• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2000.04a
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• pp.714-719
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• 2000

This paper describes a transfer matrix approach to analyze the dynamics of a high sped flexible rotor system supported at 2 positions by five ceramic bearings. The rotor system is modelled as lumped parameters in which many factors are considered not only lumped inertia or mass, bending moment, shear force but also gyroscopic effect and unbalance. The equation of motion is derived in the transfer matrix form, from which the eigenvalues equation is also derived. The transfer natural frequencies and modes. The eigenvalues, eigenmodes, campbell diagram, whirling critical speed, whirling modes, and the response of unbalance are calculated and discussed.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.12
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• pp.1914-1922
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• 2004

This paper provides a comprehensive study of optimum design of a helicopter tailrotor driveshaft made of the flexible matrix composites (FMCs). Since the driveshaft transmits power while subjected to large bending deformation due to aerodynamic loadings, the FMCs can be ideal for enhancing the drivetrain performance by absorbing the lateral deformation without shaft segmentation. However, the increased lateral flexibility and high internal damping of the FMCs may induce whirling instability at supercritical operating conditions. Thus, the purpose of optimization in this paper is to find a set of tailored FMC parameters that compromise between the lateral flexibility and the whirling stability while satisfying several criteria such as torsional buckling safety and the maximum shaft temperature at steadystate conditions. At first, the drivetrain was modeled based on the finite element method and the classical laminate theory with complex modulus approach. Then, an objective function was defined as a combination of an allowable bending deformation and external damping and a genetic algorithm was applied to search for an optimum set with respect to ply angles and stack sequences. Results show that an optimum laminate consists of two groups of layers: (i) one has ply angles well below 45$^{\circ}$ and the other far above 45$^{\circ}$ and (ii) the number of layers with low ply angles is much bigger than that with high ply angles. It is also found that a thick FMC shaft is desirable for both lateral flexibility and whirling stability. The genetic algorithm was effective in converging to several local optimums, whose laminates exhibit similar patterns as mentioned above.

• Advances in nano research
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• v.8 no.3
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• pp.245-254
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• 2020

This work examines the fundamental vibrational characteristics of a spinning CNT-based nano-rotor assuming a nonlocal elasticity Euler-Bernoulli beam theory. The rotary inertia, gyroscopic, and rotor mass unbalance effects are all taken into consideration in the beam model. Assuming a nonlocal theory, two coupled 6th-order partial differential equations governing the vibration of the rotating SWCNT are first derived. In order to acquire the natural frequencies and dynamic response of the nano-rotor system, the nonlinear equations of motion are numerically solved. The nano-rotor system frequency spectrum is shown to exhibit two distinct frequencies: one positive and one negative. The positive frequency is known as to represent the forward whirling mode, whereas the negative characterizes the backward mode. First, the results obtained within the framework of this numerical study are compared with few existing data (i.e., molecular dynamics) and showed an overall acceptable agreement. Then, a thorough and detailed parametric study is carried out to study the effect of several parameters on the nano-rotor frequencies such as: the nanotube radius, the input angular velocity and the small scale parameters. It is shown that the vibration characteristics of a spinning SWCNT are significantly influenced when these parameters are changed.

• International Journal of Fluid Machinery and Systems
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• v.3 no.3
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• pp.235-244
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• 2010

Recent studies on the moment whirl due to leakage flow in the back shroud clearance of hydro-turbine runners or centrifugal pump impellers are summarized. First, destabilizing effect of leakage flow is discussed for lateral vibrations using simplified models. Then it is extended to the case of whirling motion of an overhung rotor and the criterion for the instability is obtained. The fluid moment caused by a leakage clearance flow between a rotating disk and a stationary casing was obtained by model tests under whirling and precession motion of the disk. It is shown that the whirl moment always destabilizes the whirl motion of the overhung rotor while the precession moment destabilizes the precession only when the precession speed is less than half the rotor speed. Then vibration analyses considering both whirl and precession are made by using the hydrodynamic moments determined by the model tests. For larger overhung rotors, the whirl moment is more important and cause whirl instability at all rotor speed. On the other hand, for smaller overhung rotors, the precession moment is more important and cancels the destabilizing effect of the whirl moment.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.14 no.1
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• pp.32-39
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• 2004

