Formula For Thickness Research Articles

The Multi-Objective Optimization for Cycloidal Gear Drive Based on the Elastohydrodynamic Lubrication Theory

For improving the designed quality of the cycloidal gear planetary drive, the paper derives a calculation formula of the minimum film thickness, which is between cycloidal gear teeth, based on elastohydrodynamic lubrication theory and gear geometry. A mathematical model for constrained multi-objective optimization is established and the model satisfies three constrains:maximize minimum film thickness between gear teeth( minimize the reciprocal ), minimize average value of m points’s absolute error value on active section that is between the tooth curves of positive shift optimal combination and tooth curves of rotated angle’s modification, minimize the total volume of gear drive. The paper abandons traditional designed method of the multi-objective optimization , improves two-objective particle swarm optimization and offers a new designed model for constrained three-objective optimization. The example is analyzed and the optimization program is complied using Matlab. The optimization’s process and result shows that the method of improved constrained multi-objective particle swarm optimization could effectively improve the products’ synthesize economical and technical indexes.

New minimum film thickness formula for EHL rolling/sliding line contacts considering shear thinning behavior

Full EHL line contact simulations have been carried out to obtain a new minimum film thickness formula pertaining to thin film EHL line contacts for Carreau-type shear-thinning lubricants. The present analysis uses Doolittle’s free volume based viscosity model with Tait’s equation to describe the density–pressure relationship. The load parameter ( W) used in the present simulations ranges from 2 × 10−5 to 5 × 10−4, while the piezo-viscous coefficient varies from 15 to 30 GPa −1 using different sets of Doolittle–Tait parameters. The curve-fitted values of minimum film thickness are found to conform well with the corresponding simulated values. Further, the present equation is shown to accurately capture the effect of increased scale and load sensitivities due to shear-thinning behavior.

Research on Cushioning Package Design Methods Based on Infinitive Equations

The cushion design methods based on cushioning coefficient - maximum stress curve were studied. In research work, the cushioning coefficient - maximum stress curve was equivalent to an infinitive equation, and then composed to infinitive equations together with the cushion area and thickness formula. The cushion design methods based on cushioning coefficient - maximum stress curve was characterized as the problem of solving infinitive equations. By this method, the classic cushion area and thickness calculation methods were analyzed. It is believed that the essence of the classic design methods is increasing a restriction to the infinitive equations, as changed the original infinitive equations to posed equations. The research work can help designers deep understanding the traditional cushioning design methods and theories, and can be used to flexible design the cushion structure.

Assessments of total corneal power and intraocular lens power in post-LASIK eyes

To compare the different evaluations of corneal power in post-laser-assisted in situ keratomileusis (LASIK) eyes and assess the accuracy and differences of intraocular lens (IOL) power prediction with corneal powers through different calculation methods. For this prospective study, 71 eyes of 39 candidates undergoing LASIK and 3 months later returning for reexamination were included. All subjects were divided into 2 groups according to the axial length: Group A (23.46 - 25.97 mm) 44 eyes, Group B (26.00 - 28.52 mm) 27 eyes. The ranges of spherical equivalents were -1.75 - -9.50 D with an average of (-4.82 ± 1.98) D. Subjective refraction and Pentacam Scheimpflug analyzer were performed at pre-operation and subjective refraction, IOLMaster and Galilei II dual Scheimpflug analyzer at over 3 months post-operation. The following values were obtained: SimK by Galilei II dual Scheimpflug analyzer, Kn calculated with Gaussion thick lens formula, Kray with ray tracing method, Kchm calculated with clinical history method and Km by IOLMaster. Repeated measures analysis of variance analyze the differences between SimK, Kn, Kray, Km and Kchm. Repeated measurement analysis of variance was employed to analyze the differences between SimK, Kn, Kray, Km combining intraocular lens power formula and Kchm combining intraocular lens power formula. Pearson's analysis was performed to analyze the correlations between SimK, Kn, Kray, Km and Kchm. Those combining with formulas for IOL power calculations were also analyzed. P < 0.05 indicated statistical significance. The values of SimK, Kn, Kray, Km and Kchm were (39.02 ± 1.8), (37.8 ± 1.51), (36.8 ± 1.84), (39.18 ± 1.75) and (38.55 ± 1.83) D respectively. The differences between SimK, Kn, Kray, Km and Kchm had statistical significances (P < 0.01). High correlations existed between SimK, Kn, Kray, Km and Kchm (r > 0.9, P < 0.01). In the same IOL formula, Kray had the highest IOL power value, Kn followed, Kchm the third, SimK and Km the smallest. Among the IOL formulas, Haigis-L and Haigis predicted the highest IOL power, HofferQ followed, Holladay the third and SRK/T the smallest. Kn/Kray combining with Haigis formula may be a new and effective method for predicting the IOL power in post-LASIK eyes.

