Klocke F. Manufacturing Processes 1: Cutting

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5.10 The Use of FEM in Cutting Technology 211

Material speed/(m/min)

Initial contact

Shear initiation

Crack initiation

iii

Sliding

End of sliding

New segmentation

Cracking

viii

Shear initiation

vii

12,5

37,5

62,5

Fig. 5.7 Simulation of the segmented chip formation with v

= 70 m/ min, f = 0.25 mm and

γ =−6

◦

(ADI-900)

material [Kloc07]. As soon as an element in the FE simulation exceeds the critical

damage value, it is erased.

crit



f (σ , ε, a)dε (5.9)

Figure 5.7 provides an example of a simulation of segmented chip formation

based on the integration of a fracture hypothesis when cutting ADI-900. B

ROZZO’s

criterion was used as a fracture hypothesis, which relates the tensile stress to the

largest shear stress [Broz72]. Because experimental investigations have shown that

the formation of segmented chips when machining ADI-900 is based on two differ-

ent mechanisms, C

HUZHOY’s material model additionally assumes material damage

as a function of the state values deformation and deformation velocity in order to

take into account the accelerated sliding of the chip segments due to high shear

stresses and the heterogeneous graphite sphere structure.

In the case of the segmented chip formation under consideration, after ﬁrst con-

tact and shear initiation a crack develops on the free surface which runs along the

shear zone. The stagnation area disappears and the chip segment begins to slide

jerkily from the cutting edge. Due to the crack which has developed, the supporting

cross-section between the chip segment and the base material becomes smaller. The

shear angle gets larger so that the chip segment is further pushed out of the chip root

area. Starting from a critical shear angle, the original shear zone collapses and splits

212 5 Finite Element Method (FEM)

up: one part wanders with the chip segment across the rake face; the other part re-

forms after repeated compression in from of the cutting edge, and the segmentation

process repeats itself [Kloc07].

5.10.3 Simulation of the Cutting Process

5.10.3.1 Simulation of the Turning Process

Computing power is becoming increasingly cheaper and faster with the rapid

development of the computer industry. This makes it possible to simulate cutting

processes that do not allow for the assumption of a plane strain state three-

dimensionally. Figure 5.8 gives an example of chip formation simulation for the

external cylindrical turning of a normally annealed heat-treated steel C45E+N. I n

order to reduce computing time, only one section of the workpiece was treated in

the model. The values for friction and heat transfer were taken from the model

for machining C45E+N veriﬁed by H

OPPE [Hopp03]. The mechanical material

properties of the normally annealed heat-treated steel C45E+N were determined by

L -MAGD with the help of tensile and compression tests [Elma06]. The tool used

was a Al

/TiN-coated insert of the form CNMG120408.

When wear models are integrated into the simulation, not only stresses, tempera-

tures and chip forms can be predicted, but also possible tool wear. U

SUI discovered

in experimental investigations that wear velocity dW/dt can be calculated with the

= 300 m/min

= 1 mm

= 0.3 mm

0 ms

= 0.34 ms

= 1.03 ms t

= 2.46 ms

Fig. 5.8 Simulated ﬁrst cut in external turning of C45E+N

5.10 The Use of FEM in Cutting Technology 213

Cutting time

K+1

Δt = t

K+1

PHASE 1

Thermo-mechanical

FE-analysis of the

turning process

PHASE 2

Calculation of the

thermo-mechanical

load collective in

steady state

condition

PHASE 3

Calculation of the

nodal wear rate and

the resulting wear

PHASE 4

Adaptation of the

tool geometry

dependant on wear

Tool

−

⋅

Integration of the

wear model

tool

chip

Fig. 5.9 Simulation of tool wear

following equation when the normal stress σ

, sliding velocity v

and surface

temperature of the tool ϑ are known [Usui78]:

= σ

· v

· C

· exp



−



(5.10)

The material constants C

and C

are dependent on the material/cutting tool

material combination. To determine them, A

LTAN has suggested a numerically com-

bined calibration method in which the speciﬁc material constants can be determined

based on experimental results for wear velocity and numerically calculated values

for σ

, v

and ϑ [Alta02]. Figure 5.9 shows the basic sequence of a wear simu-

lation. After the collected thermo-mechanical load for the stationary state has been

calculated in the ﬁrst and second phases, the current wear rate dW/dt is calculated

in the third phase based on the wear model provided in the user subroutine. This is

followed by the modelling of the worn tool in the fourth phase, whereby the nodes

of the tool contour are shifted as a function of the calculated wear volume W.This

4-phase wear calculation cycle is continued until a user-deﬁned tool life criterion is

reached, and the simulation is stopped.

