Mathematical formulation of the film thickness in a multi-pad externally adjustable hydrodynamic bearing using the transformation technique

2021 ◽  
Vol 21 (3) ◽  
pp. 525-534
Author(s):  
A. Ganesha ◽  
Pai Raghuvir ◽  
S.M. Abdul Khader
Keyword(s):  
Film Thickness ◽  
High Speed ◽  
Mathematical Formulation ◽  
Approximation Error ◽  
Conventional Technique ◽  
Fine Tuning ◽  
Transformation Technique ◽  
Hydrodynamic Bearing ◽  
Thickness Profile ◽  
Projection Approximation

Instability problem of a hydrodynamic plain journal bearing at higher speeds is conventionally resolved by using the non-circular bearings. High speed precision rotating shafts demands accurate positioning of the journal centres. A multi-pad adjustable bearing is a non-circular bearing, provides a fine-tuning option of the journal centre by continuously changing the bearing profile. In the present study, the bearing has a configuration of four bearing pads that are adjustable both in the radial and tilt directions. The fluid film thickness profile is conventionally obtained using the trigonometric relations, which has computational limitations, especially in multi-pad adjustable bearings. In this investigation, the film thickness profile of a multi-pad adjustable bearing is mathematically formulated using the transformation technique. The results obtained are compared with those available in the literature for a similar bearing. The observation shows that transformation technique eliminates the projection approximation error present in the conventional technique.

Vision-based high speed wafer film thickness profile estimation with nonlinear regression

2020 ◽  
Author(s):  
Doo-Hyun Cho ◽  
Hyounggon Kim ◽  
Jaehyeon Son ◽  
Sungha Kim ◽  
Taejoong Kim ◽  
...  
Keyword(s):  
Film Thickness ◽  
Nonlinear Regression ◽  
High Speed ◽  
Thickness Profile ◽  
Profile Estimation

Study of the Fluid Dynamics of Thin Liquid Films Flowing Down a Vertical String With Counterflow of Gas

2015 ◽  
Author(s):  
Zezhi Zeng ◽  
Gopinath Warrier ◽  
Y. Sungtaek Ju
Keyword(s):  
Heat Transfer ◽  
Fluid Dynamics ◽  
Film Thickness ◽  
Liquid Film ◽  
Direct Contact ◽  
High Speed ◽  
Small Diameter ◽  
Liquid Films ◽  
Thin Liquid Films ◽  
Liquid Coolant

Direct-contact heat transfer between a falling liquid film and a gas stream yield high heat transfer rates and as such it is routinely used in several industrial applications. This concept has been incorporated by us into the proposed design of a novel heat exchanger for indirect cooling of steam in power plants. The DILSHE (Direct-contact Liquid-on-String Heat Exchangers) module consists of an array of small diameter (∼ 1 mm) vertical strings with hot liquid coolant flowing down them due to gravity. A low- or near-zero vapor pressure liquid coolant is essential to minimize/eliminate coolant loss. Consequently, liquids such as Ionic Liquids and Silicone oils are ideal candidates for the coolant. The liquid film thickness is of the order of 1 mm. Gas (ambient air) flowing upwards cools the hot liquid coolant. Onset of fluid instabilities (Rayleigh-Plateau and/or Kapitza instabilities) result in the formation of a liquid beads, which enhance heat transfer due to additional mixing. The key to successfully designing and operating DILSHE is understanding the fundamentals of the liquid film fluid dynamics and heat transfer and developing an operational performance map. As a first step towards achieving these goals, we have undertaken a parametric experimental and numerical study to investigate the fluid dynamics of thin liquid films flowing down small diameter strings. Silicone oil and air are the working fluids in the experiments. The experiments were performed with a single nylon sting (fishing line) of diameter = 0.61 mm and height = 1.6 m. The inlet temperature of both liquid and air were constant (∼ 20 °C). In the present set of experiments the variables that were parametrically varied were: (i) liquid mass flow rate (0.05 to 0.23 g/s) and (ii) average air velocity (0 to 2.7 m/s). Visualization of the liquid flow was performed using a high-speed camera. Parameters such as base liquid film thickness, liquid bead shape and size, velocity (and hence frequency) of beads were measured from the high-speed video recordings. The effect of gas velocity on the dynamics of the liquid beads was compared to data available in the open literature. Within the range of gas velocities used in the experiments, the occurrence of liquid hold up and/or liquid blow over, if any, were also identified. Numerical simulations of the two-phase flow are currently being performed. The experimental results will be invaluable in validation/refinement of the numerical simulations and development of the operational map.

