Effects of Nonlinear Damping Washers on the Automatic Ball Balancer for Optical Disk Drives

2005 ◽  
Author(s):  
Cheng-Kuo Sung ◽  
Paul C. P. Chao ◽  
Ben-Cheng Yo
Keyword(s):  
Nonlinear Dynamics ◽  
Steady State ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Dynamic Performance ◽  
Nonlinear Damping ◽  
Disk Drives ◽  
Optical Disc ◽  
Scaled Model ◽  
Jump Phenomena

This study is devoted to explore the effect of nonlinear dynamics of damping washers on the dynamic performance of automatic ball balancer (ABB) system installed in optical disc drives. The ABB is generally used on rotational system to reduce vibration. Researches have been conducted to study the performance of the ABB by investigating the nonlinear dynamics of the system; however, the model adopted often consider the damping washer in a typical ABB suspension system as a linear one, which does not reflect the fact that the practical washers are inevitably exhibit nontrivial nonlinear dynamics at some range of operation, deviating the ABB performance away from the expecteds. In this study, a complete dynamic model of the ABB including a detailed nonlinear model of the damping washers based on experimental data for practical wahers is established. The method of multiple scales is then applied to formulate a scaled model to find all possible steady-state ball positions and analyze stabilities. It is found that with reasonable level of nonlinearity, the balancing balls of the ABB are still reside at the desired positions at steady state, rendering expected vibration reduction; however, jump phenomena also occurs as the spindle operated through natural frequency of the suspension, causing unwanted system vibrations. Numerical simulations and experiments are conducted to verify the theoretical findings. The obtained results are used to predict the level of residual vibration, with which the guidelines on choices of the nonlinear damping washers are distilled to achieve desired performance.

Effects of Rolling Friction of the Balancing Balls on the Automatic Ball Balancer for Optical Disk Drives

2005 ◽  
Vol 127 (4) ◽  
pp. 845-856 ◽  
Author(s):  
Paul C.-P. Chao ◽  
Cheng-Kuo Sung ◽  
Hui-Chung Leu
Keyword(s):  
Steady State ◽  
Multiple Scales ◽  
Rolling Friction ◽  
Friction Model ◽  
Optical Disk ◽  
Contact Dynamics ◽  
Hertzian Contact ◽  
Disk Drives ◽  
Scaled Model ◽  
Stick Slip

This study is devoted to evaluating the performance of an automatic ball-type balance system (ABB) installed in optical disk drives (ODDs) with consideration of the rolling friction between the balancing balls and the ball-containing race of the ABB. Research has been conducted to study the performance of the ABB by investigating the nonlinear dynamics of the system; however, the model adopted to describe the rolling friction between the balancing balls and their race was a simple stick-slip type, which does not reflect the realistic contact dynamics, leading to an inaccuracy in predicting ABB performance. In this study, a complete dynamic model of the ABB including a detailed rolling friction model for the balls based on Hertzian contact mechanics and hysteresis loss is established. The method of multiple scales is then applied to formulate a scaled model to find all possible steady-state ball positions and analyze stabilities. It is found that possible steady-state residing positions of the ball inside the race are multiple and form continuous ranges. Numerical simulations and experiments are conducted to verify the theoretical findings, especially for the rolling friction model. The obtained results are used to predict the level of residual vibration, with which the guidelines on dimension design and material choices of the ABB are distilled to achieve desired performance.