Figure 5.10 provides an example of wear prediction of uncoated cemented car-

bide inserts. Until the wear criterion of VB

= 200 μm is reached, a total of seven

214 5 Finite Element Method (FEM)

Vergrößerung 50-fach

Ti6-4, depth of cut a

= 1 mm, HW-K20

cutting speed v

= 100 m/min and feed f = 0.2 mm

100

150

200

250

300

0 50 100 150 200 250

Cutting time t

Flank wear width VB/µm

Simulation

Experiment

Tool

Work piece

= 250 s

200

µm

600 µm

Vergrößerung 200-fach

200 µm

Vergrößerung 200-fach

200 µm200 µm

50x-magnification

200x-magnification

Fig. 5.10 Simulation of the ﬂank face wear and comparison with the experimental results

4-phase cycles are calculated in the wear simulation. As the comparison of the wear

curves of the simulation and the experiment shows, the simulation deviates only in

the last calculation cycle. The SEM image of the cutting edge, which was taken at

cutting time t = 250 s in the experiment, makes it clear that width of ﬂank wear

width VB increases erratically in the experiment as a result of the displacement of

the cutting edge. As this point, the crater broke t hrough the cutting edge and thus

led to an acceleration of ﬂank face wear. Since wear in the area of the rake face

was ignored because of lacking material constants for crater wear in the FE s imu-

lation, simulating cutting edge displacement in the direction of the ﬂank face was

impossible.

5.10.3.2 Simulation of the Milling Process

The following example shows how cutting simulation has been applied in the

industrial sector (Fig. 5.11):

Based on a numerical chip form simulation, the tool geometry of an inserted-

tooth cutter was optimized with respect to chip ﬂow in the product development

5.10 The Use of FEM in Cutting Technology 215

Ultimate design

of tool holder and

cutting insert

CAD-Model

of the tool holder:

miller Ø 100 mm

equipped with 10 PCD

die heads

f,c,p

Chip shape simulation

for the calculation of the

thermo-mechanical load

spectrum

Fig. 5.11 Chip form simulation for the development of the tool body and the tool holder (Source:

Kennametal)

phase. In the typical product development process for indexable inserts for metal

machining, prototypes are manufactured and tested in several iteration stages in

order to identify the ideal design.

The development process is time-consuming, extremely costly and usually lasts

up to 8 weeks. By integrating FE simulations of chip formation into the development

process, the number of iteration cycles in the design process can be signiﬁcantly

reduced. Furthermore, the design of the tool holder can be improved with the help

of FE simulation; however, this type of simulation requires very exact input data

regarding force and directions of force, which in the past could only be acquired

with costly cutting experiments. Chip form simulation can be of assistance here. By

simulating the chip ﬂow, which essentially is determined by the lead angle of the

cutting edge to the cutting direction as well as the chip former geometry, which is

ﬁxed in the t ool body, predictions can be made not only about chip form but also

216 5 Finite Element Method (FEM)

about forces and temperatures. These can then be utilized to help design the tool

holder.

By incorporating chip formation simulation into the tool prototype development

process, in the above example of an inserted-tooth cutter, we can ﬁnd an optimal

combination of adjusted, positive axial and radial lead angles as well as an opti-

mized cutting edge bevel. This in turn leads to a considerably better surface quality

after cutting. The chip is removed from the surface being produced, resulting in a

very smooth surface. The two-tier cutting edge bevel results in lower cutting f orces,

which can minimize burr formation.

5.10.3.3 Simulation of the Drilling Process

Drilling is the most common means used in tool production. From the standpoint

of cost and productivity, modelling and optimizing drilling processes is thus an of

1 3 5 7 9

Diameter d / mm

ratio (d

/ d) %

Experiment

Simulation

12345678910

Drill diameter d/mm

Specific feed force k

f,max

/(kN/mm

)

f,max

= 2 * F

z,max

/ ( d * f )

Drill

Workpiece

Material : C45E+N

Cutting speed

: v

= 35 m / min

Feed : f =

0.012 * d

Cutting tool material : HW-K20

Cutting edge radius

: r

= 4 µm

Cooling : dry

Temperature T/°C

400

200

Experiment

Simulation

Fig. 5.12 FE-model of the drilling process compared with the experiment

5.10 The Use of FEM in Cutting Technology 217

enormous importance in the manufacturing industry. The drilling process is particu-

larly challenging for 3D-FE simulation, demanding a lot of computing power from

the hardware and efﬁcient simulation tools due to the numerous inﬂuencing parame-

ters involved (e.g. the complex geometry of the drill, cutting edge rounding, different

contact friction processes, difﬁculty deﬁnable heat transfer and thermo-mechanical

material properties) [Kloc06].

