Vibration Localization in Rotating Shafts: Part I — Theory

1995 ◽  
Author(s):  
A. Galip Ulsoy ◽  
Christophe Pierre ◽  
Suhyun Choi
Keyword(s):  
Cross Section ◽  
Rotational Speed ◽  
Theoretical Study ◽  
Circular Cross Section ◽  
Rotating Shaft ◽  
Vibration Localization ◽  
Rotating Shafts ◽  
Principal Directions ◽  
Internal Coupling ◽  
Perturbation Solutions

Abstract This paper presents a theoretical study of vibration localization in single-span, flexible, rotating shafts. 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 shown, using both exact and perturbation solutions, that directional vibration localization can occur for certain appropriate combinations of disorder and coupling.

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.

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.

Vibration Localization in Rotating Shafts, Part 2: Experiment

1998 ◽  
Vol 120 (1) ◽  
pp. 149-155
Author(s):  
A. Galip Ulsoy ◽  
Christophe Pierre ◽  
Suhyun Choi
Keyword(s):  
Cross Section ◽  
Companion Paper ◽  
Rotating Shaft ◽  
Vibration Localization ◽  
State Response ◽  
Mass Unbalance ◽  
Rotating Shafts ◽  
Principal Directions ◽  
Gyroscopic Coupling ◽  
Internal Coupling

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 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 experimentally demonstrated here that directional vibration localization can occur for 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.

Dynamic Analysis of High-Speed Rotating Shafts Using the Flexible Multibody Approach

2018 ◽  
Author(s):  
Vesa-Ville Hurskainen ◽  
Babak Bozorgmehri ◽  
Marko K. Matikainen ◽  
Aki Mikkola
Keyword(s):  
Dynamic Analysis ◽  
Cross Section ◽  
High Speed ◽  
Capture Cross Section ◽  
Absolute Nodal Coordinate Formulation ◽  
Beam Element ◽  
Capture Cross ◽  
Rotating Shaft ◽  
Absolute Nodal Coordinate ◽  
Rotating Shafts

In this study, a higher-order finite element based on the absolute nodal coordinate formulation (ANCF) is applied in the dynamic analysis of high-speed rotating shafts. Static and modal tests are carried out to analyze the performance and accuracy of the introduced ANCF element. Also, via a transient dynamic benchmark test involving a rotating flexible shaft, the accuracy of the examined beam element in high-speed applications is analyzed. According to the results, the introduced beam element can adequately capture cross-section deformationin high-speed rotating shaft analysis.

scholarly journals Influence of rotatory inertia on stochastic stability of a viscoelastic rotating shaft

2008 ◽  
Vol 35 (4) ◽  
pp. 363-379
Author(s):  
Ratko Pavlovic ◽  
P. Kozic ◽  
G. Janevski
Keyword(s):  
Cross Section ◽  
Stochastic Stability ◽  
Circular Cross Section ◽  
Longitudinal Axis ◽  
Physical Parameters ◽  
Rotatory Inertia ◽  
Rotating Shaft ◽  
Axial Forces ◽  
Constant Rate ◽  
Mean And Variance

The stochastic stability problem of a viscoelastic Voigt-Kelvin balanced rotating shaft subjected to action of axial forces at the ends is studied. The shaft is of circular cross-section, it rotates at a constant rate about its longitudinal axis of symmetry. The effect of rotatory inertia of the shaft cross-section and external viscous damping are included into account. The force consists of a constant part and a time-dependent stochastic function. Closed form analytical solutions are obtained for simply supported boundary conditions. By using the direct Liapunov method almost sure asymptotic stability conditions are obtained as the function of stochastic process variance, external damping coefficient, retardation time, angular velocity, and geometric and physical parameters of the shaft. Numerical calculations are performed for the Gaussian process with a zero mean and variance ?2 as well as for harmonic process with amplitude H.

scholarly journals HYDRODYNAMIC ANALYSES OF THE FLOW PATTERNS IN STIRRED VESSEL OF TWO-BLADED IMPELLER

2020 ◽  
Vol 14 (2) ◽  
pp. 117-132
Author(s):  
Houssem Laidoudi
Keyword(s):  
Reynolds Number ◽  
Fluid Flow ◽  
Laminar Flow ◽  
Cross Section ◽  
Rotational Speed ◽  
Circular Cross Section ◽  
Three Dimensions ◽  
Governing Equations ◽  
Stirred Vessel ◽  
New Correlation

