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.

Imbalance Vibration Suppression of Supercritical Shafts With Automatic Balancing Devices

2007 ◽  
Author(s):  
Hans DeSmidt
Keyword(s):  
Vibration Suppression ◽  
Hard Disk Drives ◽  
Type Systems ◽  
Disk System ◽  
Single Plane ◽  
Cd Rom ◽  
Flexible Shaft ◽  
Flexible Mode ◽  
Rotating Coordinates ◽  
Automatic Balancing

This research explores the use of automatic balancing devices (autobalancers) for imbalance suppression of flexible shafts operating at supercritical speeds. Essentially, autobalancers are passive devices consisting of several balls free to roll within an oil-filled circular track mounted on a rotor or shaft to be balanced. At certain speeds, the stable equilibrium positions of the balls is such that they reduce or cancel the rotor imbalance. This “automatic balancing” phenomena occurs as a result of the non-linear dynamic interaction between the balancer balls and the rotor transverse vibrations. Thus, autobalancer devices can passively compensate for unknown imbalance without the need for a control system and naturally adjust for gradually changing imbalance conditions. Single-plane autobalancers are widely utilized for imbalance correction of computer hard-disk drives and CD-ROM drives as well as for balancing machine tools. While autobalancers can effectively compensate for imbalance of planar disk-type systems and rigid rotors, the use of autobalancing devices on flexible shafts has not been fully considered. This study explores the dynamics and stability of an imbalanced flexible shaft-disk system equipped with a dual ball autobalancer by solving a coupled set of nonlinear equations to determine the fixed-point equilibrium conditions in rotating coordinates. Stability is assessed via eigenvalue analysis of a 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 stiffness, autobalancer/imbalance-plane axial offset distance, and relative ball-track viscous damping are each explored. This investigation yields valuable analysis methods and insights for the application of automatic balancing devices to flexible shaft and rotor systems operating at supercritical speeds.

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.

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.

An Online Automatic Balancing System to Actively Reduce Vibration of Machine Tool Motorized Spindle

2014 ◽  
Author(s):  
Hongwei Fan ◽  
Minqing Jing ◽  
Jingjuan Zhi ◽  
Heng Liu ◽  
Wenhui Xin
Keyword(s):  
Machine Tool ◽  
Vibration Suppression ◽  
Angular Position ◽  
Work Piece ◽  
Influence Coefficient ◽  
Negative Effects ◽  
Motorized Spindle ◽  
Single Plane ◽  
Influence Coefficient Method ◽  
Automatic Balancing

Mass imbalance is one of main vibration sources for rotating machine tool spindle, which has many negative effects on spindle bearing and work-piece surface. In order to reduce these harmful effects, an online automatic balancing system is investigated in this paper. The system proposed is composed of sensor, electromagnetic ring balancer and active controller. The electromagnetic ring balancer uses an annular coil to generate the pulsing drive magnetic field and uses the counterweight plate to obtain the required correction mass. When the spindle rotates, if unbalance occurs the proposed balancer will be driven to reach the predetermined angular position under the electromagnetic field to then realize balance, the balanced position can be determined according to the measured signals and the adaptive influence coefficient method. The new single-plane self-balancing motorized spindle and DSP-based controller were developed to validate design of the proposed online active balancing system. The experimental results show that the developed balancing system is effective for vibration suppression of rigid spindle.

Disk Position Nonlinearity Effects on the Chaotic Behavior of Rotating Flexible Shaft-Disk Systems

2012 ◽  
Vol 28 (3) ◽  
pp. 513-522 ◽  
Author(s):  
H. M. Khanlo ◽  
M. Ghayour ◽  
S. Ziaei-Rad
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Dynamic Behavior ◽  
Chaotic Behavior ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Disk System ◽  
Partial Differential ◽  
Rayleigh Beam ◽  
Flexible Shaft

AbstractThis study investigates the effects of disk position nonlinearities on the nonlinear dynamic behavior of a rotating flexible shaft-disk system. Displacement of the disk on the shaft causes certain nonlinear terms which appears in the equations of motion, which can in turn affect the dynamic behavior of the system. The system is modeled as a continuous shaft with a rigid disk in different locations. Also, the disk gyroscopic moment is considered. The partial differential equations of motion are extracted under the Rayleigh beam theory. The assumed modes method is used to discretize partial differential equations and the resulting equations are solved via numerical methods. The analytical methods used in this work are inclusive of time series, phase plane portrait, power spectrum, Poincaré map, bifurcation diagrams, and Lyapunov exponents. The effect of disk nonlinearities is studied for some disk positions. The results confirm that when the disk is located at mid-span of the shaft, only the regular motion (period one) is observed. However, periodic, sub-harmonic, quasi-periodic, and chaotic states can be observed for situations in which the disk is located at places other than the middle of the shaft. The results show nonlinear effects are negligible in some cases.

scholarly journals Strain Sensing With Piezoelectric Zinc Oxide Thin Films for Vibration Suppression in Hard Disk Drives

2008 ◽  
Author(s):  
Sarah Felix ◽  
Stanley Kon ◽  
Jianbin Nie ◽  
Roberto Horowitz
Keyword(s):  
Vibration Suppression ◽  
Transfer Functions ◽  
Hard Disk Drives ◽  
Hard Disk ◽  
Disk Drive ◽  
Strain Sensing ◽  
Linear Quadratic ◽  
H2 Control ◽  
Hard Drives ◽  
Optimization Methodology

This paper describes the integration of thin film ZnO strain sensors onto hard disk drive suspensions for improved vibration suppression for tracking control. Sensor location was designed using an efficient optimization methodology based on linear quadratic gaussian (LQG) control. Sensors were fabricated directly onto steel wafers that were subsequently made into instrumented suspensions. Prototype instrumented suspensions were installed into commercial hard drives and tested. For the first time, a sensing signal was successfully obtained while the suspension was flying on a disk as in normal drive operation. Preliminary models were identified from experimental transfer functions. Nominal H2 control simulations demonstrated improved vibration suppression as a result of both the better resolution and higher sensing rate provided by the sensors.

MEMS-based Accelerometers and their Application to Vibration Suppression in Hard Disk Drives

MEMS/NEMS ◽  
2007 ◽  
pp. 993-1022
Author(s):  
Roberto Oboe ◽  
Ernesto Lasalandra ◽  
Matthew T. White
Keyword(s):  
Vibration Suppression ◽  
Hard Disk Drives ◽  
Hard Disk ◽  
Disk Drives

Operational Shock Response of Ultrathin Hard Disk Drives

2014 ◽  
Author(s):  
Shengkai Yu ◽  
Jianqiang Mou ◽  
Wei Hua ◽  
Weidong Zhou ◽  
Chye Chin Tan
Keyword(s):  
Hard Disk Drives ◽  
Hard Disk ◽  
Element Model ◽  
System Level ◽  
Disk Drives ◽  
Disk System ◽  
Shock Response ◽  
Shock Simulation ◽  
Resistance Performance ◽  
Operational Shock

Operational shock is one of key challenges for designing the ultrathin mobile hard disk drives (HDDs) due to the reduced thickness of mechanical components and their stiffness. Some simplifications in the conventional methods for operational shock simulation are not valid. In this paper, a method for system level modelling and simulation of operational shock response of HDDs has been proposed by coupling the structural finite element model of the HDD and the air bearing model. The dynamic shock response of the head-disk system in a 5 mm ultrathin HDD design is investigated. The effects of drive base stiffness, disk-ramp contact, disk spinning and disk distortion have been studied. The results reveal that the drive base deformation and ramp contact are critical for the operational shock resistance performance of ultrathin drives.

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