Evolution and breakup of viscous rotating drops

We study the evolution of a viscous fluid drop rotating about a fixed axis at constant angular velocity $Omega$ or constant angular momentum L surrounded by another viscous fluid. The problem is considered in the limit of large Ekman number and small Reynolds number. The analysis is carried out by combining asymptotic analysis and full numerical simulation by means of the boundary element method. We pay special attention to the stability/instability of equilibrium shapes and the possible formation of singularities representing a change in the topology of the fluid domain. When the evolution is at constant $Omega$, depending on its value, drops can take the form of a flat film whose thickness goes to zero in finite time or an elongated filament that extends indefinitely. When evolution takes place at constant L and axial symmetry is imposed, thin films surrounded by a toroidal rim can develop, but the film thickness does not vanish in finite time. When axial symmetry is not imposed and L is sufficiently large, drops break axial symmetry and, depending on the value of L, reach an equilibrium configuration with a 2-fold symmetry or break up into several drops with a 2- or 3-fold symmetry. The mechanism of breakup is also described

Size and dimensionality effects in superconducting Mo thin films

Molybdenum is a low Tc, type I superconductor whose fundamental properties are poorly known. Its importance as an essential constituent of new high performance radiation detectors, the so-called transition edge sensors (TESs) calls for better characterization of this superconductor, especially in thin film form. Here we report on a study of the basic superconducting features of Mo thin films as a function of their thickness. The resistivity is found to rise and the critical temperature decreases on decreasing film thickness, as expected. More relevant, the critical fields along and perpendicular to the film plane are markedly different, thickness dependent and much larger than the thermodynamic critical field of Mo bulk. These results are consistent with a picture of type II 2D superconducting films, and allow estimates of the fundamental superconducting lengths of Mo. The role of morphology in determining the 2D and type II character of the otherwise type I molybdenum is discussed. The possible consequences of this behaviour on the performance of radiation detectors are also addressed

Multiple Frequency Solidly Mounted BAW Filters

This paper reports the simultaneous fabrication of Receive and Transmit Bulk Acoustic Wave filters for the WCDMA standard on the same die. Both filters are based on Solidly Mounted Resonators using a common Bragg mirror, but with each having a specific piezoelectric film thickness. Electrical measurements reveal that the process steps required to provide the two different piezoelectric film thicknesses on the same die does not impact the electrical performances of resonators and filters and that this approach could thus be generalised to more than two filters.

Influence of the rheological behaviour of the lubricant on the appearance of pitting in elastohydrodynamic eegime

This paper analyses the influence of lubricant behaviour on the appearance of pitting. It attempts to study the effect of viscosity?pressure relation, compressibility, film thickness?roughness relation and friction coefficient on pitting failure of the contacting elements.To explain these effects, we first deal with the influence of the oil on the lubrication of the contact using elastohydrodynamic theory and secondly two multiaxial fatigue criteria are used, Crossland criterion and Dang Van criterion, to evaluate the influence of the rheology on the appearance of pitting. Finally, different applications are presented together with a discussion on the results obtained.

Análisis de la influencia de los diferentes parámetros de diseño en la aparición de fatiga superficial en contactos mecánicos

