抄録
The relation between the traverse motion x=x(t) and the shape of a thread reeled up on the cylindrical reel, ξ=ξ(t) is given as follows
where, r: diameter of reel, ω0: Angular velocity, so rω0: reeling velocity, l: tangential length between reel and traverse bar.
By this equation we can obtain the gains i. e. the ratio of both amplitudes. So when the traverse motion x=x(t) is given, we can solve this equation.
Generally, when x=x(t) is given as the form of the Fourier series, we can obtain its gain as the sum of each gains. But in the proper assumptive cases, we can analyse some important motions approximately. Traverse limit, i. e. upper limit of ω/ω0, depends upon the two factors, frictional cofficient between the surface of reeled thread and the thread, and yarn stiffness; the latter is negligible in this case, so we obtain the result as follows:
General determination of the sectional shape of thread layers, reeled on the reel surface, is very difficult, but in the case of S. H. M., it becomes:
but, this slightly different from that of the experimental result, because of the neglect of geometrical form factors of the thread.
