In a turning operation on stainless steel with hardness = 200 HB, the cutting speed = 200 m/min, feed = 0.25 mm/rev, and depth of cut = 3.5 mm. How much power will the lathe draw in performing this operation if its mechanical efficiency = 90%?

Respuesta :

Answer:

Gross power perform this operation is 9.07 kW

Explanation:

Given :

Cutting speed [tex]v = 200 \times 10^{3}[/tex] [tex]\frac{mm}{min}[/tex]

Feed [tex]f = 0.25[/tex] mm

Depth of cut [tex]d = 3.5[/tex] mm

Mechanical efficiency [tex]\eta = 0.90[/tex]

First find the material removal rate,

  [tex]R = v \times f \times d[/tex]

  [tex]R = 200 \times 10^{3} \times 0.25 \times 3.5[/tex]

  [tex]R = 175000[/tex] [tex]\frac{mm^{2} }{min}[/tex]

  [tex]R = \frac{175000}{60} = 2916.67[/tex] [tex]\frac{mm^{2} }{sec}[/tex]

From the standard table,

Specific cutting energy [tex]U = 2.8 \frac{J}{mm^{2} }[/tex]

Cutting power,

  [tex]P = 2916.67 \times 2.8[/tex]

  [tex]P = 8166.67[/tex] W

We know that gross power is given by,

 [tex]P_{gross} = \frac{P}{\eta}[/tex]

 [tex]P_{gross} = \frac{8166.67}{0.90}[/tex]

 [tex]P_{gross} = 9074.07[/tex] W

 [tex]P_{gross} = 9.07[/tex] kW

Therefore, gross power perform this operation is 9.07 kW

The amount of power that the lathe will draw in performing the given operation at the given mechanical efficiency is; 9.074 kW

We are given;

  • Cutting speed; v = 200 m/min = 200000 mm/min
  • Feed; f = 0.25 mm/rev
  • Depth of cut; d = 3.5 mm
  • Mechanical efficiency; η = 90% = 0.9

  • Formula for material removal rate is;

R = vfd

Thus;

R = 200000 × 0.25 × 3.5

R = 175,000 mm³/min

Converting to mm³/s gives;

R = 2916.67 mm³/s

  • From the table attached and by interpolation, the specific cutting energy is; U = 2.8 J/mm³

Thus;

Gross power = RU/η

Gross power = 2916.67 × 2.8/0.9

Gross power = 9074.08 W

Gross power = 9.074kW

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