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.

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.

Thermal Elastohydrodynamic Lubrication Analysis for Point Contact Transmission

2009 ◽  
Author(s):  
Hai-zhou Huang ◽  
Xi-chuan Niu ◽  
Xiao-yang Yuan
Keyword(s):  
Film Thickness ◽  
Numerical Solutions ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Surface Velocity ◽  
Squeeze Film ◽  
Elastic Displacement ◽  
Circular Arc ◽  
Tooth Width ◽  
Contact Transmission

To investigate the thermal EHL (elastohydrodynamic lubrication) in point contact transmission, a model considering the two-dimensional surface velocity of tooth face and the running-in is proposed. The numerical solutions for pressure, temperature and film thickness distribution in the contact zone are obtained by solving equations including the Reynolds, Energy and the elastic displacement with variable dimension meshing method. The model was used to study the point contact transmission of the circular arc gear in a windlass. The main results show that it is pure rolling along the direction of tooth width, and the rolling speed plays a leading role in improving the lubricating performance and transmission efficiency of circular arc gear. The squeeze film effect makes the pressure peak tend to be gentle and the film thickness increase slightly.

Oil Film Thickness and Pressure Distribution in Elastohydrodynamic Point Contacts

1982 ◽  
Vol 24 (4) ◽  
pp. 173-182 ◽  
Author(s):  
A. Mostofi ◽  
R. Gohar
Keyword(s):  
Contact Problem ◽  
Film Thickness ◽  
Numerical Solutions ◽  
Point Contact ◽  
Point Contacts ◽  
Rolling Velocity ◽  
Oil Film ◽  
Static Contact ◽  
Theoretical Predictions ◽  
Interferometry Method

In this paper, a general numerical solution to the elastohydrodynamic point contact problem is presented for moderate loads and material parameters. Isobars, contours and regression formulae describe how pressure and oil film thickness vary with geometry, material properties, load, and squeeze velocity, when the rolling velocity vector is at various angles to the static contact ellipse long axis. In addition, the EHL behaviour under spin is examined. The theoretical predictions of film thickness compare favourably with other numerical solutions to the point contact problem, as well as with experimental results which use the optical interferometry method to find film thickness and

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.

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

2005 ◽  
Vol 128 (2) ◽  
pp. 267-274 ◽  
Author(s):  
H. Hashimoto ◽  
M. Okajima
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Numerical Solutions ◽  
Experimental Investigations ◽  
Curve Fit ◽  
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 curve fit 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: 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 quantitatively 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.

Two-dimensional generalized non-Newtonian EHL lubrication: Shear rate-based solution versus shear stress-based solution

2021 ◽  
pp. 135065012110504
Author(s):  
Hai Chao Liu ◽  
Bin Bin Zhang ◽  
Volker Schneider ◽  
C.H. Venner ◽  
G. Poll
Keyword(s):  
Shear Stress ◽  
Shear Rate ◽  
Film Thickness ◽  
Numerical Solutions ◽  
Point Contact ◽  
Shear Thinning ◽  
High Shear ◽  
Two Dimensional ◽  
Ehl Lubrication ◽  
Ehl Contact

Lubricant behaves non-Newtonian at high shear stress and high shear rate. The non-Newtonian shear behavior of oil such as shear-thinning, viscoelasticity, and limiting shear stress could have influences on almost all characteristics of an elastohydrodynamic lubrication (EHL) contact, that is, the central film thickness, the coefficient of friction, and the temperature rise in the lubricating film. For example, for lubricants of large molecular weight or of polymer blended ones, there can be inlet shear-thinning, which would reduce the EHL film thickness. For the EHL traction in a rolling/sliding EHL contact, it cannot be reasonably predicted without the consideration of non-Newtonian rheology. In EHL numerical studies, the non-Newtonian properties and the constitutive equations are expressed by the concept of generalized viscosity [Formula: see text], which can be either a function of shear rate [Formula: see text] or a function of shear stress [Formula: see text]. In this way, a non-Newtonian lubrication problem could be solved as a generalized Newtonian problem based on solvers for a Newtonian EHL problem. According to the function of the generalized viscosity [Formula: see text], numerical solutions can be classified into shear rate-based ones and shear stress-based ones. In this work, these two kinds of numerical solutions are revisited. And their efficiency is compared for a two-dimensional (2D) non-Newtonian point contact EHL problem (here 2D means non-Newtonian flow in both the x and y directions). Results show that the shear rate-based numerical solution has a higher efficiency than the shear stress-based one. The shear rate-based 2D generalized Newtonian method is more suitable to analyze multiple EHL contacts in angular contact ball bearings and gears with complex 2D flow and/or transient EHL lubrication problems.

