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A CNC vertical milling machine has to cut a straight slot of 10 mm width and 2 mm depth by a cutter of 10 mm diameter between points (0, 0) and (100, 100) on the XY plane (dimensions in mm). The feed rate used for milling is 50 mm/min. Milling time for the slot (in seconds) is
- a)120
- b)170
- c)180
- d)240
Correct answer is option 'B'. Can you explain this answer?
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To determine the milling time for the slot, we need to consider the following factors:
1. Cutting speed
2. Feed rate
3. Slot dimensions
1. Cutting Speed:
The cutting speed is the speed at which the cutter moves through the material. It is usually measured in meters per minute (m/min) or millimeters per minute (mm/min). In this case, the cutting speed is not provided directly, but we can calculate it using the cutter diameter and the rotational speed.
Given that the cutter diameter is 10 mm, we can calculate the circumference of the cutter using the formula:
C = π * d
where C is the circumference and d is the diameter.
C = π * 10 mm = 31.42 mm
To convert the cutting speed from mm/min to m/min, we divide by 1000:
Cutting speed = 31.42 mm/min / 1000 = 0.03142 m/min
2. Feed Rate:
The feed rate is the speed at which the workpiece moves relative to the cutter during the milling operation. It is usually measured in meters per minute (m/min) or millimeters per minute (mm/min). In this case, the feed rate is given as 50 mm/min.
3. Slot Dimensions:
The slot has a width of 10 mm and a depth of 2 mm. The distance between the two points (0, 0) and (100, 100) on the XY plane is the length of the slot. We can calculate the length using the distance formula:
Length = √[(x2 - x1)^2 + (y2 - y1)^2]
Length = √[(100 - 0)^2 + (100 - 0)^2]
Length = √(100^2 + 100^2)
Length = √(20000)
Length = 141.42 mm
Now, let's calculate the milling time for the slot:
Milling time = Length / (Cutting speed * Feed rate)
Milling time = 141.42 mm / (0.03142 m/min * 50 mm/min)
Milling time = 141.42 mm / (0.001571 m²/min)
Milling time = 90,000 min
Converting minutes to seconds:
Milling time = 90,000 min * 60 s/min
Milling time = 5,400,000 s
Therefore, the milling time for the slot is approximately 5,400,000 seconds, which is not one of the given options. It seems there might be an error in the options provided, as none of them match the calculated milling time.
1. Cutting speed
2. Feed rate
3. Slot dimensions
1. Cutting Speed:
The cutting speed is the speed at which the cutter moves through the material. It is usually measured in meters per minute (m/min) or millimeters per minute (mm/min). In this case, the cutting speed is not provided directly, but we can calculate it using the cutter diameter and the rotational speed.
Given that the cutter diameter is 10 mm, we can calculate the circumference of the cutter using the formula:
C = π * d
where C is the circumference and d is the diameter.
C = π * 10 mm = 31.42 mm
To convert the cutting speed from mm/min to m/min, we divide by 1000:
Cutting speed = 31.42 mm/min / 1000 = 0.03142 m/min
2. Feed Rate:
The feed rate is the speed at which the workpiece moves relative to the cutter during the milling operation. It is usually measured in meters per minute (m/min) or millimeters per minute (mm/min). In this case, the feed rate is given as 50 mm/min.
3. Slot Dimensions:
The slot has a width of 10 mm and a depth of 2 mm. The distance between the two points (0, 0) and (100, 100) on the XY plane is the length of the slot. We can calculate the length using the distance formula:
Length = √[(x2 - x1)^2 + (y2 - y1)^2]
Length = √[(100 - 0)^2 + (100 - 0)^2]
Length = √(100^2 + 100^2)
Length = √(20000)
Length = 141.42 mm
Now, let's calculate the milling time for the slot:
Milling time = Length / (Cutting speed * Feed rate)
Milling time = 141.42 mm / (0.03142 m/min * 50 mm/min)
Milling time = 141.42 mm / (0.001571 m²/min)
Milling time = 90,000 min
Converting minutes to seconds:
Milling time = 90,000 min * 60 s/min
Milling time = 5,400,000 s
Therefore, the milling time for the slot is approximately 5,400,000 seconds, which is not one of the given options. It seems there might be an error in the options provided, as none of them match the calculated milling time.
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A CNC vertical milling machine has to cut a straight slot of 10 mm width and 2 mm depth by a cutter of 10 mm diameter between points (0, 0) and (100, 100) on the XY plane (dimensions in mm).The feed rate used for milling is 50 mm/min. Milling time for the slot (in seconds) isa)120b)170c)180d)240Correct answer is option 'B'. Can you explain this answer?
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