• Title/Summary/Keyword: Stiffness and Damping Coefficients

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Analysis of Tilting Pad Journal Bearings Considering Pivot Stiffness (피봇 강성을 고려한 틸팅 패드 저널 베어링의 해석)

  • Choi, Tae Gyu;Kim, Tae Ho
    • Tribology and Lubricants
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    • v.30 no.2
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    • pp.77-85
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    • 2014
  • This study set out to predict the load capacity and rotordynamic coefficients of tilting-pad journal bearings, taking the pivot stiffness into account. The analysis uses rocker-back (cylindrical) and ball in socket (spherical) pivot models, both of which are based on Hertzian contact stress theory. The models ascertain the non-linear elastic deformation of the pivots according to the applied load, pivot geometry, and material properties. At present, the Reynolds equation for an isothermal, isoviscous, and incompressible fluid is used to calculate the film pressure by using the finite-element method, after which the Newton-Raphson method is used to simultaneously find the journal center location, pad angles, and pivot deflections. The bearing analysis, excluding the pivot models, is validated using predictions those are readily available in the literature. As the rotor speed increases, the predicted journal eccentricity and damping coefficients decrease, but the stiffness coefficients increase, as expected. Most importantly, the implementation of the pivot models increases the journal eccentricity but significantly decreases the stiffness and damping coefficients of the tilting-pad journal bearings.

Added Mass, Viscous Damping and Fluid-stiffness Coefficients on the Rotating Inner Cylinder in Concentric Annulus (동심환내의 회전체 진동에 의한 부가질량, 유체감쇠계수 및 유체탄성계수에 관한 연구)

  • 심우건;박진호;김기선
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2001.05a
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    • pp.695-701
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    • 2001
  • While a rotating inner cylinder executes a periodic translational motion in concentric annulus, the vibration of the rotating inner cylinder is induced by fluid-dynamic forces acting on the cylinder. In the previous study related to journal bearing, the unsteady viscous flow in the annulus and the fluid-dynamic forces were evaluated based on a numerical approach. Considering the dynamic-characteristics of unsteady viscous flow, an approximate analytical method has been developed for estimating added mass, viscous damping and fluid-stiffness coefficients. For the study of flow-induced vibrations and related instabilities, it is of interest to separate the coefficients from the fluid-dynamic forces. The added-mass and viscous damping coefficients for very narrow annular configurations, as journal bearing. can be approximated by considering the gap ratio to the radius of inner cylinder, while the fluid-stiffness coefficient is related to the Reynolds number, the oscillatory Reynolds number and the gap ratio.

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Effect of Seal Wear on the Rotordynamics of a Multistage Turbine Pump (시일의 마멸이 다단 터빈 펌프 동특성에 미치는 영향)

  • 김영철;이동환;이봉주
    • Journal of KSNVE
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    • v.7 no.6
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    • pp.1015-1023
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    • 1997
  • Rotordynamic analysis of a multistage turbine pump using finite element method is performed to investigate the effects of seal wear on its system behavior. Stiffness and damping coefficents of the 2-axial grooved bearing are obtained as functions of rotating speed. Stiffness and damping coefficients of plane annuler seals are calculated as functions of rotating speed as well as seal clearance of seals become larger, these stiffness and damping coefficients decrease drastically so that there can be significant changes in whirl natural frequencies and damping characteristics of the pump rotor system. Although a pump is designed to operate with a sufficient seperation margin from the 1st critical speed, seal wear due to long operation may cause a sudden increase in vibration amplitude by resonance shift and reduce seal damping capability.

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Dynamic Analysis of a Large Tilting Pad Journal Bearing Including the Effects of Temperature Rise and Turbulence (온도상승 및 난류효과를 고려한 대형 틸팅패드 저널베어링의 동특성 해석)

  • 하현천;김경웅
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.19 no.2
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    • pp.313-321
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    • 1995
  • The effects of the temperature rise and the turbulence are very important factors to predict the accurate performance of a large tilting pad journal bearing. In this study, the dynamic characteristics of a large tilting pad journal bearing are analyzed, taking into account the three dimensional variation of lubricant viscosity and turbulence. The effects of the temperature rise and the turbulence on the stiffness and damping coefficients are investigated in comparison with the results from the laminar or isothermal theory. The stiffness and damping coefficients increase due to the turbulence but decrease due to the temperature rise. The results show that the effects of both the temperature rise and turbulence must be considered simultaneously in order to predict the dynamic characteristics of a large tilting pad journal bearing more accurately.

