Mechanical Engineering Exam > Mechanical Engineering Questions > In a certain machining operation with cutting...
Start Learning for Free
In a certain machining operation with cutting speed of 50m/min, tool life of 45 min was observed; when the cutting speed was increased to 100m/min, tool life decreased to 10 min. The cutting speed for maximum productivity if tool change time is 2 minutes is:
- a)194.5 m/min
- b)110 m/min
- c)54 m/min
- d)260 m/min
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
In a certain machining operation with cutting speed of 50m/min, tool l...
Most Upvoted Answer
In a certain machining operation with cutting speed of 50m/min, tool l...
Given information:
- Cutting speed = 50 m/min, Tool life = 45 min
- Cutting speed = 100 m/min, Tool life = 10 min
- Tool change time = 2 min
Analysis:
Tool life is the time taken for a cutting tool to become worn out or damaged to an extent that it needs to be replaced. It is affected by factors like cutting speed, feed rate, and depth of cut.
To maximize productivity, we need to find the cutting speed that gives the maximum tool life.
Solution:
We can use Taylor's tool life equation to find the relationship between cutting speed and tool life:
VT^n = C
Where V is the cutting speed, T is the tool life, n is the tool life exponent, and C is a constant.
Step 1: Find the tool life exponent (n)
Using the given data:
50^𝑛 × 45 = 𝐶
(100/2)^𝑛 × 10 = 𝐶
Simplifying the equations:
50^𝑛 × 45 = 𝐶
5000^𝑛 = 𝐶
Taking the ratio of the two equations:
(50^𝑛 × 45) / (5000^𝑛 × 10) = 45 / 10
Simplifying the ratio:
5000^𝑛 / 50^𝑛 = 9
Taking the logarithm of both sides:
log(5000^𝑛 / 50^𝑛) = log(9)
n × log(5000/50) = log(9)
n = log(9) / log(5000/50)
Calculating the value of n:
n ≈ 0.256
Step 2: Find the cutting speed for maximum productivity
Substituting the values of n and tool life into the Taylor's tool life equation:
V × 45^0.256 = C
V × 10^0.256 = C
Simplifying the equations:
V × 1.517 = C
V × 1.080 = C
Taking the ratio of the two equations:
(V × 1.517) / (V × 1.080) = 1.517 / 1.080
Simplifying the ratio:
1.517 / 1.080 = V / V
1.405 = 1
Since the ratio is equal to 1, it means that the cutting speed has no effect on the tool life.
Step 3: Find the cutting speed for maximum productivity
To maximize productivity, we need to minimize the total machining time. The total machining time is the sum of the tool life and the tool change time.
Total machining time = Tool life + Tool change time
For the given data:
Total machining time = 45 + 2 = 47 min
Total machining time = 10 + 2 = 12 min
To maximize productivity, we need to minimize the total machining time.
Since the cutting speed has no effect on the tool life, we can choose the cutting speed that gives the minimum total machining time.
Therefore, the cutting speed for maximum productivity is the one that gives the minimum total machining time, which is 50 m
- Cutting speed = 50 m/min, Tool life = 45 min
- Cutting speed = 100 m/min, Tool life = 10 min
- Tool change time = 2 min
Analysis:
Tool life is the time taken for a cutting tool to become worn out or damaged to an extent that it needs to be replaced. It is affected by factors like cutting speed, feed rate, and depth of cut.
To maximize productivity, we need to find the cutting speed that gives the maximum tool life.
Solution:
We can use Taylor's tool life equation to find the relationship between cutting speed and tool life:
VT^n = C
Where V is the cutting speed, T is the tool life, n is the tool life exponent, and C is a constant.
Step 1: Find the tool life exponent (n)
Using the given data:
50^𝑛 × 45 = 𝐶
(100/2)^𝑛 × 10 = 𝐶
Simplifying the equations:
50^𝑛 × 45 = 𝐶
5000^𝑛 = 𝐶
Taking the ratio of the two equations:
(50^𝑛 × 45) / (5000^𝑛 × 10) = 45 / 10
Simplifying the ratio:
5000^𝑛 / 50^𝑛 = 9
Taking the logarithm of both sides:
log(5000^𝑛 / 50^𝑛) = log(9)
n × log(5000/50) = log(9)
n = log(9) / log(5000/50)
Calculating the value of n:
n ≈ 0.256
Step 2: Find the cutting speed for maximum productivity
Substituting the values of n and tool life into the Taylor's tool life equation:
V × 45^0.256 = C
V × 10^0.256 = C
Simplifying the equations:
V × 1.517 = C
V × 1.080 = C
Taking the ratio of the two equations:
(V × 1.517) / (V × 1.080) = 1.517 / 1.080
Simplifying the ratio:
1.517 / 1.080 = V / V
1.405 = 1
Since the ratio is equal to 1, it means that the cutting speed has no effect on the tool life.
Step 3: Find the cutting speed for maximum productivity
To maximize productivity, we need to minimize the total machining time. The total machining time is the sum of the tool life and the tool change time.
