Question

A deep drawing operation is performed in which the inside of the cylindrical cup has a diameter of 4.25 in and a height = 2.65 in. The stock thickness = 3/16 in, and the starting blank diameter = 7.7 in. Punch and die radii = 5/32 in. The metal has a tensile strength = 65,000 lb/in2, a yield strength = 32,000 lb/in2, and a shear strength of 40,000 lb/in2. Determine (a) drawing ratio, (b) reduction, (c) drawing force, and (d) blankholder force

Answer 1

Answer:

drawing ratio = 1.81176

reduction = 0.4480 = 44.80 %

drawing force is = 162724.682 lb

blank holder force = 95481.10 lb

Explanation:

given data

cylindrical cup diameter = 4.25 in

cup height = 2.65 in

stock thickness = 3/16 in

blank diameter = 7.7 in

Punch and die radii = 5/32 in

so Punch diameter will be = 2 ×  5/32 in = 0.3125 in

tensile strength = 65,000 lb/in²

yield strength = 32,000 lb/in²

shear strength of 40,000 lb/in²

to find out

(a) drawing ratio, (b) reduction, (c) drawing force, and (d) blankholder force

solution

first we get drawing ratio hat is express as

drawing ratio = $\frac{blank\ diameter}{cup\ diameter}$     ..................1

put here value

drawing ratio = $\frac{7.7}{4.25}$

drawing ratio = 1.81176

and

reduction will be here

reduction = $\frac{blank\ diameter - cup\ diameter}{blank\ diameter}$  .................2

reduction = $\frac{7.7 - 4.25}{7.7}$

reduction = 0.4480 = 44.80 %

and

drawing force will be

drawing force is = k× π× cup diameter ×  stock thickness × tensile strength   ........................3

here k = 1

so put here value

drawing force is = 1 × π× 4.25 × $\frac{3}{16}$ × 65000

drawing force is = 162724.682 lb

and

blank holder force will be here as

blank holder force = maximum punch load × $\frac{1}{3}$     ........................4

so here maximum punch load will be

maximum punch load = π × punch diameter × stock thickness × tensile strength × ( $\frac{blank\ diameter}{punch\ diameter}$ - 0.7 )     .......................5

here 0.7 is correction factor

maximum punch load = π × 0.3125 × $\frac{3}{16}$  × 65000 × ( $\frac{7.7}{0.3125}$ - 0.7 )

maximum punch load  = 286443.30 lb

so

blank holder force =  286443.30 × $\frac{1}{3}$

blank holder force = 95481.10 lb