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.

Stability of Water-Lubricated, Hydrostatic, Conical Bearings With Spiral Grooves for High-Speed Spindles

2001 ◽  
Vol 124 (2) ◽  
pp. 398-405 ◽  
Author(s):  
S. Yoshimoto ◽  
S. Oshima ◽  
S. Danbara ◽  
T. Shitara
Keyword(s):  
High Speed ◽  
Water Pressure ◽  
Rotating Shaft ◽  
Pressurized Water ◽  
High Speeds ◽  
Theoretical Predictions ◽  
The Stability ◽  
Stability Of Water ◽  
Spiral Grooves ◽  
Good Agreement

In this paper, the stability of water-lubricated, hydrostatic, conical bearings with spiral grooves for high-speed spindles is investigated theoretically and experimentally. In these bearing types, pressurized water is first fed to the inside of the rotating shaft and then introduced into spiral grooves through feeding holes located at one end of each spiral groove. Therefore, water pressure is increased due to the effect of the centrifugal force at the outlets of the feeding holes, which results from shaft rotation. In addition, water pressure is also increased by the viscous pumping effect of the spiral grooves. The stability of the proposed bearing is theoretically predicted using the perturbation method, and calculated results are compared with experimental results. It was consequently found that the proposed bearing is very stable at high speeds and theoretical predictions show good agreement with experimental data.

The whirling of a spinning top

1950 ◽  
Vol 2 (1) ◽  
pp. 9-14
Author(s):  
J. Morris
Keyword(s):  
High Speed ◽  
Moments Of Inertia ◽  
Prime Movers ◽  
Rotating Shafts ◽  
The Common ◽  
The Stability ◽  
Spinning Top

SummaryThis paper has been compiled because of the applicability of the treatment of the stability of the motion of the common spinning top to the problem of the whirling of rotating shafts, carrying loads of appreciable moments of inertia. This problem is assuming renewed interest and importance, especially in the drives of contra-propeller systems and the more recent high speed prime movers.

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 Frequencies in High-Speed Milling Processes or a Positive Answer to Davies, Pratt, Dutterer and Burns

2004 ◽  
Vol 126 (3) ◽  
pp. 481-487 ◽  
Author(s):  
T. Insperger ◽  
G. Ste´pa´n
Keyword(s):  
High Speed ◽  
Period Doubling ◽  
Flip Bifurcation ◽  
Vibration Frequencies ◽  
High Speed Milling ◽  
Machine Tool Chatter ◽  
Special Cases ◽  
Universal Approach ◽  
The Stability ◽  
Excitation Model

The stability charts of high-speed milling are constructed. New unstable regions and vibration frequencies are identified. These are related to flip bifurcation, i.e. period doubling vibrations occur apart of the conventional self-excited vibrations well-known for turning or low-speed milling with multiple active teeth. The Semi-Discretization method is applied for the delayed parametric excitation model of milling providing the connection of the two existing and experimentally verified results of machine tool chatter research. The two extreme models in question, that is, the traditional autonomous delayed model of time-independent turning, and the recently introduced discrete map model of time-dependent highly interrupted machining, are both involved as special cases in the universal approach presented in this study.

Floquet Stability Analysis of a Rotor Supported on Rolling Element Bearings With Clearance and Static Load

2013 ◽  
Author(s):  
C. A. Kitio Kwuimy ◽  
A. S. Das ◽  
C. Nataraj
Keyword(s):  
Static Load ◽  
Rotation Speed ◽  
Approximate Model ◽  
Hertzian Contact ◽  
Rolling Element Bearings ◽  
Rotating Shaft ◽  
Second Order Differential Equations ◽  
Rolling Element ◽  
Small Clearance ◽  
The Stability

A rotating shaft supported on rolling element bearings is considered. The system is known to be modeled by a pair of coupled second order differential equations involving Hertzian contact force and thus parametric excitations. In studying the stability of the system, the static equilibrium in the direction of the static load is found to linearly increases with clearance. An approximate model is obtained and conditions of validity of such a model are discussed. Cage rotation speed, static load and clearance are revealed as key parameters. Considering the Floquet formalism for stability, in the domain (clearance,speed), it is found that the domain of stability decreases for large clearance and increases for small clearance. Higher number of rolling element as well as smaller static load positively affect the stability as well.

