Calculated Film Thickness Research Articles

Optimization of cycloid wheel shaping based on thermal mixed lubrication and wear characteristics

The cycloid pinwheel mechanism plays a key role in the function of RV reducers, making the lubrication and wear characteristics of the cycloid tooth profile vital areas of research. This study uses the RV-20E reducer as a case study to analyze the time-varying contact force and relative velocity between the cycloid wheel and the pinwheel, factoring in the system's dynamic properties. A transient contact model for thermal mixed lubrication of the cycloid tooth profile was developed, incorporating friction and temperature rise, and was based on a rough surface model of the dynamic bonding interface. This model enabled the calculation of oil film thickness, contact stress, and wear volume at the interface between the cycloid wheel and the pinwheel. Additionally, the study assessed the impact of traditional shaping methods on wear characteristics and derived a fitted cycloid tooth profile for the profile grinding process. These findings provide valuable insights into improving the lifespan of RV reducers.

Ultrasound enabled simultaneous measurement of coating wear depth and lubricant film thickness in a sliding bearing

Sliding bearings, serving as critical supporting components in rotating machinery, often work by riding on an ultra-thin oil film. The rupture of this oil film can cause wear of the soft coating on the bearing and even lead to catastrophic failures. This paper introduces a novel ultrasonic reflection-based approach to simultaneously measure both lubricant film thickness and coating wear depth. Through an analysis of the ultrasonic wave propagation in a worn bearing, it is observed that the echo waveform remains independent of wear depth but correlates with changes in the time of flight back to the transducer. Given this, the captured time or phase shift between the reflected and incident waves, together with the reduction in the wave amplitude, enables a simultaneous calculation of both oil film thickness and coating wear depth. The efficacy of the proposed method is validated through acoustic simulations and experiments with varied coating roughness.

Computational domain optimization for circular EHL contacts

This paper introduces an optimized computational domain for fully flooded circular elastohydrodynamic lubrication (EHL) contacts, enhancing the accuracy of numerical calculations of pressure and oil film thickness. First, the computational domain was configured based on Kapitza's analytical solution. Then, a resolution sensitivity study for the mesh of the 2D computational domain for the Reynolds equation was conducted to investigate the effect of mesh resolution on the accuracy of the numerical solution. Subsequently, the impact of the size of the full 3D computational domain on the simulation's accuracy and computational efficiency was analyzed. The main result is the 3D computational domain, which automatically adapts to operating conditions within the piezoviscous rigid, the isoviscous rigid, the piezoviscous elastic, and the isoviscous elastic regions, as well as in the transition regions between them. This results in a model which provides accurate predictions across a wide range of operational conditions. Another outcome is a new approximate expression for the central oil film thickness, showing a maximum relative difference of less than 4.6% compared to the numerical model.

Enhancing practical modeling: A neural network approach for locally-resolved prediction of elastohydrodynamic line contacts

When modeling bearings in the context of entire transmissions or drivetrains, there are practical limits to the calculation resources available to calculate single bearings or even contacts. In settings such as these, curve-fitting methods have historically been deployed to estimate the elastohydrodynamic lubrication conditions. Machine learning methods have the potential to enable more sophisticated physical modeling in the context of larger computation environments, as the evaluation time of a trained model is typically negligible. We present a neural network that accurately evaluates the locally variable elastohydrodynamic film pressure and film thickness distributions and explore its application to (e.g.) cylindrical roller bearings. Employing a neural network for the EHL film thickness calculations rather than the curve-fitted, simplified methods that are today’s standard can enable a more physically precise modeling strategy at almost no additional computational cost.

Electron Energy-Loss Spectroscopy Method for Thin-Film Thickness Calculations with a Low Incident Energy Electron Beam

