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 drive point radius, a web takeoff point radius, a drive point correction factor, a web takeoff point correction factor and a total 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;
• correlating each of the data collection sectors, 1, 2, . . . n, at the web takeoff point with a corresponding one of the data collection sectors, 1, 2, . . . n, at the drive 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 driving speed for the parent roll and Ωi(1, 2, . . . n) is the 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;
• 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, Cdp(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(1, 2, . . . n)/Rtp
• 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;
• calculating the total correction factor, Ct(1, 2, . . . n), for each of the data collection sectors, 1, 2, . . . n, as a function of the drive point correction factor, Cdp(1, 2, . . . n), and the web takeoff point correction factor, Ctp(1, 2, . . . n), using the formula:
• Ct(1, 2, . . . n)=Cdp(1, 2, . . . n)×Ctp(1, 2, . . . n)
• where Cdp(1, 2, . . . n) is the drive point correction factor for each of the data collection sectors, 1, 2, . . . n, and Ctp(1, 2, . . . n) is the web takeoff point correction factor for each of the data collection sectors, 1, 2, . . . n;
• entering the total correction factor, Ct(1, 2, . . . n), in the data table for each of the data collection sectors, 1, 2, . . . n, in the column for entering the total correction factor;
• multiplying the total correction factor, Ct(1, 2 . . . n), for each of the data collection sectors, 1, 2 . . . n, by the ideal speed reference signal, SRSi, to establish a corrected speed reference signal, SRSiCorrected, 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 a corrected driving speed, MiCorrected, as each of the data collection sectors, 1, 2, . . . n, approaches or is at the drive point using the corrected speed reference signal, SRSiCorrected, to at least approximate the web feed rate of the round parent roll to reduce feed rate variations in the web material at the web takeoff point.