La fatiga superficial es uno de los principales problemas en las transmisiones mecánicas y es uno de los focos de atención de las investigaciones de los últimos anos en Tribología. La disminución de viscosidad de los lubricantes para la mejora de la eficiencia, el aumento de las potencias a transmitir, el aumento de la vida de los componentes o la mejora de su fiabilidad han supuesto que los fenómenos de fatiga superficial hayan cobrado especial relevancia, especialmente los fenómenos de pitting y micropitting en cajas multiplicadoras/reductoras de grandes potencias de aplicación, por ejemplo, en el sector eólico. Como todo fenómeno de fatiga, el pitting y micropitting son debidos a la aplicación de cargas ciclicas. Su aparición depende de las presiones y tensiones cortantes en el contacto entre dos superficies que al encontrarse en rodadura y deslizamiento varian con el tiempo. La principal consecuencia de la fatiga superficial es la aparición de hoyuelos de diferente magnitud segun la escala del fenómeno (pitting o micropitting) en la superficie del material. La aparición de estos hoyuelos provoca la perdida de material, induce vibraciones y sobrecargas en el elemento que finalmente acaba fallando. Debido a la influencia de la presión y tensión cortante en el contacto, la aparición de fatiga depende fuertemente del lubricante que se encuentre entre las dos superficies y de las condiciones de funcionamiento en las cuales este trabajando. Cuando el contacto trabaja en condiciones de lubricacion mixta-elastohidrodinamica tiende a aparecer micropitting debido a las altas tensiones localizadas en las proximidades de las asperezas, mientras que si el régimen es de lubricación completa el tipo de fatiga superficial suele ser pitting debido a las tensiones mas suavizadas y menos concentradas. En esta Tesis Doctoral se han analizado todos estos factores de influencia que controlan el pitting y el micropitting prestando especial atención al efecto del lubricante. Para ello, se ha dado un enfoque conjunto a ambos fenómenos resolviendo las ecuaciones involucradas en el contacto elastohidrodinamico no-Newtoniano (la ecuación de Reynolds, la deformación elástica de los sólidos y la reologia del lubricante) para conocer la presión y la tensión cortante en el contacto. Conocidas estas, se resuelve el campo de tensiones en el interior del material y, finalmente, se aplican criterios de fatiga multiaxial (Crossland, Dang Van y Liu-Mahadevan) para conocer si el material falla o no falla. Con la metodología desarrollada se ha analizado el efecto sobre las tensiones y la aparición de la fatiga superficial del coeficiente viscosidad-presion, de la compresibilidad, del espesor especifico de película y de la fricción así como de la influencia de las propiedades a fatiga del material y de las condiciones de funcionamiento (radios de contacto, velocidad, deslizamiento, carga y temperatura). Para la validación de los resultados se han utilizado resultados teóricos y experimentales de otros autores junto con normas internacionales de amplia utilización en el mundo industrial, entre otras, para el diseño y calculo de engranajes. A parte del trabajo realizado por simulación y cálculo de los diferentes modelos desarrollados, se ha realizado un importante trabajo experimental que ha servido no solo para validar la herramienta desarrollada sino que además ha permitido incorporar al estudio factores no considerados en los modelos, como los aditivos del lubricante. Se han realizado ensayos de medida del coeficiente de fricción en una maquina de ensayo puntual con la que se ha validado el cálculo del coeficiente de fricción y se ha desarrollado un proceso de mejora del coeficiente de fricción mediante texturizado superficial en contactos puntuales elastohidrodinamicos mediante fotolitografia y ataque quimico. Junto con los ensayos de medida de fricción en contacto puntual se han realizado ensayos de fricción y fatiga superficial en contacto lineal mediante una maquina de discos que ha permitido evaluar la influencia de diferentes aditivos (modificadores de fricción, antidesgaste y extrema-presion) en la aparición de fatiga superficial (pitting y micropitting) y la fricción en el contacto. Abstract Surface fatigue is one of the most important problems of mechanical transmissions and therefore has been one of the main research topics on Tribology during the last years. On the one hand, industrial demand on fuel economy has led to reduce lubricant viscosity in order to improve efficiency. On the other hand, the requirements of power and life of machine elements are continuously increasing, together with the improvements in reliability. As a consequence, surface fatigue phenomena have become critical in machinery, in particular pitting and micropitting in high power gearboxes of every kind of machines, e.g., wind turbines or cranes. In line with every fatigue phenomena, pitting and micropitting are caused by cyclic loads. Their appearance depends on the evolution of pressures and shear stresses with time, throughout the contact between surfaces under rolling and sliding conditions. The main consequence of surface fatigue is the appearance of pits on the surface. The size of the pits is related to the scale of the fatigue: pitting or micropitting. These pits cause material loss, vibrations and overloads until the final failure is reached. Due to the great influence of the pressures and shear stresses in surface fatigue, the appearance of pits depends directly on the lubricant and the operating conditions. When the contact works under mixed regime (or under elastohydrodynamic but close to mixed regime) the main fatigue failure is micropitting because of the high pressures located near the asperities. In contrast, when the contact works under elastohydrodynamic fully flooded conditions the typical fatigue failure is pitting. In this Ph.D. Thesis, the main factors with influence on pitting and micropitting phenomena are analyzed, with special attention to the effect of the lubricant. For this purpose, pitting and micropitting are studied together by solving the equations involved in the non-Newtonian elastohydrodynamic contact. Thus, pressure and shear stress distributions are found by taking into account Reynolds equation, elastic deflection of the solids and lubricant rheology. Subsequently, the stress field inside the material can be calculated and different multiaxial fatigue criteria (Crossland, Dang Van and Liu- Mahadevan) can be applied to predict whether fatigue failure is reached. The influences of the main parameters on pressure and surface fatigue have been studied, taking into account the lubricant compressibility and its viscosity-pressure coefficient, the specific film thickness, the friction coefficient and the fatigue properties of the contacting materials, together with the operating conditions (contact radius, mean velocity, sliding velocity, load and temperature). Several theoretical and experimental studies of different authors have been used to validate all the results obtained, together with international standards used worldwide in gear design industry. Moreover, an experimental stage has been carried out in order to validate the calculation methods and introduce additional influences not included previously, e.g., lubricant additives. The experimentation includes different friction tests in point contacts performed with a tribological equipment in order to validate the results given by the calculations. Furthermore, the reduction and optimization of the friction coefficient is analyzed by means of textured surfaces, obtained combining photolithography and chemical etching techniques. Besides the friction tests with point contact, friction and surface fatigue tests have also been performed with line contact in a tribological test rig. This equipment is also used to study the influence of different types of additives (friction modifiers, anti-wear and extreme-pressure additives) on surface fatigue (pitting and micropitting).

