On the Structural Nonlinearity of Rotating Shafts

1994 ◽  
Vol 116 (3) ◽  
pp. 404-407 ◽  
Author(s):  
Tatu Leinonen
Keyword(s):  
Theoretical Model ◽  
General Theory ◽  
Nonlinear Model ◽  
Rotating Shaft ◽  
Structural Nonlinearity ◽  
Rotating Shafts ◽  
Bending Behavior

This paper presents a nonlinear model to describe the bending behavior of a rotating shaft, based on the general theory of a bending bar. Justification for this theoretical model is provided by tests, the resulting curves fitting the observed results more closely than those of other models. In particular, the model explains why infinite points of deformation coming from linear theories can be avoided.

On the Nonlinear Behavior of Rotating Shafts

1991 ◽  
Author(s):  
Tatu Leinonen
Keyword(s):  
Theoretical Model ◽  
General Theory ◽  
Nonlinear Model ◽  
Nonlinear Behavior ◽  
Rotating Shaft ◽  
Rotating Shafts ◽  
Bending Behaviour

Abstract This paper presents a nonlinear model to describe the bending behaviour of a rotating shaft, based on the general theory of a bending bar. Justification for this theoretical model has been provided by tests, the resulting curves more closely fitting observed results than those of other models.

Bisynchronous Torsional Vibrations in Rotating Shafts

1987 ◽  
Vol 54 (4) ◽  
pp. 893-897 ◽  
Author(s):  
O. Bernasconi
Keyword(s):  
Angular Momentum ◽  
Nonlinear Term ◽  
Rotation Frequency ◽  
Longitudinal Component ◽  
Torsional Vibrations ◽  
Rotating Shaft ◽  
Rotating Shafts

In this study, the intrinsic behavior of rotating shafts with residual unbalance is considered. The longitudinal component of the angular momentum caused by synchronous precession (whirling) induces torsional vibrations with a frequency of twice the rotation frequency (bisynchronous). The nonlinear term which represents this coupling is characteristic of the asymmetrical aspect of rotating shaft kinematics. This result has been obtained analytically and confirmed experimentally.

Vibration Localization in Rotating Shafts: Part II — Experiment

1995 ◽  
Author(s):  
A. Galip Ulsoy ◽  
Christophe Pierre ◽  
Suhyun Choi
Keyword(s):  
Cross Section ◽  
Circular Cross Section ◽  
Companion Paper ◽  
Rotating Shaft ◽  
Vibration Localization ◽  
State Response ◽  
Mass Unbalance ◽  
Rotating Shafts ◽  
Principal Directions ◽  
Gyroscopic Coupling

Abstract This paper presents an experimental study of vibration localization in single-span, flexible, rotating shafts. It was shown in a companion paper (Part I) that a non-circular cross-section of the rotating shaft, leading to dissimilar lateral moments of inertia, can introduce disorder. Internal coupling between the principal directions of vibration is provided by the rotational speed through the gyroscopic moments. It is experimentally demonstrated here that directional vibration localization can occur for certain appropriate combinations of disorder and coupling. The steady state response, due to mass unbalance, of a simply supported rotating shaft is considered. It is shown that disorder and gyroscopic coupling lead to directional vibration localization; i.e., larger vibration amplitudes in one of the two orthogonal principal directions of the shaft cross section.

A Finite Rotating Shaft Element Using Timoshenko Beam Theory

1980 ◽  
Vol 102 (4) ◽  
pp. 793-803 ◽  
Author(s):  
H. D. Nelson
Keyword(s):  
Timoshenko Beam ◽  
Beam Theory ◽  
Timoshenko Beam Theory ◽  
Internal Damping ◽  
Theory Analysis ◽  
Rotating Shaft ◽  
Element Analysis ◽  
Rotor Systems ◽  
The Finite Element Analysis ◽  
Rotating Shafts

The use of finite elements for simulation of rotor systems has received considerable attention within the last few years. The published works have included the study of the effects of rotatory inertia, gyroscopic moments, axial load, and internal damping; but have not included shear deformation or axial torque effects. This paper generalizes the previous works by utilizing Timoshenko beam theory for establishing the shape functions and, thereby including transverse shear effects. Internal damping is not included but the extension is straight forward. Comparison is made of the finite element analysis with classical dosed form Timoshenko beam theory analysis for nonrotating and rotating shafts.

Rotating Shafts Affected by Transverse Cracks: A Sensitivity Analysis

2008 ◽  
Author(s):  
Nicolo` Bachschmid ◽  
Ezio Tanzi ◽  
Paolo Pennacchi
Keyword(s):  
Sensitivity Analysis ◽  
Element Model ◽  
Dynamical Behaviour ◽  
Crack Model ◽  
Transverse Cracks ◽  
Rotating Shaft ◽  
Shaft Line ◽  
Linear Approach ◽  
Turbo Generator ◽  
Rotating Shafts

The dynamic behaviour of heavy, horizontal axis, rotating shaft-lines affected by transverse cracks can be analysed in the frequency domain by a quasi linear approach, using a simplified breathing crack model applied to a traditional finite element model of the shaft-line. This allows to perform a series of analyses with affordable efforts. The analysis of the modelling procedure allows to define an approximated approach for simulating the dynamical behaviour, which allows to predict the severity of the crack excited vibrations, combined to modal analysis. this answers to the old-age question on how deep a crack must be to be detected by means of vibration measurements. The model of a 320 MW turbo-generator group has been used to perform a numerical sensitivity analysis, in which the vibrations of the shaft-line, and more in detail the vibrations of the shafts in correspondence to the bearings, have been calculated for all possible positions of the crack along the shaftline and for two different values of the depth of the crack. The calculated results confirm the predicted behaviour.

