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.

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 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.

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.

Mitigation of nonlinear rub-impact of a rotor system with magnetorheological damper

2019 ◽  
Vol 31 (3) ◽  
pp. 321-338
Author(s):  
Jun Wang ◽  
Liang Ma ◽  
Junhong Zhang ◽  
Xin Lu ◽  
YangYang Yu
Keyword(s):  
Magnetic Field Intensity ◽  
Element Model ◽  
Considerable Effect ◽  
Rotor System ◽  
Magnetorheological Damper ◽  
Self Healing ◽  
Nonlinear Dynamic Response ◽  
Rotor Systems ◽  
Adaptive Ability ◽  
The Relationship

In this work, a new method of using a magnetorheological damper to improve the self-adaptive ability of a rotor system to rub-impact is developed. To validate the feasibility of this method, a finite element model of the rub-impact rotor system with magnetorheological damper is investigated. A revised formula describing the relationship between the yielding shear stress and magnetic field intensity is proposed. Focusing on the mitigation effect of magnetorheological damper on the nonlinear dynamic response of the rotor system, numerical simulation is conducted. The results show that magnetorheological damper has a considerable effect on the vibration and stability of a rub-impact rotor system. When a suitable current is applied, magnetorheological damper can effectively mitigate the vibration of the rotor system to prevent rub-impact. If contact of the rotor/stator is inevitable, magnetorheological damper can further stabilize heavy rub-impact to slight rub-impact by adjusting the current to an appropriate value. This research reveals the influence mechanisms of magnetorheological damper on normal and rub-impact rotor systems and is helpful for vibration control and fault self-healing of rotating machinery.

scholarly journals Time Frequency Features of Rotor Systems with Slowly Varying Mass

2011 ◽  
Vol 18 (1-2) ◽  
pp. 29-44
Author(s):  
Tao Yu ◽  
Qingkai Han
Keyword(s):  
Numerical Method ◽  
Element Model ◽  
Rotor System ◽  
Analytic Method ◽  
Rotor Systems ◽  
Time Frequency ◽  
First Order ◽  
General Rules ◽  
Frequency Features ◽  
Varying Mass

With the analytic method and numerical method respectively, the asymptotic solutions and finite element model of rotor system with single slowly varying mass is obtained to investigate the time frequency features of such rotor system; furthermore, with given model of slowly varying mass, the rotor system with dual slowly varying mass is studied. For the first order approximate solution is used, there exists difference between the results with analytic method and numerical method. On the base of common characteristics of rotor system with dual slowly varying mass, the general rules and formula describing the frequency distribution of rotor system with multiple slowly varying mass are proposed.

scholarly journals Rub-Impact Force Induces Periodic, Quasiperiodic, and Chaotic Motions of a Controlled Asymmetric Rotor System

2021 ◽  
Vol 2021 ◽  
pp. 1-27
Author(s):  
N. A. Saeed ◽  
Emad Mahrous Awwad ◽  
Ali Maarouf ◽  
Hassan M. H. Farh ◽  
Fahd A. Alturki ◽  
...  
Keyword(s):  
Impact Force ◽  
Equations Of Motion ◽  
Rotor System ◽  
Control Law ◽  
Slow Flow ◽  
Response Curves ◽  
Chaotic Motions ◽  
Flow Equations ◽  
Impact Forces ◽  
Asymmetric Rotor

This article aims to explore the oscillatory characteristics of a controlled asymmetric rotor system when subjected to rub and impact forces between the rotor and stator. Four electromagnetic poles are used to control the whirling motion of the rotor system through a linear proportional-derivative control law. The equations of motion that govern the whole system dynamics are derived including the rub and impact forces. The derived mathematical model is analyzed in two basic steps. Firstly, the obtained model is treated as a weakly nonlinear system using perturbation analysis to obtain the slow-flow modulating equations when neglecting the rub and impact forces. Depending on the obtained slow-flow equations, different response curves are plotted to explore the system’s periodic vibrations and determine the conditions at which the system can exhibit rub and impact force. Secondly, the whole system model including the rub and impact forces is investigated by using the bifurcation diagrams, Poincare map, frequency spectrums, and temporal oscillations. The obtained results revealed that the applied control law could mitigate the system whirling oscillations and prevent the rub and impact forces if the control gains are tuned properly. However, the system can perform period-n, quasiperiodic, or chaotic motion depending on the shaft spinning speed if the controller fails to eliminate the contact between the rotor and stator.

Simulation of Rotor System Vibrations Using Experimentally Verified Super Elements

2016 ◽  
Author(s):  
Sergei Semenov ◽  
Mikhail Nikhamkin ◽  
Nikolai Sazhenkov ◽  
Irina Semenova ◽  
Grigorii Mekhonoshin
Keyword(s):  
Numerical Technique ◽  
Element Model ◽  
3D Models ◽  
Rotor System ◽  
Vibration Modes ◽  
Frequency Range ◽  
Test Rig ◽  
Rotor Systems ◽  
Operating Frequency Range ◽  
Analysis Of Results

A numerical technique based on finite element model reduced by using experimentally verified superelements is presented in the paper. This method can be used for modelling of rotor systems with elements which can produce nonaxisymmetrical vibration modes (fan, flexible disks and etc.) in operating frequency range thus forcing to calculate 3D models without cycle symmetry. Testing of proposed mathematical modeling method is produced using special rotor test rig. The procedure of superelements creation and verification is provided. Critical speeds of test rotor system were determined numerically and experimentally. Comparative analysis of results is provided.

Sign in / Sign up

Export Citation Format

Share Document