Alternative method for reducing web feed rate variations induced by parent roll geometry variations

A method for reducing feed rate variations in a web material when unwinding a parent roll by transporting the web material away from the parent roll at a web takeoff point, the method comprising the steps of:

• dividing the parent roll into a selected number 1, 2, . . . n, of data collection sectors to be analyzed;
• creating a data table having a sector column for entering a sector number for each of the data collection sectors, 1, 2, . . . n, the data table also having a column for entering a web takeoff point radius and a web takeoff point correction factor for each of the data collection sectors, 1, 2, . . . n;
• using an ideal speed reference signal, SRSi, to drive the parent roll at a driving speed corresponding to a web feed rate of a round parent roll and at a drive point being disposed on the outer surface either coincident with or spaced from the web takeoff point;
• measuring the web takeoff point radius, Rtp(1, 2, . . . n), at or near the web takeoff point of the parent roll for each of the data collection sectors, 1, 2, . . . n, as the parent roll is being driven at the drive point;
• calculating an ideal web takeoff point radius, Rtpi, by adding the web takeoff point radii, Rtp(1, 2, . . . n), for all of the data collection sectors, 1, 2, . . . n, to determine a sum and dividing the sum by the total number, n, of the data collection sectors, 1, 2, . . . n;
• calculating the web takeoff point correction factor, Ctp(1, 2, . . . n), for each of the data collection sectors, 1, 2, . . . n, as a function of the web takeoff point radius, Rtp(1, 2, . . . n), and the ideal web takeoff point radius, Rtpi, using the formula:
• Ctp(1,2, . . . n)=Rtpi/Rtp(1,2, . . . n)
• where Rtp(1, 2, . . . n) is the web takeoff point radius for each of the data collection sectors, 1, 2, . . . n, and Rtpi is the ideal web takeoff point radius;
• entering the web takeoff point correction factor, Ctp(1, 2, . . . n), in the data table for each of the data collection sectors, 1, 2, . . . n, in the column for entering the web takeoff point correction factor;
• multiplying the web takeoff point correction factor, Ctp(1, 2, . . . n), for each of the data collection sectors, 1, 2 . . . n, by the ideal speed reference signal, SRSi, to establish an improved speed reference signal, SRSiImproved, for each of the data collection sectors (1, 2 . . . n);
• and,
• adjusting the driving speed, Mi, of the parent roll for each of the data collection sectors, 1, 2, . . . n, to an improved driving speed, MiImproved, as each of the data collection sectors, 1, 2, . . . n, approaches or is at the drive point using the improved speed reference signal, SRSiImproved, to at least reduce fluctuations in feed rate of the web material caused by variations in the web takeoff point radii.

A method for reducing feed rate variations in a web material when unwinding a parent roll about a longitudinal axis to transport the web material away from the parent roll at a web takeoff point, the method comprising the steps of:

• dividing the parent roll into a plurality of angular sectors disposed about the longitudinal axis;
• using an ideal speed reference signal to drive the parent roll at a driving speed corresponding to a web feed rate of a round parent roll and at a drive point being disposed on the outer surface either coincident with or spaced from the web takeoff point;
• determining a rotational speed for each of the sectors, while at the drive point, as the parent roll is being driven;
• calculating a drive point radius of each of the sectors by calculating the radius at the drive point of the parent roll for each of the sectors as a function of the driving speed and the rotational speed;
• calculating an ideal drive point radius by determining an average for the drive point radii for all of the sectors;
• calculating a drive point correction factor for each of the sectors as a function of the drive point radius and the ideal drive point radius;
• multiplying the drive point correction factor for each of the sectors by the ideal speed reference signal to establish an improved speed reference signal for each of the sectors;
• and,
• adjusting the driving speed of the parent roll for each of the sectors to an improved driving speed as each of the sectors approaches or is at the drive point using the improved speed reference signal to maintain a substantially consistent rotational speed to reduce feed rate variations in the web material at the web takeoff point caused by fluctuations in drive point radii.

A method for reducing feed rate variations in a web material when unwinding a parent roll by transporting the web material away from the parent roll at a web takeoff point, the method comprising the steps of:

• dividing the parent roll into a selected number 1, 2, . . . n, of data collection sectors to be analyzed;
• creating a data table having a sector column for entering a sector number for each of the data collection sectors, 1, 2, . . . n, the data table also having a column for entering a drive point radius and a drive point correction factor for each of the data collection sectors, 1, 2, . . . n;
• using an ideal speed reference signal, SRSi, to drive the parent roll at a driving speed corresponding to a web feed rate of a round parent roll and at a drive point being disposed on the outer surface either coincident with or spaced from the web takeoff point;
• determining a rotational speed for each of the data collection sectors, 1, 2, . . . n, while at the drive point, as the parent roll is being driven;
• calculating the drive point radius, Rdp(1, 2, . . . n), for each of the data collection sectors, 1, 2, . . . n, from the driving speed and the rotational speed using the formula:
• Rdp(1,2, . . . n)=Mi/2πΩi(1,2, . . . n)
• where Mi is the instantaneous driving speed for the parent roll and Ωi(1, 2, . . . n) is the instantaneous rotational speed when each of the data collection sectors, 1, 2, . . . n, is at the drive point;
• entering the drive point radius, Rdp(1, 2, . . . n), in the data table for each of the data collection sectors, 1, 2, . . . n, in the column for entering the drive point radius;
• calculating an ideal drive point radius, Rdpi, by adding the drive point radii, Rdp(1, 2, . . . n), for all of the data collection sectors, 1, 2, . . . n, to determine a sum and dividing the sum by the total number, n, of the data collection sectors, 1, 2, . . . n;
• calculating the drive point correction factor, Cdp(1, 2, . . . n), for each of the data collection sectors, 1, 2, . . . n, as a function of the drive point radius, Rdp(1, 2, . . . n), and the ideal drive point radius, Rdpi, using the formula:
• Cdp(1,2, . . . n)=Rdp(1,2, . . . n)/Rdpi
• where Rdp(1, 2, . . . n) is the drive point radius for each of the data collection sectors, 1, 2, . . . n, and Rdpi is the ideal drive point radius;
• entering the drive point correction factor, Cdp(1, 2, . . . n), in the data table for each of the data collection sectors, 1, 2, . . . n, in the column for entering the drive point correction factor;
• multiplying the drive point correction factor, Cdp(1, 2 . . . . n), for each of the data collection sectors, 1, 2 . . . n, by the ideal speed reference signal, SRS, to establish an improved speed reference signal, SRSiImproved, for each of the data collection sectors (1, 2 . . . n);
• and,
• adjusting the driving speed, Mi, of the parent roll for each of the data collection sectors, 1, 2, . . . n, to an improved driving speed, MiImproved, as each of the data collection sectors, 1, 2, . . . n, approaches or is at the drive point using the improved speed reference signal, SRSiImproved, to maintain a substantially consistent rotational speed to reduce feed rate variations in the web material at the web takeoff point caused by fluctuations in drive point radii.