11.5 Zero error of screw gauge

  Basic Mathematics and Measurements

If the zero of the main scale does not coincide with the zero of the circular scale when left of the thimble touches the zero mark of the main scale, then the instrument has an error called zero error.

Note: Zero-error is always algebraically subtracted from the measured length.

Types of zero error.

1. Positive zero error: If the zero of the circular scale lies to the bottom of the main scale, then the zero error is called as positive zero error. (As shown in fig. (b)).
$${\text{Positive zero error}} = \left( {M.S.R. + n \times L.C.} \right)$$
where,

$n:$ Number of circular scale division on the thimble that coincides with the main scale on the sleeve

2. Negative zero error: If the zero of the circular scale lies to the top of the main scale, then the zero error is called as negative zero error. (As shown in fig. (c)).

Illustration: Calculate the positive and negative zero as shown in the figure given below. Screw gauge pitch is $1\ mm$ and has $50$ circular scale divisions.

Least count of screw gauge can be calculated as,
$$L.C. = \frac{{{\text{Pitch}}}}{{{\text{Number of circular scale divisions}}}}$$$$L.C. = \frac{{1\,mm}}{{50}} = 0.02\,mm$$

Process of taking zero error reading is same as the screw gauge reading.

(a) For positive zero error:
$${\text{Positive zero error}} = M.S.R. + n \times L.C.$$$$R_+ = 0 + 2 \times 0.02\,mm$$$$R_+ = 0.04\,mm$$

(b) For negative zero error:
$${\text{Negative zero error}} = - \left( {M.S.R. + n \times L.C.} \right)$$$${R_ - } = - \left( {0 + 4 \times 0.02\,mm} \right)$$$${R_ - } = - 0.08\,mm$$

Correction of zero error

True reading $=$ Observed reading $-$ zero error