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.

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 Effect of Disk Warpage/Skew on the Deflection and Vibration of a Flexible Disk Spinning Above a Baseplate and in Contact With a Point-Head

1997 ◽  
Vol 119 (1) ◽  
pp. 64-70 ◽  
Author(s):  
R. Y. Wu ◽  
G. G. Adams
Keyword(s):  
Film Thickness ◽  
Rotational Speed ◽  
Numerical Solutions ◽  
Point Contact ◽  
Angle Variation ◽  
Coupled Equations ◽  
Close Proximity ◽  
Small Change ◽  
Flexible Disk ◽  
Air Film

A flexible disk, with small initial warpage/skew, is spinning in close proximity to a stationary baseplate. The partial differential equation for the disk deflection is coupled to the Reynolds equation of the stabilizing air-film. Disk warpage/skew produces a small change in the deflection which rotates with the disk. These deflections are obtained by linearizing the coupled equations about the axisymmetric configuration corresponding to a perfect disk. Numerical solutions are obtained and compared for different values of rotational speed and air-film thickness. The results show that among the three skewed/warped disks modeled, the skewed disk (i.e., the plane of the disk is skewed with respect to its axis of rotation) produces the largest deflection change (axial runout). With the effect of a point-contact head included, the existence of disk warpage/skew causes the head to produce a spatially-fixed harmonically varying force. The total disk motion is determined by superposition of the deflection pattern fixed on the disk and the space-fixed head-induced vibration. The disk pitch angle variation at the head is obtained and the results are compared for various values of the rotational speed and air-film thickness.

Experimental Measurement of a Three Lobe Air Bearing Rotordynamic Coefficients

2006 ◽  
Author(s):  
Rafael O. Ruiz ◽  
Marcelo H. Di Liscia ◽  
Sergio Di´az ◽  
Luis Medina
Keyword(s):  
Reynolds Equation ◽  
Ideal Gas ◽  
Magnetic Bearing ◽  
Experimental Results ◽  
Rotating Speed ◽  
Rotordynamic Coefficients ◽  
Fluid Film Bearings ◽  
Bearing Force ◽  
Air Film ◽  
Gas Journal Bearing

This work presents direct experimental measurements of air film rotordynamic coefficients on a three lobe bearing. The test rig uses two magnetic bearing actuators to impose desired test orbits to the journal. Tests are conducted at several rotating speeds up to 12,000rpm. Journal whirling excitation is independent of the rotating speed, thus allowing asynchronous excitations. One-dimensional orbits in the horizontal and vertical axes are applied as excitations at each rotating speed. The experimental results show the behavior of the rotordynamic coefficients of the air film bearing under synchronous and asynchronous excitation. The synchronous experimental results are compared to numerical estimation of the bearing force coefficients through solution of the isotropic ideal gas journal bearing Reynolds equation coupled with the pressure drop through the feeding holes. The results of this work prove the suitability of the rig to identify both the synchronous and nonsynchronous response of air fluid film bearings.

The Influence of Orifice Restriction on the Stability of Rigid Rotor-Aerostatic Bearing System

2009 ◽  
Author(s):  
Cheng-Hsien Chen ◽  
Ding-Wen Yang ◽  
Yuan Kang ◽  
Ren-Ming Hwang ◽  
Shrh-Shyong Shyr
Keyword(s):  
Reynolds Equation ◽  
Inertial Force ◽  
Adiabatic Process ◽  
Rigid Rotor ◽  
Double Row ◽  
Stability Threshold ◽  
Spindle Rotation ◽  
The Stability ◽  
Air Film ◽  
Bearing System

This paper has studied the influence of the restriction effect on the stability of a rigid rotor in rotation supported by double-row, orifice compensated aerostatic bearings. The air which is assumed to be perfect gas, passes through orifice restrictor into the bearing clearance undergoing the adiabatic process is governed by Reynolds equation including the coupled effects of wedge due to spindle rotation and squeezed film due to journal oscillation. The Ph-method is used to analyze Reynolds equation and which is then solved by the finite difference method and numerical integration to yield static and dynamic characteristics of air film. The motion equation of the rotor-bearing system is obtained by using the perturbation method and the eigensolution method is used to determine the stability threshold and critical whirl ratio. The variations of stability threshold of both critical inertial force and critical whirl ratio with restriction parameters are analyzed for various whirl ratios, speed of journal rotation and eccentricity ratios.

High Knudsen Number Molecular Rarefaction Effects in Gas-Lubricated Slider Bearings for Computer Flying Heads

1987 ◽  
Vol 109 (2) ◽  
pp. 276-282 ◽  
Author(s):  
Y. Mitsuya ◽  
T. Ohkubo
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Flow Model ◽  
Slip Flow ◽  
Ambient Air ◽  
Mean Free Path ◽  
Lubricating Film ◽  
Modified Reynolds Equation ◽  
Air Film ◽  
Rarefaction Effects

This paper presents a study into the gas lubrication capability of an ultra-thin 0.025 μm film (converted value for ambient air film). The experimental results obtained using subambient helium as the lubricating film are compared with the calculated results using the modified Reynolds equation considering flow slippage due to the molecular mean free path effects. This comparison confirms that the slip flow model holds true within the range of the present experiments, and that the modified Reynolds equation is applicable for designing the computer flying heads operating at such thin spacing. The reason for the excellent agreement is discussed considering the locality of rarefaction effects on the lubricating surfaces and the anisotropy of these effects between the film thickness and the slider width.

