If α is the rake angle of the cutting tool, φ is the shear angle and \upsilon is the cutting velocity, then the velocity of chip sliding along the shear plane is given by (A) {\upsilon\cos\alpha}/{\sin(\phi -\alpha) (B) {\upsilon\sin\alpha}/{\sin\alpha(\phi -\alpha) (C) {\upsilon\sin\alpha}/{\cos(\phi -\alpha) (D) {\upsilon\cos\alpha}/{\cos(\phi -\alpha)

SSC JE Mechanical Engineering 2018 Set 1 Paper

Question : 186 of 200

Marks: +1, -0

If α is the rake angle of the cutting tool, φ is the shear angle and

υ

is the cutting velocity, then the velocity of chip sliding along the shear plane is given by
(A)

{υ\cosα}/{\sin(φ -α)

(B)

{υ\sinα}/{\sinα(φ -α)

(C)

{υ\sinα}/{\cos(φ -α)

(D)

{υ\cosα}/{\cos(φ -α)

Solution:

From Lami’s theorem

V_c/{\sinϕ}=V_s/{\sin(90-α)}

=V/{\sin (90-(ϕ-α))}

V/{\cos(ϕ-α)}

where

V_c

= chip velocity

V_s

= shear velocity
V = cutting velocity
α = rake angle
ϕ = shear angle
velocity of chip along the shear plane

V_c/{\sinϕ}=V_s/{\cosα}

⇒V_c={V_s\sinϕ}/{\cosα}

V_c/{\sinϕ}=V/{\cos(ϕ-α)}

V_c={V\sinϕ}/{\cos (ϕ-α)}

Go to Question:

Prev Question

Next Question