Due to its complexity, the process can not be represented by 2D simulation as

can the orthogonal cross section in turning. A plane strain deformation state can-

not be assumed in the case of drilling, since there are different cutting speeds along

the drill radius and usually very complex, curved cutting edge geometries, causing

a transverse material ﬂow. For this reason, only a three-dimensional approach is

purposeful. However, this increases the costs of both implementation and computa-

tion exponentially, whereby the computing time with today’s computer technology

is increased by the third power of the model size. Nevertheless, the tool and work-

piece must be discretized in detail as volume bodies into ﬁnite elements. In order to

reach a satisfactory level of accuracy i n the simulation results, the most crucial area

of the major cutting edge should be meshed especially ﬁnely [Kloc06]. Figure 5.12

gives an example of an FE model of the drilling process. In order to shorten com-

puting time, the drilling process is considered from the point at which the entire

major cutting edge is ﬁrst engaged. The cylindrical workpiece model is adjusted to

the material of the ﬁrst cut process by notching a conic section on the cylinder. To

verify the drilling model, both the chip form and the calculated feed force are com-

pared with experimental results. The high level of agreement between them shows

that even for such complex processes as drilling, numerical simulation of diverse

target ﬁgures is possible.

Chapter 6

Cutting Fluids

6.1 The Functions of Cutting Fluids

By fulﬁlling its main functions, cooling and lubricating the machining site as well

as carrying away the chips, modern cutting ﬂuid systems make a substantial con-

tribution to the high performance level of many manufacturing processes. This is

achieved by removing process heat from the tool/workpiece contact area by cooling

and slowing the progress of heat via lubrication. Not only must excessive heating

of the workpieces, which leads to expansion, be avoided, but also temperature load

on the cutting tool material be reduced. The fulﬁlment of these functions may at

ﬁrst sound simple, but often requires cutting ﬂuid properties which are not readily

combined with each other.

6.2 Types of Cutting Fluids

According to DIN 51385, cutting ﬂuids are classiﬁed as non water-miscible, water-

miscible or water-based. Water-based cutting ﬂuids are fabricated simply by adding

the water-miscible concentrate to water (Fig. 6.1).

Cutting fluid

Emulsifiable

cutting fluid

Water-soluble

cutting fluid

Coolant-

emulsion

Coolant-

solution

Water-miscible

cutting fluid

Non water-miscible

cutting fluid

Water based

cutting fluid

Fig. 6.1 Division of the most important metalworking cutting ﬂuids, acc. to DIN 51385

219

F. Klocke, Manufacturing Processes 1, RWTH edition,

DOI 10.1007/978-3-642-11979-8_6,



Springer-Verlag Berlin Heidelberg 2011

220 6 Cutting Fluids

6.2.1 Non Water-Miscible Cutting Fluids

Non water-miscible cutting ﬂuids are mostly mineral oils that contain additional

active agents to improve lubrication, wear protection, corrosion protection, durabil-

ity and foaming properties. Additives that improve lubrication (“antiwear additives”

or AW-additives) help to reduce friction at the cutting location. To this end, natu-

ral fat oils (palm oil, rapeseed oil) or synthetic fatty substances (ester) are added.

The polar structure of these additives gives the additives good adhesive properties

on the metal surface, on which they form a half-solid lubricating ﬁlm called “metal

soap”. However, the effectiveness of this lubricating ﬁlm is reduced in temperatures

higher than its melting point (120–180

◦

C). EP-additives (EP = extreme pressure)

are also added to the mineral oils. Compounds containing phosphorous and sulphur

as well as free sulphur are used. The chlorine compounds also shown in Fig. 6.2 are

now of secondary importance in Germany. Burning used cutting ﬂuids containing

chlorine is now only allowed in special incineration sites, since toxic dioxins can

possibly be generated in case of uncontrolled burning. This makes disposal much

more expensive, so additives containing chlorine are largely avoided. On the metal

surface, the additives form metal salts at different temperatures. These salts can

absorb high pressures and exhibit only a low level of shear strength. In this way, not

only are forces lowered but also heat arising at the cutting location is reduced. The

temperature spheres of action of the individual additives can be seen in Fig. 6.2.

In addition to mineral oils, low-viscosity ester oils are also used as cutting ﬂuids

in machining. Presently, mostly mineral oils (about 90%) are utilized. The reason for

this is the lower cost required to procure it in comparison to synthetic ester oils. This

Kind of additive

Temperature

sphere of action

Lubrication

improving

additives

Fatty oils

(animal, vegetable)

Synthetic Fats (ester)

Chloric compounds

Phosphoric

compounds

Sulfidic compounds

Free sulfur

until ca. 120 °C

until ca. 180 °C

until ca. 400 °C

until ca. 600 °C

until ca. 800 °C

until ca. 1000 °C

EP-additives

Fig. 6.2 Temperature range of coolant additives (Source: Mobil Oil)