A 20 mm diameter drill with point angle 120° is used to drill a throu...
Given data:
Diameter of drill (D) = 20 mm
Point angle (α) = 120°
Thickness of plate (L) = 30 mm
Feed rate (f) = 0.1 mm/rev
Cutting velocity (V) = 20 m/min
Length of approach (a) = 2 mm
Length of over travel (o) = 3 mm
Calculating the time required for drilling:
To calculate the time required for drilling, we need to determine the total distance traveled by the drill.
1. Calculating the distance traveled during approach:
During the approach, the drill advances into the material until it reaches the desired depth. The length of approach is given as 2 mm.
Therefore, the distance traveled during approach (Da) can be calculated as:
Da = π * D * a
= π * 20 mm * 2 mm
= 40π mm
2. Calculating the distance traveled during drilling:
During drilling, the drill advances through the entire thickness of the plate. The length of drilling is equal to the thickness of the plate (L) minus the length of approach (a) and over travel (o).
Therefore, the distance traveled during drilling (Dd) can be calculated as:
Dd = π * D * (L - a - o)
= π * 20 mm * (30 mm - 2 mm - 3 mm)
= π * 20 mm * 25 mm
= 500π mm
3. Calculating the distance traveled during retraction:
During retraction, the drill is withdrawn from the hole. The length of retraction is equal to the over travel (o).
Therefore, the distance traveled during retraction (Dr) can be calculated as:
Dr = π * D * o
= π * 20 mm * 3 mm
= 60π mm
4. Calculating the total distance traveled:
The total distance traveled (Dt) is the sum of the distances traveled during approach, drilling, and retraction.
Therefore, the total distance traveled (Dt) can be calculated as:
Dt = Da + Dd + Dr
= 40π mm + 500π mm + 60π mm
= 600π mm
5. Calculating the time required:
The time required for drilling can be calculated using the formula:
Time = Distance / Velocity
Therefore, the time required for drilling can be calculated as:
Time = Dt / V
= (600π mm) / (20 m/min)
= (600π mm) / (0.02 m/min)
≈ 9549.3 min
Final answer:
Rounding off to one decimal place, the time required for drilling is approximately 1.1 min.