scholarly journals A New Structural Bump Foil Model With Application From Start-Up to Full Operating Conditions

2019 ◽  
Vol 141 (10) ◽  
Author(s):  
Mihai Arghir ◽  
Omar Benchekroun
Keyword(s):  
Film Thickness ◽  
Numerical Solutions ◽  
Operating Conditions ◽  
Experimental Results ◽  
Static Loads ◽  
Contact Algorithm ◽  
Start Up ◽  
Theoretical Predictions ◽  
Full Speed ◽  
Contact Pressures

Abstract This paper presents a new structural bump foil model that can handle all operating conditions from start-up to full speed. The model is based on a nonlinear contact algorithm with friction and gaps. The top foil is modeled as a curved beam while bump foil uses a coupled truss model. The model considers the gaps between the bump foil and the bearing casing, between the bump foil and the top foil and between the rotor and the top foil. Thus, any numerical interference between the rotor and the top foil is avoided. A mixed lubrication model is used for the thin film pressures. Following this algorithm, contact pressures appear if the film thickness is less than three times the equivalent roughness of the rotor and of the top foil. Fluid pressures are calculated from numerical solutions of Reynolds equation while contact pressures, if present, are calculated with the model of Greenwood and Williamson. The model is validated by comparisons with the experimental results obtained for start-up operating conditions of a first-generation foil bearing of 38.1 mm diameter with static loads of 10–50 N. Theoretical predictions of the start-up torque and takeoff speed compare well with experimental results. It is also shown how manufacturing bump height errors can explain the differences between theoretical and experimental predictions. Further validations are presented for the same bearing operating at high speeds (30, 45, and 55 krpm) and heavy static loads (up to 200 N). The calculated minimum film thickness and attitude angle are compared with experimental data from the literature.

scholarly journals A New Structural Bump Foil Model With Application From Start-Up to Full Operating Conditions

2019 ◽  
Author(s):  
Mihai Arghir ◽  
Omar Benchekroun
Keyword(s):  
Film Thickness ◽  
Numerical Solutions ◽  
Operating Conditions ◽  
Experimental Results ◽  
Static Loads ◽  
Contact Algorithm ◽  
Start Up ◽  
Theoretical Predictions ◽  
Full Speed ◽  
Contact Pressures

Abstract The paper presents a new structural bump foil model that can handle all operating conditions from start-up to full speed. The model is based on a non-linear contact algorithm with friction and gaps. The top foil is modeled as a curved beam while bump foil uses a coupled truss model. The model considers the gaps between the bump foil and the bearing casing, between the bump foil and the top foil and between the rotor and the top foil. Thus, any numerical interference between the rotor and the top foil is avoided. A mixed lubrication model is used for the thin film pressures. Following this algorithm, contact pressures appear if the film thickness is less than three times the equivalent roughness of the rotor and of the top foil. Fluid pressures are calculated from numerical solutions of Reynolds equation while contact pressures, if present, are calculated with the model of Greenwood and Williamson. The model is validated by comparisons with the experimental results obtained for start-up operating conditions of a first generation foil bearing of 38.1 mm diameter with static loads of 10 N to 50 N. Theoretical predictions of the start-up torque and take-off speed compare well with experimental results. It is also shown how manufacturing bump height errors can explain the differences between theoretical and experimental predictions. Further validations are presented for the same bearing operating at high speeds (30, 45 and 55 krpm) and heavy static loads (up to 200 N). The calculated minimum film thickness and attitude angle are compared with experimental data from the literature.

