Physics-Based Process Modeling
offering cost reduction, time saving, and engineering decision assistance
for machining and other processes
Tahany El-Wardany
December 8th, 2005
Overview
• Objective of process simulation
• Classification of different machining models
• Overview of Process Modeling
• Physic-Based Models
 Mechanistic Models
 Finite Element Models
2
Modeling tools Lead to best practice machining process
Objective of process simulation:
To create scientific requisites, development of recipes and identify and model new
manufacturing technologies for affordable manufacturing of any part any material any
where with no waste.
Justification:
•
New features and materials designed for better part functionality are always difficult to
implement and cause high scrap rate.
•
Current products manufacturing parameters were set and approved decades ago.
New tooling, coating, coolant, and machines technologies are not utilized to reduce
cost.
•
Transferring and outsourcing manufacturing processes without proper evaluation of
sources of errors lead to long time to market and waste of unacceptable parts
•
Experimentally dependent analysis of new products manufacturing processes is not
enough to identify the underlying physics of problems generated and develop the
proper solutions
Payback:
•
•
50% reduction of manufacturing cost and time to market can be achieved.
Introduction of new processes and material is simplified
3
Why Process Modeling
 Process Simulation provides fundamental understanding of the relationships
between process variables:
 Optimal range of cutting parameters
 Chip morphology and cutting forces
 Development of temperatures and stresses
 Influence of tool wear and premature tool failure
 Dynamics of the tool/workpiece/machine system
 Workpiece surface integrity and residual stress
 Process simulation reduce number of iterations and results in a substantial
cost savings
4
Tools Available/Required to Eliminate Sources of Waste
Product cycle to market utilize CAE tools for:
•
Product Design and planning
•
Time management
•
Layout planning
•
Ergonomics
•
Processes simulation
•
Logistics
Tolerances &
Overproduction
Inventory
Unnecessary motion
Unnecessary risk
Inefficient processing
& Product defects
5
Process Simulation Lead to New Promising Technologies
New materials and manufacturing processes can solve many problems if utilized
Change drive
Combine
parts /
components
Modify
Dimension &
Tolerance
Reduce size
Superplastic forming
New Lightweight &
high performance
material
Online Monitoring
Advanced monitoring
New manufacturing
methods &
processes
On line part repair
Laser
repair
Enable function
Flow Forming
6
Classification of different machining models
Categories
Slip line field models
Heuristic models
Atomistic models
Finite Element models
Methodology
Various slip line fields
beginning with the
shear plane solutions
for representing the
deformation in
machining
Model machining
process as sum of
various small
individual events in
the regions of
deformation
Modeling the
microscale cutting at
the level of individual
atoms of the
workpiece and tool
Describe the behavior of
the workpiece being
machined as a collective
behavior of an
assemblage of small
element regions.
Advantages
Accurate prediction of
forces and strain rate
Reasonable
prediction of cutting
forces and its
variation with
process parameters
Yield useful
information about
the strain distribution
in the chip and the
subsurface of the
machined layer
Offers significant promise
towards furthering the
understanding of
machining and for
prediction of the outputs of
the machining process
Disadvantage
Required pre-existing,
experimentally
determined flow field,
which limits their
accuracy, ability to
predict the process
outputs under different
machining conditions
Analysis can be
complicated if:
 Work hardening
is introduced
 Tool nose radius
is considered
Material is dependent
on strain rate
Prediction of
machining output is
accurate only within
the range of
experiments used to
determine the
coefficient.
Each material/tool
combination needs a
small set of
experiments
Need accurate
interatomic force
laws for the work
and tool materials.
Accurate results can
be obtained only
when a 3ad analysis
is used
Can not be scaled
for most practical
machining process
Time consuming
Problems in 3-D
machining
A remesher technique
must be used
Accuracy depends on the
presentation of the work
and tool material
.
7
Overview of Process Modeling
Workpiece Tool Nose
Geometry radius and
angles
Nominal
Cutting
Conditions
Chip Load
Chip flow
and effective
cutting angles
Model
Wokpiece
fixture
Adaptive
meshing
&
separatio
n criteria
Cutting edge
radius + Wear
Cutting
Coefficients
Cutting
Force
Model
+ Ploughing
Residual stress prediction
Finite Element Model
Isotherms prediction
Finite Element Model
Coolant
properties
Contact length
friction coefficients
Forces Chip/tool
Force
Model
Interface
Friction
Model
Heat
Generated
Model
Tool and work
thermal properties
8
Process Modeling
Physic-Based Models
To developed Finite Element and/or Mechanistic models to investigate
specific aspects of manufacturing process
3D FE Face Milling model
To optimize high pressure coolant application
Prediction of instantaneous temperature distribution
along chip/tool/WP interface
Temperature
Isotherms
Insert
Chip
Result
Innovative Tool Design - High pressure, integral
and adjustable coolant nozzle
23.6 ci/min Metal
Removal Rate on
Titanium Demonstrated
Prediction of instantaneous cutting Forces
Normal force  K n  Ac
Tool
Tangential force  K f  Ac
chip load
Ac = tc * dz / cos(lead)
Kn, Kf – specific cutting forces
depending on material & cutting condition
Hollow Fan Blade leading/trailing edge machining
Predicted 70% machining time reduction
Cutting Force (N)
Application
Mechanistic 3-axis milling model
To reduce machining time
Original Production
Force Optimization
PW 4000 LE/TE
Cutting Time (Sec.)
Machining
9
Physics-Based Model - Concept of Mechanistic Models

