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.

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.

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.

The Buckling and Postbuckling of Fibrils Adhering to a Rigid Surface

2013 ◽  
Vol 80 (4) ◽  
Author(s):  
Sebastian Stark ◽  
Matthew R. Begley ◽  
Robert M. McMeeking
Keyword(s):  
Aspect Ratio ◽  
Numerical Results ◽  
Rigid Surface ◽  
Displacement Control ◽  
Load Displacement ◽  
Adhesive Performance

Recent experiments in which arrays of compliant fibrils are compressed axially against a rigid surface and then released have shown that there is load-displacement hysteresis during this process, accompanied by buckling and unbuckling of the fibrils. Furthermore, the adhesive performance of the system is decreased by such prior buckling. We present a model describing the buckling and postbuckling characteristics of a fibril with an aspect ratio of 10 or greater. The possibility during buckling of partial detachment of the end of the fibril is taken into account. The results are presented and discussed for both load and displacement control and the load-displacement hysteresis is identified. It is found that due to instabilities sudden spreading and shrinkage of the adhered area at the end of the fibril can accompany the hysteresis. Numerical results are provided to substantiate the findings and possible reasons for the observed influence of buckling on adhesive performance are reviewed.

Non-Newtonian Micropolar Fluid Squeeze Film Between Conical Plates

2012 ◽  
Vol 67 (6-7) ◽  
pp. 333-337 ◽  
Author(s):  
Jaw-Ren Lin ◽  
Chia-Chuan Kuo ◽  
Won-Hsion Liao ◽  
Ching-Been Yang
Keyword(s):  
Micropolar Fluid ◽  
Reynolds Equation ◽  
Fluid Model ◽  
Load Capacity ◽  
Numerical Results ◽  
Squeeze Film ◽  
Micropolar Fluids ◽  
Newtonian Case ◽  
Film Characteristics ◽  
Film Lubrication

By applying the micropolar fluid model of Eringen (J. Math. Mech. 16, 1 (1966) and Int. J. Mech. Sci. 31, 605 (1993)), the squeeze film lubrication problems between conical plates are extended in the present paper. A non-Newtonian modified Reynolds equation is derived and applied to obtain the solution of squeeze film characteristics. Comparing with the traditional Newtonian case, the non-Newtonian effects of micropolar fluids are found to enhance the load capacity and lengthen the approaching time of conical plates. Some numerical results are also provided in tables for engineer applications

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.

A Comparison of Homogenization and Direct Techniques for the Treatment of Roughness in Non-Newtonian-Modified Reynolds Equation: Numerical Results

Volume 1 ◽  
2004 ◽  
Author(s):  
Malal Kane ◽  
Benyebka Bousaid
Keyword(s):  
Exact Solution ◽  
Reynolds Equation ◽  
Direct Methods ◽  
Homogenization Method ◽  
Numerical Results ◽  
Homogenization Theory ◽  
Lubricated Contact ◽  
A New Technique ◽  
Direct Inspection ◽  
Theoretical Developments

This article is concerned with the simulation of a lubricated contact in severe running conditions considering the fluid as Non-Newtonian of Maxwell type. To overcome some limitations that become apparent at very small film thickness, notably when the roughness is two-dimensional, Jai in 1995 introduced a new technique based on a rigorous homogenization theory in the case of compressible fluid flow. This procedure was mathematically developed by Jai [1] and Buscaglia and Jai [2], and applied to tribological problems by Jai and Bou-Sai¨d [3]. The theoretical developments have been presented and discussed elsewhere [6] of this work and we present here some numerical results obtained from the homogenized technique. The obtained results were discussed and compared with the direct methods of calculation, and seem to us valid for a definitive validation of this method said about homogenization. These results have been compared to the exact solution obtained from a numerical simulation. By direct inspection it is clear that the symmetry predicted by the homogenization method is not present in the exact solution which qualitatively agrees with the homogenized solution.

