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1. 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, 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 sectors at the web takeoff point with a corresponding one of the sectors at the drive 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 for each of the sectors by calculating the radius at the drive point for each of the sectors from the driving speed and the rotational speed using the formula:
Rdp=Mi/2πΩi where Mi is the instantaneous driving speed for the parent roll and Ωi, is the instantaneous rotational speed when each of the sectors is at the drive point; calculating an ideal drive point radius by adding the drive point radii for all of the sectors to determine a sum and dividing the sum by the total number of 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 using the formula:
Cdp=Rdp/Rdpi where Rdp is the drive point radius for each of the sectors and Rdpi is the ideal drive point radius; calculating a modified drive point correction factor for each of the sectors using the formula:
Cdpmodified=1−(1−Cdp)*x, where Cdp is the drive point correction factor for each of the sectors and x is drive point adjustment percentage; measuring a web takeoff point radius for each of the sectors by measuring the radius at or near the web takeoff point of the parent roll for each of the sectors as the parent roll is being driven at the drive point; calculating an ideal web takeoff point radius by adding the web takeoff point radii for all of the sectors to determine a sum and dividing the sum by the total number of sectors; calculating a web takeoff point correction factor for each of the sectors as a function of the web takeoff point radius and the ideal web takeoff point radius using the formula:
Ctp=Rtpi/Rtp where Rtp is the web takeoff point radius for each of the sectors and Rtpi is the ideal web takeoff point radius; calculating a modified total correction factor for each of the sectors as a function of the modified drive point correction factor and the web takeoff point correction factor using the formula:
CTmodified=Cdpmodified×Ctp where Cdpmodified is the modified drive point correction factor for each of the sectors and Ctp is the web takeoff point correction factor for each of the sectors; multiplying the modified total correction factor, CTmodified, for each of the sectors by the ideal speed reference signal, SRSi, to establish an improved speed reference signal, SRSiImproved for each of the sectors; and, adjusting the driving speed, Mi, of the parent roll for each of the sectors to an improved driving speed, MiImproved, as each of the sectors approaches or is at the drive point using the improved speed reference signal, SRSiImproved to at least reduce feed rate variations in the web material at the web takeoff point. |
