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.

Limit-Cycle Analysis of Planar Rotor/Autobalancer System Influenced by Alford's Force

2016 ◽  
Vol 138 (2) ◽  
Author(s):  
DaeYi Jung ◽  
H. A. DeSmidt
Keyword(s):  
Steady State ◽  
Limit Cycle ◽  
Limit Cycles ◽  
Journal Bearing ◽  
Dynamic Interactions ◽  
Rotor Imbalance ◽  
Synchronous Condition ◽  
Freely Moving ◽  
Automatic Balancing ◽  
Special Case

In recent years, there has been much interest in the use of so-called automatic balancing devices (ABDs) in rotating machinery. Essentially, ABDs or “autobalancers” consist 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” 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 and 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 steady-state positions resulting in increased rotor vibration. In this paper, an approximate analytical harmonic solution for the limit cycles is obtained for the special case of symmetric support stiffness together with the so-called Alford's force cross-coupling term. The limit-cycle stability is assessed via Floquet analysis with a perturbation. It is found that the stable balanced synchronous conditions coexist with undesirable nonsynchronous limit cycles. For certain combinations of bearing parameters and operating speeds, the nonsynchronous limit-cycle can be made unstable guaranteeing global asymptotic stability of the synchronous balanced condition. Additionally, the analytical bifurcation of the coexistence zone and the pure balanced synchronous condition is derived. Finally, the analysis is validated through numerical time- and frequency-domain simulation. The findings in this paper yield important insights for researchers wishing to utilize ABDs on rotors having journal bearing support.

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.

Dynamic Analysis of a Coupled Dual-Rotor With Squeeze Film Damper Considering Sudden Unbalance

2021 ◽  
Author(s):  
Ying Cui ◽  
Yuxi Huang ◽  
Guogang Yang ◽  
Yongliang Wang ◽  
Han Zhang
Keyword(s):  
Steady State ◽  
Transient Response ◽  
Rotor System ◽  
Lubricating Oil ◽  
Squeeze Film ◽  
Radial Clearance ◽  
Oil Viscosity ◽  
Squeeze Film Damper ◽  
Damping Effect ◽  
Bistable State

Abstract A nonlinear multi-degree-of-freedom dynamic model of a coupled dual-rotor system with an intershaft bearing and uncentralized squeeze film damper is established by using finite element method. Based on the model, the critical speed characteristic diagram and vibration modes of the system were calculated. The steady-state unbalance response is obtained by using Newmark-β algorithm. The numerical results show the effect of SFD position in the dual-rotor system on response amplitude. It is found that with the decrease of radial clearance and the increase of length-diameter ratio and lubricating oil viscosity, the damping effect of SFD is enhanced and the bistable state phenomenon can be suppressed. The transient response of the system in case of sudden unbalance occurring at the fan was simulated by applying a step function. It is demonstrated that the SFD can effectively reduce the duration and maximum amplitude of the transient process, but at certain speeds, the SFD will increase the amplitude after the system returns to steady state, the damping effect on the transient response is also enhanced with the increase of length-diameter and the decrease of radial clearance, and with the increase of the sudden unbalance value, the response is more likely to stabilized at the high amplitude state of the bistable state.

Multiobjective optimization of journal bearing using mass conserving and genetic algorithms

2005 ◽  
Vol 219 (3) ◽  
pp. 235-248 ◽  
Author(s):  
H Hirani
Keyword(s):  
Thermal Analysis ◽  
Genetic Algorithms ◽  
Film Thickness ◽  
Journal Bearing ◽  
Operating Conditions ◽  
Radial Clearance ◽  
Pareto Optimal ◽  
Optimization Strategy ◽  
Oil Viscosity ◽  
Film Pressure

An optimal design of hydrodynamic journal bearing using mass conserving thermal analysis and genetic algorithms is presented. Simultaneous minimization of power loss and oil flow, subjected to constraints on film thickness, film pressure, and temperature rise between the bearing surfaces, is the objective of this study. The radial clearance, L/D ratio, oil groove location, feed pressure, and the oil viscosity are the design variables. The rank-based genetic algorithm is used to deal with the discrete variables and multimodal objective functions and to capture Pareto optimal points. In view of computation economics and robustness, initial guesses of oil film pressure distribution, eccentricity ratio, and attitude angle obtained by two-dimensional analytical approach are provided for mass conserving thermal analysis. The complete optimization strategy is illustrated by a step-by-step (in four steps) approach. A comparative study of thermal and isothermal analyses is illustrated. Effects of constraints on temperature, pressure, and film thickness on the design vector are enlightened. The mass conserving thermal analysis is validated against experimental results. Pareto optimal fronts for various operating conditions are presented.

scholarly journals Viscosity Effect on Stiffness of Non-conventional (Five Tilted Pads) Journal Bearing

2018 ◽  
Vol 25 (3) ◽  
pp. 53-57
Author(s):  
Mohammed Oawed Atteaa Alhassany ◽  
Ali Khalid Aldulaimy
Keyword(s):  
High Speed ◽  
Journal Bearing ◽  
Cross Coupling ◽  
High Viscosity ◽  
Lubricating Oil ◽  
Coupling Coefficients ◽  
Oil Viscosity ◽  
Viscosity Change ◽  
Oil Film ◽  
Stiffness Coefficients

