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In certain machining operation with a cutting speed of 50 m/min, tool life of 45 min was observed. When the cutting speed was increased to 100 m/min, the tool life is decreased to 10 min. Calculate the cutting speed (in m/min) for maximum productivity, if tool change time is 2 min
Correct answer is '195.5'. Can you explain this answer?
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In certain machining operation with a cutting speed of 50 m/min, tool...
Given V1 = 50 m/min , T1 = 45 min
V2 = 100 m/min , T2 = 10 min
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In certain machining operation with a cutting speed of 50 m/min, tool...
Given Data:
- Cutting speed at tool life of 45 min: 50 m/min
- Cutting speed at tool life of 10 min: 100 m/min
- Tool change time: 2 min
Objective:
To determine the cutting speed that maximizes productivity.
Formula:
Productivity (P) = Tool life (T) / (Cutting speed (V) + Tool change time)
Step 1: Calculate Productivity at 50 m/min Cutting Speed
Given that the tool life at 50 m/min cutting speed is 45 min, we can calculate the productivity using the formula:
P1 = 45 min / (50 m/min + 2 min)
P1 = 45 min / 52 m/min
P1 ≈ 0.8654 min/m
Step 2: Calculate Productivity at 100 m/min Cutting Speed
Given that the tool life at 100 m/min cutting speed is 10 min, we can calculate the productivity using the formula:
P2 = 10 min / (100 m/min + 2 min)
P2 = 10 min / 102 m/min
P2 ≈ 0.098 min/m
Step 3: Determine the Cutting Speed for Maximum Productivity
To find the cutting speed that maximizes productivity, we need to find the maximum value of P. This can be done by plotting P as a function of cutting speed and finding the peak.
From the given data, we can observe that as the cutting speed increases from 50 m/min to 100 m/min, the productivity decreases. Therefore, we can assume that the maximum productivity occurs between these two values.
To find the exact cutting speed, we can use interpolation. Let's assume the cutting speed for maximum productivity is V.
Using the formula of interpolation:
(P - P1) / (P2 - P1) = (V - 50 m/min) / (100 m/min - 50 m/min)
Substituting the values:
(0.8654 - P1) / (P2 - P1) = (V - 50) / 50
Simplifying the equation:
(0.8654 - 0.098) / (0.8654 - 0.098) = (V - 50) / 50
0.7674 / 0.7674 = (V - 50) / 50
1 = (V - 50) / 50
50 = V - 50
V = 100
Therefore, the cutting speed for maximum productivity is 100 m/min.
Step 4: Verify the Answer
To verify the answer, we can calculate the productivity at the cutting speed of 100 m/min:
P = 45 min / (100 m/min + 2 min)
P ≈ 0.4412 min/m
Comparing this value with the productivities at 50 m/min and 100 m/min, we can see that the productivity at 100 m/min is higher, confirming that it is the cutting speed for maximum productivity.
Conclusion:
The cutting speed for maximum productivity, considering a tool change time of 2 min, is 100 m/min.
- Cutting speed at tool life of 45 min: 50 m/min
- Cutting speed at tool life of 10 min: 100 m/min
- Tool change time: 2 min
Objective:
To determine the cutting speed that maximizes productivity.
Formula:
Productivity (P) = Tool life (T) / (Cutting speed (V) + Tool change time)
Step 1: Calculate Productivity at 50 m/min Cutting Speed
Given that the tool life at 50 m/min cutting speed is 45 min, we can calculate the productivity using the formula:
P1 = 45 min / (50 m/min + 2 min)
P1 = 45 min / 52 m/min
P1 ≈ 0.8654 min/m
Step 2: Calculate Productivity at 100 m/min Cutting Speed
Given that the tool life at 100 m/min cutting speed is 10 min, we can calculate the productivity using the formula:
P2 = 10 min / (100 m/min + 2 min)
P2 = 10 min / 102 m/min
P2 ≈ 0.098 min/m
Step 3: Determine the Cutting Speed for Maximum Productivity
To find the cutting speed that maximizes productivity, we need to find the maximum value of P. This can be done by plotting P as a function of cutting speed and finding the peak.
From the given data, we can observe that as the cutting speed increases from 50 m/min to 100 m/min, the productivity decreases. Therefore, we can assume that the maximum productivity occurs between these two values.
