Functional diagram of the lab stand

The functional diagram of the lab stand is presented in Fig. 2. The band is coiled from unwind roll UR on the roll WR. The control of the velocity of the tight band is done through the controller (control unit SC) with feedback from transducer ST, reference unit HS through the frequency converter U1, and induction motor M.

The tension force of the band is controlled by changing current is of the friction clutch FC winding. The elongation of the band is proportional to tension force F of the band. It is evident that signal of transducer FT measures the tension force of the band. So, the second closed loop regulates the tension force of the band and consists of the controller GC, transducer FT, reference unit HG, and converter U2.

Development of the block diagram of the laboratory stand

Functional diagram of the laboratory stand is shown in Fig. 2. As it was discussed previously, the tension force of the band depends on the friction clutch FC. The increased torque, developed by friction clutch, increases the tension force of the band. As a result the tight band will elongate. Process of band coiling might be illustrated by the simplified kinematical diagram (Fig. 3).

Investigated process of the tight band coiling is made by assuming that the band is elastic and has no weight [4]. In diagram: L is the length of the band for range B when the band is not tight (Fig. 3); l is elongation of band due to tension force. During the stabilized process, the amount of material coming into the range B equals to the amount of leaving material. That does not happen during transient response, because the tension force F and elongation l are being changed.

Length of the band coming into range B is L2 (winded-off length), and L1 (winded-on length) is the length of band coming out of the range, recalculated to the length of the loose band. The elongation of the band due tension force in the range B equals to:

l=L₁L₂+l₀ (1)

where l₀ the initial elongation of the tight band, at the starting moment t=0 s.

The relative elongation is proportional to the tension force F and it equals to:

δ=l/L. (2)