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Discuss the geometry and design steps for a broach tool with the help of diagram

Diagram of broach :

Let,

n = Total number of teeth in the broach

L = Effective length of a broach in mm

P - Tool pitch in mm

L = Length to be broached in mm

t - Rise per tooth in mm

$n_s$ = Number of safety teeth

$n_f$ Number of finishing teeth ( Range, 3 to 6 )

1) Tool pitch (p) : p = 1.75 $\sqrt{l}$

2) Rise per tooth (t) :

Total rise = No. of teeth in broach x rise per tooth

= n x t

3) Total number of teeth in the broach (n)

n = (Roughing teeth) + (finishing teeth)

n = ( $\frac{depth \ of \ cut}{cut \ per \ tooth}$ ) + ( $n_s$ + $n_f$)

n = ( $\frac{total \ rise}{rise \ per \ tooth}$ ) + ( $n_s$ + $n_f$)

4) Effective length (L)

L = No. of teeth in broach x pitch

= n x p

5) Total load on a broach (F)

a) for round holes

f = Hole circumference x N X t x K

= $\pi$ d x N X t x K

b) For square holes

f = Hole perimeter x N X t x K

= 4 H x N x t x K

Where,

d = finished hole dia in mm

N = Maximum no. of teeth cutting at a time

t = Rise per tooth in mm

K = Force required to cut 1 mm and 2 mm of metal at a given rise per tooth

H = Finished length of one side of square hole in mm

6) Total effective length ( $L_T$ )

$L_T$ = Length of roughing teeth + Length of finishing teeth = No. of roughing teeth x pitch + No. of finishing teeth x $\frac{pitch}{2}$

$L_T$ = $n_r$ x p + $n_f$ x $\frac{p}{2}$

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