Design of Pivoted-Pad Journal Bearings

1969 ◽  
Vol 91 (1) ◽  
pp. 87-103 ◽  
Author(s):  
R. C. Elwell ◽  
J. A. Findlay
Keyword(s):  
Numerical Solution ◽  
Incompressible Flow ◽  
Digital Computer ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Journal Bearings ◽  
Numerical Results ◽  
Load Direction ◽  
Numerical Examples ◽  
Calculated Load

Calculated load capacity and friction for complete pivoted-pad journal bearings are presented, for use in design computations. Dimensionless numerical results are given for the following variations in bearing geometry: 3 and 5 pads, L/D ratios of 1/2 to 1, pivot locations of 40, 50, and 60 percent, on pivot and between pivot loading, and ratios of “assembled” to “ground” clearance of 0.6, 0.8, and 1.0. The numerical results are an extension of the work of Castelli, et al., reference [1],1 and were generated in the same manner i.e., numerical solution of Reynolds’ equation by digital computer. Laminar, incompressible flow, and subambient pressures in diverging portions of the films were assumed. Illustrative numerical examples are included and significant conclusions with respect to major variables (L/D ratio, number of pads, clearances, pivot location, load direction) are drawn from the range of data produced.

Hybrid Finite-Discrete Element Modelling of Dynamic Fracture of Rocks with Various Geometries

2012 ◽  
Vol 256-259 ◽  
pp. 183-186 ◽  
Author(s):  
Hong Yuan Liu
Keyword(s):  
Discrete Element Method ◽  
Dynamic Fracture ◽  
Discrete Element ◽  
Numerical Results ◽  
Discrete Element Modelling ◽  
Rigid Surface ◽  
Element Modelling ◽  
Impact Area ◽  
The Impact ◽  
Rock Specimens

The hybrid finite-discrete element method Y-2D/3D IDE is applied to model the dynamic fracture of rock specimens with various geometries during impacting a fixed rigid surface. It is found that the modelled primary fractures are highly dependent on the rock geometry determining the weakest plane for a given impact, which agrees well with others' experimental and SPH numerical results. Compared with others' SPH results, Y-2D/3D IDE better simulates the actinomorphic pattern of primary fractures around the impact area and the secondary & tertiary fractures observed in the dynamic fracture experiments. It is concluded that the proposed Y-2D/3D IDE is a valuable tool to model rock dynamic fracture compared with FEM and DEM.

Calculation of the Hydrodynamic Interaction Between Two Encountering Bodies in Coupling Multi-Freedom Motions

2015 ◽  
Vol 157 (A4) ◽  
pp. 219-226
Keyword(s):  
Hydrodynamic Interaction ◽  
Interaction Effects ◽  
Numerical Results ◽  
Motion Equations ◽  
Flow Equations ◽  
Close Proximity ◽  
Lateral Distance ◽  
Body Sizes ◽  
Two Bodies ◽  
Good Agreement

"The sway and yaw motion will be induced additionally due to the interaction effects when two encountering bodies sail in close proximity, which may lead to the collision accident. In the present study, two ellipsoids are taken as an example. By coupling the motion equations of the two bodies and the fluid flow equations, the interaction forces and moments are calculated, and the tracks are predicted. The numerical results for the model fixed motion (only free to surge) at constant speed are compared with those published in literature for the validation of the method proposed in this paper, and good agreement is found. On this basis, more complicated multi-degree of freedom motions in surge, sway and yaw directions induced by the interaction effects are simulated. By systematically comparing and analyzing the numerical results obtained at different speeds, lateral distances and body sizes, the influences of speed and lateral distance and body size on the hydrodynamic forces are elucidated."

Wave propagation phenomena at an irregular infinite interface: Part III: Rigid boundary

1964 ◽  
Vol 54 (6B) ◽  
pp. 2233-2242
Author(s):  
W. M. Adams ◽  
E. Schlesinger ◽  
E. K. Schubel
Keyword(s):  
Wave Propagation ◽  
Acoustic Wave ◽  
Numerical Results ◽  
Rigid Surface ◽  
Rigid Boundary

Abstract The problem is the scattering of a plane, simple harmonic acoustic wave from a rigid surface. The boundary is taken to be infinite and irregular, as defined in Part I. Numerical results obtained with an IBM 7094 computer are given. Suggestions for further research are presented also.

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