Machining Time Calculation for Turning

This question asks us to determine the total machining time required to turn a cylindrical surface using a single point cutting tool. We are given the feed rate, workpiece rotation speed, and the length of the surface to be machined.

Given Parameters

• Feed rate ($f$) = 3 mm/revolution
• Workpiece rotation speed ($N$) = 600 r.p.m. (revolutions per minute)
• Length of workpiece surface to be turned ($L$) = 300 mm

Calculating Machining Time

The total machining time ($T$) for turning a cylindrical surface with a single pass can be calculated using the formula:

$$T = \frac{L}{f \times N}$$

Where:

• $T$ is the machining time
• $L$ is the length of the cut (length of the workpiece surface)
• $f$ is the feed rate
• $N$ is the rotation speed of the workpiece

Let's substitute the given values into the formula:

$$T = \frac{300 \text{ mm}}{3 \text{ mm/revolution} \times 600 \text{ revolutions/minute}}$$

First, calculate the product of feed rate and rotation speed, which gives the feed speed (the distance the tool travels along the workpiece per minute):

Feed speed = $f \times N = 3 \text{ mm/revolution} \times 600 \text{ revolutions/minute} = 1800 \text{ mm/minute}$

Now substitute this back into the machining time formula:

$$T = \frac{300 \text{ mm}}{1800 \text{ mm/minute}}$$

$$T = \frac{300}{1800} \text{ minutes}$$

$$T = \frac{1}{6} \text{ minutes}$$

Converting Time to Seconds

The options are given in seconds. We need to convert the calculated time from minutes to seconds. There are 60 seconds in 1 minute.

$$T = \frac{1}{6} \text{ minutes} \times 60 \text{ seconds/minute}$$

$$T = 10 \text{ seconds}$$

Therefore, the total machining time required to turn the cylindrical surface is 10 seconds.

Summary

Given:

• Feed rate ($f$) = 3 mm/rev
• Speed ($N$) = 600 rpm
• Length ($L$) = 300 mm

Formula:

$$T = \frac{L}{f \times N}$$

Calculation:

$$T = \frac{300 \text{ mm}}{(3 \text{ mm/rev}) \times (600 \text{ rev/min})} = \frac{300 \text{ mm}}{1800 \text{ mm/min}} = \frac{1}{6} \text{ min}$$

Convert to seconds:

$$T = \frac{1}{6} \text{ min} \times 60 \text{ sec/min} = 10 \text{ seconds}$$

The calculated machining time of 10 seconds matches one of the provided options.