Normal force and friction force proportional to chip load:
Ff  K f  A c


n
Fn  K n  A c
Chip load determined from cutting geometry
Kn and Kf dependent on material combination, cutting
conditions and cutting geometry
i
Tool
c
Workpiece
Specific cutting pressures depend on uncut chip
thickness, cutting velocity and normal rake angle

V
ln(K n )  a0  a1 ln(t c )  a2 ln(V )  a3n  a4 ln(V ) ln(t c )
ln(K f )  b0  b1 ln(t c )  b 2 ln(V )  b3n  b 4 ln(V ) ln(t c ).




For given workpiece-tool material combination, conduct cutting tests over a designed
range of cutting conditions
Transform the measured external cutting forces to obtain the rake face force
components
Based on the chip load, determine the specific normal pressure and friction pressure
Determine the constants a’s and b’s by linear regression
10
Physics-Based Model - Concept of Mechanistic Models
Mechanistic-based modeling enables optimization of all machining process
Machining Loads Proportional To:
1) Chip load
Interaction Forces Defined & Summed
z
work
y
x
2) Cutter speed
3) Material Properties
tool

n
Tool
c
i
y
P
Workpiece
V
chip
Each cutting segment is simulated as
simple oblique cutting
Approach Using Physics
Based Simulation
Traditional Process Approach
Variable, acceptable loads
Variable feed rate
Constant
feed rate
Processing Time
100
Optimized Loads
Process simulator
and optimizer
Time
Slow and constant feed
• acceptable forces and chip loads
• long cycle time
Savings
100
Variable feed
• safe, optimized loads
• shortened cycle time
UTC PROPRIETARY
11
Physics-Based Model - Concept of Mechanistic Models
• Model predict details of cutter-work contact parameters
• Cutting parameters such as chip thickness and feed rate vary significantly
along tool axis and tool path
UTC PROPRIETARY
12
Mechanistic Modeling Prediction of the tool deflection
Edge definition in space
13
Dynamics Characterization of Flexible Part
Flexible part representation
Real and Imaginary parts representing
the dynamics of the part/fixture system
0 degree phase
90 degree phase
180 degree phase
270 degree phase
Effect of part dynamics on tool geometry
14
Prediction of Dynamic Forces and tool deflection
Optimize machining process for flexible tool
Predicted dynamic forces
Predicted dynamic tool deflection
15
Physics-Based Model – Concept of FE Modeling
 Finite Element method (FEM) provides a good approximate solution to
continuum problems using a numerical discretization scheme
 FEM models allow for real geometric relations and complex boundary
conditions.
 FEM allows studying the effect of various material models on surface produced
 Detailed information can be obtained from FE simulation of machining process
 Excessive computational times and the need of carefully designed calibration
experimentation limit the use of FEM in predicting residual stress.
16
Physics-Based Model – Concept of FE Modeling
1- Simulation of chip separation criteria
 Cutting is simulated by forcing the tool to move into the workpiece in
small steps.
 Untied the nodes on previously defined parting line. Arbitrary influence the residual stress prediction.
 Mesh is fixed in space and the material flow through the mesh.
Iterative modification of the chip geometry to satisfy the velocity
boundary conditions.
 Assume parting criteria such as a stress or strain value. Eliminates
the effect of cutting conditions on the prediction of some process
output.
 More accurate to simulate the chip separation resulting from plastic
flow of the material.
 Automatic remeshing occurs to represent the deformed configuration
of the workpiece based on the following criteria:




