Lecture-12 Work done and Power required in metal cutting

The total work done is cutting is equal to the sum of the work done in shearing the metal and

the work done in overcoming the friction.

Now, if

 W = Total work done

W_s = Work done in shear

 W_f = Work done against friction

Then,                                                   W=W_s +W_f ……………………………………………..(1)

If no work is lost, the total work done must-be equal to the work supplied by the motor.

i.e., work supplied by the motor should be = W_s + W_f

Now, the work supplied by the motor is partly used in cutting and partly in feeding the tool. If Wm be the work supplied by the motor, then:

W_m = Work consumed in cutting+ Work spent in feeding

                   = F_e x V_e + F_t x feed velocity

In comparison to the cutting velocity the feed velocity is very nominal.

Similarly, F_t is very small as compared to F_e. So, the work spent in feeding can be considered as negligible.

Therefore,                                                          W_m = F_c x V_c   ……………………………………………….(2)

A so , under ideal conditions, i.e. when there is no loss of work ,

W_m = W

Therefore,                                                          F_c x V_c = W_s + W_f ……………………………………….(3)

Now,                                                     W_s = F_s x V_s (Shear Force x shear velocity)

And,                                                       W_f = F x V_f (Friction force x velocity of chip flow)

Or,                                                          (Fc x Vc) = (Fs x Vs) + (F x V_f)  ……………………………………(4)

In the forces are taken in KG and velocities in meters per minute, the work done will be in kgf-m/min.

Total work done per unit volume of the metal removed unit time.