Nonlinear friction dynamics on fibrous materials, application to the characterization of surface quality. Part I: global characterization of phase spaces

The diversity and the complexity of fibrous materials (woven fabrics, nonwovens or knitted fabrics) make the control of surface qualities very difficult. The control and the comprehension of the tribological phenomena generated by a dynamic friction are of major importance. Whereas the traditional investigations such as measurements of average parameters like roughness or friction coefficient quickly find their limits on such deformable, heterogeneous and flexible fibrous surfaces with very heterogeneous relief, this series of two publications proposes a new manner of observing the interactions of friction. Our laboratory has developed a patented method of measurements, called MODALSENS, which aims at rubbing a very fine and flexible blade on the analyzed surface. Dynamic friction with the contact generates nonlinear vibrations, and the response of the sensor is analyzed in its phase space using the tools of nonlinear analysis of time series. Then, when the evaluated surfaces change, this first part endeavors to characterize the portraits of phases related to the nonlinear vibrations of MODALSENS in a global way, by quantifying its invariants such as dimensions, Shannon entropies, diameters of attractors and largest Lyapunov exponents. From this first part, a classification of studied fibrous surfaces is built and is expected to give rise to new estimators for the surface quality analysis of fibrous media.