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In a single pass turning operation the cutting speed is the only variable based on the cutting time cost and the cutting edge cost. The tool life for minimum cost given that cost of 1 cutting edge is Rs. 5, operator wages including the machine tool cost is Rs. 75/hour and tool life equation is VT0.1 is 100
[PI 1995]
- a)10
- b)17
- c)29
- d)36
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
In a single pass turning operation the cutting speed is the only varia...
Topt = 36 min
Most Upvoted Answer
In a single pass turning operation the cutting speed is the only varia...
The tool life equation given in the question is VT^0.1 = 100. Here, V represents the cutting speed and T represents the tool life. We need to find the tool life that minimizes the cost.
To find the cost, we need to consider two factors: cutting time cost and cutting edge cost.
1. Cutting time cost:
The cutting time cost is given by the equation C1 = (T/V) * W, where C1 is the cutting time cost, T is the tool life, V is the cutting speed, and W is the operator wages including the machine tool cost.
2. Cutting edge cost:
The cutting edge cost is given by the equation C2 = (T * E * C), where C2 is the cutting edge cost, T is the tool life, E is the number of cutting edges, and C is the cost of one cutting edge.
To minimize the cost, we need to find the tool life that minimizes the sum of the cutting time cost and the cutting edge cost. This can be expressed as the equation C = C1 + C2.
Substituting the equations for C1 and C2, we get C = (T/V) * W + (T * E * C).
To find the minimum value of C, we can differentiate it with respect to T and set the derivative equal to zero. This will give us the tool life that minimizes the cost.
Differentiating C with respect to T, we get dC/dT = (W/V) + E * C.
Setting dC/dT = 0, we get (W/V) + E * C = 0.
Simplifying the equation, we get T = -W/(E * C).
Given that C = 5 (cost of one cutting edge), W = 75 (operator wages including machine tool cost), and E = 1 (number of cutting edges), we can substitute these values into the equation to find the tool life.
T = -75/(1 * 5) = -15.
Since tool life cannot be negative, we take the absolute value of T, which gives us T = 15.
Therefore, the tool life for minimum cost is 15.
To find the cost, we need to consider two factors: cutting time cost and cutting edge cost.
1. Cutting time cost:
The cutting time cost is given by the equation C1 = (T/V) * W, where C1 is the cutting time cost, T is the tool life, V is the cutting speed, and W is the operator wages including the machine tool cost.
2. Cutting edge cost:
The cutting edge cost is given by the equation C2 = (T * E * C), where C2 is the cutting edge cost, T is the tool life, E is the number of cutting edges, and C is the cost of one cutting edge.
To minimize the cost, we need to find the tool life that minimizes the sum of the cutting time cost and the cutting edge cost. This can be expressed as the equation C = C1 + C2.
Substituting the equations for C1 and C2, we get C = (T/V) * W + (T * E * C).
To find the minimum value of C, we can differentiate it with respect to T and set the derivative equal to zero. This will give us the tool life that minimizes the cost.
Differentiating C with respect to T, we get dC/dT = (W/V) + E * C.
Setting dC/dT = 0, we get (W/V) + E * C = 0.
Simplifying the equation, we get T = -W/(E * C).
Given that C = 5 (cost of one cutting edge), W = 75 (operator wages including machine tool cost), and E = 1 (number of cutting edges), we can substitute these values into the equation to find the tool life.
T = -75/(1 * 5) = -15.
Since tool life cannot be negative, we take the absolute value of T, which gives us T = 15.
Therefore, the tool life for minimum cost is 15.
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In a single pass turning operation the cutting speed is the only varia...
Topt = 36 min
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In a single pass turning operation the cutting speed is the only variable based on the cutting time cost and the cutting edge cost. The tool life for minimum cost given that cost of 1 cutting edge is Rs. 5, operator wages including the machine tool cost is Rs. 75/hour and tool life equation is VT0.1 is 100[PI 1995]a)10b)17c)29d)36Correct answer is option 'D'. Can you explain this answer?
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In a single pass turning operation the cutting speed is the only variable based on the cutting time cost and the cutting edge cost. The tool life for minimum cost given that cost of 1 cutting edge is Rs. 5, operator wages including the machine tool cost is Rs. 75/hour and tool life equation is VT0.1 is 100[PI 1995]a)10b)17c)29d)36Correct answer is option 'D'. 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 a single pass turning operation the cutting speed is the only variable based on the cutting time cost and the cutting edge cost. The tool life for minimum cost given that cost of 1 cutting edge is Rs. 5, operator wages including the machine tool cost is Rs. 75/hour and tool life equation is VT0.1 is 100[PI 1995]a)10b)17c)29d)36Correct answer is option 'D'. 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 a single pass turning operation the cutting speed is the only variable based on the cutting time cost and the cutting edge cost. The tool life for minimum cost given that cost of 1 cutting edge is Rs. 5, operator wages including the machine tool cost is Rs. 75/hour and tool life equation is VT0.1 is 100[PI 1995]a)10b)17c)29d)36Correct answer is option 'D'. Can you explain this answer?.
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