Elastohydrodynamic Film Thickness in Concentrated Contacts: Part 2: Correlation of Experimental Results with Elastohydrodynamic Theory

1986 ◽  
Vol 200 (3) ◽  
pp. 219-226 ◽  
Author(s):  
R J Chittenden ◽  
D Dowson ◽  
C M Taylor
Keyword(s):  
Film Thickness ◽  
Experimental Studies ◽  
Elastohydrodynamic Lubrication ◽  
Operating Conditions ◽  
Experimental Results ◽  
Experimental Techniques ◽  
Dimensionless Parameters ◽  
Wide Range ◽  
Theoretical Predictions ◽  
Computational Procedures

The existence of a coherent film of lubricant between highly loaded machine elements has been recognized for many years. Over this period of time measurements of film thickness have gone hand in hand with theoretical analyses in the field now known as elastohydrodynamic lubrication. The experimental techniques of capacitance, electrical resistance and X-ray measurement have been supplemented by the use of optical interferometry while the analytical expressions obtained with the use of elegant simplifications have been superseded by those developed from extensive and comprehensive computational procedures. These developments in experimental techniques have yielded a substantial number of measurements of both minimum and central film thickness. Likewise, the advent of the digital computer has allowed the derivation of a large number of solutions to the problem of elastohydrodynamic lubrication of concentrated contacts. All these results, covering a wide range of geometrical conditions, are to be found in the literature, yet little attempt appears to have been made to assemble a representative set of experimental data to permit a detailed evaluation of the theoretical formulae for elliptical contacts. The second part of this paper therefore considers the correlation between a number of experimental studies covering a wide range of operating conditions and geometries, and the predictions of recent elastohydrodynamic theory. Some of the important aspects of each set of experimental results are then considered and examples are provided which illustrate the following points: 1. Good estimates of lubricant film thickness may be obtained from the theoretical expressions recently derived, even when the dimensionless parameters involved are outside the ranges considered in the derivation of the formulae. 2. The discrepancies which exist between theoretical predictions and some of the measured film thicknesses are nevertheless quite large, even when the dimensionless parameters are within their usual limits. On the whole there is good agreement between experiment and theory, while the general trend of the results indicates that theoretical predictions may underestimate the minimum film thickness by about 10 per cent and the central film thickness by about 25 per cent. This measure of agreement is quite remarkable when the extreme difficulty of interpreting the magnitudes of effective and very thin mean film thicknesses between machined components in various forms of experimental equipment is considered.

The Improvement of the Micro Torsional Mirror by a Reinforced Folded Frame

2000 ◽  
Author(s):  
Hung-Yi Lin ◽  
Weileun Fang
Keyword(s):  
Thin Film ◽  
Residual Stresses ◽  
Film Thickness ◽  
Experimental Results ◽  
Dynamic Loads ◽  
Inertia Force ◽  
Optical Performance ◽  
Thin Film Thickness ◽  
Static Loads ◽  
Dynamic Inertia

Abstract Stiffness of micromachined structures is limited by thin film thickness. Hence, static loads such as thin film residual stresses, or dynamic loads such as the inertia force could significantly deform the thinness micromachined torsional mirror. This work aims to stiffen the thin film micromachinined torsional mirror. The proposed torsional mirror exploits a reinforced frame to improve the stiffness of the mirror plate. Consequently, the mirror plate has less deformation no matter subject to the residual stresses or to the dynamic inertia force. In addition the reinforced frame stiffen the mirror without increasing the mass significantly. In application of this technique, the micro torsional mirror was fabricated through the integration of DRIE, conventional bulk and surface micromachining processes. The experimental results demonstrated that the proposed design significantly improves the flatness of the mirror plate in both static and dynamic conditions. Consequently, the optical performance of the micro torsional mirror was improved.

An Interpolation Procedure for the Minimum Film Thickness in Point Contacts

1990 ◽  
Vol 204 (3) ◽  
pp. 199-206 ◽  
Author(s):  
C J Hooke
Keyword(s):  
Film Thickness ◽  
Contact Geometry ◽  
High Accuracy ◽  
Operating Conditions ◽  
Experimental Results ◽  
Point Contacts ◽  
Design Charts ◽  
Minimum Film Thickness ◽  
Interpolation Procedure

Most engineering point contacts operate in, or close to, the elastic piezoviscous regime. A general interpolation procedure is presented by which the minimum film thickness in any such contact may be estimated. This procedure matches all existing numerical and experimental results with high accuracy. Design charts are provided and these enable the minimum film thickness to be read directly and also allow the effect of changes in contact geometry and operating conditions to be assessed.

