Secondary critical speed of flexible rotors with inertia slots

Sakata, Masaru; Endo, Mitsuru; Kishimoto, Kikuo; Hayashi, Naoki

doi:10.1016/0022-460x(83)90439-x

Cited by 5 publications

(5 citation statements)

References 2 publications

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“…Unstable whirl in the region of "rst order critical vibrations was dealt with previously in references [7,8]. Sakata et al [6] discussed and analyzed the slots both experimentally and theoretically using both transfer matrix and three-dimensional "nite element method. However, the model rotors treated in reference [6] are simpli"ed ones in which the reduction of #exural rigidity due to the longitudinal slots for the electric windings has been represented by parallel #ats on the model rotors.…”

Section: Introductionmentioning

confidence: 98%

“…The dynamics of slotted shaft needs more attention particularly with the emergence of new materials such as composites. Sakata et al [6], summarized second order (or twice per revolution) forced vibrations excited by the weight of the rotor. Unstable whirl in the region of "rst order critical vibrations was dealt with previously in references [7,8].…”

Section: Introductionmentioning

confidence: 99%

“…Sakata et al [6] discussed and analyzed the slots both experimentally and theoretically using both transfer matrix and three-dimensional "nite element method. However, the model rotors treated in reference [6] are simpli"ed ones in which the reduction of #exural rigidity due to the longitudinal slots for the electric windings has been represented by parallel #ats on the model rotors. Goodwin [9] points out that it is important for the designer to be aware of the potential region of instability de"ned by the eigenfrequencies associated with the di!erent lateral sti!nesses of the rotor in two orthogonal directions.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Vibration Characteristics of Slotted Shafts

Sekhar

Srinivas

2002

Journal of Sound and Vibration

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Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Vibration Characteristics of Slotted Shafts

Sekhar

Srinivas

2002

Journal of Sound and Vibration

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“…critical speed (Smith 1933). The relevant literature primarily identifies these gravity critical speeds (Coleman & Feingold 1958;Genta 2005), with subsequent linear analyses under various idealizations: Jeffcot rotor models on rigid bearings (Taylor 1940;Childs 1993;Rajalingham et al 1993;Genta 2005), Jeffcot rotors on flexible pedestals (Kondo & Kimura 1991), Euler-Bernoulli beam models (Bishop & Parkinson 1965;Sakata et al 1983) and three-dimensional finite element (FE) models (Rao & Sreenivas 2003). Experimental results on horizontal cantilever shafts were reported, for example, by Hull (1961), and on a simply supported shaft with a centrally mounted wheel were reported by Bishop & Mahalingam (1965).…”

Section: Introductionmentioning

confidence: 99%

Nonlinear secondary whirl of an overhung rotor

Nandakumar

Chatterjee

2009

Proc. R. Soc. A.

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Gravity critical speeds of rotors have hitherto been studied using linear analysis, and ascribed to rotor stiffness asymmetry. Here, we study an idealized asymmetric nonlinear overhung rotor model of Crandall and Brosens, spinning close to its gravity critical speed. Nonlinearities arise from finite displacements, and the rotor's static lateral deflection under gravity is taken as small. Assuming small asymmetry and damping, slow modulations of whirl amplitudes are studied using the method of multiple scales. Inertia asymmetry appears only at second order. More interestingly, even without stiffness asymmetry, the gravity-induced resonance survives through geometric nonlinearities. The gravity resonant forcing does not influence the resonant mode at leading order, unlike the typical resonant oscillations. Nevertheless, the usual phenomena of resonances, namely saddle-node bifurcations, jump phenomena and hysteresis, are all observed. An unanticipated periodic solution branch is found. In the three-dimensional space of two modal coefficients and a detuning parameter, the full set of periodic solutions is found to be an imperfect version of three mutually intersecting curves: a straight line, a parabola and an ellipse.

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“…The method has since been used widely for rotordynamics analysis (e.g. Flack & Rooke 1980;Sakata et al 1983;Hsieh et al 2006). Several papers have concentrated on finite beam elements of various kinds (e.g.…”

Section: Literature Reviewmentioning

confidence: 99%

Modal projections for synchronous rotor whirl

2008

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We consider the synchronous whirl of arbitrary axisymmetric rotors supported on rigid bearings. Prior computational treatments of this problem were based on adding elementlevel gyroscopic terms to the governing equations. Here, we begin with a direct continuum formulation wherein gyroscopic terms need not be added on separately and explicitly: all gyroscopic effects are captured implicitly within the continuum elastodynamics. We present two new methods for obtaining the whirl speed, where we project the dynamic equilibrium equations of the rotor on to a few of its non-spinning vibration mode shapes. The first modal projection method is direct and more accurate, but requires numerical evaluation of more demanding integrals. The second method is iterative and involves a small approximation, but is simpler. Both the methods are based on one new insight: the gyroscopic terms used in other treatments are essentially the result of a prestress in the rotor caused by the non-zero spin rate, and may be incorporated as such in the continuum formulation. The accuracy of the results obtained, for several examples, is verified against detailed calculations with a commercial finiteelement package, against our own nonlinear finite-element code or against analytical estimates. For further verification and illustration, a closed-form analytical solution for a simple problem, obtained using our method, matches the results obtained with explicit gyroscopic terms.

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Secondary critical speed of flexible rotors with inertia slots

Cited by 5 publications

References 2 publications

Vibration Characteristics of Slotted Shafts

Vibration Characteristics of Slotted Shafts

Nonlinear secondary whirl of an overhung rotor

Modal projections for synchronous rotor whirl

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