Question

Consider an orthogonal machining process carried out on a steel alloy of 600 MPa shear strength, the width of the cut is 10mm. The depth of cut is 0.5 mm and the chip thickness 0.7mm. The cutting speed is 2400 m/sec, the coefficient of friction is 0.364 and the rake angle of the tool is 10 oC. Estimate : a) Material removal rate b) specific power in shear c) specific power in friction

Answer 1

GIVEN:

Shear strength() = 600Mpa

Width of cut (W) = 10 mm

depth of cut () = 0.5 mm

chip thickness () = 0.7 mm

cutting speed (V) = 2400 m/s = 2400 * 10³ mm/ s

coefficient of friction () = 0.364

rake angle ( ) =

To FInd:

a) material removal rate (MRR)

b) specific power in shear

c) specific power in friction

Solution:

a) material removal rate (MRR)

Material removal rate (MRR) =

=   

= * width of cut (W) * depth of cut ()

= Velocity (V_c) * width of cut (W) * depth of cut ()

= 2400 *(10 * * 0.5 *)

= 0.012  

MRR = 12 mm³/ sec

b) specific power in shear

Specific power in shear = F_{s *} V_s

cutting ratio (r) = uncut chip thickness(t₀) / chip thickness (t₁)

r =

r = 0.71 mm

shear angle ()

from velocity triangle

By applying sine's Law

from this

  

= 600 * 10⁶ *

=

   F_s= 4811.77 N

therefore , Specific power in shear = F_{s *} V_s

_{= 4811.77 * 3571.89 Nm/sec}

_{=17187.13 KW}

c) specific power in friction

specific power in friction = F_f * V_f

similarly,from velocity triangle

By applying sine's Law

from force analysis diagram,

F_f= F_t cos + F_{c Sin ...........................(1)}

_{.............................(2)}

_{..................(3)}

_{by friction analysis}

So , substituting in (3)

_{.........................(4)}

_{subs (4) in (2)}

_{................(5)}

_{subs (4)&(5) in (1)}

F_f= F_t cos + F_{c Sin}

F_f= 1262.73cos10 + 7161.30sin 10

F_f= 2487.09 N

specific power in friction = F_f * V_f

_{= 2487.09 * 2261.32 Nm/sec}

_{= 5624.106 KW}

Result :

a) material removal rate (MRR) = 12 mm/sec

b) specific power in shear = 17187.13 KW

c) specific power in friction = 5624.106 KW