Francesco Bottiglione

Meeting the Contact-Mechanics Challenge

This paper summarizes the submissions to a recently announced contact-mechanics modeling challenge. The task was to solve a typical, albeit mathematically fully defined problem on the adhesion between nominally flat surfaces. The surface topography of the rough, rigid substrate, the elastic properties of the indenter, as well as the short-range adhesion between indenter and substrate, were specified so that diverse quantities of interest, e.g., the distribution of interfacial stresses at a given load or the mean gap as a function of load, could be computed and compared to a reference solution. Many different solution strategies were pursued, ranging from traditional asperity-based models via Persson theory and brute-force computational approaches, to real-laboratory experiments and all-atom molecular dynamics simulations of a model, in which the original assignment was scaled down to the atomistic scale. While each submission contained satisfying answers for at least a subset of the posed questions, efficiency, versatility, and accuracy differed between methods, the more precise methods being, in general, computationally more complex. The aim of this paper is to provide both theorists and experimentalists with benchmarks to decide which method is the most appropriate for a particular application and to gauge the errors associated with each one.

Leakage mechanism in flat seals

We present a theoretical approach to estimate the fluid leakage in flat seals. The approach is based on the analogy between the seal-substrate interface and a porous medium. We assume that the interface is constituted of a random distribution of noncontact patches (the pores) and small but numerous contact spots (islands). Leakage may occur only through the pores, of which the lateral size and height are distributed according to a probability density function that we calculate on the basis of a recent theory of contact mechanics. Our theoretical approach is based on a percolation scheme that has never been proposed before and we believe it could be useful to stimulate further theoretical or experimental investigations. Within this percolation scheme we apply critical path analysis to calculate the hydraulic conductivity of the medium and compare our predictions with other calculations very recently presented to the scientific community.

Role of statistical properties of randomly rough surfaces in controlling superhydrophobicity.

We investigate the effect of statistical properties of the surface roughness on its superhydrophobicity. In particular, we focus on the liquid-solid interfacial structure and its dependence on the coupled effect of surface statistical properties and drop pressure. We find that, for self-affine fractal surfaces with Hurst exponent H > 0.5, the transition to the Wenzel state first involves the short wavelengths of the roughness and, then, gradually moves to larger and larger scales. However, as the drop pressure is increased, at a certain point of the loading history, an abrupt transition to the Wenzel state occurs. This sudden transition identifies the critical drop pressure p(W), which destabilizes the composite interface. We find that p(W) can be strongly enhanced by increasing the mean square slope of the surface, or equivalently the Wenzel roughness parameter r(W). Our investigation shows that, even in the case of randomly rough surface, r(W) is still the most crucial parameter in determining the superhydrophobicity of the surface. An analytical approach is, then, proposed to show that, for any given value of Youngs contact angle θ(Y), a threshold value (r(W))(th) = 1/(-cos θ(Y)) exists, above which the composite interface is strongly stabilized and the surface presents robust superhydrophobic properties. Interestingly, this threshold value is identical to the one that would be obtained in pure Wenzel regime to guarantee perfect superhydrophobicity.

Effect of the Ratio Spread of CVU in Automotive Kinetic Energy Recovery Systems

The Kinetic Energy Recovery Systems (KERS) are being considered as promising short-range solution to improve the fuel economy of road vehicles. The key element of a mechanical hybrid is a Continuously Variable Unit (CVU), which is used to drive the power from the flywheel to the wheels and vice versa by varying the speed ratio. The performance of the KERS is very much affected by the efficiency of the CVU in both direct and reverse operation, and the ratio spread. However, in real Continuously Variable Transmissions (CVT), the ratio spread is limited (typical value is 6) to keep acceptable efficiency and to minimize wear. Extended range shunted CVT (Power Split CVT or PS-CVT), made of one CVT, one fixed-ratio drive and one planetary gear drive, permit the designer to arrange a CVU with a larger ratio spread than the CVT or to improve its basic efficiency. For these reasons, in the literature they are sometimes addressed as devices for proficient application to KERS. In this paper, two performance indexes have been defined to quantify the effect of the ratio spread of PS-CVT on the energy recovery capabilities and overall round-trip efficiency of KERS. It is found that no substantial benefit is achieved with the use of PS-CVT instead of direct drive CVT, because the extension of the speed ratio range is paid with a loss of efficiency. It is finally discussed if new generation high-efficiency CVTs can change the scenario.

MG-IVT: An Infinitely Variable Transmission With Optimal Power Flows

The infinitely variable transmissions (IVTs) allow the transmission ratio to vary with continuity, offering the possibility of also reaching zero values for the transmission ratio and the motion inversion. In this paper an original infinitely variable transmission system is described (MG-IVT). MG-IVT is made up of the coupling of a continuously variable transmission, a planetary gear train, and two ordinary transmissions with a constant transmission ratio. By means of two frontal clutches, the MG-IVT is allowed to get two different configurations. The main purpose is to get the configurations that make the optimal efficiency of the transmission at different transmission ratios. Kinetic characteristics of single component devices are obtained, and the MG-IVT systems performance is determined by considering how the efficiency of the component devices change as a function of operating conditions. The advantages of the MG-IVT are therefore shown in terms of power and efficiency in comparison to the traditional IVT.

