ONE GRAPHICAL METHOD FOR OBTAINING THE FRICTIONAL INDEX FROM THE BELTING EQUATION

Abstract

On the fibre or yarn sliding around a cylinder, the relation of the initial tension to the final tension is given by the following equation (i. e. belting equation): where T is the final tension of fibre or yarn, T₀ is the initial tension of fibre or yarn, θ is the lapping angle of fibre or yarn against the cylinder, ρ is the radius of the cylinder, N is the frictional index, a is the constant. From the above equation, one method for calculating the approximate value of the frictional index is stated below.
1) The following equation is derived from the eqation (1): Let then a graph having gradient N and passing through the origin of the coordinate would be expected.
2) The method of the simplest calculation may be expressed by where x_i and y_i are the values based on the experimental data.
3) The value of dT/dT₀ can be obtained by the gradient of two consecutive points given in the experimental data. Then a method for estimating the value of T/T₀, is to obtain the mean value of T/T₀ for the two consecutive points.