A surface grinding operation has been performed on a Cast Iron plate having dimensions 300 mm (length) x 10 mm (width) x 50 mm (height). The grinding was performed using an alumina wheel having a wheel diameter of 150 mm and wheel width of 12 mm. The grinding velocity used is 40 m/s, table speed is 5 m/min, depth of cut per pass is 50 µm and the number of grinding passes is 20. The average tangential and average normal force for each pass is found to be 40 N and 60 N respectively. The value of the specific grinding energy under the aforesaid grinding conditions is ______________ J/mm³ (round off to one decimal place).

The correct answer is 38.4.

Step-by-Step Explanation:

1. Identify the given parameters from the grinding operation:
- Length of the Cast Iron plate = 300 mm
- Width of the plate (w) = 10 mm
- Height of the plate = 50 mm
- Grinding velocity (V) = 40 m/s
- Table speed (v) = 5 m/min
- Depth of cut per pass (d) = 50 µm = 50 × 10^-3 mm = 0.05 mm
- Average tangential force (F_c) = 40 N

2. Convert units to a consistent system (mm and seconds):
First, convert the table speed from m/min to mm/s:

$$v=5\text{m/min}=\frac{5\times 1000\text{mm}}{60\text{s}}=\frac{5000}{60}\text{mm/s}\approx 83.333\text{mm/s}$$

3. Calculate the Power consumed in grinding:
The grinding power (P) is determined by the product of the average tangential force and the grinding wheel velocity:

$$P=F_c\times V=40\text{N}\times 40\text{m/s}=1600\text{W (or J/s)}$$

4. Calculate the Material Removal Rate (MRR):
The rate at which material is removed from the workpiece during one pass is defined as:

$$\text{MRR}=v\times w\times d$$

Substituting the values:

$$\text{MRR}=\frac{5000}{60}\text{mm/s}\times 10\text{mm}\times 0.05\text{mm}=41.666{\text{mm}}^3\text{/s}$$

5. Calculate the Specific Grinding Energy (e):
Specific grinding energy is defined as the power consumed per unit volume of material removed per unit time:

$$e=\frac{P}{\text{MRR}}$$

Substituting the calculated values:

$$e=\frac{1600}{41.666}\approx 38.4{\text{J/mm}}^3$$

Thus, the value of the specific grinding energy is 38.4 J/mm³.