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Determining Tape Thickness without Knowledge of Supply-Reel Circumference

IP.com Disclosure Number: IPCOM000118422D
Original Publication Date: 1997-Feb-01
Included in the Prior Art Database: 2005-Apr-01
Document File: 2 page(s) / 68K

Publishing Venue

IBM

Related People

Winarski, DJ: AUTHOR

Abstract

This article determines d, the thickness of the tape wound on single-reel cartridges. This determination is made within the first few additional wraps. Knowledge of the thickness of the tape is valuable for setting the proper tape tension. It is assumed that the motor driving the supply reel has a fine-line tachometer and the takeup reel motor has a single-line tachometer.

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This is the abbreviated version, containing approximately 52% of the total text.

Determining Tape Thickness without Knowledge of Supply-Reel Circumference

      This article determines d, the thickness of the tape wound on
single-reel cartridges.  This determination is made within the first
few additional wraps.  Knowledge of the thickness of the tape is
valuable for setting the proper tape tension.  It is assumed that the
motor driving the supply reel has a fine-line tachometer and the
takeup reel motor has a single-line tachometer.

In this article, the following symbols are used:
  N = total number of tachometer lines on the supply reel (known)
    (i.e., N = 512 for a 512 line "fine-line" tachometer/encoder)
  N12 = number of tachometer lines on the supply reel counted
         for the first revolution of the single-line tachometer
         on the takeup reel (measured by servo)
  M1  = Integral number of wraps of tape on the takeup reel
         (measured by servo)
  SUM(N1) = total number of fine-line tachometer counts to wrap
             M1 revolutions of tape on the takeup reel
  Ri = hub radius of the supply and takeup reels (known)
  Rm = original winding radius of supply reel cartridge
        (undetermined constant)
  d   = desired thickness of the tape (undetermined constant)
  L1  = instantaneous length of tape wound from supply reel to
         takeup reel (unknown)

The length of tape, L1, on the takeup reel can be calculated by
summing the circumferences of the individual wraps.  Assuming that
there are M1 wraps of tape on the takeup reel, where M1 is an integer
greater than one, L1 is equal to PI*M1*(2*Ri+(M1-1)*d).
  L1 = PI*M1*(2*Ri + (M1-1)*d)                                (1)

Eqn. (1) represents the closed form analytical solution to the
amount of tape on a reel, based on a finite elements approach.  This
finite element approach treats the tape as incremental additions of
individual rings or individual...