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A high-speed steel tool is used to turn a steel work part with length = 350 mm and diameter = 70 mm. The parameters in the Taylor equation are n = 0.13 and C = 75 (m/min) for a feed of 0.4 mm/rev. The operator and machine tool rate = $36.00/hr, and the tooling cost per cutting edge = $4.25. It takes 5.0 min to load and unload the work part and 4.0 min to change tools. Determine the cutting speed for minimum cost.

Respuesta :

raphealnwobi

Answer:

42.85 m/min

Explanation:

To save cost, the tools should not be changed frequently if the tool cost or tool change time is high

[tex]The\ operator\ and\ machine\ tool\ rate =C_o=\$36/hr=\frac{\$36}{1\ hr*\frac{60\ min}{1\ hr} } =\$0.6/min[/tex]

The tooling cost per cutting edge = [tex]C_t[/tex] = $4.25

n = 0.13, C=75 (m/min), tool change time = [tex]t_t=4\ min[/tex]

Therefore the cutting speed for minimum cost is given as:

[tex]v_{max}=\frac{C}{[\frac{C_o}{(\frac{1}{n}-1 )(C_o*t_t+c_t)} ]^n} \\\\Substituting:\\\\v_{max}=75{[\frac{0.6}{(\frac{1}{0.13}-1 )(0.6*4+4.25)} ]^{0.13}} \\\\v_{max}=42.85\ m/min[/tex]