Grease soap particles passing through an elastohydrodynamic contact under side slip conditions

2000 ◽  
Vol 214 (4) ◽  
pp. 317-325 ◽  
Author(s):  
P Eriksson ◽  
V Wikström ◽  
R Larsson
Keyword(s):  
Film Thickness ◽  
High Speed ◽  
Previous Investigation ◽  
Video Camera ◽  
Slip Conditions ◽  
High Speed Video ◽  
Elastohydrodynamic Contact ◽  
High Speed Video Camera ◽  
Pure Rolling ◽  
Minimum Film Thickness

In a previous investigation, grease thickener fibres were tracked as they passed through an elastohydrodynamic (EHD) contact in pure rolling using interferometry in a standard ball-and-disc apparatus. In order to capture single thickener fibres, a high-speed video camera was used. Here, the experiments have been repeated introducing different amounts of side slip for different rolling speeds and a faster video camera capable of capturing 4500 frames/s. The contact was lubricated with a continuous supply of grease. Two greases, based on the same synthetic poly(α-olefin) but thickened with Li-12-OH and lithium complex soap respectively, were studied. It was observed that the thickener fibres were stretched both before entering the contact and as they passed through it. Fibres seem to avoid the minimum film thickness regions and, if they enter, the film is restored immediately after passage.

scholarly journals The Effects of Artificially-Produced Defects on the Film Thickness Distribution in Sliding EHD Point Contacts

1982 ◽  
Vol 104 (3) ◽  
pp. 365-375 ◽  
Author(s):  
C. Cusano ◽  
L. D. Wedeven
Keyword(s):  
Film Thickness ◽  
Contact Region ◽  
Thickness Distribution ◽  
Point Contact ◽  
Optical Interferometry ◽  
Point Contacts ◽  
Thickness Profile ◽  
Inlet Region

The effects of artificially-produced dents and grooves on the elastohydrodynamic (EHD) film thickness profile in a sliding point contact are investigated by means of optical interferometry. The defects, formed on the surface of a highly polished ball, are held stationary at various locations within and in the vicinity of the contact region while the disk is rotating. It is shown that the defects, having a geometry similar to what can be expected in practice, can dramatically change the film thickness which exists when no defects are present in or near the contact. This change in film thickness is mainly a function of the position of the defects in the inlet region, the geometry of the defects, the orientation of the defects in the case of grooves, and the depth of the defect relative to the central film thickness.

Some Limitations in Applying Classical EHD Film Thickness Formulas to a High-Speed Bearing

1981 ◽  
Vol 103 (2) ◽  
pp. 295-301 ◽  
Author(s):  
J. J. Coy ◽  
E. V. Zaretsky
Keyword(s):  
Film Thickness ◽  
High Speed ◽  
Heating Effects ◽  
Theoretical Predictions ◽  
Traction Fluid ◽  
Shear Heating ◽  
Thickness Measurements ◽  
Inner Race ◽  
Maximum Stresses ◽  
Good Agreement

Elastohydrodynamic film thickness was measured for a 20-mm ball bearing using the capacitance technique. The bearing was thrust loaded to 90, 448, and 778 N (20, 100, and 175 lb). The corresponding maximum stresses on the inner race were 1.28, 2.09, and 2.45 GPa (185,000, 303,000, and 356,000 psi). Test speeds ranged from 400 to 14,000 rpm. Film thickness measurements were taken with four different lubricants: (a) synthetic paraffinic, (b) synthetic paraffinic with additives, (c) neopentylpolyol (tetra) ester meeting MIL-L-23699A specifications, and (d) synthetic cycloaliphatic hydrocarbon traction fluid. The test bearing was mist lubricated. Test temperatures were 300, 338, and 393 K. The measured results were compared to theoretical predictions using the formulae of Grubin, Archard and Cowking, Dowson and Higginson, and Hamrock and Dowson. There was good agreement with theory at low dimensionless speed, but the film was much smaller than theory predicts at higher speeds. This was due to kinematic starvation and inlet shear heating effects. Comparisons with Chiu’s theory on starvation and Cheng’s theory on inlet shear heating were made.

Comprehensive design methodology for an engine journal bearing

2000 ◽  
Vol 214 (4) ◽  
pp. 401-412 ◽  
Author(s):  
H Hirani ◽  
K Athre ◽  
S Biswas
Keyword(s):  
Film Thickness ◽  
High Speed ◽  
Design Methodology ◽  
Design Procedure ◽  
Maximum Pressure ◽  
Connecting Rod ◽  
Automotive Engine ◽  
Reciprocating Engine ◽  
High Power Output ◽  
Minimum Film Thickness

The trend towards high power output, high speed and low power loss in engines requires a better understanding of bearing behaviour. Research in this area is directed more towards different aspects involved in bearing analyses, rather than providing a comprehensive guideline on design of bearing. This effort compiles the design methodology for selection of diametral clearance and bearing length by limiting the minimum film thickness, maximum pressure and temperature. The design procedure is summarized on the basis of the existing rapid bearing analyses for evaluation of the journal trajectory, minimum film thickness and maximum pressure and simplified thermal analysis. A flow chart is provided for step-by-step bearing design. Finally, two case studies of engine bearings are described: one investigates the VEB bigend connecting-rod bearing for a large industrial reciprocating engine and the other a main crankshaft bearing for an automotive engine. The methodology translates into easy-to-use expressions and the overall procedure is outlined, using practical data to demonstrate how this can be employed effectively by users.

scholarly journals Enriching particles on a bubble through drainage: Measuring and modeling the concentration of microbial particles in a bubble film at rupture

