scholarly journals A Method for Predicting the Influences of Bearing Support Stiffness and Position on the Vibrations of a Flexible Rotor System

2021 ◽  
Vol 26 (4) ◽  
pp. 287-295
Author(s):  
Jing Liu ◽  
Changke Tang
Keyword(s):  
Optimization Design ◽  
Design Method ◽  
Frequency Equation ◽  
Mode Shapes ◽  
Rotational Inertia ◽  
Flexible Rotor ◽  
Fe Method ◽  
Critical Speeds ◽  
Rotor Systems ◽  
Flexible Rotor Systems

The bearing support stiffness and position can greatly affect the vibrations of flexible rotor systems (FRSs). However, most previous works only focused on the effect of the bearing support stiffness on the critical speeds or modal characteristics including the natural frequencies and mode shapes of rigid rotor systems (RRSs). The previous studies missed the combined effects of the bearing support stiffness and position. To overcome this issue, an analytical method of a FRS based on the finite element (FE) method is proposed. Our model considers the bearing support stiffness and rotational inertia of FRS. The frequency equation of FRS is established for solving the critical speeds. The critical speeds and modal deformations of FRS from our model and the numerical model based on a commercial software are compared to verify the effectiveness of the presented method. The effects of the bearing support stiffness and position on the critical speeds of FRS are analyzed. The results show that the critical speeds are positively correlated with the bearing support stiffness. The critical speeds of FRS are also greatly affected by the bearing position. This study can provide some guidance for the optimization design method of bearing support stiffness and position in FRSs.

scholarly journals An analytical investigation for optimizing the support stiffness and positions of the bearings of a flexible rotor system

2020 ◽  
Author(s):  
Jing Liu ◽  
Changke Tang
Keyword(s):  
Optimization Design ◽  
Rotor System ◽  
Mode Shapes ◽  
Rotational Inertia ◽  
Fe Model ◽  
Flexible Rotor ◽  
Fe Method ◽  
Critical Speeds ◽  
Rotor Systems ◽  
Flexible Rotor Systems

Abstract The support stiffness and positions of the bearings can greatly affect the vibrations of flexible rotor systems. However, most previous works only focused on the effect of the support stiffness of the bearings on the critical speeds of the rigid rotor systems or modal characteristics including natural frequencies and mode shapes, which missed the combine effects of the support stiffness and positions of the bearings. To overcome this issue, an analytical dynamic model of a flexible rotor system based on the finite element (FE) method is proposed. The model considers the support stiffness of the bearings and rotational inertia of the rotor system. The frequency equation of the rotor system is established for solving the critical speeds. The critical speeds and modal deformations of the system from the presented model and the numerical model based on a commercial software are compared to verify the effectiveness of the proposed FE model. The effects of the support stiffness and positions of the bearings on the critical speeds of the flexible rotor system are analyzed. The results show that the critical speeds are positively correlated with the support stiffness. The critical speeds of the flexible rotor system are also greatly affected by the support positions of the bearing. This study can provide some guidance for the optimization design method of the support stiffness and positions of the bearings in the flexible rotor systems.

A Virtual Bearing Method for Optimal Bearing Placement of Flexible Rotor Systems

2017 ◽  
Author(s):  
Shibing Liu ◽  
Bingen Yang
Keyword(s):  
Optimization Problem ◽  
Optimization Method ◽  
Rotor System ◽  
Problem Solution ◽  
Flexible Rotor ◽  
Rotor Systems ◽  
Real Coded Genetic Algorithm ◽  
Minimum Number ◽  
Distributed Transfer Function ◽  
Flexible Rotor Systems

Flexible multistage rotor systems have a variety of engineering applications. Vibration optimization is important to the improvement of performance and reliability for this type of rotor systems. Filling a technical gap in the literature, this paper presents a virtual bearing method for optimal bearing placement that minimizes the vibration amplitude of a flexible rotor system with a minimum number of bearings. In the development, a distributed transfer function formulation is used to define the optimization problem. Solution of the optimization problem by a real-coded genetic algorithm yields the locations and dynamic coefficients of bearings, by which the prescribed operational requirements for the rotor system are satisfied. A numerical example shows that the proposed optimization method is efficient and accurate, and is useful in preliminary design of a new rotor system with the number of bearings unforeknown.

