32—A USEFUL METHOD FOR CALCULATING COEFFICIENTS OF FRICTION OF WOOL FIBRES FROM CAPSTAN MEASUREMENTS

An account is given of an investigation in which a variant of the capstan method was used to study the dependence of the frictional properties of wool fibres on the tension in the fibres when they slid at a very low speed over a rod of horn immersed in water (to which a wetting agent had been added). Some ofthe fibres had been given a mild shrinkproofing treatment with KMnO₄ in saturated salt solution. The curves relating the tensions T ₁ and T ₀ in the two ends of a sliding fibre, with T ₁ > T ₀, were found to be accurately linear in the range from T ₀=O up to T ₁=05 gf. For with-scale sliding, they all passed very close to the origin, but nevertheless the coefficient of with-scale friction,μ_w(={1/π}ln{T ₁/T ₀}), was markedly dependent on the tension owing to the high sensitivity of the logarithm to ‘zero error’ in the range of T ₁/T ₀ appropriate to with-scale sliding. For against-scale sliding, the intercept was larger and more variable, so that μ_a also depended markedly on the tension. It is suggested that the most satisfactory parameters to use for characterization of the friction are the coefficients of friction calculated from the slopes of the curves of T ₁ against T ₀, without regard to the intercepts.

It is shown that these new parameters reveal satisfactorily a previously determined difference between the shrinkproofed and the untreated fibres, namely, that the with-scale coefficient is significantly larger for the shrinkproofed fibres.

The measured coefficients for untreated fibres depend on the state of polish of the horn surface. For treated fibres, repolishing the horn greatly increases the variance of the measurements. The best conditions to use for particular applications are dicussed.