A Mixed-Lubrication Study of Journal Bearing Conformal Contacts

1997 ◽  
Vol 119 (3) ◽  
pp. 456-461 ◽  
Author(s):  
Qian (Jane) Wang ◽  
Fanghui Shi ◽  
Si C. Lee
Keyword(s):  
Film Thickness ◽  
Contact Pressure ◽  
Contact Area ◽  
Numerical Solutions ◽  
Mixed Lubrication ◽  
Lubricant Film ◽  
Operating Conditions ◽  
Asperity Contact ◽  
Lubricant Film Thickness ◽  
Asperity Contacts

Numerical analyses of finite journal bearings operating with large eccentricity ratios were conducted to better understand the mixed lubrication phenomena in conformal contacts. The average Reynolds equation derived by Patir and Cheng was utilized in the lubrication analysis. The influence function, calculated numerically using the finite element method, was employed to compute the bearing deformation. The effects of bearing surface roughness were incorporated in the present analysis for the calculations of the asperity contact pressure and the asperity contact area. The numerical solutions of the hydrodynamic and asperity contact pressures, lubricant film thickness, and asperity contact area were evaluated based on a simulated bearing-journal geometry. The calculations revealed that the asperity contact pressure may vary significantly along both the width and the circumferential directions. It was also shown that the asperity contacts and the lubricant film thickness were strongly dependent on the bearing width, asperity orientation, and operating conditions.

Report Paper 2: Approximate Short Bearing Analysis and Experimental Results Obtained Using Plastic Bearing Liners

1969 ◽  
Vol 184 (12) ◽  
pp. 190-196 ◽  
Author(s):  
J. P. O'Donoghue ◽  
P. R. Koch ◽  
C. J. Hooke
Keyword(s):  
Approximate Solution ◽  
Film Thickness ◽  
Journal Bearings ◽  
Experimental Results ◽  
Approximate Theory ◽  
Hydrodynamic Problem ◽  
Dynamic Conditions ◽  
Oil Film ◽  
Theoretical Predictions ◽  
Bearing Analysis

This paper outlines a new approximate theory for liquid lubricated plain journal bearings with elastic liners. This is a modified form of Ocvirk's theory and includes the effect of circumferential flow. The results of a series of tests on short plastic bearings are presented to compare with the theoretical predictions of the new theory. The authors conclude that for short bearings the theory gives reasonably good predictions of performance, but the elasticity assumptions cause major errors for length/diameter ratios greater than 0·5 due to the decrease in oil film thickness that occurs near the ends of the bearing. The approximate solution adopted for the hydrodynamic problem may be of use for considering dynamic conditions taking the Reynolds conditions for cavitation.

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

A Study of Roughness and Non-Newtonian Effects in Lubricated Contacts

2005 ◽  
Vol 127 (3) ◽  
pp. 575-581 ◽  
Author(s):  
Malal Kane ◽  
Benyebka Bou-Said
Keyword(s):  
Film Thickness ◽  
Numerical Solutions ◽  
Operating Conditions ◽  
Homogenization Theory ◽  
Roughness Effects ◽  
Small Surface ◽  
Lubricated Contacts ◽  
Lubricated Contact ◽  
A New Technique ◽  
Numer Anal