Total machining time = Tool life + Tool change time
For the given data:
Total machining time = 45 + 2 = 47 min
Total machining time = 10 + 2 = 12 min
To maximize productivity, we need to minimize the total machining time.
Since the cutting speed has no effect on the tool life, we can choose the cutting speed that gives the minimum total machining time.
Therefore, the cutting speed for maximum productivity is the one that gives the minimum total machining time, which is 50 m
Attention Mechanical Engineering Students!
To make sure you are not studying endlessly, EduRev has designed Mechanical Engineering study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Mechanical Engineering.
|
Explore Courses for Mechanical Engineering exam
|
|
Similar Mechanical Engineering Doubts
Top Courses for Mechanical EngineeringView all
In a certain machining operation with cutting speed of 50m/min, tool life of 45 min was observed; when the cutting speed was increased to 100m/min, tool life decreased to 10 min. The cutting speed for maximum productivity if tool change time is 2 minutes is:a)194.5 m/minb)110 m/minc)54 m/mind) 260 m/minCorrect answer is option 'A'. Can you explain this answer?
Question Description
In a certain machining operation with cutting speed of 50m/min, tool life of 45 min was observed; when the cutting speed was increased to 100m/min, tool life decreased to 10 min. The cutting speed for maximum productivity if tool change time is 2 minutes is:a)194.5 m/minb)110 m/minc)54 m/mind) 260 m/minCorrect answer is option 'A'. 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 certain machining operation with cutting speed of 50m/min, tool life of 45 min was observed; when the cutting speed was increased to 100m/min, tool life decreased to 10 min. The cutting speed for maximum productivity if tool change time is 2 minutes is:a)194.5 m/minb)110 m/minc)54 m/mind) 260 m/minCorrect answer is option 'A'. 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 certain machining operation with cutting speed of 50m/min, tool life of 45 min was observed; when the cutting speed was increased to 100m/min, tool life decreased to 10 min. The cutting speed for maximum productivity if tool change time is 2 minutes is:a)194.5 m/minb)110 m/minc)54 m/mind) 260 m/minCorrect answer is option 'A'. Can you explain this answer?.
In a certain machining operation with cutting speed of 50m/min, tool life of 45 min was observed; when the cutting speed was increased to 100m/min, tool life decreased to 10 min. The cutting speed for maximum productivity if tool change time is 2 minutes is:a)194.5 m/minb)110 m/minc)54 m/mind) 260 m/minCorrect answer is option 'A'. 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 certain machining operation with cutting speed of 50m/min, tool life of 45 min was observed; when the cutting speed was increased to 100m/min, tool life decreased to 10 min. The cutting speed for maximum productivity if tool change time is 2 minutes is:a)194.5 m/minb)110 m/minc)54 m/mind) 260 m/minCorrect answer is option 'A'. 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 certain machining operation with cutting speed of 50m/min, tool life of 45 min was observed; when the cutting speed was increased to 100m/min, tool life decreased to 10 min. The cutting speed for maximum productivity if tool change time is 2 minutes is:a)194.5 m/minb)110 m/minc)54 m/mind) 260 m/minCorrect answer is option 'A'. Can you explain this answer?.
Solutions for In a certain machining operation with cutting speed of 50m/min, tool life of 45 min was observed; when the cutting speed was increased to 100m/min, tool life decreased to 10 min. The cutting speed for maximum productivity if tool change time is 2 minutes is:a)194.5 m/minb)110 m/minc)54 m/mind) 260 m/minCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
Download more important topics, notes, lectures and mock test series for Mechanical Engineering Exam by signing up for free.
Here you can find the meaning of In a certain machining operation with cutting speed of 50m/min, tool life of 45 min was observed; when the cutting speed was increased to 100m/min, tool life decreased to 10 min. The cutting speed for maximum productivity if tool change time is 2 minutes is:a)194.5 m/minb)110 m/minc)54 m/mind) 260 m/minCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
In a certain machining operation with cutting speed of 50m/min, tool life of 45 min was observed; when the cutting speed was increased to 100m/min, tool life decreased to 10 min. The cutting speed for maximum productivity if tool change time is 2 minutes is:a)194.5 m/minb)110 m/minc)54 m/mind) 260 m/minCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for In a certain machining operation with cutting speed of 50m/min, tool life of 45 min was observed; when the cutting speed was increased to 100m/min, tool life decreased to 10 min. The cutting speed for maximum productivity if tool change time is 2 minutes is:a)194.5 m/minb)110 m/minc)54 m/mind) 260 m/minCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of In a certain machining operation with cutting speed of 50m/min, tool life of 45 min was observed; when the cutting speed was increased to 100m/min, tool life decreased to 10 min. The cutting speed for maximum productivity if tool change time is 2 minutes is:a)194.5 m/minb)110 m/minc)54 m/mind) 260 m/minCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice In a certain machining operation with cutting speed of 50m/min, tool life of 45 min was observed; when the cutting speed was increased to 100m/min, tool life decreased to 10 min. The cutting speed for maximum productivity if tool change time is 2 minutes is:a)194.5 m/minb)110 m/minc)54 m/mind) 260 m/minCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
|
|
Explore Courses for Mechanical Engineering exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup