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Drawing Force F= D p t (TS )
Blank Holder Force Fh= 0.015 (YS) ( Db2 − ( D p + 2.2t + 2Ra ) 2 )
Volume of cylinder πr2 h
True Stress = Y f = K n
Forging Factor = K f = 1 +
Bending force= F =
K bf (TS ) wt 2
, Kbf for the V bending is 1.33, edge bending 0.33
Forging Force F = K f Y f A
True Strain = ln
K x = 0.98 + 0.02 x
x = a + b ln rx
p = K x average flow stress ( x +
Merchant equation= = 45 +
Average Flow Stress=
True Strain = ln
2πr(rotational speed)= Linear speed
Theoretical surface finish=(f2/32NR)
vTN=C (Taylor tool life)
1. The workpart in a turning operation is 88 min in diameter and 400 mm long. A feed of 0.25
mm/rev is used in this operation. If cutting speed is 3.5 m/s, the too should be changed in
every 3 workparts, but if the cutting speed is 2.5 m/sec, the tool can be used to produce 20
pieces between the tool changes. Determine the cutting speed that will allow the tool to be
used for 50 parts between tool changes.
2. Tool life tests in turning yield the following data: (1) when cutting speed is 100 m/min, tool
life is 10 min; (2) when cutting speed is 75 m/min, tool life is 30 min. (a) Determine the n
and C values in the Taylor tool life equation. Based on your equation, compute (b) the tool
life for a speed of 110 m/min, and (c) the speed corresponding to a tool life of 15 min.
3. A sheet metal 5 mm thick and 20 mm long is bent to included angle of 60° and a bend
radius of 7.5 mm in an edge bending die. The metal has a yield strength of the 220 MPa,
and tensile strength of 340 MPa. Compute the required force to bend the part, given that the
die opening dimension is 15 mm.
4. A cup-drawing operation is performed in which the inside diameter = 80 mm and the
height = 50 mm. Stock thickness = 3.0 mm, and starting blank diameter = 130 mm. Punch
and die radii = 4 mm. Tensile strength = 400 MPa and yield strength = 180 MPa for this
sheet metal. Determine (a) drawing ratio, (b) reduction, (c) drawing force, and (d)
5. Bar stock of initial diameter = 90 mm is drawn with a draft = 10 mm. The draw die has an
entrance angle = 18, and the coefficient of friction at the work-die interface = 0.08. The
metal behaves as a perfectly plastic material with yield stress = 105 MPa. Determine (a)
area reduction, (b) draw stress, (c) draw force required for the operation, and (d) power to
perform the operation if exit velocity = 1.0 m/min.
A face milling operation is to be performed on a cast iron part to finish the surface to 30 μin. The cutter uses four inserts and its diameter is 3.0 in. The cutter rotates at 480 rev/min.
To obtain the best possible finish, a type of carbide insert with 4/64 in nose radius is to be
used. Determine the required feed rate (in/min) that will achieve the 36 μ-in finish.
Please use the 30 μ-in surface finish, so the last sentence of the problem should read
as: "Determine the required feed rate (in/min) that will achieve the 30 μ-in finish".
Hint: Please consider the actual to theoretical surface finish ratio graph I posted with the
lecture notes previously to find out the actual feed rate. Please note that theoretical surface
finish can be calculated by (f^2)/(32*Tool Nose radius) formula
7. A direct extrusion operation produces the cross section shown in Figure (c) from an
aluminum billet whose diameter = 150 mm and length = 900 mm. The flow curve
parameters for the aluminum are K = 240 MPa and n = 0.16. In the Johnson strain equation,
a = 0.8 and b = 1.5. Determine (a) the extrusion ratio, (b) the shape factor, (c) the force
required to drive the ram forward during extrusion at the point in the process when the
billet length remaining in the container = 850 mm, and (d) the length of the extruded
section at the end of the operation if the volume of the butt left in the container is 600,000
8. A drilling operation is performed in which 0.5 in diameter holes are drilled through cast
iron plates that are 1.0 in thick. Sample holes have been drilled to determine the tool life at
two cutting speeds. At 80 surface ft/min, the tool lasted for exactly 50 holes. At 120 surface
ft/min, the tool lasted for exactly 5 holes. The feed of the drill was 0.003 in/rev. (Ignore
effects of drill entrance and exit from the hole. Consider the depth of cut to be exactly 1.00
in, corresponding to the plate thickness.) Determine the values of n and C in the Taylor tool
life equation for the above sample data, where cutting speed v is expressed in ft/min, and
tool life T is expressed in min.
9. Casting is a forming operation T/F?
10. In milling operation, the cutting tool rotates T/F?
11. In slab milling, the milling cutter rotates at an axis perpendicular to the cutting surface of
the work-part T/F?
12. Decreasing the feed speed usually improves the surface finish T/F?
13. What is the difference between peripheral milling and face milling?
14. What is the difference between roughing cut and finishing cuts?
15. What is difference between Industry 4.0 and smart factories?
16. What is the difference between metal forming and the machining?
17. Holding force is generally higher as compared to drawing force in deep cup drawing? T/F
18. State the factors that might lead to infeasibility in deep cup drawing?
19. What is the wrinking in deep cup drawing, state the reasons why it might happen?
20. With the extrudate having a cross sectional area other that the circle requires higher
extrusion forces. Please specify the main reason.
21. Distinguish between generating and forming when machining workpart geometries.
22. What is he difference between blanking and punching