Stresses in Rotating Disks at High Temperatures

1946 ◽  
Vol 13 (1) ◽  
pp. A45-A52
Author(s):  
A. Stanley Thompson
Keyword(s):  
Radial Stress ◽  
Coefficient Of Thermal Expansion ◽  
Variable Temperature ◽  
Rotating Disk ◽  
Allowable Stress ◽  
Tabular Form ◽  
Rotating Disks ◽  
Elasticity Coefficient ◽  
Plastic Disk ◽  
General Method

Abstract A general method was found by which the problem of the rotating disk with any arbitrary profile could be solved, including the effect of plastic flow and of variable temperature, and including the change with temperature of modulus of elasticity, coefficient of thermal expansion, and allowable stress. The solution requires for its application to a specific disk only the elementary arithmetic involved in completion of a tabular form sheet. Two applications of the method are made. For an arbitrary disk profile, an integral equation was found which converges rapidly to the radial stress distribution in a series of successive substitutions. For an arbitrary choice of radial stress, the necessary disk profile can be found in one calculation. Appendix 1 gives an example of the use of the method for the design of a partially plastic disk with a central hole.

Vibration Measurement and Monitoring of a Rotating Disk Using Contactless Laser Excitation

2013 ◽  
Author(s):  
Itsuro Kajiwara ◽  
Naoki Hosoya
Keyword(s):  
Laser Doppler Vibrometer ◽  
Rotating Disk ◽  
Disk Drive ◽  
Vibration Characteristics ◽  
Vibration Measurement ◽  
Testing System ◽  
Rotating Disks ◽  
Vibration Testing ◽  
Structural Surface ◽  
Theoretical Analyses

This paper proposes a contactless vibration testing system for rotating disks based on an impulse response excited by a laser ablation. High power YAG pulse laser is used in this system for producing an ideal impulse force on structural surface without contact. The contactless vibration testing system is composed of a YAG laser, laser Doppler vibrometer and spectrum analyzer. This system makes it possible to measure vibration characteristics of structures under operation, such as vibration measurement of a rotating disk. The effectiveness of this system is confirmed by experimental and theoretical analyses. In this paper, a platter of hard disk drive is employed as an experimental object. Vibration characteristics of a rotating and non-rotating platter are measured and compared with the results of theoretical analysis.

Nonlinear Resonant Motion of Traveling Waves in Rotating Disks

2000 ◽  
Author(s):  
Albert C. J. Luo ◽  
Chin An Tan
Keyword(s):  
Traveling Waves ◽  
Rotation Speed ◽  
Rotating Disk ◽  
Disk Drive ◽  
Computer Memory ◽  
Rotating Disks ◽  
Resonant Wave ◽  
Linear And Nonlinear ◽  
Resonant Spectrum ◽  
Disk Drive Industry

Abstract The resonant conditions for traveling waves in rotating disks are derived. The nonlinear resonant spectrum of a rotating disk is computed from the resonant conditions. Such a resonant spectrum is useful for the disk drive industry to determine the range of operational rotation speed. The resonant wave motions for linear and nonlinear, rotating disks are simulated numerically for a 3.5-inch diameter computer memory disk.

Thermo-mechanical analysis and optimization of functionally graded rotating disks

2020 ◽  
Vol 55 (5-6) ◽  
pp. 159-171
Author(s):  
Hassan Mohamed Abdelalim Abdalla ◽  
Daniele Casagrande ◽  
Luciano Moro
Keyword(s):  
Finite Element ◽  
Equivalent Stress ◽  
Rotating Disk ◽  
Mechanical Analysis ◽  
Theory Of Elasticity ◽  
Functionally Graded ◽  
Rotating Disks ◽  
Maximum Equivalent Stress ◽  
Quadratic Programming Method ◽  
Stress Uniformity

The behavior of thermo-mechanical stresses in functionally graded axisymmetric rotating hollow disks with variable thickness is analyzed. The material is assumed to be functionally graded in the radial direction. First, a two-dimensional axisymmetric model of the functionally graded rotating disk is developed using the finite element method. Exact solutions for stresses are then obtained assuming that the plane theory of elasticity holds. These solutions are in accordance with finite element ones, thus showing the validity of the assumption. Finally, in order to reduce the maximum equivalent stress along the radius, the optimization of the material distribution is addressed. To avoid subsequent finite element simulations in the optimization process, which can be computationally demanding, a nonlinear constrained optimization problem is proposed, for which the solution is obtained numerically by the sequential quadratic programming method, showing prominent results in terms of equivalent stress uniformity.

