M E A S U R I N G THE MEAN V E L O C I T Y OF A T A P E

V. Y a . S i d o r e n k o UDC 531.112

A widety used method for measuring the mean velocity of a tape in tape-propell ing mechanisms consists o f

the application of a measuring rolier [1, 2].

The intrinsic error which then arises in measuring the mean velocity of a tape is due first to the fact that for

a measured t ime interval the roller may produce a nonintegral number of pulses and, second, to the possibility that

the beginning of the t ime interval wllI not coincide with the regular velocity transducer's pulse.

The maximum measurement error AVma x for one measurement is evaluated by the possible variation of the counter indicator by one unit. All the measured values of the tape mean velocities are then distributed in therange of ~Avmax. Let us determine the root-mean-square error in measuring the mean velocity of a tape by means of the

measuring roller.

The tape length drawn by the tape-propell ing mechanism during one velocity measurement is

L t = L . n + l ,

where L = 7rd/M is the tape length per one pulse of the measuring roller's vetocity converter, d is the diameter of

the roller, M is the number of pulses of the measuring roller's velocity converter per one rotation, n is the reading

of the pulse counter at the end of the measurement, l is a positive value which we shall henceforth ca l l addendum.

Let us now examine the aggregate of all the mean velocity values subject to measurement, assuming that alI

the values of the addendum l from 0 to L and all the positions of the beginning of the vetoci ty-measurement time

interval with respect to the pulses of the measuring-roller 's vetocity transducer are equiprobable.

The aggregate of the measurement errors of the mean velocities subject to measurement follows the tri-

anguIar disrrtbution law with a precision which rises with the number of measurements [3]

,( l ll) ( A t ) = T 1 L '

where A/ is the possible error in measur trig the length of a tape segment, 0 < [A/I< L.

The dispersion of the measurement error is

L

o - - f Al, ---1(1 -- V az, ) c, J L \ C d A l = 6-

--L

The root-mean-square measurement error of a tape length drawn by the tape-propell ing mechanism during

a velocity measurement is

a t ---- 1 / ' D - ~ 0 , 4 1 L .

Therefore, the root-mean-square error in measuring the mean velocity of the tape will be

L nd o'v ~ 0,41 --7 ~ 0.41

Mt

Transhaeed from Izmeri te l 'naya Tekhnika, No. 10, p. 89, October, 1970. Original article submitted May 12,

1970.

�9 197l Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New

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It will be seen that the measurement error of the roller method is determined by the measuring t ime and the number of pulses produced by the measuring rol ler ' s veloci ty transducer for a single revolution. In order to reduce the error in measuring the mean veloci ty of the tape by the measuring-rol ler method it is necessary to select a measuring t ime t = 100 sec. However, it is l imi ted by the length of the tape on the reel of the part icular t ape-pro- pel l ing mechanism.

The measurement error can be reduced by increasing the number of pulses produced per one revolut ion of the roller, i .e . , by producing an improved design of the vetocity converter. For this purpose it is possible to use photo- e lectr ic , capaci t ive , or inductive transducers.

L I T E R A T U R E C I T E D

1. D . P . Vasilevskii, "Laboratory testing technique for tape recorders," Trudy VNIIRT, No. 12 (1964). 2. V . G . Korol 'kov, Tape Recorder Testing [in Russian], ~nergiya, Moscow (1965). 3. ~. V. Mikhalev and V. A. Malev, Voprosy radio~lektroniki, 12, No. 16 (1966).

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