To Measure Diameter of a Given Wire and Thickness of a Given Sheet Using Screw Gauge
1. Aim
To determine:
- The diameter of a given wire using a screw gauge.
- The thickness of a given sheet using a screw gauge.
2. Apparatus Used
- Screw gauge with least count 0.01 mm
- Wire sample (preferably copper or aluminum)
- Metal sheet sample
- Cleaning cloth
- Magnifying glass (optional)
3. Diagram
Fig 1: Labeled diagram of a screw gauge showing its various parts
4. Theory
A screw gauge is a precision measuring instrument used to measure the diameter of thin wires or the thickness of thin sheets with a high degree of accuracy. It works on the principle of a micrometer screw.
The screw gauge consists of a U-shaped frame with a fixed anvil on one end and a movable spindle on the other end. The spindle moves when the thimble is rotated due to the screw mechanism. The spindle has a fine pitch thread that advances by a specific distance (usually 0.5 mm or 1.0 mm) for each complete rotation of the thimble.
The main scale (pitch scale) is marked on the sleeve, and a circular scale (thimble scale) is marked on the thimble. The pitch scale typically has markings in 0.5 mm or 1.0 mm, while the thimble scale has 50 or 100 divisions for one complete rotation.
Zero Error and Zero Correction
Before using the screw gauge, it is essential to check for zero error:
- Positive Zero Error: When the screw gauge shows a reading above zero when the anvil and spindle are in contact.
- Negative Zero Error: When the screw gauge shows a reading below zero when the anvil and spindle are in contact.
Zero correction is applied by subtracting the zero error from the observed reading if the error is positive, and adding the zero error to the observed reading if the error is negative.
5. Formula
The least count of the screw gauge is calculated as:
$\text{Least Count} = \frac{\text{Pitch}}{\text{Number of divisions on circular scale}}$
For a typical screw gauge with pitch 1 mm and 100 divisions:
$\text{Least Count} = \frac{1 \text{ mm}}{100} = 0.01 \text{ mm}$
The total reading of the screw gauge is determined as:
$\text{Total Reading} = \text{Main Scale Reading} + \text{Circular Scale Reading} - \text{Zero Correction}$
Where:
$\text{Main Scale Reading} = \text{Visible divisions on pitch scale} \times \text{Pitch}$
$\text{Circular Scale Reading} = \text{Coinciding division on circular scale} \times \text{Least Count}$
$\text{Zero Correction} = \text{Zero Error (with sign)}$
6. Procedure
A. Determination of Zero Error
- Clean the anvil and spindle faces using a clean cloth.
- Rotate the ratchet until the anvil and spindle come in contact. The ratchet mechanism produces a clicking sound when proper contact is made.
- Note the reading on the main scale and the circular scale.
- If the zero of the circular scale coincides with the reference line on the sleeve, there is no zero error.
- If the zero of the circular scale does not coincide with the reference line, note the reading as zero error with appropriate sign.
- Repeat this step 3-5 times to get an accurate zero error value.
B. Measurement of Wire Diameter
- Place the wire between the anvil and spindle.
- Rotate the ratchet gently until the wire is held firmly between the anvil and spindle (the ratchet will make a clicking sound).
- Note down the reading on the main scale (MSR) and the division on the circular scale that coincides with the reference line (CSR).
- Take measurements at different points along the length of the wire (at least 5 points).
- Apply zero correction to each reading.
C. Measurement of Sheet Thickness
- Place the sheet between the anvil and spindle.
- Rotate the ratchet gently until the sheet is held firmly (the ratchet will make a clicking sound).
- Note down the MSR and CSR.
- Take measurements at different points on the sheet (at least 5 points).
- Apply zero correction to each reading.
7. Observation Table
A. Zero Error Determination
| Observation | Main Scale Reading (mm) | Circular Scale Reading (mm) | Zero Error (mm) |
|---|---|---|---|
| 1 | |||
| 2 | |||
| 3 | |||
| Mean Zero Error | |||
B. Wire Diameter Measurement
| Observation | Main Scale Reading (mm) | Circular Scale Reading (mm) | Total Reading (mm) | Corrected Reading (mm) |
|---|---|---|---|---|
| 1 | ||||
| 2 | ||||
| 3 | ||||
| 4 | ||||
| 5 | ||||
| Mean Diameter of Wire | ||||
C. Sheet Thickness Measurement
| Observation | Main Scale Reading (mm) | Circular Scale Reading (mm) | Total Reading (mm) | Corrected Reading (mm) |
|---|---|---|---|---|
| 1 | ||||
| 2 | ||||
| 3 | ||||
| 4 | ||||
| 5 | ||||
| Mean Thickness of Sheet | ||||
8. Calculations
Example Calculation
Given:
- Pitch of the screw gauge = 1 mm
- Number of divisions on circular scale = 100
- Least count = 0.01 mm
For Zero Error Calculation:
If the zero of circular scale is at 96 division when spindle and anvil are in contact:
$\text{Zero Error} = 96 \times 0.01 = +0.96 \text{ mm (Positive)}$
or
$\text{Zero Error} = (100 - 96) \times 0.01 = -0.04 \text{ mm (Negative)}$
depending on how the gauge is designed.