Remeshing is required after specific number of increments
Remeshing is required if tool penetrate the workpiece
Remeshing is required if element distorted
Remeshing is required if element angle deviation exceed a specified value
17
Physics-Based Model – Concept of FE Modeling
2. Presentation of the physical properties of workpiece materials
•Accuracy of the FE analysis is principally dictated by the accuracy in presenting
the material physical properties.
•The constitutive equation of D2 tool steel in its hardened state is

  147000  75000.2
3.38 

T

68

1  





 2714  68 


0.312


 
 1  0.012 ln 
 

 o





(1)
•units of stress, strain rate, and temperature are psi, 1/s, and deg F, respectively.
18
Physics-Based Model – Concept of FE Modeling
Effect of material flow stress equation on Chip Formation and temperature
distribution
Chip Formation
Heat generated on
the flank and rake face
 = (148000 +114000 0.2976 )
(1+0.00031log(. / .o)(1-((T-527.67) /
(2475-527.67))1.78
Chip Formation
Heat generated on
the flank and rake face
 = (109700 +90240 0.03549 )
(1+0.0387log(. / .o)(1-((T-527.67) /
(2475-527.67))1.201
19
Physics-Based Model – Concept of FE Modeling
3. Friction characteristics in the interface zone
Friction occurs at the chip tool interface under extreme conditions of temperature, pressure,
and strain. It is important to determine the coefficient of friction experimentally since it is
dependent on cutting conditions and tool geometry.
Friction conditions affect the chip formation and consequently the accuracy of the results
obtained
Stick-slip friction analysis
No Friction analysis
Force
Temperature
20
Physics-Based Model – Concept of FE Modeling
4. Type of Analysis- Coupled Thermo - Mechanical Finite Element
Thermal
expansion
Temperature
dependent
material
Temperature
dependent
boundary conditions
Heat Transfer
Analysis
Temperature
Thermal stress
Material properties
Heat generated
due to plastic
deformation and friction
Changing
geometry (remeshing) due
to large deformation
Changing contact
conditions
Mechanical Analysis
Stresses - Plastic strain - Strain rate
Nodal coordinates - Contact forces
21
Physics-Based Model – Concept of FE Modeling
5. Finite Element Assumption




Large strain theory
Plane Strain
Updated Lagrangian formulation
Remeshing occurs as tool advanced to the workpiece, element
distortion, or tool penetration in the workpiece;
 Stick slip friction representation at the tool-chip interface is used
 Material flow stress is function of strain, strain rate and temperature
(Johnson-Cook constitutive equation)
22
Physics-Based Model – Concept of FE Modeling
6. Boundary Conditions
T = Tambient
On surface ST
) On surfaces S1
KT =hair(T- Tambient
 n
V
) On surfaces Sc
KT =h(T- Tambient
 n c
KT =0
n
N
N
hair  usselt 0*Kair
partDiameter
On surfaces Sa
ST
Air Convection Coefficients
Nusselt N0  Re [cutting velocity (V), part diameter (D), air/coolant viscosity (u)]
and Pr (Prandtl number)
Where Re Reynolds NO.
23
Physics-Based Model – Concept of FE Modeling
6. Boundary Conditions
Contact heat transfer coefficients
wp = 0.29 and tool 0.71 Btu/in^2/sec/oF
K
Cp
v

V
heat conductivity
specific heat
fluid viscosity
fluid dynamic viscosity
Coolant velocity component
on the tool face or chip
am
  coolantV jet  x  Dnozzle 
  coolantC coolant 
 A x , D  

hc  1.1222 K coolant 



 coolant
K coolant




V
ST
 x,D 
24
Physics-Based Model – Concept of FE Modeling
7- Output
 Tremendous amount of machining data can be obtained from each
run, the following results are of general interest:




