Method of Operating an Off-LIne Finishing Device for Fiber Webs, in Particular an Off-Line Slitter-Winder for Winding Fiber Webs

Abstract

A method of operating an off-line finishing device for fiber webs, in particular an off-line slitter-winder for winding fiber webs, wherein in operating the off-line device the running speed is automatically optimized to minimize cost of web breaks. The method considers the costs associated with a web break during unwinding in addition to the cost benefit of maximizing web unwind speed so as to maximize machine utilization. The method determines an optimal web break stopping time in a web break situation and how often a web break is predicted. Automatic optimization incorporates limitations including the maximum rotation speed of the parent roll, the maximum speed of the fiber web being unwound, the maximum positive torque which can be applied to the parent roll to accelerate the parent roll to a rotation rate which produces a desired web speed, and maximum braking torque.

Claims

1. A method of operating an off-line finishing device for fiber webs, having an unwinder and a parent roll mounted thereto, the parent roll having a fiber web with a fiber web length, the unwinder having at least one torque drive motor for controlling an unwind velocity of the parent roll, and at least one torque brake, wherein said at least one torque brake comprises at least one of said torque drive motor and a mechanical brake, the at least one torque brake having a selected braking torque, the method comprising the steps of: unwinding the fiber web from the parent roll; continuously calculating an inertia of the parent roll as the parent roll is unwound; continuously calculating a maximum deceleration of the parent roll by dividing the selected braking torque by the inertia; and controlling the unwind velocity of the parent roll so that said calculated maximum deceleration will bring the parent roll to a stop in no more than a selected time.

2. The method of claim further comprising: collecting continuously data relating to frequency of occurrence of web breaks per parent roll and determining probability of occurrence of a web break during the unwinding of a fiber web from the parent roll; determining a cost function for the unwind of the parent roll as a function of time; determining a cost function for a web break as a function of the selected time and the probability of occurrence of a web break during the unwinding of a fiber web from the parent roll; and setting the selected time to a time interval which minimizes the total cost of unwinding a fiber web from the parent roll.

3. The method of claim 1 wherein the off-line finishing device is a slitter winder, and further comprising: collecting continuously data relating to frequency of occurrence of web breaks per parent roll and determining probability of occurrence of a web break during the unwinding of a fiber web from the parent roll; determining a cost function for the unwinding of the parent roll as a function of time; determining a cost function for a web break as a function of the selected time and the probability of occurrence of a web break during the unwinding of a fiber web from the parent roll; setting the selected time to a time interval which minimizes the total cost of unwinding a fiber web from the parent roll; and slitting and winding the fiber web length into customer rolls.

4. A method of operating an off-line slitter winder finishing device for fiber webs, having an unwinder and a parent roll mounted thereto, the parent roll having a fiber web with a fiber web length, the unwinder having a maximum web speed, and at least one torque drive motor for controlling an unwind velocity of the parent roll, and at least one torque brake, wherein said at least one torque brake comprises at least one of said torque drive motor and a mechanical brake, the at least one torque brake having a selected braking torque, the method comprising the steps of: using a model of the off-line slitter winder finishing device for fiber webs to pre-calculate a limit of a web break stopping time required by the selected braking torque in relation to the parent roll inertia and web unwind speed and how much setting a maximum web break stopping time decreases capacity of the finishing device for fiber webs by decreasing average web unwind speed; collecting continuously data relating to frequency of occurrence of web breaks per parent roll to determining probability of occurrence of a web break; calculating expected value of capacity loss based on the determined probability of occurrence of a web break and the web break stopping a time; and while the web unwind speed is lower than maximum running speed, adjusting the maximum web break stopping time and thus the web unwind speed such that the expected value of capacity loss is minimized, wherein the expected value of capacity loss is continuously adjusted as the probability of occurrence of a web break is updated.

5. A method of operating an off-line finishing device for fiber webs, the device having an unwinder and a parent roll mounted thereto, the unwinder having a torque drive and a torque break, the method comprising: selecting a maximum web speed for unwinding the fiber web; determining a web break frequency based on a history for a selected number of parent rolls which have been unwound most recently, by dividing the number of web breaks by the number of the selected number of parent rolls which have been unwound; defining a web break cost as a function of rotation a selected stop time of the parent roll; defining a cost of incremental increased time to unwind the parent roll caused by reducing web speed below the maximum web speed to achieve the selected stop time of the parent roll, until the parent roll decrease in inertia is such that the parent roll can stop in the selected time at maximum web speed; minimizing a total cost, due to web breaks and cost of increased time to unwind the parent roll do to unwinding at less than the selected maximum web speed by choice of the selected stop time of the parent roll.