Effects of Rolling Friction of the Balancing Balls on the Automatic Ball Balancer for Optical Disk Drives

2004 ◽  
Author(s):  
Paul C.-P. Chao ◽  
Chi-Wei Chiu ◽  
Cheng-Kuo Sung ◽  
Hui-Chung Leu
Keyword(s):  
Steady State ◽  
Multiple Scales ◽  
Rolling Friction ◽  
Friction Model ◽  
Optical Disk ◽  
Contact Dynamics ◽  
Disk Drives ◽  
Scaled Model ◽  
Stick Slip ◽  
Balance System

This study is devoted to evaluate the performance of an automatic ball-type balance system (ABB) installed in optical disk drives (ODD) with consideration of the rolling friction between the balancing balls and the ball-containing race of the ABB. Researches have been conducted to study the performance of the ABB by investigating the nonlinear dynamics of the system; however, the rolling friction model adopted was a simple stick-slip type, which does not reflect the true contact dynamics between rolling balls and their races, leading to an inaccuracy in predicting ABB performance. In this study, a complete dynamic model of the ABB including a detailed rolling friction model based on contact mechanics is established. The method of multiple scales is then applied to formulate a scaled model to find all possible steady-state ball positions and analyze stabilities. It is found that possible steady-state residing positions of the ball inside the race are multiple and form continuous ranges. Numerical simulations and experiments are conducted to verify the validness of the theoretical findings. The obtained results are used to predict the level of residual vibration, with which the guidelines on dimension design and material choices of the ABB are distilled to achieve desired performance.

Dynamic Analysis of the Optical Disk Drives Equipped with an Automatic Ball Balancer with Consideration of Torsional Motions

2005 ◽  
Vol 72 (6) ◽  
pp. 826-842 ◽  
Author(s):  
Paul C. P. Chao ◽  
Cheng-Kuo Sung ◽  
Chun-Chieh Wang
Keyword(s):  
Multiple Scales ◽  
Spindle Motor ◽  
Optical Disk ◽  
Torsional Stiffness ◽  
Torsional Motion ◽  
Disk Drives ◽  
Scaled Model ◽  
Supporting Plate ◽  
Steady State Solutions ◽  
Balanced Solution

This study is dedicated to evaluate the performance of an automatic ball-type balancer system (ABS) installed in optical disk drives (ODDs) with consideration of the relative torsional motion between the ODD case and the spindle-disk-ABS-turntable system, noting that the turntable is the supporting plate structure for disk, pickup, and spindle motor inside the ODD. To this end, a complete dynamic model of the ABS considering the torsional motion is established with assuming finite torsional stiffness of the damping washers, which provides suspension of the spindle-disk-ABS-turntable system to the ODD case. Considering the benchmark case of a pair of balancing balls in an ABS, the method of multiple scales is then applied to formulate a scaled model for finding all possible steady-state solutions of ball positions and analyzing corresponding stabilities. The results are used to predict the levels of residual vibration, with which the performance of the ABS can then be reevaluated. Numerical simulations are conducted to verify theoretical results. It is deduced from both analytical and numerical results that the spindle speed of an ODD could be operated above both primary translational and secondary torsional resonances in order to guarantee stabilization of the desired balanced solution for a substantial vibration reduction.

Multi-Frequency Multi-Modal Excitation of a Heated Annular Plate

2006 ◽  
Author(s):  
Haider N. Arafat ◽  
Ali H. Nayfeh
Keyword(s):  
Nonlinear Dynamics ◽  
Internal Resonance ◽  
Radial Direction ◽  
Natural Frequencies ◽  
Annular Plate ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Plate Theory ◽  
Frequency Excitation ◽  
The Difference

The forced nonlinear dynamics of a pre-buckled thermally loaded annular plate are investigated. The plate is modeled using the von Ka´rma´n plate theory and the heat equation. The heat, which is generated by the difference between the uniformly distributed temperatures at the inner and outer boundaries, is assumed to symmetrically flow in the radial direction. The amount of heat affects the natural frequencies, which may give rise to different internal resonance conditions. The method of multiple scales is used to examine the system axisymmetric responses when it is driven by an external multi-frequency excitation. The plate responses could be very complex exhibiting Hopf and cyclic-fold bifurcations, quasi-periodicity, chaos, and multiplicity of attractors.