Predicted Residual Stress
Predicted Cutting Forces
Predicted Temperature
Predicted Stresses on tool face
25
Stresses on the tool and workpiece
To define the possible areas of
tool chipping during machining,
stress concentration on the tool
should be predicted
Maximum Principal Stress Component
Minimum Principal Stress Component
Cutting speed is 80 SFM, Feed is 0.004 in/tooth,
Axial Depth of cut is 0.3 in, Tool material is Carbide,
Workpiece material is Titanium, Materials properties
is function, of strain, strain rate and temperature.
Shear Stress Component
26
Strain and strain rate on the tool and workpiece
Shear strain Component
Cutting speed is 80 SFM, Feed is 0.004
in/tooth,
Axial Depth of cut is 0.3 in, Tool material is
Carbide,
Workpiece material is Titanium, Materials
properties is function, of strain, strain rate
and temperature.
Strain rate 1/sec
27
Temperature generated during machining
Cutting Temperature oF
Cutting speed is 80 SFM, Feed is 0.004 in/tooth, Axial Depth of cut is
0.3 in, Tool material is Carbide, Workpiece material is Titanium,
Materials properties is function of strain, strain rate and temperature
Temperature Isotherms on the tool and workpiece
Time (sec) in
28
Definition of Residual Stresses in Metal Cutting
 Residual stress is defined as the stress that exists in an elastic body
after all the external loads are removed.
29
Concept of Residual Stress Generation
1-Due to Thermal Load
I
II
warm, compressive
cold, no stress
II
II
cold
Y
Y
x
x
Y
Y
III
IV
hot, plastic flow
cold, tension
warm, compressive
cold
II
cold
Y
x
Y
II
Y
x
Y
30
Concept of Residual Stress Generation
2-Due to Mechanical Load
Chip
Primary Deformation
Zone
Tool
Elastic-Plastic
Deformation Zone
0
1
Tension Test Bar
Compressive
Zone
2
3
Path of material flow
Tensile
Zone 4
5 (Position Nr.)
stress
stress
predominantly
compressive load
3
tensile residual
3
4
stress
5
0
predominantly tensile
load
4
(tension)
(compression)
(compression)
compressive
residual stress
(tension)
0
5
2
1
2
strain
1
strain
31
Residual stress classification
Residual stress is classified into two different types
depending on how it is developed:

Mechanical residual stresses

Contingent residual stresses
These two types may occur simultaneously during machining,
although they are generated by different mechanisms.
32
Mechanical residual stresses
generated following inhomogeneous plastic flow caused by







External forces
Thermal gradients
glide (descend or flow)
kinking (imperfection)
grain boundary effects
orientation effects
dislocation
33
Contingent residual stresses
Those stresses that are dependent on the coexistence of the source from which
they are derived





Chemical reactions.
Alloying.
Percipitation.
phase transformation.
Thermal effects causing relative expansion between different
constituents.
 Non uniform heating and cooling at the machined surface.
34
Parameters affect pattern & magnitude of residual stress









Material hardness and non uniform plastic strain.
Mechanical properties of workpiece materials.
Cutting conditions.
Tool geometry and edge preparations.
Tool wear.
Coolant.
Mechanical deformation of the workpiece surface.
Phase transformation of the workpiece structure.
Restrains placed on the workpiece due to its fixture.
35
Causes of Residual Stress - and how to model it
Thermal Load
cutting
conditions
material
properties
Cutting
Process
tool geometry
coolant fixture
chip
load
Elast./plast.
deformation
tool
wear
Residual
Stress
friction
Mechanical Load
FEM model
+ exact geometry
+ inclusion of several physical effects
- long calculation times
analytical model
+ fast calculation
+ easy to use
- simplified geometries and physical laws
=> necessity to simplify the process
36
Assumption usually used when mathematically
predicting Residual stresses




