Calculating Specific Cutting Pressure in Turning

The question asks us to find the specific cutting pressure during a turning operation, given the main cutting force, depth of cut, and feed rate. Specific cutting pressure is a key parameter in machining that represents the resistance of the material to cutting.

Specific cutting pressure ($\boldsymbol{k_c}$) is defined as the cutting force ($\boldsymbol{F_c}$) per unit area of the undeformed chip cross-section ($\boldsymbol{A}$).

Mathematically, it is expressed as:

$$k_c = \frac{F_c}{A}$$

The undeformed chip cross-sectional area ($\boldsymbol{A}$) in a turning operation is determined by the depth of cut ($\boldsymbol{d}$) and the feed rate ($\boldsymbol{f}$).

$$A = d \times f$$

Let's identify the given values from the question:

• Main cutting force, $F_c = 400$ N
• Depth of cut, $d = 2$ mm
• Feed rate, $f = 0.1$ mm/rev

Step-by-Step Calculation

Step 1: Calculate the undeformed chip cross-sectional area ($A$).

Using the formula $A = d \times f$, we plug in the given values:

$$A = (2 \text{ mm}) \times (0.1 \text{ mm/rev})$$

$$A = 0.2 \text{ mm}^2$$

The undeformed chip area is 0.2 square millimeters.

Step 2: Calculate the specific cutting pressure ($k_c$).

Using the formula $k_c = \frac{F_c}{A}$, we plug in the main cutting force and the calculated chip area:

$$k_c = \frac{400 \text{ N}}{0.2 \text{ mm}^2}$$

To simplify the fraction, we can multiply both the numerator and the denominator by 10:

$$k_c = \frac{4000}{2} \text{ N/mm}^2$$

$$k_c = 2000 \text{ N/mm}^2$$

Thus, the specific cutting pressure is 2000 N/mm².

Comparing with Options

Let's compare our calculated specific cutting pressure with the given options:

1. 1000 N/mm²
2. 4000 N/mm²
3. 2000 N/mm²
4. 3000 N/mm²

Our calculated value of 2000 N/mm² matches option 3.

The specific cutting pressure is a material property that varies with cutting conditions. It indicates the force required per unit area of material being cut.