Effect of Flexible Damped Bearing-Supports on the Dynamic Stability of High-Speed Turbochargers

2013 ◽  
Author(s):  
A. Alsaeed ◽  
G. Kirk ◽  
S. Bashmal
Keyword(s):  
Dynamic Stability ◽  
Dynamic Characteristics ◽  
High Speed ◽  
Element Model ◽  
Dynamic Coefficients ◽  
Speed Range ◽  
Rotor Bearing ◽  
The Stability ◽  
The Finite Element Model ◽  
Bearing System

The aim of this study is to analytically design flexible damped bearing-supports in order to improve the dynamic characteristics of the rotor-bearing system. The finite-element model of the turbocharger rotor with linearized bearing dynamic coefficients is used to solve for the logarithmic decrements and hence the stability map. The design process attempts to find the optimum dynamic characteristics of the flexible damped bearing-support that would give best dynamic stability of the rotor-bearing system. The method is successful in greatly improving the dynamic stability of the turbocharger and may also lead to a total linear stability throughout the entire speed range when used besides the enhanced-performance hydrodynamic bearings.

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.

Passive Control of Critical Speeds of a Rotating Shaft Using Eccentric Sleeves: Model Development

2016 ◽  
Author(s):  
A. J. Kirk ◽  
J. Griffiths ◽  
C. Bingham ◽  
G. Knowles ◽  
R. Bickerton
Keyword(s):  
High Speed ◽  
Passive Control ◽  
Equations Of Motion ◽  
Variable Mass ◽  
Model Development ◽  
Three Dimensional ◽  
Practical Case ◽  
Rotating Shaft ◽  
Critical Speeds ◽  
Rotating Shafts

This paper considers the passive control of lateral critical speeds in high-speed rotating shafts through application of eccentric balancing sleeves. Equations of motion for a rotating flexible shaft with eccentric sleeves at the free ends are derived using the extended Hamilton Principle, considering inertial, non-constant rotating speed, Coriolis and centrifugal effects. A detailed analysis of the passive control characteristics of the eccentric sleeve mechanism and its impact on the shaft dynamics, is presented. Results of the analysis are compared with those from three-dimensional finite element simulations for 3 practical case studies. Through a comparison and evaluation of the relative differences in critical speeds from both approaches it is shown that consideration of eccentric sleeve flexibility becomes progressively more important with increasing sleeve length. The study shows that the critical speed of high-speed rotating shafts can be effectively controlled through implementation of variable mass/stiffness eccentric sleeve systems.

Combination Parametric Resonance of Nonlinear Unbalanced Rotating Shafts

2018 ◽  
Vol 13 (11) ◽  
Author(s):  
M. S. Qaderi ◽  
S. A. A. Hosseini ◽  
M. Zamanian
Keyword(s):  
Parametric Excitation ◽  
Multiple Scales ◽  
Nonlinear Differential Equations ◽  
Geometrical Nonlinearity ◽  
Primary Resonance ◽  
Rotating Shaft ◽  
Rotating Shafts ◽  
Slow Evolution ◽  
The Stability ◽  
Parametric And External Excitations

In this paper, dynamic response of a rotating shaft with geometrical nonlinearity under parametric and external excitations is investigated. Resonances, bifurcations, and stability of the response are analyzed. External excitation is due to shaft unbalance and parametric excitation is due to periodic axial force. For this purpose, combination resonances of parametric excitation and primary resonance of external force are assumed. Indeed, simultaneous effect of nonlinearity, parametric, and external excitations are investigated using analytical method. By applying the method of multiple scales, four ordinary nonlinear differential equations are obtained, which govern the slow evolution of amplitude and phase of forward and backward modes. Eigenvalues of Jacobian matrix are checked to find the stability of solutions. Both periodic and quasi-periodic motion were observed in the range of study. The influence of various parameters on the response of the system is studied. A main contribution is that the parametric excitation in the presence of nonlinearity can be used to suppress the forward synchronous vibration. Indeed, in the presence of combination parametric excitation, the energy is transferred from forward whirling mode to backward one. This property can be applied in control of rotor unbalance vibrations.

A Statistical Study of Process Variables to Optimize a High Speed Curtain Coater: Part I

TAPPI Journal ◽  
2009 ◽  
Vol 8 (1) ◽  
pp. 20-26 ◽  
Author(s):  
PEEYUSH TRIPATHI ◽  
MARGARET JOYCE ◽  
PAUL D. FLEMING ◽  
MASAHIRO SUGIHARA
Keyword(s):  
Boundary Layer ◽  
Experimental Design ◽  
High Speed ◽  
Statistical Study ◽  
Process Variables ◽  
High Speeds ◽  
The Stability ◽  
Air Removal ◽  
Removal System

Using an experimental design approach, researchers altered process parameters and material prop-erties to stabilize the curtain of a pilot curtain coater at high speeds. Part I of this paper identifies the four significant variables that influence curtain stability. The boundary layer air removal system was critical to the stability of the curtain and base sheet roughness was found to be very important. A shear thinning coating rheology and higher curtain heights improved the curtain stability at high speeds. The sizing of the base sheet affected coverage and cur-tain stability because of its effect on base sheet wettability. The role of surfactant was inconclusive. Part II of this paper will report on further optimization of curtain stability with these four variables using a D-optimal partial-facto-rial design.

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