SIMULATION OF CHIP FORMATION IN AN ORTHOGONAL
CUTTING PROCESS USING FEM
Hugo Manuel Correia Costa
Sponsored by: European Community, Socrates/ Erasmus Program
Introduction
The final workpiece quality is a more and more important factor in all cutting processes.
It is, without any doubt, dependent on the cutting conditions.
Metal cutting is a very complex process and its complexity is mostly due to the
problematic of chip formation. It involves hard mechanical events with high stresses and
strains that must be known to improve the whole process. Machining process modelling is
becoming recognized in the industrial and academic worlds as a proper way to identify and
analyse this problem and its dependence on parameters such as: temperature, cutting angles,
work material, friction conditions (namely on the rake face), velocity, tool tip radius and
depth of cut.The most important research activities on this subject are described in [2] and [3].
Objectives
The objectives of this work are:
• To develop an orthogonal cutting process simulation model with the available process
conditions.
• To validate the simulation, i.e. to confirme the simulation capabilities using the available
process conditions by comparing the results with those of Lin and Yarng [1].
• To analyse the orthogonal cutting events with respect to the following parameters: plastic
strain, equivalent stress and applied external force.
Developed work
The initial cutting conditions are practically the same as in [1] for all the experiments
except EXP 1-5. The goal was to insure, as far as possible, the quality of the simulations. By
selecting mild steel as work material and a tool velocity of v = 400 mm/s the following
outputs were analysed: displacement, equivalent stress, equivalent strain, equivalent plastic
strain rate and external force.
This work is based on a large deformation-large strain finite elements theory using a
incremental approach in a 2D elastic-plastic model of an adiabatic steady state cutting, using
the Marc Autoforge software package. The work was carried out through several experiments,
each one with an EXPi file name, where “i” is the sequence number.
The tool is considered as a rigid body, not meshed and without any kind of deformation.
Because of software limitations due to the non availability of material fissuration subroutines, a cutting process simulation starting with reference to an already advanced state was
carried out, with the already formed chip in total contact with the tool rake face. The
workpiece material has a plastic deformation behaviour descrived by the flow stress law [1]:
σ = Ao (T,ε’’)*(ε’’/1000)^0.0195*ε’^0.21 where:
Ao (T,ε’’) = 1394e^ (-0.00118*T)+339e^ (-0.0000184*[T-(943+23.5*ln(ε’’*1000))]^2
With: T = 298 °K (constant temperature)
ε’’ - total strain rate
ε’ - total strain (in an adimensional range = 0.05 to 2 mm/mm)
σ - flow stress (MPa)
For the considered range of ε’, the σ values were obtained through this formulation.
These material data were introduced in marc autoforge as a plastic stress-strain diagram.
In Tab. 1 all the EXP files with the principal model conditions are reported:
EXP 1-5
EXP 7-13
EXP 14-16
EXP 17-19
EXP 20-22
EXP 24-36
Depth of cut
0.20 mm
0.27 mm
0.27 mm
0.27 mm
0.27 mm
0.27 mm
Velocity
400 mm/s
400 mm/s
400 mm/s
400 mm/s
400 mm/s
400 mm/s
RF angle Tool tip rad. Thickness
12°
0.1 mm
0.6 mm
20°
0.1 mm
0.6 mm
20°
0.1 mm
0.6 mm
20°
0.1 mm
0.6 mm
20°
0.1 mm
0.6 mm
20°
0.1 mm
0.6 mm
Work length
3.2 mm
1.8 mm
3.2 mm
1.8 mm
2.4 mm
Tab. 1 - Principal cutting conditions for the various simulation groups of files.
1
The EXP 1- 5 workpiece length is not specified since it is not an important input parameter.
Material description
In Tab. 2, the work material mechanical properties are reported:
E
188 GPa
Mild steel
ν
0.3
τ lim
400 MPa
fy
176 MPa
Tab. 2 – Work material mechanical properties.
Description of the EXP models
In Tab. 3, the models synthetic design descriptions are presented:
EXP 1-5
EXP 7 - 36
Single workpiece body models with simple elastic-plastic deformation
outputs without any kind of chip formation. [5]
Workpiece composed by two distinct bodies, one becoming the chip,
"worksu", and the other the machined surface, "workju", after the cutting
process development [1].
Tab. 3 - Models design description.
In EXP 7 - 36, mostly two types of chip separation criteria were implemented: 1) with
the "contact table" software option, 2) with shear boundary conditions applied on the elements
edges, mostly on the primary deformation zone.
Contact parameters
The defined bodies are:
q The tool as a rigid body with an advance velocity of 400 mm/s
q The workpiece as a deformable body, with the material properties specifications
q The holder as a static rigid body with the aim of stopping the workpiece relative
movement during the cutting process. *
In "contact table" option, all the contact relationships between the contact bodies are
entered. The contacts can be glued (G) or touch type (T) contacts, always with a possible
Distance tolerance, Separation force and Friction coefficient. This contact table parameters
are specified in Tab. 4
EXP 7
EXP 9
EXP 10 - 14
EXP 15 - 36
Contact condition
Glued all
Glued all
Touch all
Touch all
Separation force
1e12 N
1,76e6 N
176 N
0N
Dist. tolerance
0.0000 mm
0.0001 mm
0.0001 mm
0.0001 mm
Friction coeff.
0.16
0.16
0.16
0.16
Tab. 4 - Contact conditions. In EXP 9 the unit area was 1 dm^2 instead of 1 mm^2
From the EXP 15, instead of the contact table option, it was chosen to use a boundary
conditions approach. The load on the cutting plane has a calculated value Fs = σs*A = 12 N,
where: σs = limit shear stress (400 N/mm^2 for mild steel)
A = area of a mesh element = Length*Thickness = 0.05*0.6 mm^2
Remeshing parameters
EXP 1- 5
EXP 7-13
EXP 14
EXP15 - 16
EXP17
EXP18-36
Elem. distortion
Y
Y
Y
Y
Y
Y
Tool penetrat.
