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.

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.

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.

Hybrid Adaptive Rotor Imbalance Vibration Control via Passive Autobalancer and Active Bearing Actuation

2011 ◽  
Author(s):  
DaeYi Jung ◽  
Hans DeSmidt
Keyword(s):  
Steady State ◽  
Vibration Control ◽  
Vibration Isolation ◽  
Dynamic Interactions ◽  
Control Approach ◽  
Rotor Systems ◽  
Rotor Imbalance ◽  
Globally Attractive ◽  
Storage Batteries ◽  
Automatic Balancing

Many researchers have explored the use of active bearings, such as non-contact Active Magnetic Bearings for example, to control imbalance vibration in rotor systems. This paper develops a new hybrid adaptive imbalance vibration control approach based on an active bearing augmented with a passive automatic balancing device (ABD) to enhance the balancing and vibration isolation capabilities. Essentially, an ABD or “autobalance” consists of several freely moving eccentric balancing masses mounted on the rotor, which, at supercritical operating speeds, act to cancel the rotor’s 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 to cancel the imbalance. Since the ABD acts directly on the rotor in the rotating frame, rotor whirl amplitudes are passively reduced without any forces transmitted between rotor and bearing. Therefore, this hybrid ABD/active bearing approach enables increased rotor balancing capability and reduced steady-state control power consumption. However, due to the inherent nonlinearity of the autobalancer, the potential for other, non-synchronous limit-cycle behavior exists. In such situations, the balancer masses do not reach their desired synchronous balanced steady-state equilibrium positions resulting in increased rotor vibration. To address this, a new adaptive active control algorithm for the rotor/bearing/ABD system is derived based on the Lyapunov approach which guarantees global asymptotic stability of the synchronous balanced condition. This approach enables the controller to cope with both the system nonlinearity introduced by the passive ABD and with the rotor imbalance uncertainty. Here, the controllability of system is established through an accessible distribution Lie bracket operational analysis. The simulation results demonstrate the advantages of the hybrid ABD/active bearing system. In particular, it is shown that the balanced equilibrium can be made globally attractive under the action of the adaptive bearing control law, and that the steady-state power levels are significantly reduced via the addition of the ABD. These findings are relevant to limited power applications such as in satellite reaction wheels or flywheel energy storage batteries.

An hourglass-type electromagnetic isolator with negative resistance electromagnetic shunt circuit

2020 ◽  
Vol 64 (1-4) ◽  
pp. 549-556
Author(s):  
Yajun Luo ◽  
Linwei Ji ◽  
Yahong Zhang ◽  
Minglong Xu ◽  
Xinong Zhang
Keyword(s):  
Vibration Isolation ◽  
Electromechanical Coupling ◽  
Coupling Effect ◽  
Negative Resistance ◽  
Isolation System ◽  
Amplitude Vibration ◽  
Vibration Responses ◽  
The Stability ◽  
Isolation Performance ◽  
Shunt Circuit

The present work proposed an hourglass-type electromagnetic isolator with negative resistance (NR) shunt circuit to achieve the effective suppression of the micro-amplitude vibration response in various advanced instruments and equipment. By innovatively design of combining the displacement amplifier and the NR electromagnetic shunt circuit, the current new type of vibration isolator not only can effectively solve the problem of micro-amplitude vibration control, but also has significant electromechanical coupling effect, to obtain excellent vibration isolation performance. The design of the isolator and motion relationship is presented firstly. The electromechanical coupling dynamic model of the isolator is also given. Moreover, the optimal design of the NR electromagnetic shunt circuit and the stability analysis of the vibration isolation system are carried out. Finally, the simulation results about the transfer function and vibration responses demonstrated that the isolator has a significant isolation performance.

Chaos Anti-Synchronization between Chen System and Lu System

2014 ◽  
Vol 631-632 ◽  
pp. 710-713 ◽  
Author(s):  
Xian Yong Wu ◽  
Hao Wu ◽  
Hao Gong
Keyword(s):  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Lyapunov Theory ◽  
State Variables ◽  
Chen System ◽  
System Parameters ◽  
Control Scheme ◽  
Error Dynamics ◽  
The Stability ◽  
Different Chaotic Systems

Anti-synchronization of two different chaotic systems is investigated. On the basis of Lyapunov theory, adaptive control scheme is proposed when system parameters are unknown, sufficient conditions for the stability of the error dynamics are derived, where the controllers are designed using the sum of the state variables in chaotic systems. Numerical simulations are performed for the Chen and Lu systems to demonstrate the effectiveness of the proposed control strategy.

Energy flow and performance evaluation of inerter-based vibration isolators mounted on finite and infinite flexible foundation structures

2022 ◽  
Vol 14 (1) ◽  
pp. 168781402110704
Author(s):  
Zhuang Dong ◽  
Jian Yang ◽  
Chendi Zhu ◽  
Dimitrios Chronopoulos ◽  
Tianyun Li
Keyword(s):  
Power Flow ◽  
Vibration Isolation ◽  
Vibration Suppression ◽  
Flow Behavior ◽  
Flexible Beam ◽  
Vibration Isolators ◽  
Force Transmissibility ◽  
And Performance ◽  
Flexible Foundation ◽  
Isolation Performance

This study investigates the vibration power flow behavior and performance of inerter-based vibration isolators mounted on finite and infinite flexible beam structures. Two configurations of vibration isolators with spring, damper, and inerter as well as different rigidities of finite and infinite foundation structures are considered. Both the time-averaged power flow transmission and the force transmissibility are studied and used as indices to evaluate the isolation performance. Comparisons are made between the two proposed configurations of inerter-based isolators and the conventional spring-damper isolators to show potential performance benefits of including inerter for effective vibration isolation. It is shown that by configuring the inerter, spring, and damper in parallel in the isolator, anti-peaks are introduced in the time-averaged transmitted power and force transmissibility at specific frequencies such that the vibration transmission to the foundation can be greatly suppressed. When the inerter is connected in series with a spring-damper unit and then in-parallel with a spring, considerable improvement in vibration isolation can be achieved near the original peak frequency while maintaining good high-frequency isolation performance. The study provides better understanding of the effects of adding inerters to vibration isolators mounted on a flexible foundation, and benefits enhanced designs of inerter-based vibration suppression systems.

A New CRONE Suspension: More Compact and More Efficient: Part 2—Synthesis and Achievement

2009 ◽  
Author(s):  
Audrey Rizzo ◽  
Xavier Moreau ◽  
Alain Oustaloup ◽  
Vincent Hernette
Keyword(s):  
Transfer Function ◽  
Fractional Derivative ◽  
Vibration Isolation ◽  
Suspension System ◽  
Technological Parameters ◽  
Stability Degree ◽  
Parallel Arrangement ◽  
The Stability ◽  
Crone Suspension ◽  
The Ideal

In a vibration isolation context, fractional derivative can be used to design suspensions which allow to obtain similar performances in spite of parameters uncertainties. This paper presents the synthesis and the achievement of a new Hydractive CRONE suspension system. After the study of the different constraint in suspension in the first paper, the ideal transfer function of the hydractive CRONE suspension is created and simulated in different case. Then a method to determine the technological parameters is proposed. A parallel arrangement of dissipative and capacitive components and a gamma arrangement are compared. They lead to the same unusual performances: the stability degree robustness and the rapidity robustness.

Sign in / Sign up

Export Citation Format

Share Document