Rough Air-Soft Elastohydrodynamic Lubrication

2013 ◽  
Vol 420 ◽  
pp. 30-35
Author(s):  
Khanittha Wongseedakaew ◽  
Jesda Panichakorn
Keyword(s):  
Surface Roughness ◽  
Film Thickness ◽  
Modulus Of Elasticity ◽  
Contact Region ◽  
Elastohydrodynamic Lubrication ◽  
Multilevel Methods ◽  
Inlet Temperature ◽  
Film Pressure ◽  
Air Inlet ◽  
Air Film

This paper presents the effects of rough surface air-soft elastohydrodynamic lubrication (EHL) of rollers for soft material under the effect of air molecular slip. The time independent modified Reynolds equation and elasticity equation were solved numerically using finite different method, Newton-Raphson method and multigrid multilevel methods were used to obtain the film pressure profiles and film thickness in the contact region. The effects of amplitude of surface roughness, modulus of elasticity and air inlet temperature are examined. The simulation results showed surface roughness has effect on film thickness but it little effect to air film pressure. When the amplitude of surface roughness and modulus of elasticity increased, the air film thickness decreased but air film pressure increased. However, the air inlet temperature increased when the air film thickness increased.

scholarly journals Optical Analysis of Ball Bearing Starvation

1971 ◽  
Vol 93 (3) ◽  
pp. 349-361 ◽  
Author(s):  
L. D. Wedeven ◽  
D. Evans ◽  
A. Cameron
Keyword(s):  
Film Thickness ◽  
Ball Bearing ◽  
Point Contact ◽  
Experimental Measurements ◽  
Line Contact ◽  
Optical Analysis ◽  
Grease Lubrication ◽  
Theoretical Predictions ◽  
Pressure Stress ◽  
Starvation Conditions

Elastohydrodynamic oil film measurements for rolling point contact under starvation conditions are obtained using optical interferometry. The experimental measurements present a reasonably clear picture of the starvation phenomenon and are shown to agree with theoretical predictions. Starvation inhibits the generation of pressure and, therefore, reduces film thickness. It also causes the overall pressure, stress, and elastic deformation to become more Hertzian. Additional experiments using interferometry illustrate: the cavitation pattern, lubricant entrapment, grease lubrication, ball spin, and edge effects in line contact.

scholarly journals A thermal resistances-based approach for thermal-elastohydrodynamic calculations in point contacts

2017 ◽  
Vol 232 (11) ◽  
pp. 2088-2102 ◽  
Author(s):  
Eduardo de la Guerra Ochoa ◽  
Javier Echávarri Otero ◽  
Enrique Chacón Tanarro ◽  
Benito del Río López
Keyword(s):  
Friction Coefficient ◽  
Film Thickness ◽  
Thermal Effects ◽  
Good Accuracy ◽  
Computational Cost ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Point Contacts ◽  
New Approach ◽  
Ball On Disc

This article presents a thermal resistances-based approach for solving the thermal-elastohydrodynamic lubrication problem in point contact, taking the lubricant rheology into account. The friction coefficient in the contact is estimated, along with the distribution of both film thickness and temperature. A commercial tribometer is used in order to measure the friction coefficient at a ball-on-disc point contact lubricated with a polyalphaolefin base. These data and other experimental results available in the bibliography are compared to those obtained by using the proposed methodology, and thermal effects are analysed. The new approach shows good accuracy for predicting the friction coefficient and requires less computational cost than full thermal-elastohydrodynamic simulations.

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