11.4 Screw Gauge

  Basic Mathematics and Measurements

The screw gauge is an instrument used for measuring accurately the diameter of a thin wire or the thickness of a sheet of metal. It consists of a U-shaped frame fitted with a screwed spindle which is attached to a thimble.

Screw gauge are used to measure,

• the diameter of the given lead shot
• the diameter of a given wire and find its volume
• the thickness of a given glass plate and find its volume
• the volume of an irregular lamina

The detailed description of every component of screw gauge is given below,

3. Thimble: It is the part through which measuring screw is rotated, this screwing results in the displacement of spindle and thimble itself.

4. Ratchet: Ratchet is itself a small device which is used to provide a limited applied force. It is installed at the right end of screw gauge, ratchet acts as a safety device for instruments and also adds more precision in measurement. Final adjustment is made by a making three turns of a ratchet.

5. Frame: The body used to hold the different components of a screw gauge in their place is called frame.

6. Main scale: The scale found on a stationary sleeve which is called the main scale.

7. Circular scale: The rotating scale which can be found on its rotating cylindrical part it is also called circular scale.

8. Pitch: Pitch of a screw gauge is defined as the distance moved by the tip of the screw when its thimble is turned through one complete revolution.

(A). Least count of screw gauge $(L.C.)$: Least count of a screw gauge is the smallest distance moved by the tip of the screw when the screw turns through one division.

In other words least count of screw-gauge is defined as the ratio of its pitch to the total number of divisions.

Mathematically,
$$L.C. = \frac{{{\text{Pitch}}}}{{{\text{Number of circular divisions}}}}$$
Let the pitch of the screw gauge be $1\ mm$ and number of divisions on a circular scale be $100$.

So, the least count is,
$$L.C. = \frac{{1\,mm}}{{100}} = 0.01\,mm$$

(B). Reading of a screw gauge $(R)$.

The reading of a screw gauge is given as,

Reading of screw gauge$=$Main scale reading $(M.S.R.)$ $+$ Circular scale reading $(C.S.R.)$

CIrcular scale reading is given by,
$$C.S.R. = n \times L.C.$$
So,
$$R = M.S.R. + n \times L.C.$$

where,

$M.S.R.:$ Main scale reading just to the left of the thimble
$n:$ Number of circular scale division on the thimble that coincides with the main scale on the sleeve

Let us understand how to take the reading with screw gauge better with the help of an illustration.

Illustration: The screw gauge has $50$ circular division with a pitch of $1\ mm$. The main scale is graduation in $mm$. Find the reading of the screw gauge as shown in the figure.

Least count $(L.C.)$ of the screw gauge is,
$$L.C. = \frac{{1\,mm}}{{50}} = 0.02\,mm$$
From the diagram, main scale reading $(M.S.R.)=20.5\ mm$

$n=11$

So, circular scale reading is,
$$C.S.R. = n \times L.C.$$$$C.S.R. = 11 \times 0.02\,mm$$$$C.S.R. = 0.22\,mm$$
So, the reading of the screw gauge is,
$$R = M.S.R. + C.S.R.$$$$R = \left( {20.5 + 0.22} \right)\,mm$$$$R = 20.72\,mm$$