# Measure Diameter of Given Wire Using Screw Gauge

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## What is a Screw Gauge?

A screw gauge is an instrument that measures the diameter of thin objects like a wire. The name screw gauge is provided because it is most commonly used to measure the diameters of wire which in turn are governed by the standard numbers that are called the standard wire gauge.

A screw gauge also measures the thickness of small sheets such as glass and plastic.

Since a screw gauge works on the principle of a micrometer, that’s why we call it the principle of a micrometer screw.

### Screw Gauge

When accurately cut, a single threaded screw is placed inside a closely fitted nut and rotated. The two types of motions occur, one is circular and the other is a linear motion of the screw along its axis.

The distance moved by the screw in one complete rotation of the screw equals the distance between the two consecutive threads of the screw gauge. This distance is called ‘Pitch’ and it is always a constant value.

Since the linear motion (the small distances) made by the screw gauge is hard to be measured so these linear distances are amplified into larger distances by the rotational motion of the screw. These rotations are easily measurable. The screw gauge is constructed in a way that follows the principle of ‘micrometer screw.’

Now, to measure the diameter of a given wire using a screw gauge, we need to know its structure.

### Structure of a Screw Gauge

In the above figure, we can see a U-shaped frame.

On the right side of this frame, we have a net that is called a sleeve. The readings on the sleeve measure the linear distance moved by the screw; this scale is called the ‘linear scale’ or the ‘pitch scale’.

If 15 mm is written on the U-frame, it means there are 15 divisions on the sleeve.

On the left side of the U-shape, there is a metal projection called ‘stud’. When this screw is moved forward, the stud and the screw together hold the wire or a sheet firmly.

The screw is attached to a milled head with a sloping edge that rotates over the sleeve; the sloping edge is called the circular or a head scale.

Now, let’s study the two terms used to find diameter of wire using screw gauge:

### Determine the Diameter of Wire Using Screw Gauge

• Determine the Linear scale division (number of visible and undiscovered divisions).

• Find and record the pitch and L.C. of the screw gauge.

• Record the zero error, if there’s any, otherwise, keep it nill.

• Let ‘m’ = number of divisions of the circular scale lying on the reference line.

• Firstly, we will find the direction of the wire in a perpendicular direction, we rotate the wire to 90°.

• Now, we will rotate the wire in different directions. We will repeat the above steps 6 times and note the total reading and the zero error.

• We will take the average of different values of diameters.

• Now, we will take a half-length ruler to ascertain the length of the wire. Repeat this step four times and record our observations.

### Pitch

$\text{Pitch } - \frac{\text{linear distance moved by the screw}}{\text{One rotation of the screw}}$

We can determine the pitch by rotating the circular scale to reach the zero mark on the reference line. In this way, we note down the pitch scale reading.

To Determine the Diameter of A Wire By Screw Gauge

Firstly, we count the number of divisions on the linear scale on a place completely uncovered by the cap. Let’s suppose that we got the reading as 4.0 mm as a linear scale reading.

Now, we rotate the screw 3 times till the zero mark of the head scale reaches the reference line, it means one rotation is complete.

After four rotations, we note the reading and it comes out 6.0 mm. We got the linear distance mode as:   7.0 mm -  4.0 mm  = 3.0 mm.

So, the pitch can be calculated as:

$= \frac{\text{linear distance moved by the screw}}{\text{One rotation of the screw}} = \frac{3mm}{3}$ = 1 mm

So, the pitch of the screw is 1 mm or 0.1 cm.

So, the distance moved by the screw in one complete rotation of the circular cap is 1 mm.

Least Count of the Screw Gauge

A circular cap has 100 divisions, if the cap moves one division, then the distance moved is 1/100 of the pitch, which is the least count of the screw gauge.

So, the formula for the least count is:

$L.C. = \frac{\text{Pitch}}{\text{No. of divisions in a circular/head scale}} = \frac{1}{100}$ = 0.01 mm or 0.001 cm.

1.  …… mm

2. ……..mm

3. ……..mm

Mean zero error…….mm.

Table for the diameter of wire using screw gauge:

 S.No. LSR (N) in mm Circular Scale Reading Total Reading No. of circular scale divisions on the reference line  (n) n * L.C. Observed readingG = N + n * L.C. (mm) CorrectedD = G + c

Question 1: How do Errors Occur?

Answer: Because of the manufacturing defect of the screw gauge, the wear and tear of the screw threads lead to increasing gaps; these irregular gaps may lead to zero and backlash errors.

Question 2: What are the Zero Errors?

Answer: Due to the manufacturing defect in the screw gauge, when the screw completely touches the fixed dead and zero of the circular scale doesn’t coincide with the reference line. The type of error that occurs is the zero error.

Question 3: What is a Backlash Error?

Answer: When we rotate the ratchet, we find a certain lag in the linear movement of this screw that is indicated by the jerky movement of the screw.

In certain cases, on rotating the ratchet, the screw doesn’t move immediately in the opposite direction, instead, it rotates in the reverse direction which happens due to improper alignment in threads (rise in gaps in threads) so the type of error that occurs is the backlash error.

Question 4: State the Sources of Error in a Screw Gauge.