determine the following

Question

When a work piece of 75 mm in diameter is machined on a lathe, the cutting force applied to the cutting tool is 2 500 N. Assuming that 15 Nm of torque is lost due to friction in the bearings of the spindle, Determine the following: 1. The torque required at the driving pulley of the lathe 2. The driving force required at the driving pulley of the lathe if it has an effective diameter of 250 mm. 3. The power required at the driving pulley of the lathe if it rotates at 275 r/min

Answer 1

Diameter ofthe pulley, D_P  = 75 mm = 0.075 m

Cuttingforce, F _C   = 2500 N

Torque lost due to friction , T _F   = 15 N-m

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1.

Calculate the torque required at the driving pulley:

T - T _F   = (F _C ) (D_P  / 2)

T - 15   = (2500 ) (0.075 / 2)

T  = 952.5  N-m

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2.

Calculate driving force:

T  = ( F _D  ) (Effective diameter / 2)

952.5 = ( F _D  ) (0.25/ 2)

F _D  = 7620 N

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3.

Calculate the power required:

P = 2piNT/60

    = 2piNT / 60

    = 2pi(275)(952.5) / 60

    = 99.8  W