Simulations of sliding adhesive contact between microgear teeth in silicon-based MEMS work in a vacuum environment

Sliding friction and adhesive contact interactions between microgear silicon-based MEMS teeth working in a clean and vacuum environment have been modelled using a multiscale hierarchical elastic structure. Here the results of numerical simulations based on the use of multiscale block model are presented. The tooth is modelled as a bulk silicon-based MEMS surface covered by roughness having two subscales specified by the character of interactions: atomic subscale level and adhesive subscale. Friction over completely meshing teeth surfaces is estimated by calculation of the total energy dissipated during sliding. The dissipation is caused by the different physical and chemical mechanisms. Due to the vacuum environment, these mechanisms reduced to the energy lost by the dissociation of chemical and van der Waals bonds, and by the elastic interlocking between the asperities located on the meshing micro-tooth surfaces. It is argued that due to the Polonsky-Keer effect, there is no plastic deformation of the MEMS tooth surface asperities because the asperity sizes are within the validity of this effect. The adhesion layer is defined employing ideas of the Maugis approximation. The adhesion force of each nanoasperity has assumed to be equal to the pull-off force in the Boussinesq-Kendall model corrected by the Borodich no-slip coefficient. The simulations show that MEMS with the clean silicon surfaces of teeth cannot work due to stiction between surfaces, while friction between tooth surfaces functionalised by carbon-based layer is much smaller. If the functionalised coating is worn away then stiction may occur

Probabilistic, fractal, and related techniques for analysis of engineering surfaces

n many engineering fields surface topography is of crucial importance solving problems offriction and other problems of tribology. A review of mathematical approaches for descriptionof topography of engineering surfaces is presented. Firstly, we give a brief introduction to someof statistical parameters used for description of surface roughness. It is argued that althoughsome of these parameters may be quite useful for specific engineering problems, a set of finitenumbers of parameters cannot describe contact properties of rough surfaces. Then we discussvarious models of surface roughness based on Gaussian models of the asperity heights.The results of application of various modern tests of normality for checking whether thedistribution of the asperity heights is Gaussian, are presented. Further fractal models of rough-ness are discussed. Using fractal parametric-homogeneous (PH) surfaces, it is demonstratedthat tribological properties of a rough surface cannot be characterized just by the fractaldimension of the surface. It is also shown that models based solely on the power-spectraldensity function (PSDF) are quite similar to fractal models and these models do not reflecttribological properties of surfaces. In particular, it is demonstrated that different profiles mayhave the same PSDF

A macro model for electroadhesive contact of a soft finger with a touchscreen

A contact problem of electroadhesion for a conductive elastic body pressed against a rigid plane surface of a dielectric coating covering a conductive substrate is formulated applying the Johnsen-Rahbek approximation for the attractive surface stresses and the Derjaguin-Muller-Toporov (DMT) hypothesis about the influence of the adhesive stresses on the deformable shape of the elastic body. An approximate solution is obtained using the Winkler--Fuss deformation model with the equivalent (contact load dependent) stiffness coefficient evaluated according to the Xydas--Kao soft finger model. The friction force under applied voltage is evaluated as the product of the coefficient of friction and the integral of the macro contact pressure over the apparent contact area. The upper and lower estimates for the friction force are discussed in the case of absence of any external normal load

Contact probing of stretched membranes and adhesive interactions: graphene and other two-dimensional materials

Contact probing is the preferable method for studying mechanical properties of thin two-dimensional (2D) materials. These studies are based on analysis of experimental force–displacement curves obtained by loading of a stretched membrane by a probe of an atomic force microscope or a nanoindenter. Both non-adhesive and adhesive contact interactions between such a probe and a 2D membrane are studied. As an example of the 2D materials, we consider a graphene crystal monolayer whose discrete structure is modelled as a 2D isotropic elastic membrane. Initially, for contact between a punch and the stretched circular membrane, we formulate and solve problems that are analogies to the Hertz-type and Boussinesq frictionless contact problems. A general statement for the slope of the force–displacement curve is formulated and proved. Then analogies to the JKR (Johnson, Kendall and Roberts) and the Boussinesq–Kendall contact problems in the presence of adhesive interactions are formulated. General nonlinear relations among the actual force, displacements and contact radius between a sticky membrane and an arbitrary axisymmetric indenter are derived. The dimensionless form of the equations for power-law shaped indenters has been analysed, and the explicit expressions are derived for the values of the pull-off force and corresponding critical contact radius

Size effect and multiscale fracture

We study fracture of notched samples made of quasi-brittle, polyphase materials like rock, concrete or ceramics. The fracture demonstrates the size effect during loading. This means that a full-size sample made of such a material exhibits different fracture behaviour than a laboratory-size sample. The effect is explained by the existence of an extended zone of distributed defects and cracks (process zone) that surrounds the tip of the propagating fracture. The growth mechanisms of the process zone is scale-dependent: in an unbounded sample or a full-size structure, the zone develops until its maximum width and then it remains of the same width, while in a bounded sample that is less than some critical size, the process zone cannot be fully developed. Various similarity and scaling approaches to mechanics of multiple fracture are discussed. The growing process zone is modelled as a pattern of fractures having fractal properties on the intermediate stage of the development of the pattern. A formula is derived for the critical tensile stress that depends on both the sample size and the size of the process zone

Simulations of sliding adhesive contact between microgear teeth in silicon-based MEMS work in a vacuum environment

Sliding friction and adhesive contact interactions between microgear silicon-based MEMS teeth working in a clean and vacuum environment have been modelled using a multiscale hierarchical elastic structure. Here the results of numerical simulations based on the use of multiscale block model are presented. The tooth is modelled as a bulk silicon-based MEMS surface covered by roughness having two subscales specified by the character of interactions: atomic subscale level and adhesive subscale. Friction over completely meshing teeth surfaces is estimated by calculation of the total energy dissipated during sliding. The dissipation is caused by the different physical and chemical mechanisms. Due to the vacuum environment, these mechanisms reduced to the energy lost by the dissociation of chemical and van der Waals bonds, and by the elastic interlocking between the asperities located on the meshing micro-tooth surfaces. It is argued that due to the Polonsky-Keer effect, there is no plastic deformation of the MEMS tooth surface asperities because the asperity sizes are within the validity of this effect. The adhesion layer is defined employing ideas of the Maugis approximation. The adhesion force of each nanoasperity has assumed to be equal to the pull-off force in the Boussinesq-Kendall model corrected by the Borodich no-slip coefficient. The simulations show that MEMS with the clean silicon surfaces of teeth cannot work due to stiction between surfaces, while friction between tooth surfaces functionalised by carbon-based layer is much smaller. If the functionalised coating is worn away then stiction may occur