<i>Linear and Nonlinear Rotordynamics: A Modern Treatment with
                        Applications</i>

Yamamoto, Toshio; Ishida, Yukio; Kirk, R. G.

doi:10.1115/1.1470671

Cited by 73 publications

(86 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…This is in contrast to assertion of [26][27]. In these references, the authors stated that the chaos occurs in rotors with strong nonlinearity or in rotors with weak nonlinearity but in the presence of internal resonance.…”

Section: Introductioncontrasting

confidence: 43%

“…In other words, it is shown that the chaotic response is possible for a shaft with weak nonlinearity without the existence of any internal resonance. It is observed that the chaotic motion occurs in the rotor for any value of rotary inertia and it is not necessary that the rotor has a small gyroscopic moment with asymmetry nonlinearity [26][27].…”

Section: Introductionmentioning

confidence: 99%

“…In references [26][27], the authors stated that the chaos occurs in rotors with strong nonlinearity or in rotors with weak asymmetry nonlinearity but in the presence of internal resonance. Internal resonances occurs when the gyroscopic moment is small.…”

Section: A Short Lightly Damped Rotating Shaftmentioning

confidence: 99%

“…Yamamoto and Ishida [26] pointed out that the chaotic vibration in a rotor with weak nonlinearity is possible when the effect of gyroscopic moment is small. Indeed, when the shaft is slender, and the gyroscopic effect is small, internal resonances of type 1:(-1) may occur due to nonlinear asymmetry and this in turn may lead to a chaotic response.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Chaos and Bifurcation in Nonlinear Inextensional Rotating Shafts

Hosseini

2018

Scientia Iranica

View full text Add to dashboard Cite

In this paper, bifurcation and chaotic behavior of in-extensional rotating shafts are investigated. The shaft is modeled as a Rayleigh simply supported beam, spinning with constant rotational speed. Using two-mode Galerkin truncation, the partial differential equations of motion are discretized and then with the aid of numerical simulations, the dynamical behavior of the rotating shaft is studied. Using tools from nonlinear dynamics, such as time history, bifurcation diagram, Poincaré map, Lyapunov exponents, and amplitude spectra, a comprehensive analysis is made to characterize the complex behavior of the rotating shaft. Periodic (synchronous), quasiperiodic, chaotic and transient chaotic responses are observed in the neighborhood of the second critical speed. The effect of rotary inertia and damping on the dynamics of the rotating shaft is considered. It is shown that the chaotic response is possible for a shaft with weak nonlinearity without the existence of any internal resonance.

show abstract

Section: Introductioncontrasting

confidence: 43%

Section: Introductionmentioning

confidence: 99%

Section: A Short Lightly Damped Rotating Shaftmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Chaos and Bifurcation in Nonlinear Inextensional Rotating Shafts

Hosseini

2018

Scientia Iranica

View full text Add to dashboard Cite

show abstract

“…All components of cutting tool, holder, spindle-bearings assembly are modeled as elements of discrete disk and bearings and the multisegment beams with elasticity and distributed mass. Based on procedure of the finite element discretization in many literatures (Lalanne and Ferraris, 1998;Friswell et al, 2001;Yamamoto and Ishida, 2001), the detail of equations will not be derived here and only the equation of motions are shown below. …”

Section: Theoretical Formulationmentioning

confidence: 99%

Identification of a Machine Tool Spindle Critical Frequency through Modal and Imbalance Response Analysis

Jauhari¹,

Widodo²,

Haryanto³

2016

American Journal of Engineering and Applied Sciences

View full text Add to dashboard Cite

Abstract:The most important part for machine tool system is spindle system. The structural properties of spindle will affect to the productivity of machining process and the work pieces quality. Thus it is necessary and very important to know its spindle dynamic behaviors for avoiding forced vibration due to resonance. The Finite Element Method (FEM) has been adopted for obtaining spindle dynamic behaviors. FEM model and analysis of dynamic behaviors for the spindle system are similar to those developed in rotor-dynamic. The main purpose of this study, we implemented an ANSYS Parametric Design Language (APDL) program based on finite element method for obtaining full analysis of rotor dynamic in order to investigate the spindle dynamic behaviors. The programs efficiently performed the full analysis by determining the Campbell diagrams, critical speeds and response of imbalance due to mass unbalance at the cutting tool. Results show that the critical speeds were calculated previously are far enough from the spindle speeds operating range, then the spindle would not experience resonance and the maximum response of imbalance occurs on operating speed is also in acceptable limit. ANSYS Parametric Design Language (APDL) can be used by spindle designer as tools in order to increase the product quality, reducing cost and time consuming in the design and development stages.

show abstract

An efficient approach for whirling speeds and mode shapes of uniform and nonuniform Timoshenko shafts mounted by arbitrary rigid disks

Hsu

2020

Engineering Reports

View full text Add to dashboard Cite

In theory, the whirling motion of a shaft-disk system is three-dimensional (3D), however, if the transverse displacement in the vertical principal xy-plane and that in the horizontal principal xz-plane for the cross-section of the shaft located at the axial coordinate x are represented by a complex number, then the mass moment of inertia for unit shaft length (at x) and that for each rigid disk i can be combined with their associated gyroscopic moments (GMs) to form the frequency-dependent equivalent mass moments of inertia, respectively, in the equations of motion for the rotating Timoshenko shaft carrying arbitrary rigid disks. It is found that the above-mentioned equations for the rotating 3D shaft-disk system take the same forms as the corresponding ones for the associated stationary two-dimensional (2D) Timoshenko beam carrying the same number of disks, so that the approaches for the free vibration analyses of the stationary 2D beam-disk system can be used to solve the title problem for obtaining the whirling speeds and mode shapes of a rotating 3D shaft-disk system. Since the order of the eigenproblem equation derived from the presented approach is much smaller than that derived from the conventional finite element method (FEM), the computer time consumed by the former is much less than that by the latter. In addition, the solutions obtained from the presented approach are exact and may be the benchmark for evaluating the accuracy of solutions of the other approximate methods. Numerical examples reveal that the presented approach is available for the uniform or nonuniform shaft-disk system, and the obtained results are very close to those obtained from existing literature or the FEM. The formulation of this article is available for a shaft-disk system with various boundary conditions (BCs), to save space, only the cases with pinned-pinned BCs are illustrated. K E Y W O R D S Timoshenko shaft, gyroscopic moment, equivalent mass moment of inertia, whirling speeds and mode shapes This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

show abstract

Linear and Nonlinear Rotordynamics: A Modern Treatment with Applications

Cited by 73 publications

References 0 publications

Chaos and Bifurcation in Nonlinear Inextensional Rotating Shafts

Chaos and Bifurcation in Nonlinear Inextensional Rotating Shafts

Identification of a Machine Tool Spindle Critical Frequency through Modal and Imbalance Response Analysis

An efficient approach for whirling speeds and mode shapes of uniform and nonuniform Timoshenko shafts mounted by arbitrary rigid disks

Contact Info

Product

Resources

About