Nonsynchronous Vibration of Planar Autobalancer/Rotor System With Asymmetric Bearing Support

2017 ◽  
Vol 139 (3) ◽  
Author(s):  
DaeYi Jung ◽  
Hans DeSmidt
Keyword(s):  
Limit Cycle ◽  
Harmonic Balance ◽  
Nonlinear Behavior ◽  
Rotor System ◽  
Cycle Stability ◽  
Rotor Vibration ◽  
Rotor Systems ◽  
Asymmetric Behavior ◽  
Automatic Balancing ◽  
Comprehensive Study

Due to inherent nonlinearity of the autobalancer, the potential for other, undesirable, nonsynchronous limit-cycle vibration exists. In such undesirable situations, the balancer masses do not reach their desired synchronous balanced steady-state positions resulting in increased rotor vibration. Such behavior has been widely studied and is well understood for rotor systems on idealized bearings with symmetric supports. However, a comprehensive study into this nonlinear behavior of an imbalanced planar-rigid rotor/autobalancing device (ABD) system mounted on a general bearing holding asymmetric damping and stiffness forces including nonconservative effects cross-coupling ones has not been fully conducted. Therefore, this research primarily focuses on the unstable nonsynchronous limit-cycle behavior and the synchronous balancing condition of system under the influence of the general bearing support. Here, solutions for rotor limit-cycle amplitudes and the corresponding whirl speeds are obtained via a harmonic balance approach. Furthermore, the limit-cycle stability is assessed via perturbation and Floquet analysis, and all the possible responses including undesirable coexistence for the bearing parameters and operating speeds have been thoroughly studied. It is found that, due to asymmetric behavior of bearing support, the multiple limit cycles are encountered in the range of supercritical speeds and more complicate coexistences are invited into the ABD–rotor system compared to the case with idealized symmetric bearing supports. The findings in this paper yield important insights for researchers wishing to utilize automatic balancing devices in more practical rotor systems mounted on a asymmetric general bearing support.

scholarly journals Supercritical Coexistence Behavior of Coupled Oscillating Planar Eccentric Rotor/Autobalancer System

2018 ◽  
Vol 2018 ◽  
pp. 1-19 ◽  
Author(s):  
DaeYi Jung
Keyword(s):  
Limit Cycle ◽  
Vibration Isolation ◽  
Washing Machine ◽  
Rotor Systems ◽  
System Parameters ◽  
Eccentric Rotor ◽  
Mechanical Subsystem ◽  
The Stability ◽  
Flexible Foundation ◽  
Automatic Balancing

The automatic balancing and undesirable nonsynchronous behavior of coupled oscillating configured flexible foundation and planar eccentric rotor equipped with a passive autobalancer (AB) system has been thoroughly investigated here. Specifically, it is described that the unified AB/rotor unit is attached to a foundation via a symmetric support and the foundation is also mounted on the spring-damper isolator which allows oscillating only vertically. Therefore, the AB/rotor unit dynamically interacts with the flexible foundation, which is quite analogous to well-known vertically coupled two-spring and two-mass oscillator. Although the single unit AB/rotor system is widely explored in the related AB studies, such coupled arrangement with AB discussed here has not been previously investigated and thus needs to be explored for further application of AB into various vibration isolation problems of other complicated machines/settings. Therefore, solutions for the synchronous stable balanced and the nonsynchronous unstable limit cycle response of AB/rotor/foundation system are obtained via a fixed equilibrium condition and a harmonic like balancing approach. Furthermore, the stability of each response is assessed via a perturbation and Floquet analysis and, for the system parameters and operating speeds, the undesirable coexistence of the wanted stable balanced synchronous response and undesirable nonsynchronous limit cycle has been thoroughly studied. Due to coupled oscillating feature, it is newly found that the multiple limit cycles are encountered in the range of supercritical speeds and more complicated coexistence is attracted into the system, as well as the damping parameters of coupled components (i.e., flexible foundation) influences of the undesirable limit cycle of AB on the particular supercritical speeds. The findings in this paper yield important insights for researchers wishing to utilize automatic balancing devices in more practical rotor systems coupled with additional vibrating mechanical subsystem such as a washing machine or a reciprocating air conditioning compressor with a flexible foundation.