On Nonlinear Dynamics of Nanotweezers

2016 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Bin Liu
Keyword(s):  
Nonlinear Dynamics ◽  
Frequency Response ◽  
Parametric Resonance ◽  
Taylor Series ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Van Der Waals ◽  
Van Der Waals Forces ◽  
The Other ◽  
Amplitude Frequency Response

This paper deals with amplitude-frequency response of electrostatic nanotube nanotweezer device system. Soft alternating current (AC) of frequency near natural frequency actuates the nanotubes. This leads the system into parametric resonance. The Method of Multiple Scales (MMS) in which the nonlinear electrostatic and van der Waals forces are expanded in Taylor series is used to compare two expansions, one up to third power and the other up to fifth power. The frequency response of the system is reported and the effects of van der Waals forces, electrostatic forces, and damping forces on the frequency response are investigated.

scholarly journals Principal Parametric Resonance of Axially Accelerating Viscoelastic Beams: Multi-Scale Analysis and Differential Quadrature Verification

2012 ◽  
Vol 19 (4) ◽  
pp. 527-543 ◽  
Author(s):  
Li-Qun Chen ◽  
Hu Ding ◽  
C.W. Lim
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Steady State ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Steady State Response ◽  
Governing Equations ◽  
State Response ◽  
Non Linear ◽  
Axial Speed

Transverse non-linear vibration is investigated in principal parametric resonance of an axially accelerating viscoelastic beam. The axial speed is characterized as a simple harmonic variation about a constant mean speed. The material time derivative is used in the viscoelastic constitutive relation. The transverse motion can be governed by a non-linear partial-differential equation or a non-linear integro-partial-differential equation. The method of multiple scales is applied to the governing equations to determine steady-state responses. It is confirmed that the mode uninvolved in the resonance has no effect on the steady-state response. The differential quadrature schemes are developed to verify results via the method of multiple scales. It is demonstrated that the straight equilibrium configuration becomes unstable and a stable steady-state emerges when the axial speed variation frequency is close to twice any linear natural frequency. The results derived for two governing equations are qualitatively the same, but quantitatively different. Numerical simulations are presented to examine the effects of the mean speed and the variation of the amplitude of the axial speed, the dynamic viscosity, the non-linear coefficients, and the boundary constraint stiffness on the instability interval and the steady-state response amplitude.

A Nonlinear Oscillator Lanchester Damper

1987 ◽  
Vol 109 (4) ◽  
pp. 343-347 ◽  
Author(s):  
K. R. Asfar ◽  
A. H. Nayfeh ◽  
K. A. Barrash
Keyword(s):  
Steady State ◽  
Nonlinear Oscillator ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Harmonic Excitation ◽  
Second Order ◽  
Numerical Results ◽  
Nonlinear Spring ◽  
Uniform Expansion ◽  
Steady State Solutions

The method of multiple scales is used to investigate the effect of a nonlinear spring in the main system on the performance of Lanchester-type absorbers. A second-order uniform expansion is obtained for the response of the system to a harmonic excitation. Numerical results for steady-state solutions illustrating the influence of the nonlinearity and damping factors on the response are presented. A softening-type effective nonlinearity dominates the system and considerably improves its damping.

Nonlinear Dynamics of a Parametrically Excited Laminated Beam: Deterministic Excitation

2011 ◽  
Vol 464 ◽  
pp. 260-263 ◽  
Author(s):  
Xiang Jun Lan ◽  
Zhi Hua Feng ◽  
Hong Lin ◽  
Xiao Dong Zhu
Keyword(s):  
Nonlinear Dynamics ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Plate Theory ◽  
Third Order ◽  
Force Amplitude ◽  
Laminated Beam ◽  
Galerkin Approach ◽  
Nonlinear Dynamic Equation ◽  
Nonlinear Behaviors

The nonlinear dynamic equation of a laminated beam subject to parametrically deterministic excitation is derived based on the general von Karman-type equations and the Reddy third-order shear deformation plate theory. The first mode parametric resonance is taken into consideration using Galerkin approach. The modulation equations are obtained with the method of multiple scales. The frequency-amplitude and force-amplitude characters are investigated. Results show that the nonlinear behaviors belong to hardening effect.

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