6. The method of claim 6 wherein web break cost is a function of one half of the velocity at break, times the selected stop time of the parent roll plus a fixed cost corresponding to a web break at zero web speed.

7. The method of claim 7 wherein the cost of increased time to unwind the parent roll is a function of an allocation of total cost of operating cost of the off-line finishing device for fiber webs in a time basis.

8. The method of claim 7 wherein the time to stop rotation of the parent roll is determined based on a self-learning algorithm using multiple data instances selected from at least one of: an occurrence of web breaks, total time to unwinder and the parent rolls in the off-line finishing device for fiber webs, cost of web breaks, total cost of processing the parent rolls in the off-line finishing device, and stop time of the parent roll following a web break.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In the following the invention is further described referring to the accompanying schematic figures in which

[0047] In FIG. 1 is shown a flow diagram of the method steps of the invention for limiting the deceleration time for a parent roll when the web breaks.

[0048] In FIG. 2 is shown graphs of speed, torque, and parent roll diameter vs time for a simulated run of a slitter-winder where the maximum running speed of the web Vmax is not reduced until the last set where running speed is reduced below Vmax required by a limit on the maximum rotation rate of the parent roll.

[0049] In FIG. 3 is shown graphs of speed, torque, and parent roll diameter vs time for a simulated run of a slitter-winder where Vset is less than Vmax during the first set and part of the second sets, such that running speed during the first set and part of the second, set is continuously increasing as the parent roll inertia is decreasing until Vset=Vmax.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0050] The method of this invention is used to optimize productivity of a web handling machine for processing of the web which involves unwinding a parent roll. One particular application involves an off-line slitter-winder for winding fiber webs into partial fiber web from a parent, or machine roll to form a customer roll sets 34, 35, 37, 38, and 39 as shown in FIG. 3. The process takes into account various limitations of the web handling machine, in particular limitations associated with unwinding the parent roll. These limitations include: the maximum allowed rotation speed of the parent roll as shown in FIGS. 2 and 3 which limits web speed when the parent roll diameter is about 1.9 meters and is rotating at 500 rpm, the maximum speed of the fiber web Vmax (3000 m/minutes) being unwound, the maximum negative torque is ((D(m))/2(Tm (Nm)+Tb(Nm))Z) which can be applied to the parent roll to bring the parent roll to a stop when the web breaks. The invention is particularly concerned with taking into account the costs associated with a web break during unwinding. A break has cost associated therewith, including the amount of fiber web which must be recycled and the time lost due to cleaning up the web break and restarting the unwinding process. These costs are related to how long it takes to stop the rotation of the parent roll when a break is detected, because the longer stopping time results in more fiber web which must be recycled, and more time required for cleanup and restarting of the unwinding process. The total cost of web breaks depends on how often they happen and how much time is required to restart the unwinding process after a break happens. It is desirable to minimize or eliminate breaks thereby minimizing or completing eliminating the cost associated with a web break. However, practically web breaks cannot be completely eliminated, and their frequency may change over time due to many reasons associated with the fiber web, the operation of the unwinder, etc. The nature of web breaks are such that their occurrence is random or at least cannot be predicted in the short run, however the frequency of web breaks, although changing, can be predicted based on recent history.

[0051] Reducing the maximum stopping time reduces the amount of paper which must be recycled and the time to recover, and thus reduces the costs associated with a web break. However, reducing stopping time itself has costs if it reduces the speed of the fiber web as it is unwound. These costs tend to be constant while the costs associated with a fiber web break vary with the frequency of the web breaks. Given a known correlation between stopping time and cost of a web break, and historical data concerning past web breaks, a stopping time which minimizes overall cost can be selected.

