A statistical analysis of the frictional forces generated between monofilaments during intermittent sliding

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Abstract
The friction between poly(ethylene terephthalate) monofilaments (about 20 mu m diameter), known by the acronym PET, with a range of titanium contents has been measured. In addition, some experiments were carried out with PET fibres sliding over glass and human hair. The configuration used produces a nominal point contact and involves a taut fibre against which a second fibre is brought to form a cantilever. Movement of the first fibre invariably generates discontinuous or stick-slip motion in the cantilevered fibre. The equipment developed for friction measurements was capable of recovering and storing data from a large number of stick-slip events. Much of the static frictional force data could be fitted (at the 95% confidence limit of the chi 2 goodness-of-fit test) to the gamma, Weibull or log-normal distributions. The exact form of the distribution depended on the conditions of the experiment and, additionally in the case of human hair, on the direction of sliding. Some of the data which could not be modelled by these distributions were found to be associated with time-dependent effects. This non-stationarity, which arises from a low-level wear process, increased with the imposed sliding velocity and the total load at the contact point. By the use of simple regression models of frictional force against time, it was possible to 'correct' some of the non-stationary data so that they became (nominally) stationary. Distributions fitted to these modified data showed good continuity in both the functionality and the numerical values of the distribution parameters with the distributions fitted to the stationary data. The study also revealed the occurrence of a type of microslip prior to gross slip. This microslip manifests itself as a continuous velocity of the contact point of the fibre. Microslip was found to occur under nearly all circumstances and is dependent on a large number of factors. There was a close relationship between the extent of microslip and the degree of non-stationarity.

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