Analysis of High-Speed Rotating Disks With Variable Thickness and Inhomogeneity

1994 ◽  
Vol 61 (1) ◽  
pp. 186-191 ◽  
Author(s):  
Kai-Yuan Yeh ◽  
R. P. S. Han
Keyword(s):  
High Speed ◽  
Elevated Temperatures ◽  
Rotating Disk ◽  
Rotating Disks ◽  
Analytic Expressions ◽  
Inhomogeneous Temperature ◽  
Inhomogeneous Temperature Field ◽  
Thermoelastic Stresses ◽  
Shrink Fit ◽  
Annular Disks

A rotating disk with varying thickness and inhomogeneity, and subjected to a steady, inhomogeneous temperature field is analyzed. To handle the arbitrary profile, the disk is discretized into a series of uniform annular disks possessing constant material properties and then solved by the step-reduction method. Analytic expressions for thermoelastic stresses are given, and based on these results, the formulation is extended to include the calculation of shrink fit, the solving of the inverse problem for equistrength rotating disks, and the computations of plastic stresses and creep at elevated temperatures.

scholarly journals Controlled Double-Jet Mixing of Light Speeds in the Trigonometric Realm

2018 ◽  
Vol 10 (1) ◽  
pp. 53
Author(s):  
Jiri Stavek
Keyword(s):  
Special Relativity ◽  
Light Beam ◽  
Doppler Effect ◽  
Michelson Interferometer ◽  
Rotating Disk ◽  
Rotating Disks ◽  
Jet Mixing ◽  
Null Result ◽  
Michael Faraday ◽  
Light Beams

We were inspired by three great concepts: 1. Pythagorean means, 2. Pierre de Fermat´s principle of the least time, 3. Michael Faraday´s concept of vibrating rays in longitudinal and transverse directions. We have formulated an extended Doppler formula for rectilinear motions in the absolute spacetime where both postulates of the special relativity are valid. The second postulate of the special relativity for rectilinear motions was derived as the harmonic mean speed based on the Pythagoras-Fermat-Faraday (PF2) model. The null result of the Michelson-Morley experiment is valid for the arms of that interferometer separated by the angle π/2. However, for the angles smaller than π/2 a predicted fringe shift should be observed. For the circular motions the Doppler formula combines the longitudinal and transverse speeds in such a way that the frequency of the rotating light beam is diluted by a factor [1-(v/c)2]0.5 and the wavelength of that light beam is extended by the same factor. The Doppler formula for light beams can be tested for the rotating source and the detector placed close to the rim of that rotating disk in a defined position. In order to obtain new experimental data we propose to construct the Michelson-Morley-Harress-Sagnac interferometer where rotating disks have being attached to both arms of the Michelson interferometer. In rotating disks we might prepare light beams with defined independent values of their longitudinal speeds and after the mixing of these two light beams on their return path to the detector we might observe predicted fringe shifts. In these circular paths the second postulate of the special relativity is not valid. The full composition of Doppler formula is given by the interplay of the macro Doppler effect (the relative motion of the source and observer) and the micro Doppler effect (the combination of the longitudinal and transverse vibration speeds of that oscillating particle – the elasticity of the photon wave).

Creep deformation and stress analysis in a transversely material disk subjected to rigid shaft

2019 ◽  
Vol 25 (1) ◽  
pp. 17-25
Author(s):  
Pankaj Thakur ◽  
Monika Sethi
Keyword(s):  
Stress Analysis ◽  
Creep Deformation ◽  
Radial Stress ◽  
Hoop Stress ◽  
Rotating Disk ◽  
Angular Speed ◽  
Transition Theory ◽  
Strain Rates ◽  
Maximum Value ◽  
Inner Surface

The purpose of this paper is to present a study of creep deformation and stress analysis in a transversely material disk subjected to the rigid shaft by using Seth’s transition theory. It has been observed that radial stress has the maximum value at the inner surface of the rotating disk made of isotropic material as compared to the hoop stress and this value of radial stress further increases with the increase in the value of angular speed. Strain rates have maximum values at the inner surface for the disk made of transversely material.

scholarly journals Effects of the rotation number on flow and heat transfer in contra-rotating disk cavity with superposed flow

2019 ◽  
Vol 11 (10) ◽  
pp. 168781401988104 ◽  
Author(s):  
Shu-xian Chen ◽  
Jing-zhou Zhang
Keyword(s):  
Heat Transfer ◽  
Flow Structure ◽  
Rotation Number ◽  
Tangential Velocity ◽  
Inertial Force ◽  
Rotating Disk ◽  
Rotating Disks ◽  
Radial Temperature ◽  
Disk Rotation ◽  
Type Flow