The Bending Behavior of Porous Titanium Manufactured Using a Novel Spherical Space Holder

2019 ◽  
Vol 944 ◽  
pp. 549-556
Author(s):  
Bo Qiong Li ◽  
Xiao Ming Li ◽  
Xing Lu
Keyword(s):  
Theoretical Model ◽  
Shear Modulus ◽  
Pore Size ◽  
Polymethyl Methacrylate ◽  
Bending Strength ◽  
Porous Titanium ◽  
Spherical Space ◽  
Space Holder ◽  
Bending Behavior

Porous titanium of 10-65% porosity and 100-400 μm macro-pore size manufactured by adding spherical polymethyl methacrylate (PMMA) powders as pore makers. The bending strength of 21-453 MPa and shear modulus of 1.9-43 GPa were obtained. Increasing in porosity and macro-pore size, the bending strength and shear modulus reduced as described by theoretical model, and the macro-pores of porous titanium yielded a smaller deformation under bending.

Subcritical Large-Amplitude Vibrations of Imperfect Rotating Shafts

1989 ◽  
Vol 42 (11S) ◽  
pp. S157-S160
Author(s):  
C. E. N. Mazzilli
Keyword(s):  
Dry Friction ◽  
Large Amplitude ◽  
Critical Speed ◽  
Multiple Scales ◽  
Viscous Damping ◽  
Rotating Shaft ◽  
Geometrical Imperfection ◽  
Rotating Shafts ◽  
Large Amplitude Vibrations ◽  
Practical Implications

The effect of a geometrical imperfection, such as the axis flexural deformation, on the large-amplitude vibrations of a horizontal rotating shaft is analyzed with the aid of the Multiple Scales Method. Internal viscous damping and linear elasticity are assumed in the model. It is then seen that no matter how small the imperfection is, a “critical” speed of the order of half the classical critical speed arises, with relevant practical implications. A number of reported large-amplitude cases may eventually be explained this way. It is possible that events such as this will not appear in systems with high dry friction.

Free Vibration and Stability Analysis of Internally Damped Rotating Shafts With General Boundary Conditions

1998 ◽  
Vol 120 (3) ◽  
pp. 776-783 ◽  
Author(s):  
J. Melanson ◽  
J. W. Zu
Keyword(s):  
Boundary Conditions ◽  
Equations Of Motion ◽  
Normal Modes ◽  
Beam Theory ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Rotating Shaft ◽  
Classical Boundary ◽  
Rotating Shafts ◽  
The Stability

Vibration analysis of an internally damped rotating shaft, modeled using Timoshenko beam theory, with general boundary conditions is performed analytically. The equations of motion including the effects of internal viscous and hysteretic damping are derived. Exact solutions for the complex natural frequencies and complex normal modes are provided for each of the six classical boundary conditions. Numerical simulations show the effect of the internal damping on the stability of the rotor system.

Vibration Localization in Rotating Shafts, Part 1: Theory

1998 ◽  
Vol 120 (1) ◽  
pp. 138-148 ◽  
Author(s):  
A. Galip Ulsoy ◽  
Christophe Pierre ◽  
Suhyun Choi
Keyword(s):  
Cross Section ◽  
Rotational Speed ◽  
Theoretical Study ◽  
Rotating Shaft ◽  
Moments Of Inertia ◽  
Vibration Localization ◽  
Noncircular Cross Section ◽  
Rotating Shafts ◽  
Principal Directions ◽  
Internal Coupling

This paper presents a theoretical study of vibration localization in single-span, flexible, rotating shafts. A noncircular cross-section of the rotating shaft, leading to dissimilar lateral moments of inertia, can introduce disorder. Internal coupling between the principal directions of vibration is provided by the rotational speed through the gyroscopic moments. It is shown, both analytically and numerically, that directional vibration localization can occur for certain appropriate combinations of disorder and coupling.

Dynamic Stability of the Rotating Shaft Made of Boltzmann Viscoelastic Solid

1986 ◽  
Vol 53 (2) ◽  
pp. 424-429 ◽  
Author(s):  
W. Zhang ◽  
F. H. Ling
Keyword(s):  
Dynamic Stability ◽  
High Speed ◽  
Static Load ◽  
Viscoelastic Solid ◽  
Rotating Shaft ◽  
Special Cases ◽  
Analytical Formulas ◽  
Rotating Shafts ◽  
The Stability ◽  
Inclined Angle

A general theory is developed in this paper for studying the dynamic stability of high-speed nonuniform rotating shafts made of a Boltzmann viscoelastic solid. The equation of motion of the shaft is deduced. The stability criteria are derived by using this equation. The unstable regions for a nonhomogeneous viscoelastic shaft are worked out numerically. Analytical formulas are also given in this paper for determining the planar deflection of the shaft and its inclined angle due to a planar static load. The conclusions for special cases given in the literature known to the authors are all covered by the results in this paper.

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