Optimization of AlN thin layers on diamond substrates for high frequency SAW resonators

AlN/diamond heterostructures are very promising for high frequency surface acoustic wave (SAW) resonators. In their design, the thickness of the piezoelectric film is one of the key parameters. On the other hand, the film material quality and, hence, the device performance, also depend on that thickness. In this work, polished microcrystalline diamond substrates have been used to deposit AlN films by reactive sputtering, from 150 nm up to 3 μm thick. A high degree of the c-axis orientation has been obtained in all cases. SAW one port resonators at high frequency have been fabricated on these films with a proper combination of the film thickness and transducer size.

Approximate Analytical Model for the Squeeze-Film Lubrication of the Human Ankle Joint with Synovial Fluid Filtrated by Articular Cartilage

The aim of this article is to propose an analytical approximate squeeze-film lubrication model of the human ankle joint for a quick assessment of the synovial pressure field and the load carrying due to the squeeze motion. The model starts from the theory of boosted lubrication for the human articular joints lubrication (Walker et al., Rheum Dis 27:512–520, 1968; Maroudas, Lubrication and wear in joints. Sector, London, 1969) and takes into account the fluid transport across the articular cartilage using Darcy’s equation to depict the synovial fluid motion through a porous cartilage matrix. The human ankle joint is assumed to be cylindrical enabling motion in the sagittal plane only. The proposed model is based on a modified Reynolds equation; its integration allows to obtain a quick assessment on the synovial pressure field showing a good agreement with those obtained numerically (Hlavacek, J Biomech 33:1415–1422, 2000). The analytical integration allows the closed form description of the synovial fluid film force and the calculation of the unsteady gap thickness.