Y
Y
Y
Y
Y
Y
Increment n°
N
Y(freq=10)
N
Y (freq=3)
Y (freq=3)
Y (freq= 3)
Max.elem.length
0,3 mm
0,1 mm
0.05 mm
0.1 mm
0.05 mm
0.1 mm
Tab. 5 - Remeshing conditions.
Outside ref. levels
2
2
2
2
2
2
* In Fig. 6, the holder is represented by the X-Y axes of the diagram
2
With the tool penetration issue activated, every time the distance between the tool tip
and the nodes immediatly ahead is minor than a certain value, the remeshing is carried out.
By activating the element distortion issue, the body remeshing is dependent of this
parameter. When it reaches a certain pre-defined value, the remesh is automatically carried
out.
Finally, it is also possible to make a periodic remesh by selecting the desired frequency
on the increment option.
The elements maximum edge length was defined as about two times the undeformed
elements length, according to the software manual indications as a good compromise.
Results and discussion
Software problems were always encoutered (for example, too much deformation), since
this FE software package, without any fissuration sub-routines, is definitely not indicated for
this kind of machining process simulation. Only through some simplifications and
adaptations, some chip formation results were achieved.
EXP 1-5
Elastic-plastic deformation states with plastic strain outputs very close to the ones on
Kim's work [2] (Fig. 1). The primary deformation zone around the tool tip is easily
distinguished, with its superior values on all the outputs. This was shown as a typical study
indicated for this software package.
EXP 7-13
The first range of EXP files where the workpiece is defined as two distinct bodies. A
"contact table" option criteria was applied. The results were not the expected ones: in EXP 9,
with adaptive steps, when the cutting force reaches the nodes separation force all the upper
body (“worksu”) comes up at the same time, like a rigid body subjected to horizontal
compression. In EXP 10, with fixed time steps, the inverse results occur. The workpiece
remains glued to the tool tip and no sliding process is developed. The same procedure was
applied with a 0 separation force but the results are still unsatisfactory.
EXP 14-15
The smaller workpiece length allowed for the possibility to make a smaller elements
mesh without significant aditional solving costs improving the analysis capabilities of the
program. Despite this, the results only prove the unefitness of the “contact table” option as a
chip formation criteria. These results are mostly the same as for the former EXP range.
EXP 16
The same smaller workpiece model as for EXP 14-15, but with shear boundary
conditions (Fig. 2). The simulation of a continuous chip formation is achieved. Due to the
holder presence, the reference cutting advance of Lin (1.459 mm) is not achieved, but the
mechanical events simulation is satisfatory. The plastic strain rate distribution is close to the
one of Lin. It can be said that these are the best possible results with these cutting and process
conditions (Fig. 3).
EXP 17-19
An excessive number of mesh elements caused program running problems for these
models, as a consequence of a large workpiece length which is the same as in [1] (aprox. =
3.2 mm) with the same elements undeformed length as in EXP 14-15 and EXP 16 (0.05 mm).
EXP 24-36
Chip separation criteria defined by shear and point loads boundary conditions. The
cutting start approach is more viable in terms of mechanical events, with a node by node chip
formation. However, the cutting sliding phase is deficient. The point loads continue to act,
even after the bodies remeshing, causing too much machined sub-surface deformation and
chip sticking phenomenons on the tool tip. The external cutting force applied through the
cutting plane is easily recognizable.
3
Future work
− To implement a FORTRAN sub-routine close to the one implemented by Ceretti [4].
− To obtain the variations of the output distributions with cutting parameters such RF angle,
Tool tip radius, Sliding friction coefficient, Workpiece material, and Depth of cut.
− To utilize a lower cutting velocity = 274.8 mm/s or 137.4 mm/s for example in EXP 16 e
EXP 17 to riduce the software deformation problems. Under these conditions an easier
achievement of an exact validation is expected.
− To simulate this machining case with other software packages, more indicated for this
kind of machining processes, caracterized by workpiece fissurations.
References
[1] Lin, Z.C., Yarng, Y.-D., 1997, Three-Dimensional Cutting Process Analysis with
Different Cutting Velocities, Journal of Materials Processing Technology, Vol. 70: 22-33
[2] Astakhov, V.P., Shvets, S.V., Osman, M.O.M., 1997, Chip Structure Classification Based
on Mechanics of its Formation, Journal of Materials Processing Technology, Vol. 71:
245-257
[3] Ueda, K., Manabe, K., Okida, J., 1999, A Survey and Recent Investigations on
Computational Mechanics in Cutting, II CIRP Int. Workshop on Modeling of Machining
Operations, 25-26 Jan., Nantes, France
[4] Ceretti, E., 1999, Numerical Study of Segmented Chip Formation in Orthogonal Cutting,
II CIRP Int. Workshop on Modeling of Machining Operations, 25-26 Jan., Nantes, France
[5] Kim, K.W., Lee, W.Y., Sin, H.C., 1999, A Finite Element Analysis of a Machining with
the Tool Edge Considered, Journal of Materials Processing Technology, Vol. 86: 45-55
4
Fig. 1 - EXP 5 equivalent plastic strain
results.
Fig. 2 – EXP 16 model
with its boundary conditions
and the diagonal mesh
Fig. 3- EXP 16
plastic strain rate distribution
5
Fig. 4-EXP 17 final
plastic strain distribution
Fig. 5- EXP 26 external
force distribution
Fig. 6- EXP 9 with all
the defined bodies
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