A Numerical Study on Air-Entrainment between a Web and a Convex Guide Roller in a Web Transportation Process

2013 ◽  
Vol 392 ◽  
pp. 110-115 ◽  
Author(s):  
Puttha Jeenkour
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Numerical Study ◽  
Air Entrainment ◽  
Convex Shape ◽  
Transportation Process ◽  
Guide Roller ◽  
Shape Equation ◽  
Newton Raphson ◽  
Air Film

This paper presents a characteristic of air-entrainment between a web and a guide roller with modified convex shape. Air film thickness is derived using the modified Reynolds equation, a roller shape equation, and a web deflection equation. A finite difference method and a Newton-Raphson scheme are employed to achieve numerical results, i.e. air film thickness and air pressure distribution profiles, a minimum air film thickness, and an air film thickness at the middle of roller length under varied convex roller shapes. The results show that both minimum and central air film thicknesses decrease when the roller is designed as convex shape, and a parameter of convex roller shape affects a minimum air film thickness position.

Air Film Thickness Estimation in Web Handling Processes

1999 ◽  
Vol 121 (1) ◽  
pp. 50-55 ◽  
Author(s):  
Hiromu Hashimoto
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Experimental Results ◽  
Finite Width ◽  
Web Handling ◽  
Foil Bearing ◽  
Guide Roller ◽  
The Finite Difference Method ◽  
Air Film ◽  
The Web

In this paper, in order to estimate an air film thickness between moving web and guide roller (web spacing height), an air film thickness formula was derived based on the finite width compressible foil bearing theory. In the derivation of the air film thickness formula, the two-dimensional Reynolds equation and foil equilibrium equation were discretized by the finite difference method and solved iteratively to obtain the pressure and air film thickness distributions for various parameters. Based on the numerical results, the simplified convenience formula for the estimation of air film thickness between web and guide roller was obtained. On the other hand, the air film thickness between web and guide roller was measured by an optical sensor, and the experimental results were compared with the calculated results. Moreover, the variation of air film thickness between two layers in web winding processes was analyzed by making use of the air film thickness formula derived above. From the theoretical and experimental results obtained, the effects of air film thickness on the web transporting systems were clarified.

Slider Air Bearing Design Enhancements for High Speed Flexible Disk Recording

2005 ◽  
Vol 127 (3) ◽  
pp. 522-529 ◽  
Author(s):  
James White
Keyword(s):  
High Speed ◽  
Numerical Solutions ◽  
Hydrodynamic Pressure ◽  
Flying Height ◽  
Air Bearing ◽  
Mechanical Shock ◽  
Current Effort ◽  
Slider Air Bearing ◽  
Flexible Disk ◽  
Air Film

The current effort was motivated largely by the fact that computing and communication platforms are becoming more portable and mobile with increased demands for both speed and disk storage. This work makes use of an asymmetric opposed slider arrangement to provide both static and dynamic improvements to the recording head air bearing interface for high speed flexible disk applications. The combination of a longitudinally slotted rail opposed by an uninterrupted rail that functions as a noncontact hydrodynamic pressure pad causes the disk to deflect at the submicron level over critical areas of the slider interface. This allows the required static minimum flying height to be focused over the recording transducer while higher clearances are positioned elsewhere, resulting in minimized exposure to contact between slider and disk. The high stiffness and low flying height of the air film at the recording element together with the low stiffness and high flying height of the opposing air film provides a noncontact air bearing interface that is especially immune to mechanical shock. A computer code called FLEXTRAN was developed that provides both static and dynamic numerical solutions of the air bearing interface composed of two opposed gimbal mounted sliders loaded against a high speed flexible disk. Simulations of the asymmetric opposed slider configuration are presented and compared with those of other slider air bearing designs.

Theoretical and Experimental Investigations Into Spacing Characteristics Between Roller and Three Types of Webs With Different Permeabilities

2004 ◽  
Author(s):  
H. Hashimoto ◽  
M. Okajima
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Numerical Solutions ◽  
Experimental Investigations ◽  
First Order ◽  
Wide Range ◽  
Entrained Air ◽  
Air Diffusion ◽  
Air Film ◽  
The Web

A new theoretical model for estimating the entrained air film thickness between a web and roller is presented for both impermeable and permeable webs. A simple closed-form formula for estimating the air film thickness, which considers the effects of air leakage from the web edges and air diffusion due to the permeability of web, was obtained based on a large number of simultaneous numerical solutions of the compressible Reynolds equation and the web equilibrium equation. The variation of air film thickness with roller velocity is measured for three typical webs: PET (polyethylene terephthalate), coated paper, and newsprint. The effects of web permeability, web width and web tension on the air film thickness are examined theoretically and experimentally for a wide range of roller velocity. Reasonable agreement is seen both quantatively and qualitatively between the predicted and measured results. The validity of the formula for the first order estimation of web-roller interface problems is verified experimentally.

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