In this study, the thickness of a thin film (tc) at a low primary electron energy of less than or equal to 10 keV was calculated using electron energy-loss spectroscopy. This method uses the ratio of the intensity of the transmitted background spectrum to the intensity of the transmission electrons with zero-loss energy (elastic) in the presence of an accurate average inelastic free path length (λ). The Monte Carlo model was used to simulate the interaction between the electron beam and the tested thin films. The total background of the transmitted electrons is considered to be the electron transmitting the film with an energy above 50 eV to eliminate the effect of the secondary electrons. The method was used at low primary electron energy to measure the thickness (t) of C, Si, Cr, Cu, Ag, and Au films below 12 nm. For the C and Si films, the accuracy of the thickness calculation increased as the energy of the primary electrons and thickness of the film increased. However, for heavy elements, the accuracy of the film thickness calculations increased as the primary electron energy increased and the film thickness decreased. High accuracy (with 2% uncertainty) in the measurement of C and Si thin films was observed at large thicknesses and 10 keV, where tλ≈1. However, in the case of heavy-element films, the highest accuracy (with an uncertainty below 8%) was found for thin thicknesses and 10 keV, where tλ≤0.29. The present results show that an accurate film thickness measurement can be obtained at primary electron energy equal to or less than 10 keV and a ratio of tλ≤2. This method demonstrates the potential of low-loss electron energy-loss spectroscopy in transmission electron microscopy as a fast and straightforward method for determining the thin-film thickness of the material under investigation at low primary electron energies.

Optimum Design of Coaxial Hydraulic Sealing Systems Made from Polytetrafluoroethylene and Its Compounds

Fluidic actuation systems are optimizable as to energy consumption by reducing the friction in the hydraulic cylinders. Polymeric materials with special antifriction properties and good resistance to hydraulic fluids can be deployed to enhance the performance of hydraulic cylinders. Small friction forces can also be ensured by facilitating the hydrodynamic separation of the elements of the friction tribosystem, namely the seal and sealed-off surface, respectively. The study presented in this paper analyzed the hydrodynamic separation phenomenon in hydraulic cylinders with coaxial sealing systems of the pistons. The process underlying the forming of the fluid film between the seal and its contact surface was considered and the formula for calculating film thickness was deduced. This paper presents graphs that describe the variation of the fluid film thickness versus the dimensional and material characteristics of the sealing systems. The study yielded recommendations as to the most adequate polymeric material to be used and the optimum dimensional characteristics of the seal.

Effect of equilibrium contact angle on water equilibrium film thickness for the carbon dioxide–brine–mineral system based on surface force theory

The thickness of the thin wetting film depends on disjoining pressure forces, and it evolves with pH evolution due to brine acidification at the physical and chemical conditions of geological carbon dioxide storage becoming thinner in response to dewetting. In the literature, molecular dynamic simulation (MDS) studies have been employed to understand the effect of pressure/capillary pressure on the thin wetting film evolution. In this paper, a theoretical approach based on the Frumkin–Derjaguin Equation (FDE), models of electric double layer repulsion, and van der Waals forces have been used for the calculation of the wetting film thickness. The approach excluded hydration forces contribution to disjoining pressure forces due partly to its poorly understood nature, and partly to the high salinity conditions encountered in geological carbon storage. Due to its promising global storage capacity compared to other lithologies, the carbon dioxide–brine–silica systems was chosen to simulate sandstone saline aquifers. The validation of the model benefited much from literature resources on data and a universal model of carbon dioxide–brine interfacial tension. Calculated results confirm pH-induced dewetting and they follow trends controlled by pH and pressure as found in the literature. The novelty of the paper can be seen from the fact that it has demonstrated a theoretical supplement to MDS studies in addition to justifying the fundamental utility and versatility of the FDE. Moreover, the paper links for the first time, a transcendental equation to the thin wetting film theory encountered in the carbon dioxide–solid–brine system found in geological carbon storage.

Enhancing the Elastohydrodynamic Lubrication and Vibration Behavior of Rolling Bearings Using a Hybrid Bio-Grease Blended with Activated Carbon Nanoparticles