Limit-Cycle Analysis of Planar Rotor/Autobalancer System Supported on Hydrodynamic Journal Bearing

2011 ◽  
Author(s):  
DaeYi Jung ◽  
Hans DeSmidt
Keyword(s):  
Steady State ◽  
Limit Cycle ◽  
Journal Bearing ◽  
Cross Coupling ◽  
Numerical Continuation ◽  
Radial Clearance ◽  
Oil Viscosity ◽  
Rotor Systems ◽  
Automatic Balancing ◽  
Limit Cycle Behavior

In recent years, there has been much interest in the use of so-called automatic balancing devices (ABD) in rotating machinery. Essentially, ABDs or “autobalancers” consists of several freely moving eccentric balancing masses mounted on the rotor, which, at certain operating speeds, act to cancel rotor imbalance at steady-state. This “automatic balancing” phenomena occurs as a result of nonlinear dynamic interactions between the balancer and rotor wherein the balancer masses naturally synchronize with the rotor with appropriate phase and cancel the imbalance. However, due to inherent nonlinearity of the autobalancer, the potential for other, undesirable, non-synchronous limit-cycle behavior exists. In such situations, the balancer masses do not reach their desired synchronous balanced steady-state positions resulting in increased rotor vibration. Such automatic behavior has been widely studied and is well understood for rotor systems on idealized bearings with symmetric supports. This paper presents a comprehensive study into automatic balancing behavior of an imbalanced planar rigid rotor/ABD system mounted in two different widely-used types of hydrodynamic bearings; i) the short journal bearing with asymmetric stiffness, damping and cross-coupling terms and ii) a so-called tilting-pad bearing. In this study the non-dimensional characteristic curves of stiffness and damping of these two fluid film bearings are employed and the rotor/bearing/ABD system autobalancing behavior is studied as a function of rotor speed, bearing eccentricity and bearing journal radial clearance. These two essential bearing parameters in turn are directly determined by the rotor static loading, bearing structure, and oil viscosity. Consequently, this research focuses on the connectivity between the bearing parameters and the corresponding synchronous balancing and non-synchronous limit-cycle behavior of the system. Here, solutions for rotor limit-cycle amplitudes and corresponding autobalancer ball speeds are obtained via a harmonic balance and numerical continuation solution approach. Furthermore, an exact solution for the limit-cycle is obtained for the special case of symmetric support stiffness together with a so-called Alford’s force cross-coupling term. In each case, the limit-cycle stability is assessed via a perturbation and Floquet analysis and the coexistence of the stable balanced synchronous limit-cycle and undesired non-synchronous limit-cycle is studied. It is found that for certain combinations of bearing parameters and operating speeds, the non-synchronous limit-cycle can be made unstable thus guaranteeing global asymptotic stability of the synchronous balanced condition. Finally, the analysis is validated through numerical time-domain simulation. The findings in this paper yield important insights for researchers wishing to utilize automatic balancing devices in practical rotor systems.

ACCURACY RATING MEASUREMENT OF VIBRATION ELECTROMECHANICAL DEVICES

2019 ◽  
Vol 1 (7) ◽  
pp. 42-45
Author(s):  
V. A. Golubkov ◽  
V. F. Shishlakov ◽  
A. G. Fedorenko ◽  
E. Yu. Vataeva
Keyword(s):  
Technical Condition ◽  
Rotor System ◽  
Vibration Measurement ◽  
Random Errors ◽  
Mass Ratio ◽  
Signal Flow Graph ◽  
Bond Graphs ◽  
Rotor Systems ◽  
Electromechanical Devices ◽  
Main Components