Robust Optimization of Flexible Rotor Systems With Uncertain Parameters via Interval Analysis Method

2019 ◽  
Author(s):  
Jie Hong ◽  
ZheFu Yang ◽  
YaoYu Ni ◽  
YanHong Ma
Keyword(s):  
Interval Analysis ◽  
High Speed ◽  
Dynamic Performance ◽  
Practical Significance ◽  
Analysis Method ◽  
Flexible Rotor ◽  
Parameter Uncertainties ◽  
Rotor Systems ◽  
Interval Analysis Method ◽  
Flexible Rotor Systems

Abstract Uncertainties in the input parameters are inevitable in any design process. Along with the demands for higher rotational speed and higher efficiency of rotating machinery, parameter uncertainties (e.g. support stiffness, the effective bending stiffness of connecting structures) resulted from the increasing load on rotor systems lead to significant scatter of its dynamic performance. These parameters are “uncertain but bounded” which means the distributions are unknown, but the intervals are always got easier. This paper presents a method to robustly optimize the dynamic performance of flexible rotor systems taking into account parameter uncertainties via interval analysis method. Interval analysis methods for modal properties and dynamic response behavior of rotor systems are developed with the interval variables introduced into the equation of motion. The aim of the robust design method is to optimize the critical speed margins and dynamic load on bearings, in the meanwhile, minimizing the variability of the objective items by the means of reducing their sensitivity to parameter uncertainties. A numerical example is presented, results show that, for the high-speed flexible rotor systems, the optimal choices of design variables could reduce of sensitivity to rotor parameter uncertainties, thus optimizing the variability of dynamic performance, which has important practical significance in engineering.

Dynamic Behavior and Stability of a Rotor Under Base Excitation

2006 ◽  
Vol 128 (5) ◽  
pp. 576-585 ◽  
Author(s):  
M. Duchemin ◽  
A. Berlioz ◽  
G. Ferraris
Keyword(s):  
Dynamic Behavior ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Ritz Method ◽  
Base Excitation ◽  
Flexible Rotor ◽  
Lagrange Equations ◽  
Rotor Systems ◽  
Simple Systems ◽  
Flexible Rotor Systems

The dynamic behavior of flexible rotor systems subjected to base excitation (support movements) is investigated theoretically and experimentally. The study focuses on behavior in bending near the critical speeds of rotation. A mathematical model is developed to calculate the kinetic energy and the strain energy. The equations of motion are derived using Lagrange equations and the Rayleigh-Ritz method is used to study the basic phenomena on simple systems. Also, the method of multiple scales is applied to study stability when the system mounting is subjected to a sinusoidal rotation. An experimental setup is used to validate the presented results.

The Dynamic Analysis of SFD-Sliding Bearing Flexible Rotor System Based on Optimization Design

2012 ◽  
Vol 159 ◽  
pp. 355-360
Author(s):  
Ji Yan Wang ◽  
Rong Chun Guo ◽  
Xu Fei Si
Keyword(s):  
High Speed ◽  
Optimization Design ◽  
Critical Speed ◽  
Structural Parameters ◽  
Rotor System ◽  
Flexible Rotor ◽  
Optimization Analysis ◽  
Sliding Bearing ◽  
Critical Speeds ◽  
Design Variables

The paper establishes the mechanical model of SFD-sliding bearing flexible rotor system, adopting Runge-Kutta method to solve nonlinear differential equation, thus acquiring the unbalanced response curve and then gaining the first two critical speeds of the system. Meanwhile, the paper analyzes the sensitivity of the system on the first two critical speeds towards structural parameters, offering design variables to optimization analysis. Based on sensitivity analysis, genetic algorithm is employed to give an optimization analysis on critical speed, which aims to remove critical speed from working speed as much as possible. The critical speed ameliorates after the optimization which supplies theoretical basis as well as theoretical analysis towards the dynamic stability of high-speed rotor system and provides reference for the design of such rotor system.

Vibration Suppression of Rotating Shafts Passing Through Resonances by Switching Shaft Stiffness

1998 ◽  
Vol 120 (1) ◽  
pp. 170-180 ◽  
Author(s):  
J. Wauer ◽  
S. Suherman
Keyword(s):  
Vibration Suppression ◽  
Transient Behavior ◽  
Flexible Rotor ◽  
Nonstationary System ◽  
Rotor Systems ◽  
The Past ◽  
Limited Power ◽  
Rotating Shafts ◽  
Phase Angles ◽  
Flexible Rotor Systems

A method suggested in the past to suppress the vibrations of flexible rotor systems passing through critical speeds is reconsidered. An appropriate switching of the system stiffness (by using shape memory alloys, for instance) is utilized. To model the nonstationary system behavior more realistically, the rotor is driven by a limited power supply. A special feature is the inclusion of unequal bending stiffnesses of the shaft. The stationary and transient behavior of the motor and system characteristic and the deformation amplitudes and phase angles, are examined. Attention is focussed on the strategy for switching the stiffness to yield small resonance deflections.

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