In recent years, bio-lubricants have received a growing interest for industrial applications. Still, a full-scale implementation in machinery lubrication requires a thorough evaluation of their performance through tribological and operational tests to stand upon their performance. Additionally, the promising outcomes achieved by nanoadditives in improving the performance of synthetic lubricants have prompted research efforts to identify suitable nanoadditives for bio-grease. This paper introduces a bio-grease from a hybrid vegetable oil and glycerol monostearate as a thickener for the lubrication of rolling bearings. Activated carbon nanoparticles (ACNPs) as nanoadditives were synthesized, characterized, and incorporated into the bio-grease at concentrations of 0.5, 1, and 2% by weight. Tribo-tests were conducted on these bio-grease blends, and running tests were carried out using 6006 ball bearings on a custom test rig. Throughout a 30-min test run under a radial load of 10% of the bearing’s dynamic load rating, mechanical vibrations and power consumption were measured and analyzed for each bearing. The bio-grease with ACNPs exhibited a substantial reduction in wear scar diameter (WSD) and coefficient of friction (COF), achieving improvements of up to 73.6 and 65%, respectively, in comparison to lithium grease. Furthermore, the load carrying capacity was enhanced by 200%. The study revealed a strong correlation between measured vibration amplitudes and the viscosity of the bio-grease. The absence of high frequency resonant bands in vibration spectra indicated that the test grease samples satisfied the conditions of elastohydrodynamic lubrication, and these findings were corroborated through calculations of the minimum oil film thickness.

Lower limits of petrophysical parameters for effective reservoirs in ultradeep carbonate gas reservoirs: A case study from the Deng IV Member, Gaoshiti-Moxi Area, Sichuan Basin, SW China

Lower limits of petrophysical parameters (LLPP) of effective reservoirs are significant parameters for reserve evaluation and exploitation scheme formulation of hydrocarbon reservoirs. However, the existing LLPP determination method is not applicable to ultradeep carbonate reservoirs with diverse reservoir space and strong heterogeneity. Therefore, a systematic method for determining the LLPP of ultradeep carbonate gas reservoirs was developed in this study. First, the geological setting and reservoir characteristics were briefly introduced, and numerous cores were classified according to whether cavities and fractures were developed. Subsequently, the test data of petrophysical property, NMR, high-pressure mercury intrusion (HPMI), and fluid physical property were collected, and a series of LLPP values were obtained through static methods of cumulative frequency statistics, porosity–permeability relationship, irreducible water saturation, and minimum flowable pore throat radius (Rmin). The LLPP determined by static methods were then verified by dynamic methods of gas well testing, productivity model prediction, and productivity simulation experiment, and the LLPP of reservoirs that can form industrial gas flow were determined. Finally, the effect of reservoir heterogeneity on LLPP was revealed, the applicability of various LLPP determination methods were summarized, and the accuracy of the obtained LLPP was confirmed by well testing interpretations. The research results show that the reasonable classification of reservoir types is the prerequisite to accurately determine the LLPP of carbonate reservoirs. The lower limit of porosity is little affected by cavities, while the lower limit of permeability is greatly affected by fractures. Rmin of ultradeep carbonate reservoirs obtained by HPMI test and water film thickness calculation is approximately 60 nm. The significant heterogeneity of carbonate reservoirs requires that effective reservoirs should reach the lower limit of porosity and permeability simultaneously. LLPP determined through static methods and dynamic methods can be applied to evaluate geological and dynamic reserves, respectively. The LLPP of effective reservoirs that allow gas to accumulate, migrate, and form industrial gas production are 2.68% and 0.042 mD.

Study on Parameter Correlation of Thickness and Performance of Anodizing Film on 6061 Aluminum Alloy Frame in High Energy Laser System

As stray laser light is difficult to avoid in high-energy laser systems, it is of great significance to improve the laser damage resistance of the aluminum alloy frame anodizing film system. In this paper, the effects of anodic oxidation parameters on the thickness and performance of 6061 aluminium alloy anodic oxide composite film systems are investigated combining experiments and simulations. The thickness of the oxide film is calculated theoretically, and the simulation model is established. Then the effects of anodizing parameters and the reasons are analyzed. After characterizing the surface quality and laser damage resistance of the oxide film, the influence of anodizing parameters is summarized. This paper enables advance calculations of film thickness within a certain range, combined with the film properties, to provide a reference for the laboratory preparation of 6061 anodizing films and the preparation of structure-specific composite film systems based on the film.

Probing the Conductive and Tribological Behaviors of Solid Additives in Multiply Alkylated Cyclopentanes for Sliding Electrical Contact.