In this tribological study, we highlight the effect of lubricating oil viscosity in the Multi-pads hydrodynamic journal bearings generate important improvement in characteristics of stiffness and stability in the high speed turbomachines. Depending on viscosity of oil film (three values) variation for five tilted pads bearing, each pad is pivoted and is facilitated to be tilted with small angles, by using Matlab program, we calculate the oil film thickness for convergence layer. We applied Reynold’s equation and solved it’s numerically by using finite difference method with 5 nodes technique to find the pressure distributed on each node in the mesh of tilted pad, then calculate stiffness coefficients. Results show that there is clear effect on stiffens with viscosity change. The increase in value of Krr (for n = 0.3) between viscosity (0.04 Pas. s) and viscosity (0.058 Pas. s) is14.33 MN/m, while the increase in Krr value between viscosity (0.058 Pas. s) and viscosity (0.087 Pas. s) is 11.37 MN/m. the increase in value the of Kss (for n = 0.3) between viscosity (0.04 Pas. s) and viscosity (0.058 Pas. s) is5.921 MN/m, while increase in Kss value between viscosity (0.058 Pas. s) and viscosity (0.087 Pas. s) is9.55 MN/m respectively. the increase in value of Ksr (for n = 0.3) between viscosity (0.04 Pas. s) and viscosity (0.058 Pas. s) is 8.95 MN/m, while the increase in Ksr value between viscosity (0.058 Pas. s) and viscosity (0.087 Pas. s) is 14.41 MN/m respectively. the increase in value of Krs (for n = 0.3) between viscosity (0.04 Pas. s) and viscosity (0.058 Pas. s) are 5.08 MN/m, while the increase in Krs value between viscosity (0.058 Pas. s) and viscosity (0.087 Pas. s) is8.19 MN/m respectively. The values of the dominate principal coefficients Krr is greater than that of Ksr, also The values of the principal coefficients Kss is greater than that of cross coupling Krs for all values of viscosity that studied. From this result, we can conclude the side effect of cross coupling coefficients (Ksr ,Krs) can be overcome by great values for principal coefficient (Krr, Kss) respectively, so we can get good improvement instability for this bearing by variation the viscosity. After that, we regarded to use high viscosity lubricant in multi-pad journal bearing to improve the performance and stability by controlling the stiffness coefficients.

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 Three Dimensional Rigid Rotor/Shaft/Autobalancer System With Symmetric Bearing Support

2012 ◽  
Author(s):  
DaeYi Jung ◽  
Hans DeSmidt
Keyword(s):  
Limit Cycle ◽  
Three Dimensional ◽  
Rigid Rotor ◽  
Dynamic Interactions ◽  
Single Plane ◽  
Rotor Shaft ◽  
Gyroscopic Effects ◽  
Automatic Balancing ◽  
Transverse Deflection ◽  
Limit Cycle Behavior

In recent years, there has been much interest in the use of automatic balancing devices (ABDs) 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” 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 to 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 positions resulting in increased rotor vibration. Although several researchers have explored limit-cycle behavior of single-plane ABD-rotor systems, a limit-cycle analysis of a full three dimensional rigid ABD/shaft/rotor considering transverse deflection, out-plane tilting and gyroscopic effects has not been investigated. This paper considers an approximate harmonic analytical solution to describe the limit-cycle behavior in a three dimensional rigid rotor/ABD system. Essentially, the solutions presented here capture both in-plane transverse deflection and out-plane tilting motion of the system under the limit-cycle condition. Here the whirl speed of the ABD balancer masses is determined via the solution of a non-linear characteristic equation. Also, based upon the limit-cycle solutions, the limit-cycle stability is assessed via a perturbation and Floquet analysis exploring three main parameters; ABD balancer mass, ABD damping, and axial location of ABD along the shaft. The coexistence of the stable balanced synchronous condition and undesired non-synchronous limit-cycle is studied. It is found that for certain combinations of ABD parameters and rotor 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 simulation. The findings in this paper yield important insights for researchers wishing to utilize automatic balancing devices in rotor/shaft systems and limit-cycle mitigation.

Uncertainty Analysis of a Tilting-Pad Journal Bearing Using Fuzzy Logic Techniques

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
A. A. Cavalini ◽  
A. G. S. Dourado ◽  
F. A. Lara-Molina ◽  
V. Steffen
Keyword(s):  
Uncertainty Analysis ◽  
Journal Bearing ◽  
Relevant Information ◽  
Radial Clearance ◽  
Oil Viscosity ◽  
Present Contribution ◽  
Steady State Condition ◽  
Tilting Pad ◽  
Reaction Forces ◽  
Tilting Pad Journal Bearing

This paper is dedicated to the analysis of uncertainties affecting the load capability of a 4-pad tilting-pad journal bearing in which the load is applied on a given pad load on pad configuration (LOP). A well-known stochastic method has been used extensively to model uncertain parameters by using the so-called Monte Carlo simulation. However, in the present contribution, the inherent uncertainties of the bearing parameters (i.e., the pad radius, the oil viscosity, and the radial clearance; bearing assembly clearance) are modeled by using a fuzzy dynamic analysis. This alternative methodology seems to be more appropriate when the stochastic process that characterizes the uncertainties is unknown. The analysis procedure is confined to the load capability of the bearing, being generated by the envelopes of the pressure fields developed on each pad. The hydrodynamic supporting forces are determined by considering a nonlinear model, which is obtained from the solution of the Reynolds equation. The most significant results are associated to the changes in the steady-state condition of the bearing due to the reaction forces that are modified according to the uncertainties introduced in the system. Finally, it is worth mentioning that the uncertainty analysis in this case provides relevant information both for design and maintenance of tilting-pad hydrodynamic bearings.

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