In a batch production of mild steel shafts by machining, the following observations were made: Total idle time per piece is 20 min. Actual machining time per piece is 20 min. Life... In a batch production of mild steel shafts by machining, the following observations were made: Total idle time per piece is 20 min. Actual machining time per piece is 20 min. Life of each tool-tip is 10 min. Time required to replace a tool-tip is 5 min. The total time that will be required to produce each piece is ___ minutes.
Understand the Problem
The question is asking for the total time required to produce each piece of mild steel shafts by taking into account the idle time, actual machining time, and the time needed to replace tool-tips. We will calculate it by summing these times appropriately based on the number of tool-tips used.
Answer
The total time that will be required to produce each piece is 45 minutes.
Answer for screen readers
The total time that will be required to produce each piece is 45 minutes.
Steps to Solve
- Calculate total idle and machining time
The total idle time per piece is 20 minutes, and the actual machining time per piece is also 20 minutes.
Total idle and machining time:
$$ \text{Total idle and machining time} = \text{Idle time} + \text{Machining time} $$
$$ = 20 , \text{min} + 20 , \text{min} = 40 , \text{min} $$
- Determine the number of tool-tips needed
The life of each tool-tip is 10 minutes. For a machining time of 20 minutes, we need to calculate how many tool-tips are needed.
$$ \text{Number of tool-tips} = \frac{\text{Machining time}}{\text{Life of tool-tip}} = \frac{20 , \text{min}}{10 , \text{min}} = 2 $$
- Calculate total replacement time for the tool-tips
The time required to replace each tool-tip is 5 minutes. Since we need to replace the tool-tip after its life, we will have one replacement for the second tool-tip.
Total replacement time:
$$ \text{Total replacement time} = (\text{Number of replacements}) \times (\text{Time to replace}) $$
$$ = (2 - 1) \times 5 , \text{min} = 1 \times 5 , \text{min} = 5 , \text{min} $$
- Calculate total time to produce each piece
Now, sum all the times to find the total time required to produce each piece:
$$ \text{Total time} = \text{Total idle and machining time} + \text{Total replacement time} $$
$$ = 40 , \text{min} + 5 , \text{min} = 45 , \text{min} $$
The total time that will be required to produce each piece is 45 minutes.
More Information
This calculation takes into account the idle time, actual machining time, and the time required for tool-tip replacements, ensuring a comprehensive overview of the total production time in the machining process.
Tips
- Not calculating the number of tool-tips correctly based on the machining time and tool-tip life.
- Failing to include replacement time if more than one tool-tip is needed.
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