An Optimum Design of Herringbone Grooved Journal Bearings for Spindle Motor of Hard Disk Drive System (HDD 스핀들용 빗살무늬 저널베어링의 최적설계)

  • ;Y. Muraki;M. Tanaka
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2002.05a
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    • pp.530-532
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    • 2002
  • This paper presents an optimum design of herringbone grooved journal bearing for spindle motor of hard disk drive (HDD) system. In addition to the conventional “rectangular” groove, various groove profiles are designed. The stiffness and damping coefficients of the oil film and frictional torque are calculated and compared for tile various groove profiles. The “circular”, “valley”, and “reversed saw tooth” grooves do not produce high direct stiffness, since they partly increase the groove depths in the direction of lubricant flow, causing to reduce the pumping action of the bearing. The maximum direct stiffness can be obtained by the “rectangular”, “saw tooth”, and “step” grooves. With the same cross sectional area of the grooves, these three grooves have the same maximum stiffness, damping coefficients, and frictional torque. Among these recommendable grooves, the saw tooth groove may keep its original profile for long, enduring metal-to-metal contact during startup and shutdown.

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Eigenderivative Analysis by Modification of Design Parameter in the Proportional Damping System (설계파라미터 변경에 의한 비례 감쇠구조물의 동특성 변화 해석)

  • Lee, Jung-Woo;Oh, Jae-Eung;Lee, Jung-Youn
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.16 no.5 s.110
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    • pp.470-478
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    • 2006
  • An efficient method for change of eigenvectors and eigenvalues due to the modifying proportional damping structure using sensitivity coefficients is presented. Sensitivity coefficients are determined by iteration with eigenvalue and eigenvectors before modification of system. The proposed method is applied to examples of 3 degrees of freedom system and plate by modifying mass and stiffness. The predicted change of eigenvectors and eigenvalues are in a good agreement with these from the structural re-analysis after modification of mass and stiffness.

Tribological Induced Dynamic Characteristics Analysis of HDD Slider-Suspension Assembly (트라이볼로지 문제를 고려한 하드 디스크 슬라이더-서스펜션의 동특성 해석)

  • 김청균;차백순
    • Tribology and Lubricants
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    • v.17 no.1
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    • pp.64-71
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    • 2001
  • This paper presents dynamic responses of disk flutter and bump in HDD slider. The slider is modeled for three degree-of-freedom systems, which are capable of lifting, pitching, and rolling motions. In numerical analysis, loads from air pressure, preload and static moments from the slider, and stiffness and damping coefficients of the suspension are considered for investigating the dynamic characteristics analysis. The numerical results are presented as functions of typical parameters such as a disk velocity, stiffness and damping coefficients of the suspension, and skew angle.

Friction Effects on the Performance of Double-Bumped Air Foil Bearings (이중범프포일 공기베어링의 성능에 미치는 마찰효과)

  • Kim, Young-Cheol;Lee, Dong-Hyun;Kim, Kyung-Woong
    • Tribology and Lubricants
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    • v.23 no.4
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    • pp.162-169
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    • 2007
  • This paper deals with friction effects on the performance of double-bumped AFBs. The stiffness and damping coefficients of the double bump vary depending on the external load and its friction coefficient. The double bump can be either in the single or double active region depending on vertical deflection. The equivalent stiffness and damping coefficients of the bump system are derived from the vertical and horizontal deflection of the bump, including the friction effect. A static and dynamic performance analysis is carried out by using the finite difference method and the perturbation technique. The results of the performance analysis for a double-bumped AFB are compared with those obtained for a single-bumped AFB. This paper successfully proves that a double bumped AFB has higher load capacity, stiffness, and damping than a single-bumped AFB in a heavily loaded condition.

A Study on the Actively Controlled Aerostatic Journal Bearing using Cylindrical Capacitance Displacement Sensor (원통형 변위센서를 장착한 능동 공기 베어링에 관한 연구)

  • Park, Sang-Shin;Kim, Gyu-Ha
    • Tribology and Lubricants
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    • v.24 no.1
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    • pp.34-43
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    • 2008
  • In this paper, an actively controlled aerostatic bearing is studied to overcome the defects of air bearing such as low stiffness and damping coefficients. The actively controlled aerostatic bearing is composed of aerostatic bearings, non-contact type of displacement sensors, piezoelectric actuators and controllers. The cylindrical capacitance sensor (CCS) is used as the displacement sensor. The reason for using CCS instead of the commercial gap sensor is that it can give us the pure error motion of the spindle because it removes the roundness error or the geometric errors in the spindle. The controller is designed by the state space equation and quadratic optimal control theory. The characteristic data of the actively controlled aerostatic bearing system in the frequency domain are presented and the stiffness and damping coefficients of the bearing are mentioned. This paper shows the possibility to reduce the motion error up to 6000 rpm.