Electromechanical devices consist mainly of rotor systems. Vibration is the result of the interaction of the elements of the rotor system and is largely determined by the accuracy of manufacturing elements at the production stage and defects arising in the process of operation. The main components of the rotor systems that affect vibration are bearings. To determine the technical condition of the bearings and the service life of the rotor system, it is necessary to accurately measure the unobservable vibrations of the rotor. The article describes the model of the channel for measuring the vibration of an electromechanical system, built using the apparatus of bond graphs. The transfer function is obtained by analyzing the signal flow graph. The systematic and random errors of vibration measurement are analyzed depending on the mass ratio between the system case and the vibration transducer for various sensor masses and attachment rigidity.

scholarly journals Comparison of Common Methods in Dynamic Response Predictions of Rotor Systems with Malfunctions

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Hongliang Yao ◽  
Qian Zhao ◽  
Qi Xu ◽  
Bangchun Wen
Keyword(s):  
Frequency Domain ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Newmark Method ◽  
Incremental Harmonic Balance Method ◽  
Rotor Systems ◽  
Double Frequency ◽  
Frequency Domain Methods ◽  
Incremental Harmonic Balance

The efficiency and accuracy of common time and frequency domain methods that are used to simulate the response of a rotor system with malfunctions are compared and analyzed. The Newmark method and the incremental harmonic balance method are selected as typical representatives of time and frequency domain methods, respectively. To improve the simulation efficiency, the fixed interface component mode synthesis approach is combined with the Newmark method and the receptance approach is combined with the incremental harmonic balance method. Numerical simulations are performed for rotor systems with single and double frequency excitations. The inherent characteristic that determines the efficiency of the two methods is analyzed. The results of the analysis indicated that frequency domain methods are suitable single and double frequency excitation rotor systems, whereas time domain methods are more suitable for multifrequency excitation rotor systems.

A Transfer Matrix Technique for Evaluating the Natural Frequencies and Critical Speeds of a Rotor With Multiple Flexible Disks

1991 ◽  
Author(s):  
Fangsheng Wu ◽  
George T. Flowers
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Transfer Matrix ◽  
Natural Frequencies ◽  
Space Shuttle ◽  
Rotor System ◽  
Partial Differential ◽  
Rotor Systems ◽  
Inertial Moment ◽  
Main Engine

Abstract Modern turbomachinery is used to provide power for a wide range of applications, from steam turbines for electrical power plants to the turbopumps used in the Space Shuttle Main Engine. Such devices are subject to a variety of dynamical problems, including vibration, rotordynamical instability, and shaft whirl. In order to properly design and evaluate the performance and stability of turbomachinery, It is important that appropriate analytical tools be available that allow for the study of potentially important dynamical effects. This research effort is concerned with developing a procedure to account for disk flexibility which can readily be used for investigating how such effects might influence the natural frequencies and critical speeds of practical rotor systems. In the present work, a transfer matrix procedure is developed in which the disk flexibility effects are accounted for by means of additional terms included in the transfer matrix formulation. In this development, the shaft is treated as a discrete system while the disk is modelled as a continuous system using the governing partial differential equation. Based on this governing equation, an equivalent inertial moment Mk*, which is the generalized dynamic force coupling between shaft and disk, is then derived. Analysis shows that only the disk modes of one nodal diameter contribute to the inertial moment, Mk*, and thus influence the natural frequencies of the rotor system. To determine the Mk*, the modal expansion method is employed and the governing partial differential equation of the disk is transformed to a set of decoupled forced vibration equations in the generalized coordinates. The Mk* are then calculated in terms of modal shapes, natural frequencies, and material and geometric parameters which can be found in the literature or can be obtained from experiments. Finally the Mk* are incorporated into the point transfer matrix. By so doing, the properties of quick computational speed and ease of use are retained and the complexity of solving partial differential equations is avoided. This allows the present procedure to be easily applied to practical engineering problems. This is especially true for multiple flexible disk rotor systems. As an example, three different cases for a simplified model of the Space Shuttle Main Engine (SSME) High Pressure Oxygen Turbo-Pump (HPOTP) rotor have been studied using this procedure. Some of the more interesting results obtained in this example study are enumerated below. 1.) Disk flexibility can introduce additional natural frequency(s) to a rotor system. 2.) Disk flexibility can cause shifting of some of the natural frequencies. 3.) As disk flexibility is increased, lower natural frequencies of the rotor system will be influenced. 4.) At certain rotor speeds, disk flexibility may cause the disappearance of a natural frequency. 5.) The axial position of the disk on the rotor shaft has a significant effect on the degree of this influence.