For Wire Diameter Calculation (single reading):
Main Scale Reading = 1 mm
Circular Scale Reading = 37 divisions
Total Reading = 1 + (37 × 0.01) = 1.37 mm
Assuming a zero error of +0.03 mm:
Corrected Reading = 1.37 - 0.03 = 1.34 mm
Mean Diameter (d) = Average of all corrected readings
$d = \frac{d_1 + d_2 + d_3 + d_4 + d_5}{5}$
9. Result
After performing the experiment and necessary calculations:
- The diameter of the given wire is ________ mm with an uncertainty of ± ________ mm.
- The thickness of the given sheet is ________ mm with an uncertainty of ± ________ mm.
10. Precautions
- Always check for zero error before taking measurements.
- Clean the anvil and spindle faces properly before use.
- Use the ratchet to close the screw gauge, not the thimble, to avoid excessive pressure.
- Do not overtighten the screw gauge as it may damage the object being measured or the instrument itself.
- Take readings at multiple points of the wire/sheet to account for non-uniformity.
- Hold the screw gauge perpendicular to the wire while measuring.
- While measuring, ensure that the wire/sheet is placed at the center between the anvil and spindle.
- Keep the screw gauge away from moisture and dust when not in use.
- Handle the instrument with care to prevent dropping or damage.
- Store the screw gauge with a slight gap between the anvil and spindle to avoid wear.
11. Sources of Error
- Instrumental Errors:
- Wear and tear of the screw threads
- Imperfect or damaged anvil/spindle surfaces
- Backlash error due to worn-out threads
- Improper calibration of the screw gauge
- Observational Errors:
- Parallax error while reading the scales
- Applying excessive pressure while measuring
- Incorrect alignment of wire/sheet between anvil and spindle
- Improper determination of zero error
- Physical Errors:
- Temperature variations affecting the dimensions of both the instrument and the object
- Non-uniformity in the wire diameter or sheet thickness
- Presence of dust particles or foreign material between the measuring surfaces
- Deformation of the wire/sheet due to handling
12. Viva Voice Questions
- Question: What is a screw gauge and what is its principle of operation?
Answer: A screw gauge is a precision measuring instrument used to measure small dimensions like the diameter of wires or thickness of sheets. It works on the principle of a micrometer screw, where linear movement of the screw is converted into rotational movement of the thimble. - Question: How do you determine the least count of a screw gauge?
Answer: The least count of a screw gauge is calculated by dividing the pitch of the screw by the number of divisions on the circular scale: $\text{Least Count} = \frac{\text{Pitch}}{\text{Number of divisions on circular scale}}$ - Question: What is zero error in a screw gauge? How do you account for it in measurements?
Answer: Zero error is the reading shown by the screw gauge when its measuring faces are in perfect contact. If the zero error is positive, we subtract it from the observed reading; if it's negative, we add it to the observed reading. - Question: Differentiate between positive and negative zero error in a screw gauge.
Answer: A positive zero error occurs when the zero of the circular scale lies below the reference line when the anvil and spindle are in contact. A negative zero error occurs when the zero of the circular scale lies above the reference line when the anvil and spindle are in contact. - Question: Why is it necessary to use the ratchet while taking measurements with a screw gauge?
Answer: The ratchet ensures that a consistent pressure is applied to the object being measured, preventing over-tightening which could damage both the object and the instrument, and under-tightening which could lead to inaccurate readings. - Question: Why should measurements be taken at different points of the wire?
Answer: Measurements should be taken at different points of the wire to account for variations in diameter due to manufacturing inconsistencies or non-uniformity in the wire. - Question: How does temperature affect measurements with a screw gauge?
Answer: Temperature changes can cause thermal expansion or contraction of both the screw gauge and the object being measured, leading to inaccurate readings. Ideally, measurements should be taken at a standard temperature (usually 20°C). - Question: What is backlash error in a screw gauge and how can it be minimized?
Answer: Backlash error occurs due to wear and tear of the screw threads, resulting in a slight play between the screw and nut. It can be minimized by always approaching the final reading from the same direction (usually by closing the screw). - Question: Why is a screw gauge more accurate than a vernier caliper for measuring small dimensions?
Answer: A screw gauge is more accurate because it typically has a smaller least count (0.01 mm) compared to a vernier caliper (0.1 mm), allowing for more precise measurements of small dimensions. - Question: How would you store a screw gauge when not in use?
Answer: A screw gauge should be stored with a slight gap between the anvil and spindle to prevent wear of the measuring faces. It should be kept in a clean, dry place away from dust and moisture, preferably in its case.