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leonid [27]
3 years ago
14

In a machining operation that approximates orthogonal cutting, the cutting tool has a rake angle =100 . The chip thickness ratio

is 0.5. Calculate the shear plane angle and the shear velocity in the operation. Main Cutting force = 400N, thrust force = 200N. Calculate the percentage of the total energy dissipated into shear plane, if V = 3 m/s.
Physics
1 answer:
Rudik [331]3 years ago
6 0

Answer:

The percentage of the total energy dissipated into shear plane is 89.46%.

Explanation:

Given that,

Rake angle = 10°

Thickness ratio= 0.5

Cutting Force = 400 N

Thrust force = 200 N

Speed =3 m/s

Suppose the shear force is 345.21 N.

We need to calculate the shear plane angle

Using formula shear angle

\tan\phi=\dfrac{r\cos\alpha}{1-r\sin\alpha}

Put the value in to the formula

\tan\phi=\dfrac{0.5\cos10}{1-0.5\sin10}

\tan\phi=0.539

\phi=\tan^{-1}(0.539)

\phi=28.32^{\circ}

We need to calculate the shear velocity

Using formula of shear velocity

v_{2}=\dfrac{v\cos\alpha}{\cos(\phi-\alpha)}

Put the value into the formula

v_{2}=\dfrac{3\times\cos10}{\cos(28.32-10)}

v_{2}=3.11\ m/s

We need to calculate the percentage of the total energy dissipated into shear plane

Using formula of energy dissipated

\%d=\dfrac{P_{s}}{P}\times100

\%d=\dfrac{F_{s}\times v_{c}}{F_{c}\times v}\times100

Put the value into the formula

\%d=\dfrac{345.21\times3.11}{400\times3}\times100

d=89.46\%

Hence, The percentage of the total energy dissipated into shear plane is 89.46%.

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