Ideal Work Method
Introduction
The ideal work or uniform energy method is the simplest method for force prediction in metal
working processes. The method performs an energy balance between the external work and the
energy consumed for deforming a workpiece.
Simplifications:
• Material is homogeneous and isotropic
• Material has a rigid-plastic behaviour and all the effects that
may result from elastic deformation are ignored
• Plastic deformation is homogeneous, that is, all the sections
or slices that are initially parallel will remain parallel after
deformation
• The influence of friction and redundant work is generally
ignored but can be accounted by means of empirical
corrective factors applied in the overall energy consumed in
deforming the workpiece
• States of stress are reduced to equivalent cases of pure
tension or compression
1
Ideal Work Method
Introduction
From what was mentioned before it may be concluded that ideal work (or uniform energy)
method cannot be utilized to determine:
•Velocity fields
•Strain distribution
•Stress distribution
The method is mainly applied for force prediction based on a work or energy balance and may
be used in process design (e.g. selection of the materials for the dies and machine tools,
among other things)
2
Ideal Work Method
Rod under simple tension
A circular rod under simple tension is taken as an example.
The external work is equated to the energy consumed in
deforming the workpiece.

l
0
l0
F

n
=K
unif
wi

n
 l 
  ln 
 l0 
K n
 unif 
n 1
wi
ln ( l )
l0
0
=K
l
l
W  V   axial d axial   F dl
W  V   ij d ij   F dl

F
ln ( l )
l0

Manufacturing
process
Efficiency

Ideal work (per unit volume)

w i    axial d axial
0


K  n 1
n
   d     d   K  d  
  unif 
1

n
0
0
0
Total work (per unit volume)
w  wi  w f  wr

Uniaxial tension and
compression
~1.0
Forjing
0.2-0.95
Rolling
0.75-0.9
Extrusion
0.5-0.65
Wire drawing
0.55-0.7
Stamping
3
0.7-0.8
wi
w
Ideal Work Method
Forward rod extrusion
Again, the external work is equated to the energy consumed in deforming the workpiece.
W 
1
V  ij d ij   F dl
 

F
l
1
W  V   axial d axial   F dl
 0
l0
l 
A 
  ln   ln 0 
 A
 l0 
 unif
K n

n 1
  0.5 ~ 0.65
1
A0 dl 0 unif   pA0 dl 0

Extrusion pressure
p
1
 unif 

Extrusion force
F
1
 unif  A0

4
Ideal Work Method
Summary (steady-state vs. non steady-state plastic flow)
Steady-state (e.g. extrusion):
l 
A
 f  ln f   ln 0
 Af
 l0 



K  fn
 unif 
n 1
 saída  K  fn
Extrusion pressure
p
1
unif  f  unif Qpsteady

Extrusion force
F
1
unif  f A0

Non steady-state (ex. forging):
A 
h 
 f  ln 0   ln f    K  fn
 hf 
 A0 
Forging pressure
p
1
  Qptransient

Forging force
F
1
 Af

5
Ideal Work Method
Self-study
Solve the proposed exercises.
F
T
6