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

The included angle \( heta\) can be calculated using the formula:

$\tan(\theta) = \frac{D - d}{2L}$

Where:

• D = large diameter = 40 mm
• d = small diameter = 31.6 mm
• L = length = 60 mm

Plugging in the values:

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

To find the angle, take the arctangent:

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

You need to set the compound slide to half of the included angle calculated above:

$\text{Angle} = \frac{4.004^{\circ}}{2} \approx 2.002^{\circ}$.

The width (W) of the parallel key can be calculated as:

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

The length (L) of the parallel key is calculated using:

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

To calculate the distance X:

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

Given:

• Diameter of workpiece = 60 mm
• Thickness of cutter = 15 mm

We can substitute these values:

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

Straddle milling is a method where two or more milling cutters are mounted on the same arbor to mill two opposite sides of a workpiece simultaneously. In your sketch, label the following components:

• Arbour: the shaft on which the cutters are mounted.
• Milling cutters: the cutting tools that do the actual milling.
• Workpiece: the material being machined. Ensure the sketch clearly shows that cutters are on both sides of the workpiece, maximizing efficiency in machining.