Mechanical Hybrid KERS Based on Toroidal Traction Drives: An Example of Smart Tribological Design to Improve Terrestrial Vehicle Performance

We analyse in terms of efficiency and traction capabilities a recently patented traction drive, referred to as the double roller full-toroidal variator (DFTV). We compare its performance with the single roller full-toroidal variator (SFTV) and the single roller half-toroidal variator (SHTV). Modeling of these variators involves challenging tribological issues; the traction and efficiency performances depend on tribological phenomena occurring at the interface between rollers and disks, where the lubricant undergoes very severe elastohydrodynamic lubrication regimes. Interestingly, the DFTV shows an improvement of the mechanical efficiency over a wide range of transmission ratios and in particular at the unit speed ratio as in such conditions in which the DFTV allows for zero-spin, thus strongly enhancing its traction capabilities. The very high mechanical efficiency and traction performances of the DFTV are exploited to investigate the performance of a flywheel-based Kinetic Energy Recovery System (KERS), where the efficiency of the variator plays an important role in determining the overall energy recovery performance. The energy boost capabilities and the round-trip efficiency are calculated for the three different variators considered in this study. The results suggest that the energy recovery potential of the mechanical KERS can be improved with a proper choice of the variator.

Fluid contact angle on solid surfaces: Role of multiscale surface roughness

We present a simple analytical model and an exact numerical study which explain the role of roughness on different length scales for the fluid contact angle on rough solid surfaces. We show that there is no simple relation between the distribution of surface slopes and the fluid contact angle. In particular, surfaces with the same distribution of slopes may exhibit very different contact angles depending on the range of length-scales over which the surfaces have roughness.

Plasma-Textured Teflon: Repulsion in Air of Water Droplets and Drag Reduction Underwater

A superhydrophobic behavior can be obtained by properly modifying the surface topography of Teflon or other fluorinated polymers having an inherent hydrophobic character. According to this strategy, we have micro/nanotextured Teflon both as plane material (sheets) and as three-dimensional (3D) object (spheres) with a single step plasma process. The obtained textured Teflon samples were compared with those made of pristine Teflon in air, in terms of repulsion of impacting water droplets, and underwater, in terms of air layer behavior under static and dynamic conditions. The latter case was investigated by subjecting the spheres to a vertical fall in water. Modified surfaces present nanofilaments on the top of micrometric vertical structures, which can increase the air retaining capacity, resulting in a biomimicry effect due to a similarity with the Salvinia molesta leaf. On this surface, repulsion of impacting water droplets can be as fast as previously reached only on heated solids. Also, the air layer over the modified spheres underwater is shown to play a role in the observed reduction of hydrodynamic drag onto the moving object.

An effective medium approach to predict the apparent contact angle of drops on super-hydrophobic randomly rough surfaces

The apparent contact angle of large 2D drops with randomly rough self-affine profiles is numerically investigated. The numerical approach is based upon the assumption of large separation of length scales, i.e. it is assumed that the roughness length scales are much smaller than the drop size, thus making it possible to treat the problem through a mean-field like approach relying on the large-separation of scales. The apparent contact angle at equilibrium is calculated in all wetting regimes from full wetting (Wenzel state) to partial wetting (Cassie state). It was found that for very large values of the roughness Wenzel parameter (r(W) > -1/ cos θ(Y), where θ(Y) is the Youngs contact angle), the interface approaches the perfect non-wetting condition and the apparent contact angle is almost equal to 180°. The results are compared with the case of roughness on one single scale (sinusoidal surface) and it is found that, given the same value of the Wenzel roughness parameter rW, the apparent contact angle is much larger for the case of a randomly rough surface, proving that the multi-scale character of randomly rough surfaces is a key factor to enhance superhydrophobicity. Moreover, it is shown that for millimetre-sized drops, the actual drop pressure at static equilibrium weakly affects the wetting regime, which instead seems to be dominated by the roughness parameter. For this reason a methodology to estimate the apparent contact angle is proposed, which relies only upon the micro-scale properties of the rough surface.

Artificial Knee Joints Actuators with Energy Recovery Capabilities

The human knee absorbs more energy than it expends in level ground walking. For this reason it would be useful if the actuation system of a wearable robot for lower limbs was able to recover energy thus improving portability. Presently, we recognize three promising technologies with energy recovery capabilities already available in the literature: the Series Elastic Actuator SEA, the Clutchable Series Elastic Actuator C-SEA, and the flywheel Infinitely Variable Transmission F-IVT actuator. In this paper, a simulation model based comparison of the performance of these actuators is presented. The focus is on two performance indexes: the energy consumed by the electric motor per gait and the peak torque/power requested to the electric motor. Both quantities are related to the portability of the device: the former affects the size of the batteries for a given desired range; the latter affects the size and the weight of the electric motor. The results show that, besides some well-explained limitations of the presented methodology, the C-SEA is the most energy efficient whereas the F-IVT allows cutting down the motor torque/peak power strongly. The analysis also leads to defining how it is possible to improve the F-IVT to achieve a reduction of the energy consumption.