10.1 A two-start square thread with a 5 mm pitch must be cut on a lathe - NSC Mechanical Technology Fitting and Machining - Question 10 - 2018 - Paper 1

The helix angle is calculated using:

$\tan(\phi) = \frac{\text{Lead}}{\text{Pitch circumference}}$

Where the pitch circumference can be derived from the outer diameter (82 mm) and pitch (2.5 mm):

$\text{Pitch circumference} = \pi \times (\text{Outside diameter} - \frac{1}{2} \text{Pitch})$

Calculating:

$\text{Pitch circumference} = \pi \times (82 - 2.5) \approx 248.16 \text{ mm}$

Then,

$\tan(\phi) = \frac{10}{248.16} \approx 0.0404$

Thus,

$\phi \approx 2.29^\circ / 2^\circ 17' 24"$

The leading tool angle is calculated as follows:

$\text{Leading tool angle} = 90^\circ - (\text{helix angle} + \text{clearance angle})$

Substituting the values:

$\text{Leading tool angle} = 90^\circ - (2.29^\circ + 3^\circ) \approx 84.71^\circ / 84^\circ 42' 36"$

The following tool angle is calculated using:

$\text{Following tool angle} = 90^\circ - (\text{helix angle} - \text{clearance angle})$

Substituting the values gives:

$\text{Following tool angle} = 90^\circ - (2.29^\circ - 3^\circ) \approx 89.29^\circ / 89^\circ 17' 24"$

M indicates a Metric screw thread.

24 refers to the nominal diameter of the screw thread in millimeters.

2.5 indicates the pitch of the screw thread in millimeters.

Angle A represents the Helix angle.

Angle B represents the Clearance angle.

Angle C represents the Leading tool angle.

Angle D represents the Following tool angle.