Topic: Manufacturing Engineering
The optimum cutting speed for maximum production is ('n' is tool constant and '$T_{c}$' is time required to change the tool)
- A. $\frac{k}{[\{\frac{1}{n}+1\}T_{c}]^{\frac{n}{2}}}$
- B. $\frac{k}{[\{\frac{1}{n}-1\}T_{c}]^{n}}$
- C. $\frac{k}{[\{1-\frac{1}{n}\}T_{c}]^{2n}}$
- D. $\frac{k}{[\{\frac{1}{n}-1\}\frac{T_{c}}{2}]^{n}}$
Answer: B. $\frac{k}{[\{\frac{1}{n}-1\}T_{c}]^{n}}$
Explanation: For maximum production rate, the optimum tool life is given by $T_{opt} = \left(\frac{1}{n}-1\right)T_{c}$. According to Taylor's tool life equation $V T^n = k$, the optimum cutting speed is $V_{opt} = \frac{k}{T_{opt}^n} = \frac{k}{[\{\frac{1}{n}-1\}T_{c}]^{n}}$.