Axisymmetric Solution of a Flexible Disk Rotating Near a Rigid Surface

1988 ◽  
Vol 110 (4) ◽  
pp. 674-677 ◽  
Author(s):  
M. Carpino ◽  
G. A. Domoto
Keyword(s):  
Plane Stress ◽  
Asymptotic Expansions ◽  
Reynolds Equation ◽  
Flat Surface ◽  
Inertial Effects ◽  
Rigid Surface ◽  
Axisymmetric Solution ◽  
Spinning Disk ◽  
Rotating Flexible Disk ◽  
Flexible Disk

A rotating flexible disk separated from a rigid flat surface by a gas film is addressed. The gas film between the disk and the plate is represented by an incompressible Reynolds equation. Inertial effects are included. The disk is treated as a membrane where the tension is found from the plane stress solution for a spinning disk. Two different methods for the axisymmetric solution of this system are developed. The first uses the method of matched asymptotic expansions. The second method is a mixed numerical/perturbation procedure.

Investigation of a Flexible Disk Rotating Near a Rigid Surface

1988 ◽  
Vol 110 (4) ◽  
pp. 664-669 ◽  
Author(s):  
M. Carpino ◽  
G. A. Domoto
Keyword(s):  
Reynolds Equation ◽  
Numerical Results ◽  
Inertial Effects ◽  
Rigid Surface ◽  
Close Proximity ◽  
Flexible Disk

A flexible disk rotating in close proximity to a flat rigid surface has been studied experimentally and theoretically. A bump is located on the surface to create a non-axisymmetric disturbance. The gas film between the disk and the rigid surface is represented by an incompressible Reynolds equation with inertial effects included. The general equations of a disk including both membrane and bending effects with displacement dependent tension distributions are presented. Numerical results are developed where the effects of displacement on the tension distributions and of bending in the disk are not included.

The Effects of Baseplate Warpage and Skew on the Configuration of a Spinning Flexible Disk

1994 ◽  
Vol 116 (3) ◽  
pp. 514-520 ◽  
Author(s):  
R. Y. Wu ◽  
G. G. Adams
Keyword(s):  
Radial Direction ◽  
Reynolds Equation ◽  
Total Response ◽  
Axisymmetric Solution ◽  
Small Deviations ◽  
Close Proximity ◽  
Flexible Disk ◽  
Air Film ◽  
Axisymmetric Configuration ◽  
State Configuration

The behavior of a flexible disk, spinning in close proximity to a warped/skewed stationary baseplate, is investigated. The governing partial differential equation for the disk deflection is coupled to the Reynolds equation of the air film. Four warped/ skewed baseplate configurations are modeled. The effects of baseplate warpage and skew on the steady-state configuration of the disk are determined by investigating small deviations away from the axisymmetric configuration of the disk corresponding to a perfect baseplate. Exponential Fourier series expansions in the circumferential direction, along with finite differences in the radial direction, are used. Numerical results are determined and compared for various values of the angular velocity and initial thicknesses of the air film. Among the three warpages considered, the saddle warped baseplate provides the largest change in disk deflection whereas the spherically warped baseplate gives the smallest change. The total response of the disk is obtained by superposition of the deflection change caused by the warped/skewed baseplate and the deflection obtained from the axisymmetric solution.

Nonlinear Vibrations of a Circular Spinning Disk With a Transverse Load

2008 ◽  
Author(s):  
Xiao-Li Yang ◽  
Wei Zhang
Keyword(s):  
Parametric Resonance ◽  
Nonlinear Vibrations ◽  
Transverse Load ◽  
Rotating Speed ◽  
Coupled Equations ◽  
Nonlinear Responses ◽  
Spinning Disk ◽  
Averaged Equations ◽  
Rotating Flexible Disk ◽  
Flexible Disk

In this paper, we analyze the transverse nonlinear vibration of a rotating flexible disk with a periodically varying rotating speed, subjected to a rotating point force. Based on a small-stretch, moderate-rotation flexible disk theory of the Nowinski and the von Karman type field equations, the nonlinear governing equations of motion are derived for the rotating flexible disk, which are coupled equations among the radial, tangential and transverse displacements. According to the Galerkin approach, a four-degree-of-freedom nonlinear system governing the weakly split resonant modes are derived. The resonant case considered here is 1:1:2:2 internal resonance and a critical speed resonance. The primary parametric resonance for the first-order sin and cos modes and the fundamental parametric resonance for the second-order sin and cos modes are also considered. The method of multiple scales is used to obtain a set of eight-dimensional nonlinear averaged equations. Based on the averaged equations, the stabilities of the steady state nonlinear responses are analyzed. Using numerical simulations, the influence of different parameters on the nonlinear vibrations of the spinning disk is detected. It is concluded that there exist complicated nonlinear behaviors including multi-pulse type chaotic motions, periodic and period-n motions for the spinning disk with a varying rotating speed. It is also found that among all parameters the damping and excitation have important influence on the nonlinear responses of the spinning disk with a varying rotating speed.

