5.1 A taper with a length of 60 mm and a large diameter of 40 mm and a small diameter of 31.6 mm needs to be cut on a lathe using the compound slide method - NSC Mechanical Technology Fitting and Machining - Question 5 - 2020 - Paper 1

To calculate the included angle, we use the formula:

$an\theta = \frac{D - d}{2L}$

where:

• D = 40 mm (larger diameter)
• d = 31.6 mm (smaller diameter)
• L = 60 mm (length of the taper)

Substituting the values:

$\tan\theta = \frac{40 - 31.6}{2 \times 60} = \frac{8.4}{120} = 0.07$

Now, to find the angle, take the inverse tangent:

$\theta = \tan^{-1}(0.07) \approx 4.004^\circ$

The angle to set the compound slide is half the included angle calculated previously. Therefore:

$\text{Angle of compound slide} = \frac{\theta}{2} = \frac{4.004^\circ}{2} = 2.002^\circ$

For a 30 mm diameter shaft, the width (W) of the parallel key is calculated as:

$W = \frac{D}{4} = \frac{30}{4} = 7.5 \text{ mm}$

The length (L) of the key is given by:

$L = 1.5 \times D = 1.5 \times 30 = 45 \text{ mm}$

To calculate the distance X, use the formula:

$X = \frac{\text{diameter of workpiece} - \text{thickness of cutter}}{2}$

Substituting the given values:

$X = \frac{60 - 15}{2} = \frac{45}{2} = 22.5 \text{ mm}$

To explain straddle milling, draw a horizontal line representing the workpiece and mark two milling cutters on either side of the workpiece, showing that they are positioned parallel to each other. Label the components clearly, including the arbour which holds the milling cutters in place. Indicate how straddle milling allows for the machining of two parallel surfaces simultaneously.