The cutting edge is sharp and no rubbing occurs.
The deformation is two dimensional (i.e. no side spread).
The stresses on the shear plane are uniformly distributed.
The resultant force through the shear plane is equal, opposite, and colinear with the resultant force through the rake face of the tool.
 Plowing forces and cutting temperature were assumed to be the main
cause of residual stress.
37
Analytical Modeling of Residual Stresses in Metal Cutting
cutting
conditions
tool
geometry
(I)
wear
Force model
friction
coefficient
(II)
material
properties
Temperature
model
coolant
material
properties
(III)
material
properties
Mechanical induced
Thermal induced
residual stress model + residual stress
(MRS)
model (TRS)
Iteration Procedure
elastic stress strain
field:
elst. = 0, elst. = 0
j=0
j, j integrate
stress strain
relation
W
s xx )
2k 2
W
s yy  2G (e yy  2 s yy )
2k
W
szz  2G (ezz  2 s zz )
2k
Prandtl-Reuss
W
equations
yz  G ( yz  2  yz )
k
W
zx  G ( zx  2  zx )
k
W
xy  G ( xy  2  xy )
k
W  s xxexx  s yye yy  s zz ezz   yz yz   zx zx   xy xy
sxx  2G (exx 
Steps required of Analytical model
j = j-1+ rj-1*
j = j-1+ rj-1*
rj (xm, y, z)
rj (xm, y, z)
j = j+1
no
relaxation for
boundary
conditions
rj* (xm, y, z)
rj* < w
?
yes
residual stress
residual strain
rj* (xm, y, z)
r(y, z)
r(y, z)
boundary conditions:
free surface:
zz = 0, yz = 0, zx = 0
flat surface (symmetry):
xx = 0, yy = 0, xy = 0
38
Finite Element Modeling of Residual Stress in Metal
Cutting
0.1 mm
Chip
Tool
0.1 mm
Tool
Chip
Tool
Workpiece
920
860
0.1 mm
Chip
Workpiece
800
740
680
620
560
0.1 mm
Chip
Workpiece
500
440
380
320
260
200
140
80
20
Temperature (°C)
Tool
Workpiece
Flank wear
Flank wear
Flank wear
Flank wear
0.03 mm
0.03 mm
0.20 mm
0.20 mm
Crack module Crack module Crack module Crack module
No
Yes
No
Yes
Residual stress (MPa)
Chip formation and flank wear length on
temperature distribution
Flow chart for simulating the 3D
segmental chip formation process.
800
600
Experimental results
Without crack module,
continuous chips
With crack module,
segmental chips
(a)
Experimental results
Without crack module,
continuous chips
With crack module,
segmental chips
(b)
400
200
0
-200
-400
0 20 40 60 80 100120 0 20 40 60 80 100 120
Depth beneath machined surface (µm)
Effects of chip formation and (a) 0.03 mm and
(b) 0.20 mm flank wear length on residual stress profile
39
Residual Stress Modeling of High Speed Machining Process
Retention
Plate
Residual stress (MPa)
800
600
(b)
0.1 mm
Chip
Tool
920
860
800
740
680
620
560
500
0.1 mm
Chip
Tool
400
440
380
320
0.1 mm
Chip
(a)
260
200
Temperature (°C)
140
Experimental results
Without crack module,
continuous chips
With crack module,
segmental chips
80
Experimental results
Without crack module,
continuous chips
With crack module,
segmental chips
Tool Life Doubled - 3X increase in the MRR
Operator intervention eliminated
20
Grinding Process replaced by milling process
50% reduction in production time – Better Surface finish
Compressive residual stress
S92 Yoke
0.1 mm
Chip
Tool
Tool
200
0
Prediction of Residual Stress for HSM of Titanium
-200
-400
0 20 40 60 80 100120 0 20 40 60 80 100 120
Depth beneath machined surface (µm)
Workpiece
Workpiece
Workpiece
Workpiece
Flank
wear
Flank
wear
Flank
wearof Titanium
Flank wear
Prediction
of Temperature
for HSM
0.03 mm
0.03 mm
0.20 mm
0.20 mm
Crack module Crack module Crack module Crack module
No
Yes
No
Yes
40
Predicted residual stress for the defined Cutting
Conditions
Residual stress (ksi)
100
75
50
25
0
-25 0
10
20
30
-50
-75
-100
depth beneath the surface x0.001 in
890_0.004
80_0.004
10_003_ml
80_0.004_ml_ND
41
Predicted residual stress for 1X and 10X MRR
50
0
0
10
20
30
-50
-100
depth beneath the surface x0.001 in
890_0.004
Measured residual stress for 1X
and 4.5X MRR
80_0.004
0.0
RESIDUAL STRESS (ksi)
Residual stress (ksi)
100
-20.0
-40.0
-60.0
-80.0
-100.0
-120.0
-140.0
0.0000
0.0010
0.0020
0.0030
0.0040
0.0050
0.0060
0.0070
DEPTH (in.)
Stress Relieved
4.5X Sig 1
1X Sigma 2
1X Sigma 1
4.5X Sig 2
42
Residual stresses on the workpiece
Residual stress ksi
Cutting speed is 890 SFM, Feed is 0.004 in/tooth, Axial Depth of cut is
0.3 in, Tool material is Carbide, Workpiece material is Titanium,
Materials properties is function of strain, strain rate, and temperature
Residual stress
Depth beneath the surface x0.01 in
43
FE Simulation of Laser Assisted Machining
Laser Assisted Machining
25 µm
Conventional Machining
25 µm
Temperature Distribution
25 µm
25 µm
Shear Stress Distribution
20 µm
Crack
Sub surface damage an order of magnitude
smaller than grinding
44