The Hot-Plugging Clamp Design of the Petrochemical Equipment Pipeline

Liquid leaking accidents of petrochemical equipment were always happened in weld joint of the pipeline. In order to deal with the accidents, the hot-plugging technique was adopted. And the clamp design which was the difficult point of this technology must be valued. In this paper, the hot-plugging technique and the structure of the clamp were introduced. And the calculation formula of the clamp thickness was deduced based on the influence of the injecting hole on the clamp and GB150-98. And the results would be the fundament of further study of the hot-plugging clamp design

Optical parameters of zinc dialkyldithiophosphate in terahertz regime

The optical properties of zinc dialkyldithiophosphate (ZDDP) were investigated using a transmission-mode terahertz time-domain spectroscopy (THz-TDS) measurement. Comparing with the middle-infrared spectra of ZDDP, THz spectra of ZDDP show the weak broad absorption bands, and the absorption coefficients increased monotonously as the frequency increases within the effective frequency range. The selected frequency, where absorption constants show the lowest variance by using optimum thickness formula, was used for quantitative analysis of ZDDP with different alkyl substituents.

Research on Web-Based Elastohydrodynamic Lubrication Oil Theory of Rolling Bearing Type Planetary Friction Transmission Mechanism

Service mode and dynamic network interfere techniques are analyzed. An elastohydrodynamic lubrication oil thickness theory of rolling bearing type planetary friction transmission mechanism system based on web is presented.Elastohydrodynamic lubrication theory is adopted in rolling bearing type planetary friction transmission mechanism in this paper. Research indicates that elastohydrodynamic oil file lubrication can be realized while mechanical parts with connection between points or lines run under certain conditions. At the same time, surface disrepair of the parts has relation to lubrication state. Minimal oil film thickness formula is deduced based on the elastohydrodynamic lubrication theory. It is a part of He’nan Scientific Committee science and technology research projects 《research on collaborative design and manufacturing technique in gear manufacturing based on network and multi-Agent》

Comparison of Age-derived Lens Thickness to Optically Measured Lens Thickness in IOL Power Calculation: A Clinical Study

To assess whether lens thickness derived from age should be used in intraocular lens (IOL) power calculation. Ninety-three eyes underwent optical low coherence reflectometry (OLCR) prior to cataract surgery. Lens thickness (LT) by OLCR was used to calculate the IOL power. The mean absolute refractive error (MAE) and mean refractive error (ME) were calculated. Regression analysis between age and LT was performed. The expected IOL power, MAE, and ME were calculated with two age-derived lens thickness formulae: LT=4+(age/100) and LT=3.81+(0.0119×age). Lens thickness by OLCR was not significantly different from that by age, but the IOL power was different. Refractive outcome was better with OLCR-based LT. Correlation between age and LT was not as linear as implied by the formulae. In its current form, age-derived LT should not be used in IOL power calculation.

Central film thickness formula for shear thinning lubricants in EHL point contacts under pure rolling

Based upon an extensive set of full EHL point contact simulations, this paper offers a central film thickness formula pertaining to shear-thinning lubricants with Carreau-type behavior. In order to develop a more generic and accurate version of film thickness formula, a recent work is extended by carrying out the simulations for widely varying operating loads and piezo-viscous coefficients along with the more realistic Doolittle's free volume based pressure–viscosity model. This equation is found to conform very well with the published experimental data for EHL lubricants with widely varying rheological and piezo-viscous behaviors, i.e., polyalpha olefins and polydimethyl siloxane.

