effective stiffness content in the system at both transient and steady state operations. For wide range of crack depths and unbalance force vector angles, the effective stiffness has been found to be of negative values. This means that the cracked rotor system tends to have more resistance to deflect towards the center of its whirl orbit and less resistance to deflect away under the unbalance force excitation effect. Consequently, in the negative stiffness content zone of the unbalance force vector angles, the cracked rotor system tends to exhibit a sharp growth in the vibration whirl amplitudes. However, for positive effective stiffness values, the shaft has more resistance to deflect away from its whirl orbit center. Therefore, the cracked rotor system is at higher risk of failure in the negative effective stiffness zone of unbalance force vector angles than the positive effective stiffness zone of these angles.

Numerical Investigation on the Nonlinear Dynamics of Anisotropic Breathing Cracked Rotor Systems

2020 ◽  
Author(s):  
Zhaoli Zheng ◽  
Zixuan Li ◽  
Di Zhang ◽  
Yonghui Xie ◽  
Zheyuan Zhang
Keyword(s):  
Nonlinear Dynamics ◽  
Equations Of Motion ◽  
Crack Depth ◽  
Harmonic Balance Method ◽  
Rotor System ◽  
Breathing Crack ◽  
Cracked Rotor ◽  
Tangent Stiffness Matrix ◽  
Rotor Systems ◽  
Relative Angle

Abstract The nonlinear breathing crack behaviors and anisotropy of the bearing are important sources of severe vibration of rotor systems. However, the rotor system considering both of these factors has not gained sufficient attention in the existing studies. In this paper, the nonlinear dynamics of such anisotropic breathing cracked rotor system is investigated based on three-dimensional finite element model (FEM). Firstly, the equations of motion of the rotor system are established in the rotating frame to facilitate the modeling of the breathing crack. The fixed-interface component mode synthesis (CMS) is used to reduce the system’s degrees of freedom (DOFs). Then, in the process of solving the equations by harmonic balance method (HBM) and Newton-Raphson method, an original method for fast calculating tangent stiffness matrix is proposed. Finally, the effects of the crack depth, the anisotropy of bearing and relative angle between bearings on the nonlinear dynamics of the system are studied. The results show that the breathing behavior will complicate the vibration and introduce additional transverse stiffness. The increase of crack depth will deteriorate the vibration. The anisotropy and relative angle of bearing will lead to the splitting and merging of the resonant peaks, respectively.

scholarly journals Dynamics of Flexible Rotor Systems with an Interim Mass Unbalanced Disk Using a Spectral Element Model

2014 ◽  
Vol 2014 ◽  
pp. 1-14
Author(s):  
Sangkyu Choi ◽  
Usik Lee
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Element Model ◽  
Spectral Element ◽  
Rotor System ◽  
Dynamic Responses ◽  
Disk System ◽  
Unbalanced Mass ◽  
Rotor Systems ◽  
Blade System

A frequency domain spectral element model is developed for a rotor system that consists of two spinning shafts and an interim disk or blade system. In this study, the shafts are represented by spinning Timoshenko beam models, and the interim disk system is represented by a uniform thick rigid disk with an unbalanced mass. In our derivation of the governing equations of motion of the disk system, the disk is considered to be wobbling about the geometric center of the disk at which the spinning shafts are attached. The high accuracy of the proposed spectral element model is evaluated by comparison with the natural frequencies obtained using the conventional finite element method (FEM). The spectral element model is then used to investigate the effects of the unbalanced mass on the natural frequencies and dynamic responses of an example rotor system.

scholarly journals Experimental Verification of Lead-Lag Compensators on a Twin Rotor System

2018 ◽  
Vol 14 (2) ◽  
pp. 164-171
Author(s):  
Meryem Deniz ◽  
Enver Tatlicioglu ◽  
Alper Bayrak
Keyword(s):  
Steady State ◽  
Experimental Studies ◽  
Research Problem ◽  
Rotor System ◽  
Pid Controllers ◽  
Rotor Systems ◽  
Laboratory Setup ◽  
Nonlinear Controllers ◽  
Twin Rotor ◽  
State Error