Sliding electrical contacts need to be lubricated by conductive lubricants to perform low energy dissipation, high reliability, and long service life. This work studied the thermal stability, anti-corrosion capacity, and conductive, and tribological behaviors of several solid additives in multiply alkylated cyclopentanes (MACs), including carbon nanotubes (CNTs), multilayer graphene (MG), and silver microparticles. The results showed that all the additives possessed favorable thermal stability and corrosion resistance; in particular, CNTs and MG exhibited lower and more stable electrical contact resistance (ECR) and better lubricity abilities than Ag microparticles. Moreover, based on the characterization of the worn surfaces and the film thickness calculation, the favorable conductive and tribological properties of CNTs and MG were related to the high conductivity and specific structure of the additives and the good chemical inertness of MACs.

Film Thickness in Elastohydrodynamically Lubricated Slender Elliptic Contacts: Part II – Experimental Validation and Minimum Film Thickness

In the first paper of this series, a new formula for central film thickness of slender contacts has been proposed. In this paper, interferometry measurement of the film thickness in slender elliptic contacts is performed for comparison with film thickness distribution of EHL simulation. The new film thickness formula presented in part I of this paper series is successfully validated by comparison with the experimental data. State-of-the-art minimum film thickness formulas are compared with the experimental results and results obtained through a multilevel EHL solver. Significant deviation of the analytical minimum film thickness formulas regarding both numerical and experimental results is given. Therefore, an alternative approach for calculation of minimum film thickness via the film thickness ratio with central film thickness is proposed, which yields promising results for moderately slender elliptic EHL contacts.

The unresolved definition of the pressure-viscosity coefficient

In the classical approach to elastohydrodynamic lubrication (EHL) a single parameter, the pressure-viscosity coefficient, quantifies the isothermal pressure dependence of the viscosity for use in prediction of film thickness. Many definitions are in current use. Progress toward a successful definition of this property has been hampered by the refusal of those working in classical EHL to acknowledge the existence of accurate measurements of the piezoviscous effect that have existed for nearly a century. The Hamrock and Dowson pressure-viscosity coefficient at high temperature requires knowledge of the piezoviscous response at pressures which exceed the inlet pressure and may exceed the Hertz pressure. The definition of pressure-viscosity coefficient and the assumed equation of state must limit the use of the classical formulas, including Hamrock and Dowson, to liquids with high Newtonian limit and to low temperature. Given that this problem has existed for at least fifty years without resolution, it is reasonable to conclude that there is no definition of pressure-viscosity coefficient that will quantify the piezoviscous response for an analytical calculation of EHL film thickness at temperatures above ambient.

Misfit stress relaxation in wide bandgap semiconductor heterostructures with trigonal and hexagonal crystal structure

In this work, we consider film/substrate semiconductor heterostructures with a hexagonal (wurtzite) and trigonal (corundum) crystal structure. We show that the differences between the stress level in the α-Ga2O3/α-Al2O3 heterostructure with the corundum crystal structure and the stress level in the GaN/AlN heterostructure with the wurtzite crystal structure do not exceed 50%. We study the effect of Al composition x and growth direction of the heterostructure on the critical film thickness for misfit dislocation formation in α-(AlxGa1−x)2O3/α-Al2O3 heterostructures. We provide a comparison between theoretical calculations of the critical film thickness and experimental data on the film thickness, at which the misfit dislocations were observed in α-(AlxGa1−x)2O3/α-Al2O3 heterostructures.

Thickness Analyses of 4-(Acetyl Amino)-2-Aminobenzoic Acid on ITO Thin Film Using Analytic Based of X-Ray Photoelectron Spectroscopy Method

In this study, the binding energies of 4-(acetyl amino)-2-aminobenzoic acid molecules that coated on the Indium Tin Oxide (ITO) surface with the self-assembled technique is measured by the XPS method. The thickness of the layer formed on the modified ITO surface is calculated by using XPS technique with an analytical approach. It is reported that the formation of commercially benzoic acid -based self-assembled monolayers (SAMs) is coated surely on ITO that is proved by this technique. According to this approach, the intensity of the substrate-originated photoemission peak from a semi-infinite substrate with a uniform over layer thickness, tXPS(SAM), is obtained from the SAM peak to In3d and Sn3d oxide (ITO) intensity peaks ratio (ISAM/IITO) that the Hill equation allows thin film thickness calculation from XPS data.

Effect of Relative Humidity on the Thickness of Assembled Silica Colloidal Crystal Films.

