To calculate the cutting time, we can use the following formula for machining operations:

$\text{Cutting Time} = \frac{\text{Length of Cut} + \text{Allowance}}{\text{Feed Rate} \times \text{RPM}}$

We will break down the problem step by step.

Step 1: Calculate the RPM (Revolutions Per Minute)

First, use the formula to calculate the spindle speed (RPM) from the cutting speed and diameter:

$\text{RPM} = \frac{\text{Cutting Speed} \times 12}{\pi \times \text{Diameter}}$

Where:

• Cutting Speed = 80 fpm (feet per minute),
• Diameter = 8 inches.

$\text{RPM} = \frac{80 \times 12}{\pi \times 8} = \frac{960}{25.1327} \approx 38.2 \, \text{RPM}$

Step 2: Calculate the Total Length of Cut

The total length of cut includes the original length plus the allowance:

$\text{Total Length} = 24 + 0.5 = 24.5 \, \text{in.}$

Step 3: Calculate the Cutting Time

Now, use the formula for cutting time:

$\text{Cutting Time} = \frac{24.5}{0.030 \times 38.2}$

Let's calculate that.

$\text{Cutting Time} = \frac{24.5}{1.146} \approx 21.38 \, \text{minutes}$

Final Answer:

The cutting time is approximately 21.38 minutes.

Would you like more details or have any questions?

Here are 5 related questions:

1. How does the cutting speed affect the cutting time?
2. What would happen to the cutting time if the feed rate was reduced?
3. Can you calculate the cutting time if the diameter changes to 6 inches?
4. How would different materials influence the cutting speed?
5. Why is the allowance added to the length of cut?

Tip: Always ensure to use consistent units when calculating cutting speed and feed rate to avoid errors.