The turbulent fluid flow and convective heat transfer in counter-rotating disk cavity with central axial air inflow and radial air outflow are numerically studied based on the finite volume method. Efforts are focused upon the influence of the rotation number Rt on the flow structure, cooling performance, sealing effect, and surface tangential friction characteristics in the cavity. The stagnation point where the radial outward flow along the upstream disk driven by the rotation force meets the radial outward flow along downstream disk driven by the combination of rotation force and inflow inertial force moves from upstream disk wall to the shroud with increasing Rt. At the Rt far smaller than 1, the fluids in the core region between two disks rotate with the upstream disk like a rigid body, and the tangential velocity of the rotating core decreases with the increase of the disk cavity radius, which is different from the Batchelor-type flow. At the Rt larger than 1, the fluids on the upstream disk side rotate like the Batchelor-type flow, while the sandwich rotation disappears in the fluid on the downstream disk side. The temperature on the upstream disk wall increases and then decreases with increasing values of Rt, and the critical value of Rt for the change of temperature variation is assessed to be at about Rt = 0.69. The temperature and radial temperature gradient of the downstream disk wall decrease with increasing Rt. With increasing Rt by increasing the disk rotation rate, the pressures near the downstream disk decrease, while the frictional moments on rotating disks increase. Due to the effect of flow structure, the frictional moment on the upstream disk is smaller than that on the downstream disk.

VIBRATION OF CIRCULAR BLADED DISK WITH IMPERFECTIONS

2011 ◽  
Vol 21 (10) ◽  
pp. 2893-2904 ◽  
Author(s):  
LADISLAV PŮST ◽  
LUDĚK PEŠEK
Keyword(s):  
Dynamic Properties ◽  
Single Point ◽  
Three Dimensional ◽  
Rotating Disk ◽  
Fe Model ◽  
Rotating Disks ◽  
Response Curves ◽  
State Response ◽  
Bladed Disk ◽  
Linear Damping

The steady state response of a model of circular bladed disk with imperfection is investigated. Disk imperfection results from additional two groups of damping heads fixed on opposite ends of one diameter. These damping heads are introduced into the computing model as additional point mass, damping and stiffness. Such type of imperfection causes the bifurcation of double eigenfrequencies into pairs of close eigenfrequencies. The effect of imperfection is examined both numerically on three-dimensional nonrotating FE-model and analytically on a simplified split 2DOF model of rotating disk excited by single point harmonic force. Nonlinear friction connection is analyzed and equivalent linear damping coefficient is derived and used in the calculation procedure. It is shown that nonproportional distribution of damping strongly influences the high of resonance peaks. Some examples of response curves illustrate the dynamic properties of stationary and rotating disks with mass-damping-stiffness imperfection.

A General Approach to the Practical Solution of Creep Problems

1959 ◽  
Vol 81 (4) ◽  
pp. 585-594 ◽  
Author(s):  
A. Mendelson ◽  
M. H. Hirschberg ◽  
S. S. Manson
Keyword(s):  
Steady State ◽  
Stress Distribution ◽  
Temperature Gradient ◽  
Successive Approximations ◽  
Appreciable Effect ◽  
Rotating Disks ◽  
Transient Conditions ◽  
Practical Solution ◽  
State Stress ◽  
General Method

A general method is presented for the solution of creep problems by the use of successive approximations. The method is equally applicable to different creep laws and loading paths. Examples are presented for the creep in a flat plate with a temperature gradient and for several cases of rotating disks. In these disk problems the transient conditions prior to the establishment of steady-state stress distribution are included and shown to have an appreciable effect on the total creep strains. The use of different cumulative creep laws such as the time-hardening and strain-hardening laws are illustrated.

scholarly journals The elephant mode between two rotating disks

2008 ◽  
Vol 598 ◽  
pp. 451-464 ◽  
Author(s):  
BERTRAND VIAUD ◽  
ERIC SERRE ◽  
JEAN-MARC CHOMAZ
Keyword(s):  
Global Bifurcation ◽  
Rotating Disk ◽  
Finite Amplitude ◽  
Rotating Disks ◽  
Global Mode ◽  
Precise Analysis ◽  
Crossflow Instability ◽  
Single Disk ◽  
Source Sink ◽  
Good Agreement

Spectral direct numerical simulations (DNS) are carried out for a source–sink flow in an annular cavity between two co-rotating disks. When the Reynolds number based on the forced inflow is increased, a self-sustained crossflow instability of finite amplitude is observed. We show that this nonlinear global mode is made up of a front located at the upstream boundary of the absolutely unstable domain, followed by a saturated spiral mode, and that its properties are in good agreement with results of the local stability theory. This structure is characteristic of the so-called elephant mode of Pier & Huerre (J. Fluid Mech. vol. 435, 2001, p. 145). The global bifurcation is subcritical since only large-amplitude initial perturbations are found to trigger the elephant mode. Small-amplitude perturbations induce a long-lasting transient growth but lead eventually to a damped linear global mode, showing that non-parallel effects counteract the absolute instability and restabilize the flow. A similar linear global stabilization due to non-parallel effects has been found in the case of the flow above a single rotating disk. For the single-disk geometry, the existence of an elephant mode would imply, together with results of Davies & Carpenter (2003) a subcritical global instability, which has not yet been demonstrated. Although the present geometry differs from the single-disk case, the existence of a subcritical global bifurcation is now established, allowing a precise analysis of the transition scenarios.

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