In this paper, the governing equations of continuity and momentum subjected to suitable boundary conditions have been solved numerically to investigate the fluid flow in stirred vessel of two-bladed impeller. The numerical simulations have been carried out in three-dimensions for laminar flow. The studied fluid was considered Newtonian and incompressible. Our research studied the effects of geometrical configurations of the two-bladed impeller and its rotational speed on fluid patterns and mechanical power consumption. The innovative point in this paper is that the blades of the impeller contain three equal-sized holes of circular cross-section. The diameter of the hole (d) to the impeller diameter (D) gives the ratio d/D. the impeller speed is controlled by the Reynolds number (Re). The obtained results have been illustrated and discussed for the range of following governing parameters: d/D = 0 to 0.4 and Re = 1 to 300. The results showed that the studied parameters have significant effects on fluid flow and consumption power and the perforated blades of ratio d/D = 0.133 is more efficient than plan blades. Also, a new correlation is proposed to describe the consumption power as function of d/D and Re.

Wave propagation in a generalized piezothermoelastic rotating bar of circular cross section

2015 ◽  
Vol 11 (2) ◽  
pp. 216-237 ◽  
Author(s):  
Rajendran Selvamani ◽  
Palaniyandi Ponnusamy
Keyword(s):  
Wave Propagation ◽  
Cross Section ◽  
Rotational Speed ◽  
Relaxation Times ◽  
Circular Cross Section ◽  
Thermal Relaxation ◽  
Wave Number ◽  
Content Type ◽  
Mechanical Coupling ◽  
Thermal Relaxation Times

Purpose – The purpose of this paper is to study the wave propagation in a generalized piezothermoelastic rotating bar of circular cross-section using three-dimensional linear theory of elasticity. Design/methodology/approach – A mathematical model is developed to study the wave propagation in a generalized piezothermelastic rotating bar of circular cross-section by using Lord-Shulman (LS) and Green-Lindsay (GL) theory of thermoelasticity. After developing the formal solution of the mathematical model consisting of partial differential equations, the frequency equations have been derived by using the thermally insulated/isothermal and electrically shorted/charge free boundary conditions prevailing at the surface of the circular cross-sectional bar. The roots of the frequency equation are obtained by using the secant method, applicable for complex roots. Findings – In order to include the time requirement for the acceleration of the heat flow and the coupling between the temperature and strain fields, the analytical terms have been derived for the non-classical thermo-elastic theories, LS and GL theory. The computed physical quantities such as thermo-mechanical coupling, electro-mechanical coupling, frequency shift, specific loss and frequency have been presented in the form of dispersion curves. From the graphical patterns of the structure, the effect of thermal relaxation times and the rotational speed as well as the anisotropy of the of the material on the various considered wave characteristics is more significant and dominant in the flexural modes of vibration. The effect of such physical quantities provides the foundation for the construction of temperature sensors, acoustic sensor and rotating gyroscope. Originality/value – In this paper, the influence of thermal relaxation times and rotational speed on the wave number with thermo-mechanical coupling, electro-mechanical coupling, frequency shift, specific loss and frequency has been observed and are presented as dispersion curves. The effect of thermal relaxation time and rotational speed on wave number for the case of generalized piezothermoelastic material of circular cross-section was never reported in the literature. These results are new and original.

SAF file: It's really three dimensional file

2018 ◽  
Vol 14 (1) ◽  
pp. 1
Author(s):  
Prof. Dr. Jamal Aziz Mehdi
Keyword(s):  
Cross Section ◽  
Root Canal ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Circular Motion ◽  
Root Canal Treatment ◽  
Metal Core ◽  
Rotating Blade

The biological objectives of root canal treatment have not changed over the recentdecades, but the methods to attain these goals have been greatly modified. Theintroduction of NiTi rotary files represents a major leap in the development ofendodontic instruments, with a wide variety of sophisticated instruments presentlyavailable (1, 2).Whatever their modification or improvement, all of these instruments have onething in common: they consist of a metal core with some type of rotating blade thatmachines the canal with a circular motion using flutes to carry the dentin chips anddebris coronally. Consequently, all rotary NiTi files will machine the root canal to acylindrical bore with a circular cross-section if the clinician applies them in a strictboring manner

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