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.

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.

Imbalance Vibration Suppression of a Supercritical Shaft via an Automatic Balancing Device

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
H. A. DeSmidt
Keyword(s):  
Fixed Point ◽  
Vibration Suppression ◽  
Hard Disk Drives ◽  
Disk System ◽  
Dynamic Interactions ◽  
Single Plane ◽  
Flexible Shaft ◽  
Flexible Mode ◽  
Equilibrium Configurations ◽  
Automatic Balancing

This research explores the use of automatic balancing (AB) devices or “autobalancers” for imbalance vibration suppression of flexible shafts operating at supercritical speeds. Essentially, an autobalancer is a passive device consisting of several freely moving eccentric masses or balancer balls free to roll within a circular track mounted on a rotor that is to be balanced. At certain speeds, the stable equilibrium positions of the balls are such that they reduce or cancel the rotor imbalance. This “automatic balancing” phenomenon occurs as a result of the nonlinear dynamic interactions between the balancer balls and the rotor transverse vibration. Thus, autobalancer devices can passively compensate for unknown imbalance without the need for a control system and are able to naturally adjust for changing imbalance conditions. Autobalancers are currently utilized for imbalance correction in some single plane rotor applications such as computer hard-disk drives, CD-ROM drives, machine tools and energy storage flywheels. While autobalancers can effectively compensate for imbalance of planar, disk-type, rigid rotors, the use of autobalancing devices for nonplanar and flexible shafts with multiple modes of vibration has not been fully considered. This study explores the dynamics and stability of an imbalanced flexible shaft-disk system equipped with a dual-ball automatic balancing device. The system is analyzed by solving a coupled set of nonlinear equations to determine the fixed-point equilibrium conditions in rotating coordinates, and stability is assessed via eigenvalue analysis of the perturbed system about each equilibrium configuration. It is determined that regions of stable automatic balancing occur at supercritical shaft speeds between each flexible mode. Additionally, the effects of bearing support stiffness, axial mounting offset between the imbalance and autobalancer planes, and ball/track viscous damping are explored. This investigation develops a new, efficient, analysis method for calculating the fixed-point equilibrium configurations of the flexible shaft-AB system. Finally, a new effective force ratio parameter is identified, which governs the equilibrium behavior of flexible shaft/AB systems with noncollocated autobalancer and imbalance planes. This analysis yields valuable insights for balancing of flexible rotor systems operating at supercritical speeds.

scholarly journals Experimental investigation of a single-plane automatic balancing mechanism for a rigid rotor

2011 ◽  
Vol 330 (3) ◽  
pp. 385-403 ◽  
Author(s):  
D.J. Rodrigues ◽  
A.R. Champneys ◽  
M.I. Friswell ◽  
R.E. Wilson
Keyword(s):  
Experimental Investigation ◽  
Rigid Rotor ◽  
Single Plane ◽  
Automatic Balancing

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.

Finite Element Simulation of a Strong-Post W-Beam Guardrail System

SIMULATION ◽  
2002 ◽  
Vol 78 (10) ◽  
pp. 587-599 ◽  
Author(s):  
Ali O. Atahan
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Full Scale ◽  
Nonlinear Finite Element ◽  
Crash Test ◽  
Original Design ◽  
Dynamic Interactions ◽  
Crash Testing ◽  
Element Simulation ◽  
Test Requirements

Computer simulation of vehicle collisions has improved significantly over the past decade. With advances in computer technology, nonlinear finite element codes, and material models, full-scale simulation of such complex dynamic interactions is becoming ever more possible. In this study, an explicit three-dimensional nonlinear finite element code, LS-DYNA, is used to demonstrate the capabilities of computer simulations to supplement full-scale crash testing. After a failed crash test on a strong-post guardrail system, LS-DYNA is used to simulate the system, determine the potential problems with the design, and develop an improved system that has the potential to satisfy current crash test requirements. After accurately simulating the response behavior of the full-scale crash test, a second simulation study is performed on the system with improved details. Simulation results indicate that the system performs much better compared to the original design.

scholarly journals An anthropomorphic soft skeleton hand exploiting conditional models for piano playing

2018 ◽  
Vol 3 (25) ◽  
pp. eaau3098 ◽  
Author(s):  
J. A. E. Hughes ◽  
P. Maiolino ◽  
F. Iida
Keyword(s):  
Three Dimensional ◽  
Piano Music ◽  
Robotic Manipulators ◽  
Mechanical Stiffness ◽  
Dynamic Interactions ◽  
Conditional Model ◽  
Three Dimensional Printing ◽  
Behavioral Diversity ◽  
Research Challenge ◽  
Dimensional Printing

The development of robotic manipulators and hands that show dexterity, adaptability, and subtle behavior comparable to human hands is an unsolved research challenge. In this article, we considered the passive dynamics of mechanically complex systems, such as a skeleton hand, as an approach to improving adaptability, dexterity, and richness of behavioral diversity of such robotic manipulators. With the use of state-of-the-art multimaterial three-dimensional printing technologies, it is possible to design and construct complex passive structures, namely, a complex anthropomorphic skeleton hand that shows anisotropic mechanical stiffness. We introduce a concept, termed the “conditional model,” that exploits the anisotropic stiffness of complex soft-rigid hybrid systems. In this approach, the physical configuration, environment conditions, and conditional actuation (applied actuation) resulted in an observable conditional model, allowing joint actuation through passivity-based dynamic interactions. The conditional model approach allowed the physical configuration and actuation to be altered, enabling a single skeleton hand to perform three different phrases of piano music with varying styles and forms and facilitating improved dynamic behaviors and interactions with the piano over those achievable with a rigid end effector.

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