• Journal of the Korean Society of Manufacturing Technology Engineers
• /
• v.24 no.1
• /
• pp.110-116
• /
• 2015

This study investigates the whirling stability of a rotating shaft-disk system under parametric excitation using periodically varying torque. The equations of motion were derived using a lumped-mass model, and the Floquet method was employed to find the effects of torque fluctuation, internal and external damping, and rotational speed on whirling stability. Results indicated that the effect of torque fluctuation was considerable on the instability around resonance, but minimal on supercritical instability. Stability diagrams were sensitive to the parametric excitation frequency; critical torque decreased upon increasing excitation frequency, with faster response convergence or divergence. In addition, internal and external damping had a considerable effect on unstable regions, and reduced the effects of the parametric excitation frequency on critical torque and speed. Results obtained from the Floquet approach were in good agreement with those obtained by numerical integration, except for some cases with Floquet multipliers very close to unity.

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

• Structural Engineering and Mechanics
• /
• v.45 no.1
• /
• pp.69-93
• /
• 2013

The present study deals with the dynamics of the flapwise (out-of-plane) vibrations of a rotating, internally damped (Kelvin-Voigt model) tapered Bernoulli-Euler beam carrying a heavy tip mass. The centroid of the tip mass is offset from the free end of the beam and is located along its extended axis. The equation of motion and the corresponding boundary conditions are derived via the Hamilton's Principle, leading to a differential eigenvalue problem. Afterwards, this eigenvalue problem is solved by using Frobenius Method of solution in power series. The resulting characteristic equation is then solved numerically. The numerical results are tabulated for a variety of nondimensional rotational speed, tip mass, tip mass offset, mass moment of inertia, internal damping parameter, hub radius and taper ratio. These are compared with the results of a conventional finite element modeling as well, and excellent agreement is obtained.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.14 no.1
• /
• pp.32-39
• /
• 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 of Manufacturing Technology Engineers
• /
• v.20 no.1
• /
• pp.40-46
• /
• 2011

This paper is to investigate the effects of the asymmetrical support stiffness on the stability of a supercritical driveshaft with asymmetrical shaft stiffness and anisotropic bearings. The equations of motion is derived for a system including a rigid disk, a massless flexible asymmetric shaft, anisotropic bearings and a support beam. The Floquet theory is applied to perform the stability analysis with the variation of the support stiffness, the shaft asymmetry, the shaft damping and the shaft speed. The results show that the asymmetric support stiffness is closely related to the stability caused by primary resonance as well as the supercritical operation. First, the stiffness variation can stabilize the system around primary resonance by weakening the parametric resonance from the shaft asymmetry. Second, it also improve the stability characteristics at a supercritical operation when the support stiffness is not so high relative to the shaft stiffness.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2003.05a
• /
• pp.107-113
• /
• 2003

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.

• Transactions of the Korean Society of Machine Tool Engineers
• /
• v.15 no.2
• /
• pp.93-98
• /
• 2006

This study provides a comprehensive experimental study on the dynamic characteristics of a flexible matrix composite(FMC) driveshaft. A primary objective is to verify the analytic results of the FMC drivetrain based on the equivalent complex modulus approach and the classical lamination theory. A test rig has been constructed, which consists of a FMC shaft, a foundation beam, bearings, external dampers and a driving motor. The frequency response functions and transient responses are obtained from the external excitation and the spin-up testings. It turns out that the analytic results are in good agreement with the experimental ones.

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

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2005.11a
• /
• pp.123-126
• /
• 2005

This study provides a comprehensive experimental study on the dynamic characteristics of a flexible matrix composite(FMC) driveshaft. A primary objective is to verify the analytic results of the FMC drivetrain based on the equivalent complex modulus approach and the classical lamination theory. A testrig has been constructed, which consists of a FMC shaft, a foundation beam, bearings, external dampers and a driving motor. The frequency response functions and transient responses are obtained from the external excitation and the spinup testings. It turns out that the analytic results are in good agreement with the experimental ones.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2007.05a
• /
• pp.859-865
• /
• 2007

This paper presents a method to analyze the unbalance response of a high speed polygon mirror scanner motor supported by sintered bearing and flexible supporting structures by using the finite element method and the mode superposition method. The appropriate finite element equations for polygon mirror are described by rotating annular sector element using Kirchhoff plate theory and von Karman non-linear strain, and its rigid body motion is also considered. The rotating components except for the polygon mirror are modeled by Timoshenko beam element including the gyroscopic effect. The flexible supporting structures are modeled by using a 4-node tetrahedron element and 4-node shell element with rotational degrees of freedom. Finite element equations of each component of the polygon mirror scanner motor and the flexible supporting structures are consistently derived by satisfying the geometric compatibility in the internal boundary between each component. The rigid link constraints are also imposed at the interface area between sleeve and sintered bearing to describe the physical motion at this interface. A global matrix equation obtained by assembling the finite element equations of each substructure is transformed to a state-space matrix-vector equation, and both damped natural frequencies and modal damping ratios are calculated by solving the associated eigenvalue problem by using the restarted Arnoldi iteration method. Unbalance responses in time and frequency domain are performed by superposing the eigenvalues and eigenvectors from the free vibration analysis. The validity of the proposed method is verified by comparing the simulated unbalance response with the experimental results. This research also shows that the flexibility of supporting structures plays an important role in determining the unbalance response of the polygon mirror scanner motor.