Friction dynamics of adhesive fibrillar contact

Nowadays, it is possible to adjust contact variables (friction force, wear, etc.) by modifying at least one of the contacting surfaces, that is known as surface texturing. The surface texturing is carried out by adding or subtracting structures on the surface of any of the two surfaces in contact, with an another material or with its own material. In this way, the surface texturing in a soft dry solid-solid contact formed with soft (low elastic modulus) materials is confronted as increasing contact forces, for example, increasing the adhesive strength. In a soft dry solids-solid contact, the surface texturing is carried out with the formed mechanical structures which are primarily inspired from nature, generally, in a cylindrical shape which will be referred as a pillar, are usually made up with various visco-elastic materials. In this thesis, characterization of frictional dynamics of elastomeric pillar which is mainly inspired from nature is performed. In this way, an empiric formula to estimate friction force magnitudes of elastomeric pillars in contact with a smooth surface is proposed. In order to obtain the formulas, the frictional dynamics of elastomeric pillar is studied analytically, numerically, and experimentally in meso-scale. The friction between the pillars and the counter surface is obtained by applying a tangential motion to the pillars either with a constant velocity or with some frequency component in a harmonic excitation. The frictional dynamics are analyzed using the friction force-displacement loops which reveal the transition from stick to sliding regime, effective stiffness and dissipative energy due to the presence of friction. Two different effects on the frictional dynamics of pillars are examined, which are constructional effect of pillars such as diameter and height, and contact loading conditions such as preload, sliding velocity or excitation frequency in a harmonic loading. In the constant velocity loading, the pillars are slid on the smooth surface with various constant velocities in back and forth motions to obtain the friction force-displacement loop. The sliding velocities are in the range of 0.05 mm/s to 1 mm/s with an incremental value of 0.05 mm/s. Different pillar constructional configuration is realized in three sets, in which there are three pillars in the each set. In the first set, pillars with different height and same diameter are manufactured. In the second set, this time pillars have different diameter but same height. In the third set, ratio of pillar height to pillar diameter is kept same. Increasing the diameter or decreasing the height of pillar increases the kinetic friction force while the increase in kinetic friction force is related to higher elastic deformation energy due to higher flexural stiffness. As the sliding velocity becomes higher, the kinetic friction force and related frictional dissipative energy increase which reveals the contribution of visco-elastic behavior of pillar. Two different methodologies are evaluated to calculate the kinetic friction force magnitude of a single pillar with different dimension sliding on the surface. Those are establishing energy equilibrium at the contact interface, and modeling the behavior of pillar as a single-degree-of-freedom lumped system. In the first one, an energy balance at the contact interface is established to analyze the static and kinetic friction regime. The kinematics of sliding behavior of a pillar as well as the components of the total energy at the contact interface are identified. The kinetic friction force magnitude is estimated using the dissipative energy in the friction force-displacement loop, and validation of the estimated kinetic friction force magnitudes is accomplished by comparing with the experimental results. The relative error of the kinetic friction force estimation by using energy equilibrium approach is up to %10 under the preload with a magnitude of greater than the half of the Euler buckling load. In the second one, an approximate analytical model for the sliding motion of a single pillar on the smooth surface is built. The model is realized in frictional response of a visco-elastic pillar with hemispherical tip. The sliding motion of a pillar is described as a single-degree-of-freedom lumped parameter system, where the model is built with discrete stiffness and damping components representing the pillar dynamics and contact interaction in normal and tangential directions. The verification and limitation of the model are determined for different pillar dimension and contact loading conditions such as varying preload and sliding constant velocities. The results demonstrate that the accuracy of the model in realizing kinetic friction force magnitude is dependent on the pillar dimension, with the greatest accuracy being %95 obtained for the highest pillar under preload value close to the Euler buckling load at higher sliding velocities. The friction force of a single pillar with flat-punch tip geometry in contact with a smooth surface is examined under harmonic loading condition. The harmonic loading conditions are comprised of harmonic base excitation with various excitation frequencies which also contains the first natural frequency of the pillar in bending vibrational mode. Maximum acceleration magnitude of the harmonic base excitation is realized that the pillar stays in stick regime during the contact, where constant base acceleration magnitude is attained for each excitation frequency. The tilting behavior of the pillar in stick regime for different harmonic base displacements is discussed. Frictional-adhesion coupling of the pillar is analyzed by calculating apparent work of adhesion via establishing energy equilibrium at the contact interface. The tilting behavior reveals that the frictional response in terms of elastic deformation shape of the pillar under harmonic base excitation is similar to the results of where the pillar is slid on a surface with a constant velocity. The results demonstrate that the frictional-adhesion coupling interface of the contact may be tuned via a harmonic loading condition by carefully selecting excitation frequency and related harmonic base displacement. The kinetic friction force of a pillar array is investigated experimentally to be used as a basis for generating an empiric formulation to calculate kinetic friction force of a pillar array. Five pillar arrays in two sets, total ten pillar arrays are used. Diameter and height of a single pillar with a flat-punch tip in the sets are 1 mm and 3 mm, respectively. In these sets, the effect of different pillar number and different spacing between two pillars are examined, separately. In the first set, five pillar arrays with different pillar number, and same spacing between two pillars are used; which consists of 16, 64, 144, 256 and 400 pillars. In the second set, the pillar array with 144 pillars and various spacing between two pillars is used. The spacing displacements between two pillars are selected according to the diameter of a pillar. The two effects are separately investigated by normalizing the kinetic friction force magnitudes to the highest one in the each set and averaging the normalized kinetic friction force magnitudes for neglecting the velocity effect. By using the normalized kinetic friction force magnitudes, two formulas based on the two effects are generated by using Matlab Curve Fitting Toolbox. Furthermore, by normalizing the kinetic friction force magnitudes of all the pillar arrays to the results of the common pillar array, pillar density effect on the kinetic friction force magnitude is determined. A simple formula to estimate kinetic friction force magnitude based on pillar density is generated. The results demonstrate that as the pillar number decreases or spacing between two pillar decreases, and thus pillar density increases, the kinetic friction force magnitude of a single pillar increases. The three formulas based on different pillar array configuration can be used to estimate average kinetic friction force magnitude of a pillar array while sliding on a smooth surface before manufacturing process if the kinetic friction force magnitude of a single pillar is known. The kinetic friction force magnitude of a single pillar can be calculated by using the two methods discussed in the thesis. These are establishing energy balance at the contact interface, and solving the governing equation of motion of the pillar with contact interaction.