Temperature dependent viscosity and surface tension effects on deformations of non-isothermal falling liquid film

Theoretical and numerical investigations of the heat transfer and hydrodynamics in a liquid film flowing along an inclined substrate under the action of gravity with a local heat source have been performed. A two-dimensional model, based on the thin layer approximation, has been developed describing deformations of the film interface. Equation of a non-isothermal thin-film flow with linear dependence of viscosity and surface tension on temperature is derived. A generalized analytical formula for the film thickness as a function of liquid flow-rate is obtained. Marangoni flow, due to local temperature changes, opposes the gravitationally driven film flow and forms a horizontal bump near the upper edge of the heater. Attention is paid to the viscosity effect on the shape of the bump and the film thinning on the local heaters. A second order deformation of the free surface before the bump up to flow may exist. The criterion for the appearance of this deformation is found analytically.

The determination of the pressure–viscosity coefficient of a lubricant through an accurate film thickness formula and accurate film thickness measurements. Part 2: high L values

The pressure–viscosity coefficient of a traction fluid is determined by fitting calculation results on accurate film thickness measurements, obtained at different speeds, loads, and temperatures. Through experiments, covering a range of 5.6 &lt; M &lt; 12 000, 2.1 &lt; L &lt; 17.5, film thickness values are calculated using a numerical method and approximation formulas from 12 models. It is concluded that, to assess the pressure–viscosity coefficient of the fluid, the Chittenden et al. approximation formula applied to circular contacts is the best choice, having an inaccuracy in between (−15%, +11%). This expression has been used far outside the regime of the numerical data where it was based upon.

New film thickness formula for shear thinning fluids in thin film elastohydrodynamic lubrication line contacts

A new central film thickness formula pertaining to thin film elastohydrodynamic lubrication (EHL) line contacts has been developed for Carreau-type shear-thinning lubricants using an extensive set of full EHL simulations. The shear-thinning correction factors available in the literature are based on EHL simulations carried out for a particular value of load and piezo-viscous coefficient using the simplest exponential pressure–viscosity relationship. In the present work, therefore, the load and piezo-viscous coefficient are varied over a wide range so as to arrive at a more generic and accurate film thickness equation. Also, the pressure–viscosity relation employed herein is the Doolittle's free volume-based viscosity model, which is capable of replicating the experimental pressure–viscosity data with a high degree of accuracy. It has been demonstrated that the present film thickness equation accurately captures the recently discovered scale and load sensitivity effects.

Research on Elastohydrodynamic Lubrication Theory of Rolling Bearing Type Planetary Friction Transmission Mechanism

Elastohydrodynamic lubrication theory is adopted in rolling bearing type planetary friction transmission mechanism in this paper. Operation performance and using life-span are improved. Minimal oil film thickness formula is deduced based on the elastohydrodynamic lubrication theory. Relationship curve between minimal oil film thickness and rotate speed is presented. Variation law between minimal oil film thickness and work parameters is given.

On the issue of an equivalent oxide thickness evaluation in nanoscale MISFETs

The refinement of the evaluation formula for an equivalent oxide thickness in the case of a multi-layer gate insulator is obtained, taking into account a polarity effect in the suboxide layer at the Si/high-K dielectric interface. Calculated semiclassically and associated with the polarization dipole mechanism, the correction is negative and does not exceed 6%.

Newtonian quantitative elastohydrodynamic film thickness with linear piezoviscosity

Examples are provided for linear pressure–viscosity response at low pressures, which are said to exist in the concentrated contact inlet, including lubricants at high temperature, low viscosity liquids and water/glycol solutions. Full isothermal, Newtonian simulations of the EHL problem reveal film-forming, which is quite similar to that of exponential liquids with the exception of the reduced sensitivity to the Dowson material parameter, G, or the Moes parameter, L. Film thickness formulas are offered, which have been experimentally validated. In a significant departure from most investigations of this kind, the viscosity of the experimental liquids was not adjusted to provide successful comparisons with measurement.