This research is to investigate the performance of a flexible matrix composite driveshaft with respect to shaft design parameters such as the number of layers, ply orientations, and material properties. A finite element formulation is utilized to estimate the allowable misalignment under given driving torque, the maximum temperature at steady states, and external damping for ensuring whirling stability under supercritical speed. Results indicate that the system performance can be greatly affected by the shaft laminate parameters, especially the ply orientations. Several sets of shaft parameters that will provide satisfactory overall system performance are derived.

• Journal of the Korean Society for Precision Engineering
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• v.32 no.8
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• pp.713-718
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• 2015

This article describes the calculation procedure for the dynamic characteristics of a high-pressure labyrinth seal wherein the friction force and rotor whirling force are considered; SFCP, the commercial code developed by Lee and two colleagues, is used in the procedure. The simulation results were reviewed in comparison to those of the experiments provided by Benckert; additionally, the SFCP simulation results were verified using the CFD analysis presented by Toshio Hirano. This calculation procedure may therefore be applied to the dynamic characteristics of the labyrinth seals of high-pressure turbo machinery.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.05a
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• pp.277-282
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• 2001

Partial rotor rub occurs when an obstacle on the stator of a rotating machinery disturbs the free whirling motion of a rotor, which is more common than full annular rub for the cases of rubbing in rotating machinery. The nonlinearity due to the intermittent contacts and friction during partial rotor rub makes the phenomenon complex. The several nonlinear phenomena of superharmonics, subharmonics, and jump phenomenon are demonstrated for the partial rub using an experimental apparatus in this study. A piecewise-linear model and a rebound model using the coefficient of restitution are investigated on the basis of experimental observations in order to adopt as an analytical model of the contact between the rotor and stator during whirling motion. The contact stiffness, coefficient of restitution, and friction coefficient for the contact during partial rub are calculated from the comparison between the numerical simulation and the experimental results. Also, the numerical simulations for the model of partial rub are done for the various system parameters of clearance, contact stiffness, and friction coefficient in order to find the nonlinear behavior of partial rotor rub.

• Journal of KSNVE
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• v.6 no.6
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• pp.819-825
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• 1996

Nonlinear dynamic characteristics of rubbing phenomenon in rotor dynamics are investigated experimentally and numerically. Rubbing phenomenon occurs when rotor contacts with stator during whirling and causes the large amplitude of vibration, high whirl frequencies, and possibly catastrophic failure. Rubbing has various types of forward whirl, backward rolling, backward slipping, and partial rub depending on the system parameters of rotating machinery and running speed. Experiments are performed for forward whirl and backward whirl. And numerical analysis are conducted to explain the changes between backward rolling and backward slipping. Experimental and numerical results show that the types of whirling motion depends on the friction coefficient between rotor and stator and the eccentricity of rotor.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2008.04a
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• pp.603-607
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• 2008

This paper is to investigate the effects of support conditions on the whirling stability of a supercritical composite driveshaft. Two system parameters are rigorously considered: one is the bending stiffness of the support beam/bearings and the other is the rotating internal damping of the shaft. An analytic model is developed based on finite element methods and an eigenvalue analysis is employed to estimate the shaft stability under supercritical operating conditions. Results show that the internal damping causes the whirling instability at a supercritical speed, as demonstrated in other previous studies. However, the bending stiffness of the support beam is found to affect greatly the stability behaviors of a supercritical shaft and several combinations of the shaft/beam stiffness can be identified to guarantee the stable operation even in a supercritical region.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.109-115
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• 2003

This study intends to provide an optimum design of flexible matrix composite driveshafts using a genetic algorithm. An objective function is defined as a combination of shaft flexibility, whirling stability and torsional buckling and the design variables are selected as ply angles and the shaft thickness. Results show that the genetic algorithm can successfully find an optimum solution at which the overall performance of the FMC shafts is significantly enhanced