Abstract
In this paper, a lap-forming process is discussed by queing theory. In blowing process, tufts are transfered to the lap forming part by air flow after opening and breaking operations.
When the weight of lap is detected, each tuft which constitutes the lap on the detecing line is also served by detecting action.
Then if the lap forming and the detecting process are considered as a queing system, the eveness of lap is calculated theoretically by detecting service and arrival distributions of the tuft.
When the detecting line of lap weight is taken on the x-y plain (Fig. 1) the system can be determined by the following parameters; K: number of tufts which are being detected at the time t, 1/λ: the mean arrival time of tuft on the line, 1/μ: the mean service time of tuft on the line and size distribution of tuft. If the process of forming lap is a stationary random process, a conception of random lap can be introduced just as in the case of ramdom sliver and thus CV (%) of random lap can be calculate as the system of M/M/∞
Then, the CV (%) of random lan is where v: speed of the lap (const.) _??_: mean distance between the nearest two tufts _??_: mean length of tuft projected to X axis A•F: mean weight of tuft σw: standerd of weight of tuft. CV (%) of random lap for each mechanical operations are calculated by distribution of the length and size distribution of tuft. The result corresponds well with the experimental data reported by H. Locker. This seems to show the reality of this mathematical model.
