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A bar of 75 mm diameter is reduced to 73 mm by a cutting tool while cutting orthogonally. If the mean lengthof the cut chip is 73.5 mm, find the cutting ratio. If the rake angle is 15°, what is the shear angle?

Question

A bar of 75 mm diameter is reduced to 73 mm by a cutting tool while cutting orthogonally. If the mean lengthof the cut chip is 73.5 mm, find the cutting ratio. If the rake angle is 15°, what is the shear angle?

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Solution

The cutting ratio (r) can be calculated using the formula:

r = d/D

where: d = final diameter = 73 mm D = initial diameter = 75 mm

So, r = 73/75 = 0.9733

The shear angle (φ) can be calculated using the formula:

tan(φ) = rcos(α)/(1-rsin(α))

where: α = rake angle = 15°

So, φ = arctan[0.9733cos(15°)/(1-0.9733sin(15°))]

After calculating the above expression, you will get the value of the shear angle.

This problem has been solved

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