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

drawing ratio = 1.81176

reduction = 0.4480 = 44.80 %

drawing force is = 162724.682 lb

blank holder force = 95481.10 lb

Step-by-step 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 =
`(blank\ diameter)/(cup\ diameter)` ..................1

put here value

drawing ratio =
`(7.7)/(4.25)`

drawing ratio = 1.81176

and

reduction will be here

reduction =
`(blank\ diameter - cup\ diameter)/(blank\ diameter)` .................2

reduction =
`(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 ×
`(3)/(16)` × 65000

drawing force is = 162724.682 lb

and

blank holder force will be here as

blank holder force = maximum punch load ×
`(1)/(3)` ........................4

so here maximum punch load will be

maximum punch load = π × punch diameter × stock thickness × tensile strength × (
`(blank\ diameter)/(punch\ diameter)` - 0.7 ) .......................5

here 0.7 is correction factor

maximum punch load = π × 0.3125 ×
`(3)/(16)` × 65000 × (
`(7.7)/(0.3125)` - 0.7 )

maximum punch load = 286443.30 lb

so

blank holder force = 286443.30 ×
`(1)/(3)`

blank holder force = 95481.10 lb