Observations on the Steady-State Solution of an Extremely Flexible Spinning Disk With a Transverse Load

1983 ◽  
Vol 50 (3) ◽  
pp. 525-530 ◽  
Author(s):  
R. C. Benson
Keyword(s):  
Steady State ◽  
Hybrid System ◽  
Fourth Order ◽  
Steady State Solution ◽  
Transverse Load ◽  
System Of Differential Equations ◽  
Membrane Theory ◽  
Small Disk ◽  
Spinning Disk ◽  
Flexible Disk

The steady deflection of a transversely loaded, extremely flexible, spinning disk is studied. Membrane theory is used to predict the shapes and locations of waves that dominate the response. It is found that waves in disconnected regions are possible. Some results are presented to show how disk stiffness moderates the membrane waves, the most important result being an upper bound on the highest ordered wave of significant amplitude. A hybrid system of differential equations and boundary conditions is developed to replace the pure membrane formulation that is singular, and the full fourth-order plate formulation that is numerically sensitive. The hybrid formulation retains the salient features of the flexible disk response and facilitates calculations for very small disk stiffnesses.

Vibrational response of a moving suspension-slider loading system exciting a rotating flexible disk

2012 ◽  
Vol 331 (16) ◽  
pp. 3762-3773 ◽  
Author(s):  
Yong-Chen Pei ◽  
Qing-Chang Tan ◽  
Xin Yang ◽  
Chris Chatwin
Keyword(s):  
Vibrational Response ◽  
Loading System ◽  
Rotating Flexible Disk ◽  
Flexible Disk

A Study of the Influence of Bearing Clearance on Lateral Coupled Shaft/Disk Rotordynamics

1992 ◽  
Author(s):  
George T. Flowers ◽  
Fang Sheng Wu
Keyword(s):  
Dynamical Behavior ◽  
High Amplitude ◽  
Bladed Disk ◽  
Bearing Clearance ◽  
Shaft System ◽  
Coupling Dynamics ◽  
Bearing Loads ◽  
Rotating Flexible Disk ◽  
Flexible Disk ◽  
Clearance Nonlinearity

This study examines the influence of bearing clearance on the dynamical behavior of a rotating, flexible disk/shaft system. Most previous work in nonlinear rotordynamics has tended to concentrate separately on shaft vibration or on bladed disk vibration, neglecting the coupling dynamics between them. The current work examines the important rotordynamical behavior of coupled disk/shaft dynamics. A simplified nonlinear model is developed for lateral vibration of a rotor system with a bearing clearance nonlinearity. The steady-state dynamical behavior of this system is explored using numerical simulation and limit cycle analysis. It is demonstrated that bearing clearance effects can produce superharmonic vibration that may serve to excite high amplitude disk vibration. Such vibration could lead to significantly increased bearing loads and catastrophic failure of blades and disks. In addition, multi-valued responses and aperiodic behavior was observed.

Dynamic stability of rotating flexible disk perturbed by the reciprocating angular movement of suspension–slider system

2010 ◽  
Vol 329 (26) ◽  
pp. 5520-5531 ◽  
Author(s):  
Yong-Chen Pei ◽  
Qing-Chang Tan ◽  
Fu-Sheng Zheng ◽  
Yong-Qi Zhang
Keyword(s):  
Dynamic Stability ◽  
Angular Movement ◽  
Rotating Flexible Disk ◽  
Flexible Disk

scholarly journals ASYMPTOTICS OF STRESS AND CONTINUITY FIELDS NEAR A FATIGUE GROWING CRACK IN A DAMAGED MEDIUM IN CONDITIONS OF STATE OF PLANE STRESS

2017 ◽  
Vol 19 (9.2) ◽  
pp. 97-108
Author(s):  
S.A. Igonin ◽  
L.V. Stepanova
Keyword(s):  
Fatigue Crack ◽  
Asymptotic Solution ◽  
Plane Stress ◽  
Asymptotic Expansions ◽  
Asymptotic Representation ◽  
Stress Fields ◽  
Repeated Loading ◽  
Growing Crack

In the paper asymptotic solution to the problem of growth of fatigue crack in conditions of repeated loading in a damaged medium in the coupled elasticity-damage statement of the problem is given. Asymptotic expansions of stress fields and continuity fields in which two summands are retained in asymptotic representation are derived. The problems of determination of amplitude coeffl-cients of obtained asymptotic expansions are discussed.

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