[0052] In FIG. 1 is shown a flow chart for limiting the web break deceleration time, i.e. the web break stopping time of an unwinder according to an advantageous example of the invention. In the method first, inertia (I) of a parent roll is calculated in the inertia calculation stage 11, which is followed by a maximum web break deceleration calculation stage 12, in which the maximum web break deceleration (dmax) is calculated. In the maximum speed set value calculation stage 13 the maximum speed set value is (Vmax). In the next step 14 the set value of the speed (Vset) is compared to the maximum set value of the speed (Vmax). Depending on the result of the comparison the running speed value (Vref) is set to the set value of the speed (Vset) in stage 15 or to the maximum set value of the speed (Vmax) in stage 16, and the unwinder is run with the running speed (Vref), as shown in stage 17. After stage 17 the method is begun again from the inertia calculation stage 11.

[0053] The inertia of the parent roll is calculated based on the equation:

[00001]$\begin{array}{cc}I\left({\mathrm{kgm}}^2\right)=\frac{.Math..Math..Math..Math.W}{32}.Math.\left(D^4-D.Math..Math.0^4\right).& 1.\end{array}$

[0054] The maximum web break deceleration is calculated based on the equation:

[00002]$\begin{array}{cc}\mathrm{Liner}.Math..Math.\mathrm{deacceleratio}.Math..Math.n.Math..Math.d.Math..Math.\max \left(\frac{m}{s^2}\right)=\frac{\frac{D\left(m\right)}{2}.Math.\left(\mathrm{Tm}\left(\mathrm{Nm}\right)+\mathrm{Tb}\left(\mathrm{Nm}\right)\right).Math.Z}{I}& 2.\end{array}$

[0055] The maximum speed set value (Vset) is calculated based on the equation:

Vset(m/s)=dmax*Tstop(s)3.

[0056] In the above equations the symbols used (and their units) are: [0057] I=parent roll inertia (kgm.sup.2) [0058] p=web density (kg/m.sup.3) [0059] W=web width (m) [0060] D=parent roll diameter (m) [0061] DO=reeling shaft diameter (m) [0062] Tm=maximum motor torque (Nm) [0063] Tb=mechanical brake torque (Nm) [0064] Z=gear ratio [0065] Tstop=user given web break deceleration time (s) [0066] Vmax=machine limit speed web velocity e.g. 3000 m/minutes or 50 m/s [0067] DZ(Tm+Tb)/2=Total Brake Torque=e.g., 40,000N.Math.m (set by machine design)

[0068] In FIGS. 2-3 are shown plotted curves of example simulated runs of a slitter-winder in cases of simulating a run of 5 sets of customer rolls from a 4.5 m diameter parent roll. On the horizontal axis is shown the time (s) and on the vertical axis are shown the running speed (m/min), the torque (N.Math.m10) and the diameter (mm) of the parent roll. Curve 21 in FIG. 3 shows the speed as limited by the parent roll inertia and the web break stop time (Tstop), curve 22 shows the unwind torque divided/10, and curve 23 shows the roll diameter.

[0069] In the example of FIG. 2 the parent roll total running time is 1482 seconds, and the web break stopping time is set to a maximum of 30 seconds. No speed limitation occurs due to parent roll inertia (I) because the maximum 32 speed set value (Vmax) does not need to be further limited to control angular momentum of the roll because the 30 seconds web break stopping time can be achieved with the available braking torque when using the maximum running speed (Vmax). The speed of the last set 39 of the customer rolls is limited by an unwind maximum rotational speed. In this simulation the web braking time (Tstop) of the unwinder was limited to 30 seconds which allows operation at Vmax.

[0070] In the example of FIG. 3 the parent roll running time is 1597 seconds, and the web break stopping time (Tstop) is set to a maximum of 15 seconds. During running of the first set 34 and the second set 36 of the customer rolls the web break stopping time of 15 seconds cannot be archived at Vmax with the available braking torque. Thus until the inertia I of the roll is decreased by unwinding some of the web on the parent roll, the speed of the web 21 must be controlled to a limited web break stopping time to a maximum 15 seconds. In this simulation the web break time i.e., the web break stopping time was limited to 15 seconds by limiting the running speed reference value. When compared to the example of FIG. 2, in which the running speed is not limited it can be seen in the example of FIG. 3 how much the speed is limited in order not to exceed the 15 seconds web break stopping time and how much it increases the running time.