In order for the colloidal crystal films to be better applied, the influence of relative humidity on the preparation of silica colloidal crystal (SCC) films was systematically studied to solve the problem of different thicknesses of SCC films prepared by different batches under the conditions with the same temperature, concentration of suspension and diameter of the particles. SCC films with 190 nm particles were prepared by static vertical deposition method under different humidity regulated by saturated salt solutions, and the thickness of the films was obtained by an interferometric method. The results showed that the increase in humidity would reduce the thickness of the prepared films, which was believed to be caused by the decrease in evaporation rate after the wetting film absorbs water vapor. A new formula for calculating film thickness was proposed and verified from a series of experiments. With the control of humidity, high-quality SCC films with controlled thickness can be repeatedly prepared.

Hydrocarbons detection using surface plasmon resonance with As2S3 thin film waveguide

Surface plasmon resonance containing amorphous As2S3 film is proposed as a chemical sensor to highlight several liquid hydrocarbons. Method is label-free and is based on detection of small changes in the refractive index. As2S3 operates as plasmonic waveguide which confines the probing beam to the interface with liquid hydrocarbons. The method can easily distinguish hydrocarbons with very close refractive indices. The film thicknesses were optimized to obtain the best sensitivity and resolving power. Minimum reflectance of SPR less than 1 % was found for optimal calculated film thicknesses, the sensitivity to the refractive index changes being 2·10-5 .

A transient and time lag deformation alternating-coupling micro elastohydrodynamic lubrication model

As transient and time lag deformations occur alternately and influence each other for viscoelastic materials of dynamically loaded journal bearings, the time lag deformation per unit time is defined based on the finite element stiffness equation and the standard linear solid model, accumulating it by loop and superposing transient deformation to obtain actual deformation at every moment. Thereby, a novel temporal association deformation equation of bearing is constructed. It is used to improve the film thickness calculation method of the traditional micro elastohydrodynamic lubrication (MEHD) model. Finally, a novel transient and time lag deformation alternating-coupling micro elastohydrodynamic lubrication (TTL-MEHD) model is established. The comparison between lubrication performance parameters calculated by the new model and the MEHD model under the eccentric motion of the journal proves the new model is correct, and can effectively analyze the knocking and rough rubbing characteristics at the early stage of bearing instability. The new model is implemented to explore the effect of the time lag degree of material deformation on mixed lubrication performance. The application of the new model in connecting rod bearing of internal-combustion engine proves that it can effectively compensate for the impact lag deviation caused by the complete elasticity assumption.

A novel calculation expression for the experimental friction coefficient of the ball screw

The friction coefficient inevitably affects the friction force between balls and raceway thus might significantly change the performance of the ball screw. However, the traditional methods for determining friction coefficient are based on different empirical values which may lead to different results. To this end, this paper studies the variation law of the friction coefficient by considering different lubrication states between balls and raceway. An experiment is carried out, through which a Stribeck tribology-based expression of the friction coefficient is proposed. The given results provide two obvious stages of lubrication, and the turning point of the two stages represents the minimum value of the friction coefficient. Moreover, the rotational speed is the main factor that influences the value of the friction coefficient based on the calculation of the average central film thickness.

Research on Deformation of Flexible Side Plates in Intra-Vane Type Pumps and its Effect on Oil Film Thickness of the Flow Distribution Pair

This paper sets up both a force balance equation and a three-dimensional geometric model of a flexible side plate in an intra-vane type pump, after analyzing the structure and mechanical properties of the plate. The formulas for calculating deformation were obtained, and the theoretical curve of change in deformation was determined. Then, the contour of deformation was obtained using software simulation. The calculated and simulated values of deformation of the flexible side plate, in three positions under four working pressures, were found to be close to one another, the relative error between them being less than 2%. Next, the formula for the calculation of oil film thickness was obtained, and the curve of the change in oil film thickness relative to the distance along the radial direction of the side plate was determined, considering the flexible side plate deformation. The oil film thickness for three flexible side plate positions were then tested through experiment. The calculated values of oil film thickness were also close to the tested values. Although there was a small difference, the relative error between them was less than 5% for the oil film thickness measured at its lowest point, which indicates the accuracy of the results obtained by the theoretical calculation.