Buoyancy Arrest and Bottom Ekman Transport. Part I: Steady Flow

Abstract It is well known that along-isobath flow above a sloping bottom gives rise to cross-isobath Ekman transport and therefore sets up horizontal density gradients if the ocean is stratified. These transports in turn eventually bring the along-isobath bottom velocity, hence bottom stress, to rest (“buoyancy arrest”) simply by means of the thermal wind shear. This problem is revisited here. A modified expression for Ekman transport is rationalized, and general expressions for buoyancy arrest time scales are presented. Theory and numerical calculations are used to define a new formula for boundary layer thickness for the case of downslope Ekman transport, where a thick, weakly stratified arrested boundary layer results. For upslope Ekman transport, where advection leads to enhanced stability, expressions are derived for both the weakly sloping (in the sense of slope Burger number s = αN/f, where α is the bottom slope, N is the interior buoyancy frequency, and f is the Coriolis parameter) case where a capped boundary layer evolves and the larger s case where a nearly linearly stratified boundary layer joins smoothly to the interior density profile. Consistent estimates for the buoyancy arrest time scale are found for each case.

光溅射镀膜均匀性的优化模拟

Method of off-axis rotated scan is studied in order to improve the thickness uniformity of the film by pulse laser deposition (PLD). Based on the principle and spatial distribution of plasma,radial distribution formula of film thickness is formed. Effects on uniformity of film deposited by method of off-axis rotated scan are simulated numerically. The simulated results show that optimize of d (distance between sputtering dot and foundation) and r (interval between particle center and foundation center ) are primary means for improving the uniformity of film. In addition,influence of electromotor rotate speed,working time and laser repetition frequency is considered. Simulated with optimal parameters,maximum radius of film diameter over 40 mm is obtained when 95% uniformity is required.

Analytic Computation Method of the Equivalent Thickness of Superposition Multi-Throttle-Slices of Twin-Tubes Shock Absorber

By elastic mechanics, the deformation of single throttle-slice for shock absorber was analyzed, the formula of its deformation was established. According to the relation of the deformation of multi-throttle-slices with the pressure on each slice, the analytic formula of equivalent thickness of multi-throttle-slices was established. Followed is a practical example for the computation of the equivalent thickness of multi-throttle-slices, compared the computed results with that simulated by ANSYS. The results show that the computation method of equivalent thickness of multi-throttle-slices is accurate enough.

On the Behavior of Friction in Lubricated Point Contact With Provision for Surface Roughness

This paper presents a simple approach to predict the behavior of friction coefficient in the sliding lubricated point contact. Based on the load-sharing concept, the total applied load is supported by the combination of hydrodynamic film and asperity contact. The asperity contact load is determined in terms of maximum Hertzian pressure in the point contact while the fluid hydrodynamic pressure is calculated through adapting the available numerical solutions of elastohydrodynamic lubrication (EHL) film thickness formula for smooth surfaces. The simulations presented cover the entire lubrication regime including full-film EHL, mixed-lubrication, and boundary-lubrication. The results of friction, when plotted as a function of the sum velocity, result in the familiar Stribeck-type curve. The simulations are verified by comparing the results with published experimental data. A parametric study is conducted to investigate the influence of operating condition on the behavior of friction coefficient. A series of simulations is performed under various operating conditions to explore the behavior of lift-off speed. An equation is proposed to predict the lift-off speed in sliding lubricated point contact, which takes into account the surface roughness.

Thermoelastohydrodynamics of grease-lubricated concentrated point contacts

Isothermal and thermoelastohydrodynamic lubrication (TEHL) analyses of grease lubricated bearings are presented. A grease plug flow is formed in the conjunction that, with no shear at the boundaries with the solid surfaces, adheres to them in the region of high pressures under isothermal conditions. The elastohydrodynamic lubrication grease pressure distribution conforms fairly closely to that of its base oil alone, with the exception of inlet trail and pressure spike regions. The dependency of film thickness on speed (rolling viscosity) and load parameters for the base oil agrees with previously reported findings of the research community. For grease there are subtle differences with the base oil film thickness load and speed dependencies. However, it is clear that extrapolated oil film thickness formulae for oils can be used reasonably for the prediction of grease films, at least as a first approximation. The results presented agree well with optical interferometric measurements reported in the literature for grease-lubricated contacts at low temperatures and low surface velocities. TEHL analysis shows breakdown of the plug flow and significant reduction in film thickness, which can lead to changes in the regime of lubrication to mixed or boundary conditions.