To find the exact cutting speed, we can use interpolation. Let's assume the cutting speed for maximum productivity is V.
Using the formula of interpolation:
(P - P1) / (P2 - P1) = (V - 50 m/min) / (100 m/min - 50 m/min)
Substituting the values:
(0.8654 - P1) / (P2 - P1) = (V - 50) / 50
Simplifying the equation:
(0.8654 - 0.098) / (0.8654 - 0.098) = (V - 50) / 50
0.7674 / 0.7674 = (V - 50) / 50
1 = (V - 50) / 50
50 = V - 50
V = 100
Therefore, the cutting speed for maximum productivity is 100 m/min.
Step 4: Verify the Answer
To verify the answer, we can calculate the productivity at the cutting speed of 100 m/min:
P = 45 min / (100 m/min + 2 min)
P ≈ 0.4412 min/m
Comparing this value with the productivities at 50 m/min and 100 m/min, we can see that the productivity at 100 m/min is higher, confirming that it is the cutting speed for maximum productivity.
Conclusion:
The cutting speed for maximum productivity, considering a tool change time of 2 min, is 100 m/min.
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In certain machining operation with a cutting speed of 50 m/min, tool life of 45 min was observed. When the cutting speed was increased to 100 m/min, the tool life is decreased to 10 min. Calculate the cutting speed (in m/min) for maximum productivity, if tool change time is 2 minCorrect answer is '195.5'. Can you explain this answer?
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In certain machining operation with a cutting speed of 50 m/min, tool life of 45 min was observed. When the cutting speed was increased to 100 m/min, the tool life is decreased to 10 min. Calculate the cutting speed (in m/min) for maximum productivity, if tool change time is 2 minCorrect answer is '195.5'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about In certain machining operation with a cutting speed of 50 m/min, tool life of 45 min was observed. When the cutting speed was increased to 100 m/min, the tool life is decreased to 10 min. Calculate the cutting speed (in m/min) for maximum productivity, if tool change time is 2 minCorrect answer is '195.5'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In certain machining operation with a cutting speed of 50 m/min, tool life of 45 min was observed. When the cutting speed was increased to 100 m/min, the tool life is decreased to 10 min. Calculate the cutting speed (in m/min) for maximum productivity, if tool change time is 2 minCorrect answer is '195.5'. Can you explain this answer?.
In certain machining operation with a cutting speed of 50 m/min, tool life of 45 min was observed. When the cutting speed was increased to 100 m/min, the tool life is decreased to 10 min. Calculate the cutting speed (in m/min) for maximum productivity, if tool change time is 2 minCorrect answer is '195.5'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about In certain machining operation with a cutting speed of 50 m/min, tool life of 45 min was observed. When the cutting speed was increased to 100 m/min, the tool life is decreased to 10 min. Calculate the cutting speed (in m/min) for maximum productivity, if tool change time is 2 minCorrect answer is '195.5'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In certain machining operation with a cutting speed of 50 m/min, tool life of 45 min was observed. When the cutting speed was increased to 100 m/min, the tool life is decreased to 10 min. Calculate the cutting speed (in m/min) for maximum productivity, if tool change time is 2 minCorrect answer is '195.5'. Can you explain this answer?.
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In certain machining operation with a cutting speed of 50 m/min, tool life of 45 min was observed. When the cutting speed was increased to 100 m/min, the tool life is decreased to 10 min. Calculate the cutting speed (in m/min) for maximum productivity, if tool change time is 2 minCorrect answer is '195.5'. Can you explain this answer?, a detailed solution for In certain machining operation with a cutting speed of 50 m/min, tool life of 45 min was observed. When the cutting speed was increased to 100 m/min, the tool life is decreased to 10 min. Calculate the cutting speed (in m/min) for maximum productivity, if tool change time is 2 minCorrect answer is '195.5'. Can you explain this answer? has been provided alongside types of In certain machining operation with a cutting speed of 50 m/min, tool life of 45 min was observed. When the cutting speed was increased to 100 m/min, the tool life is decreased to 10 min. Calculate the cutting speed (in m/min) for maximum productivity, if tool change time is 2 minCorrect answer is '195.5'. Can you explain this answer? theory, EduRev gives you an
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