Elem Sci Anth ◽  
2017 ◽  
Vol 5 ◽  
Author(s):  
Peter L. L. Walls ◽  
James C. Bird
Keyword(s):  
Thin Film ◽  
Film Thickness ◽  
High Speed ◽  
Ocean Surface ◽  
Sea Surface ◽  
Bulk Liquid ◽  
Surface Microlayer ◽  
Exchange Processes ◽  
Sea Surface Microlayer ◽  
The Moment

The concentration of microbes and other particulates is frequently enriched in the droplets produced by bursting bubbles. As a bubble rises to the ocean surface, particulates in the bulk liquid can be transported to the sea surface microlayer by attaching to the bubble’s interface. When the bubble eventually ruptures, a fraction of these particulates is often ejected into the surroundings in film droplets with a particulate concentration that is higher than in the liquid from which they formed. The precise mechanisms responsible for this enrichment are unclear, yet such enrichment at the ocean surface influences important exchange processes with the atmosphere. Here we provide evidence that drainage, coupled with scavenging, is responsible for the enrichment. By simultaneously recording the drainage and rupture effects with high-speed and standard photography, we directly measured the particulate concentrations in the thin film of a bubble cap at the moment before it ruptures. We observed that the enrichment factor strongly depends on the film thickness at rupture, and developed a physical model, based on scavenging and drainage, that is consistent with our observations. We have also demonstrated that this model is quantitatively consistent with prior observations of film drop enrichment, indicating its potential for a broader range of applications in the study of the sea surface microlayer and related phenomena.

Film breakup of tilted impinging spray under various pressure conditions

2019 ◽  
Vol 21 (2) ◽  
pp. 330-339 ◽  
Author(s):  
Di Xiao ◽  
Ichikawa Yukihiko ◽  
Xuesong Li ◽  
David Hung ◽  
Keiya Nishida ◽  
...  
Keyword(s):  
Film Thickness ◽  
Boundary Conditions ◽  
Liquid Film ◽  
High Speed ◽  
Injection Pressure ◽  
Laser Induced Fluorescence ◽  
Parameter Study ◽  
Fluorescence Signal ◽  
Fuel Film ◽  
Various Boundary Conditions

Fuel film on engine walls caused by spray impingement would dramatically cause engine friction deterioration, incomplete combustion, and significant cycle-to-cycle variations. In a previous work, it has been demonstrated that fuel film would break up via wave entrainment induced by the high-speed coflow. Meanwhile, the film breakup dynamics depend on various boundary conditions, such as injection pressure, ambient pressure, and so on. However, such impact on the wall film formation was not investigated thoroughly in existing literature. This work aims to perform a parameter study to investigate possible means to enhance wave entrainment effect as to reduce the amount of impingement fuel mass. In this study, simultaneous measurements of macroscopic structure and its corresponding footprint of impinging spray are conducted using a single-hole, prototype injector in a constant volume chamber. The macroscopic spray structure was captured by high-speed backlit imaging, and the film was obtained using laser-induced fluorescence under different conditions. The laser-induced fluorescence signal is converted to film thickness following a calibration procedure where laser-induced fluorescence signals from a series of known-thickness film are captured. A mathematical processing method is used to analyze both the dynamic behavior of film thickness and amount of droplet detachment caused by high-speed coflow. It is found that at the leading edge of film waves, a remarkable amount of liquid droplets detaches from the liquid film and the quantity of film mass on the wall decreases during this process. Quantitative analysis is conducted and the mass ratio of detached droplets over residual liquid film is estimated. We hold that the film breakup percentage increases with both ambient and injection pressure due to the enhanced high-speed coflow. Then, variation laws for various boundary conditions are obtained based on the observations.

scholarly journals A Stop-Probability Approach for O-D Service Frequency on High-Speed Railway Lines

2019 ◽  
Vol 11 (24) ◽  
pp. 6996
Author(s):  
Shuo Zhao ◽  
Xiwei Mi ◽  
Zhenyi Li
Keyword(s):  
High Speed ◽  
Travel Demand ◽  
Mathematical Formulation ◽  
Real Life ◽  
Point Of View ◽  
High Speed Railway ◽  
Passenger Travel ◽  
Optimal Service ◽  
Service Frequency ◽  
Railway Operation

Train stop planning provides appropriate service for travel demand and stations and plays a significant role in railway operation. This paper formulates stop planning from the point of view of direct travel between origin-destination (O-D) stations and proposes an analytical method to theoretically derive optimal service frequencies for O-D demand on different levels. Considering different O-D demand characteristics and train service types, we introduce the concept of stop probability to present the mathematical formulation for stop planning with the objective of minimizing per capita travel time, which is solved by an iterative algorithm combined with local search. The resulting optimal stop probabilities can be used to calculate the required service frequency for each train type serving different demand categories. Numerical examples, based on three real-life high-speed railway lines, demonstrate the validity of the proposed method. The proposed approach provides a more flexible and practical way for stop planning that explicitly takes into account the importance of different stations and passenger travel characteristics.

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