This article is concerned with the simulation of a lubricated contact considering the fluid to be non-Newtonian of the Maxwell type. Severe operating conditions lead to very small surface-to-surface distances. In this situation it is necessary to take roughness effects into account. A popular method consists in averaging the film thickness following Patir and Cheng (ASME J. Lubr. Technol., 100, pp. 12–17, 1978), or more recently Wang et al. (Tribol. Trans., 45(1), pp. 1–10, 2000), with good reported results compared with experimental data. To overcome certain limitations that become apparent at very small film thickness, notably when the roughness is two-dimensional, in 1995 Jai (Math. Modell. Numer. Anal., 29(2), pp. 199–233, 1995) introduced a new technique based on a rigorous homogenization theory in the case of compressible fluid flow. This procedure was further mathematically developed by Buscaglia and Jai (Math. Probl. Eng., 7(4), pp. 355–377, 2001) and applied to tribological problems by Jai and Bou-Saı¨d (ASME J. Tribol., 124, pp. 327–355, 2002). In this paper, we propose a similar homogenized approach in the case of non-Newtonian fluids to avoid numerical problems which are often encountered in other approaches. Results in the homogenized roughness case are obtained and compared with direct numerical solutions.

Effects of Load System Dynamics on the Film Thickness in EHL Contacts During Start Up

2004 ◽  
Vol 126 (2) ◽  
pp. 258-266 ◽  
Author(s):  
G. Popovici ◽  
C. H. Venner ◽  
P. M. Lugt
Keyword(s):  
Film Thickness ◽  
Oscillatory Behavior ◽  
Contact Dynamics ◽  
Experimental Results ◽  
Force Balance ◽  
Operational Conditions ◽  
Start Up ◽  
Loading System ◽  
General Aspects ◽  
Ball On Disc

By means of numerical simulations the effects of the loading system on the contact dynamics of an EHL contact during start up have been studied. The work was initiated by experimental results obtained for the start up situation on a ball on disk apparatus in which strong film thickness oscillations were observed. In this paper it is shown how much, under operational conditions as they appear in a ball on disc rig, inertia, and stiffness related to the configuration of the loading system can influence the film thickness and mutual approach. For this purpose a model was used in which the usual force balance equation has been replaced by an equation of motion for the loading system in which an inertia and spring effect appear. It was shown that for large accelerations, the loading system does induce oscillations in the film thickness, and predictive formulas for the oscillation frequency derived from a dry contact analysis are shown to be accurate. The nature of the oscillations is explained in relation to the general aspects of time dependent solutions to EHL problems. However, the predicted oscillation amplitudes are small compared to what is seen in the experiments and although some of the phenomena shown in the solutions presented here also appear in the experimental results the experimentally observed oscillatory behavior appears to be of a different nature. As the model used here has given good predictions of the dynamic behavior of single contacts in ball on disc experiments in earlier studies it is concluded that it is unlikely that the oscillatory behavior observed in the experiments is only due to the dynamics of the loading system and other effects must play a role.

Rotational Response and Slip Prediction of Serpentine Belt Drive Systems

1994 ◽  
Vol 116 (1) ◽  
pp. 71-78 ◽  
Author(s):  
S.-J. Hwang ◽  
N. C. Perkins ◽  
A. G. Ulsoy ◽  
R. J. Meckstroth
Keyword(s):  
Numerical Solutions ◽  
Equations Of Motion ◽  
Operating Conditions ◽  
Equilibrium Analysis ◽  
Belt Drive ◽  
Theoretical Predictions ◽  
Serpentine Belt ◽  
Drive Systems ◽  
Nonlinear Equations Of Motion ◽  
Rotational Response

A nonlinear model is developed which describes the rotational response of automotive serpentine belt drive systems. Serpentine drives utilize a single (long) belt to drive all engine accessories from the crankshaft. An equilibrium analysis leads to a closed-form procedure for determining steady-state tensions in each belt span. The equations of motion are linearized about the equilibrium state and rotational mode vibration characteristics are determined from the eigenvalue problem governing free response. Numerical solutions of the nonlinear equations of motion indicate that, under certain engine operating conditions, the dynamic tension fluctuations may be sufficient to cause the belt to slip on particular accessory pulleys. Experimental measurements of dynamic response are in good agreement with theoretical results and confirm theoretical predictions of system vibration, tension fluctuations, and slip.

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