To calculate the reading on a screw gauge, you combine the measurement from the main scale (pitch scale) with the measurement from the circular scale, adjusted by the instrument's least count.
The standard formula for calculating the total reading of a screw gauge is:
Total Reading = Pitch Scale Reading + Circular Scale Reading x LC of the gauge
Let's break down this formula and the steps involved.
Understanding the Components
A screw gauge has two main scales: the Pitch Scale (or Main Scale) and the Circular Scale. It also has a specific value called the Least Count (LC).
- Pitch Scale Reading: This scale runs along the sleeve of the screw gauge and is typically marked in millimeters (mm). It measures the larger, whole-number part of the thickness or diameter being measured.
- Circular Scale Reading: This scale is marked on the thimble, the rotating part. It is divided into a certain number of equal divisions (usually 50 or 100). It measures the fractional part of the thickness or diameter.
- Least Count (LC): This is the smallest distance that can be accurately measured by the screw gauge. It is the resolution of the instrument.
How is the Least Count Calculated?
While not part of the reading formula itself, understanding the LC calculation is crucial.
The Least Count is calculated as:
LC = (Pitch of the screw) / (Total number of divisions on the circular scale)
The pitch is the distance moved by the screw's spindle for one complete rotation of the circular scale. It's typically 0.5 mm or 1 mm.
For example, if the pitch is 0.5 mm and there are 100 divisions on the circular scale, the LC would be 0.5 mm / 100 = 0.005 mm.
Steps to Calculate the Reading
Follow these steps to find the total reading of an object placed between the screw gauge's jaws:
- Note the Least Count (LC): Check the screw gauge itself, or calculate it using the formula above if the pitch and number of circular scale divisions are known.
- Read the Pitch Scale: Observe the main scale on the sleeve. Note the last division visible just before the edge of the thimble (the circular scale). This is your Pitch Scale Reading (PSR).
- Read the Circular Scale: Look at the circular scale on the thimble. Find the division that coincides with the main scale line (datum line) on the sleeve. This is your Circular Scale Division reading.
- Calculate the Circular Scale Contribution: Multiply the Circular Scale Division reading by the Least Count (LC).
- Circular Scale Reading = (Coinciding Circular Scale Division) x LC
- Calculate the Total Reading: Use the formula provided:
- Total Reading = Pitch Scale Reading + Circular Scale Reading
- Total Reading = Pitch Scale Reading + (Coinciding Circular Scale Division x LC)
Example Calculation
Let's say you are measuring the thickness of a wire using a screw gauge with:
- Pitch = 0.5 mm
- Number of circular scale divisions = 50
- Least Count (LC) = 0.5 mm / 50 = 0.01 mm
After placing the wire and tightening the ratchet, you observe:
- Pitch Scale Reading (PSR) = 4.5 mm (the last visible division on the sleeve is 4.5 mm)
- Coinciding Circular Scale Division = 25 (the 25th division on the circular scale aligns with the datum line)
Now, calculate the total reading:
- Circular Scale Reading = 25 divisions x 0.01 mm/division = 0.25 mm
- Total Reading = Pitch Scale Reading + Circular Scale Reading
- Total Reading = 4.5 mm + 0.25 mm = 4.75 mm
The thickness of the wire is 4.75 mm.
Practical Considerations
- Zero Error: Real screw gauges often have a zero error. This is the reading when the jaws are closed without any object. If there's a zero error, you must correct the total reading by subtracting the positive zero error or adding the negative zero error.
- Positive Zero Error: If the 0 on the circular scale is below the datum line when jaws are closed.
- Negative Zero Error: If the 0 on the circular scale is above the datum line when jaws are closed.
- Corrected Reading = Total Reading - Zero Error (sign included)
- Proper Usage: Always use the ratchet to tighten the screw gauge onto the object to ensure consistent pressure and avoid damaging the screw or the object.
Here's a summary of the reading process:
| Step | Action | Result |
|---|---|---|
| 1. Prepare | Note LC, check for Zero Error (and correct if necessary). | LC, Zero Error value |
| 2. Read Pitch Scale | Note last visible division on the sleeve before the thimble edge. | Pitch Scale Reading (PSR) |
| 3. Read Circular Scale | Find the circular division aligning with the datum line. | Coinciding Circular Div. |
| 4. Calculate CS Value | Multiply Coinciding Circular Div. by LC. | Circular Scale Reading |
| 5. Calculate Total | Add Pitch Scale Reading and Circular Scale Reading. | Total Reading |
| 6. Correct (If needed) | Subtract Zero Error from Total Reading (if any). | Final Corrected Reading |
By understanding the formula and following these steps, you can accurately calculate measurements using a screw gauge.
