10.1 Draw a neat sketch of a metric V-screw thread and indicate the THREE diameters of the screw thread - NSC Mechanical Technology Fitting and Machining - Question 10 - 2019 - Paper 1

The lead of a screw thread is defined as the distance a thread will advance axially in one complete revolution. It is calculated as the product of the pitch and the number of starts. For a single-start thread, the lead is the same as the pitch, while for multi-start threads, it is the pitch multiplied by the number of starts.

To calculate the lead:

$\text{Lead} = \text{Pitch} \times \text{Number of Starts}$

For this thread:

• Pitch = 4 mm
• Number of starts = 3

$\text{Lead} = 4 \text{ mm} \times 3 = 12 \text{ mm}$

The mean circumference can be calculated using the formula:

$\text{Mean circumference} = \pi \times \text{OD}$

where:

• OD = Crest diameter - 4 × Pitch
• OD = 68 mm - 4 mm = 64 mm

Thus:

$\text{Mean circumference} = \pi \times 64 \text{ mm} \approx 201.06 \text{ mm}$

The helix angle ($\theta$) can be calculated using:

$\tan(\theta) = \frac{\text{Lead}}{\text{Mean circumference}}$

Using the values calculated:

• Lead = 12 mm
• Mean circumference = 201.06 mm

Thus:

$\theta = \tan^{-1}\left(\frac{12}{207.35}\right)\approx 3.31°$

The leading tool angle ($\alpha$) is calculated as:

$\alpha = 90° - (\text{Helix angle} + \text{Clearance angle})$

Substituting values:

• Helix angle = 3.31°
• Clearance angle = 3°

Thus:

$\alpha = 90° - (3.31° + 3°) = 83.69°$

The following tool angle ($\beta$) is calculated using:

$\beta = 90° - (\text{Helix angle} - \text{Clearance angle})$

Thus:

$\beta = 90° - (3.31° - 3°) = 90.31°$