AbstractTwin rotor system is a laboratory setup resembling a simplified helicopter model that moves along both horizontal and vertical axes. The literature on control of twin rotor systems reflects a good amount of research on designing PID controllers and their extensions considering several aspects, as well as onsome nonlinear controllers. However, there is almost no previous work on design of lag-lead type compensators for twin rotor systems. In this study, by considering this open research problem, lag and lead type compensators are designed and then experimentally verified on the twin rotor system. Specifically, first, lag and lag-lag compensators are designed to obtain a reduced steady state error as compared with proportional controllers. Secondly, lead compensation is discussed to obtain a reduced overshoot. Finally, lag-lead compensators are designed to make use of their favorable properties. All compensators are applied to the twin rotor system in our laboratory. From experimental studies, it was observed that steady state error was reduced when a lag compensator was used in conjunction with a lead compensator.

ANALYSIS OF THE STEADY STATE UNBALANCE RESPONSE OF RIGID ROTORS ON MAGNETORHEOLOGICAL DAMPERS: STABILITY, FORCE TRANSMISSION AND ENERGY DISSIPATION

2014 ◽  
Vol 06 (03) ◽  
pp. 1450022 ◽  
Author(s):  
JAROSLAV ZAPOMĚL ◽  
PETR FERFECKI ◽  
PAOLA FORTE
Keyword(s):  
Steady State ◽  
Equations Of Motion ◽  
Dynamical Behavior ◽  
Squeeze Film ◽  
Magnetorheological Dampers ◽  
Force Transmission ◽  
Optimum Performance ◽  
Rotor Systems ◽  
Lateral Vibrations ◽  
Computational Procedures

The rotors working in real technological devices are always slightly imbalanced. This excites their lateral vibrations and generates forces that are transmitted to the rotor casing. These effects can be significantly reduced if damping devices are added to the support elements. The possibility of controlling the damping, in order to achieve their optimum performance, is offered by magnetorheological squeeze film dampers. In this paper, a computational modeling method is used to investigate the dynamical behavior of a rigid flexibly supported rotor loaded by its unbalance and equipped with two short magnetorheological dampers. The equations of motion of the rotor are nonlinear due to the damping forces. Computational procedures were developed to verify the applicability of such dampers by simulating their behavior and analyzing their effect on the amplitude of the rotor vibration, on the magnitude of the forces transmitted to the rotor casing and on the amount of the power dissipated in the magnetorheological films. The proposed approach to study the optimum performance of semiactive magnetorheological dampers applied in rotor systems, in terms of vibration amplitudes and transmitted forces, together with the developed efficient computational methods to calculate the system steady state response and to evaluate its stability represent the new contributions of this paper.

Transient Response Analysis of Damped Rotor Systems by the Normal Mode Method

1975 ◽  
Author(s):  
A. J. Dennis ◽  
R. H. Eriksson ◽  
L. H. Seitelman
Keyword(s):  
Steady State ◽  
Normal Mode ◽  
Transient Response ◽  
Transient Analysis ◽  
Equations Of Motion ◽  
Forced Response ◽  
Mode Shapes ◽  
Response Analysis ◽  
Rotor Systems ◽  
Incremental Formulation

A method to determine the transient response of damped single or multi-shaft rotor systems is presented. The rotor systems are idealized as rotating concentrated masses connected by massless beams, discrete springs, and dampers. The springs may have piecewise constant springs rates to simulate the stiffening effect of parts coming in contact after displacement through an initial offset. Arbitrary forcing functions are allowed. The method employs an incremental formulation in which damping gyroscopic and nonlinear terms are treated as external loads which are lagged in time. The equations of motion are uncoupled by performing a normal mode expansion of the response solution in terms of the non-rotating, undamped eigenvectors and their associated eigenvalues; modes and natural frequencies are obtained from a standard Prohl analysis. An analytical solution is used for each step of the incremental analysis. This technique has been used to study the response of a number of rotor systems to the sudden application of a rotating imbalance load. The systems studied include a dual shaft model of a rig, a single-shaft case from the written literature and a large multi-line (multi-shaft) system. The transient analysis was run out to steady-state and close agreement obtained with results from an independent steady-state forced response analysis. Orthogonality relations between the mode shapes were observed to be critical to the quality of the results. It was observed that transient analysis of multi-line systems can be accurately predicted only if the higher frequency modes which are participating in the response are included in the normal mode solution.

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