A Successive Merging and Condensation (SMAC) Method Applied to Transient Analysis of Multi-Shaft Rotor System

1993 ◽  
Author(s):  
Santosh Ratan ◽  
Jorge Rodriguez
Keyword(s):  
Transient Response ◽  
Transient Analysis ◽  
Rotor System ◽  
Time Step ◽  
Transient Dynamic Analysis ◽  
Numerical Examples ◽  
Linear Coupling ◽  
Rotor Systems ◽  
Coupling Constraints ◽  
Smac Method

Abstract A method for performing transient dynamic analysis of multi-shaft rotor system is proposed. The proposed methodology uses the reported Successive Merge and Condensation (SMAC) method [12] and a decoupling technique to decouple the shafts. Multi-shaft rotor systems are treated as systems of many independent single shaft rotor systems with external unknown coupling forces acting at the points of couplings. For each time step, first, the SMAC method is used to get the transient response in terms of the unknown coupling forces. This is followed by the application of the coupling constraints to calculate the coupling forces and, in turn, the response at the end of that time step. The proposed method preserves the efficiency advantages of the SMAC algorithm for single-shaft rotor system. Numerical examples to validate and illustrate the applicability of the method are given. The method is shown to be applicable to linear and non-linear coupling problems.

Limit-Cycle Analysis of Three-Dimensional Flexible Shaft/Rigid Rotor/Autobalancer System With Symmetric Rigid Supports

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
DaeYi Jung ◽  
H. A. DeSmidt
Keyword(s):  
Limit Cycle ◽  
Three Dimensional ◽  
Design Parameters ◽  
Rigid Rotor ◽  
Modal Shape ◽  
Flexible Shaft ◽  
Flexible Mode ◽  
Automatic Balancing ◽  
Rigid Supports ◽  
Limit Cycle Behavior

In recent years, there has been much interest in the use of automatic balancing devices (ABD) in rotating machinery. Autobalancers consist of several freely moving eccentric balancing masses mounted on the rotor, which, at certain operating speeds, act to cancel rotor imbalance. This “automatic balancing” phenomenon occurs as a result of nonlinear dynamic interactions between the balancer and rotor wherein the balancer masses naturally synchronize with the rotor with appropriate phase to cancel the imbalance. However, due to inherent nonlinearity of the autobalancer, the potential for other undesirable nonsynchronous limit-cycle behavior exists. In such situations, the balancer masses do not reach their desired synchronous balanced positions resulting in increased rotor vibration. To explore this nonsynchronous behavior of ABD, the unstable limit-cycle analysis of three-dimensional (3D) flexible shaft/rigid rotor/ABD/rigid supports described by the modal coordinates has been investigated here. Essentially, this paper presents an approximate harmonic analytical solution to describe the limit-cycle behavior of ABD–rotor system interacting with flexible shaft, which has not been fully considered by ABD researchers. The modal shape of flexible shaft is determined by using well-known fixed–fixed boundary condition due to symmetric rigid supports. Here, the whirl speed of the ABD balancer masses is determined via the solution of a nonlinear characteristic equation. Also, based upon the analytical limit-cycle solutions, the limit-cycle stability of three primary design parameters for ABD is assessed via a perturbation and Floquet analysis: the size of ABD balancer mass, the ABD viscous damping, and the relative axial location of ABD to the imbalance rotor along the shaft. The coexistence of the stable balanced synchronous condition and undesirable nonsynchronous limit-cycle is also studied. It is found that for certain combinations of ABD parameters and rotor speeds, the nonsynchronous limit-cycle can be made unstable, thus guaranteeing asymptotic stability of the synchronous balanced condition at the supercritical shaft speeds between each flexible mode. Finally, the analysis is validated through numerical simulation. The findings in this paper yield important insights for researchers wishing to utilize ABD in flexible shaft/rigid rotor systems and limit-cycle mitigation.

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