MODELING AND SIMULATION OF TURNING PROCESS

AND

TOOL EDGE RADIUS EFFECT ON MICRO-TURNING

PROCESS

USING FEM SOFTWARE

EXTENDED ABSTRACT

Submitted by

Sugan Durai Murugan V

ME09B056

Under the guidance of

Dr.G.L. Samuel

DEPARTMENT OF MECHANICAL ENGINEERING,

INDIAN INSTITUTE OF TECHNOLOGY MADRAS,

MAY 2013.

CONTENT PAGE NO

1. INTRODUCTION 1 2. MATERIAL CONSTITUTIVE LAWS 1

2.1. FLOW STRESS CURVES 1 2.2. THERMAL MODEL 3

3. BOUNDARY CONDITIONS 3 3.1. FRICITON BETWEEN TOOL AND WORK PIECE 3 3.2. SELF CONTACT 4 3.3. MOVEMENT 4

4. RESULTS ON TURNING 5 4.1. EFFECT OF CUTTING SPEED ON EFFECTIVE STRESS 5 4.2. EFFECT OF CUTTING SPEED ON TEMPERATURE 6 4.3. EFFECT OF CHANGE IN RAKE ANGLE 7

5. TOOL EDGE RADIUS EFFECT IN MICRO TURNING 8 6. RESULTS ON MICRO TURNING 9

6.1. CHIP FORMATION 9 6.2. VON-MISES EFFECTIVE STRESS 9 6.3. CUTTING FORCE 10

7. CONCLUSION 11 8. REFERENCES 13

1

1. INTRODUCTION

Understanding of the basics of metal cutting processes through the experimental studies has many

limitations. Researchers find this investigation through experiments a very time consuming and

expensive work. Using the capabilities of Finite Element Analysis, metal cutting modeling and

simulation provides an alternative and easier way for better understanding of machining process

under different cutting conditions with less number of experiments. Turning is one of the widely

used metal cutting manufacturing technique in the industry world and there are lots of studies going

on to investigate this complex process. Several models have been presented in the past with different

assumptions. In this project , application of Finite Element Method is used in simulating the effect

of cutting tool geometry and cutting speed on effective stress, cutting force and temperature changes.

DEFORM is the simulation tool used in this study. DEFORM is a Finite Element Method (FEM)

based process simulation system designed to analyze various forming processes used by metal

forming applications. It is available in both Lagrangian (Transient) and arbitrary Lagrangian and the

Eulerian (ALE Steady-State) modeling. Additional, the software is currently capability of Steady-

State function and it is required of running a transient simulation previous to steady state cutting

simulation.

2. MATERIAL CONSTITUTIVE LAWS

In DEFORM , a thermo-mechanically coupled Lagrangian incremental simulation is done with

elastic-plastic material work piece and a rigid material tool. AISI 1045 is used as the work piece

material in this study, because it has been the focus of many recent modeling and as well as

machinability. Tungsten Carbide with no coating is being used as tool material.

2.1. FLOW STRESS CURVES

As a material is deformed plastically, the amount of stress required to incur an incremental

amount of deformation is given by the flow stress curve. Actually the flow stress curve is an

extended and focused region of plasticity in the true stress-strain curve. Flow stress is strongly

dependent on several state variables, among these are accumulated strain, instantaneous strain rate

and temperature.

The Johnson-Cook model [1] is purely empirical and widely used model to represent the flow

stress equation of the materials, typically metals, subjected to large strains, high strain rates and high

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temperature. This model exhibits an unrealistically small strain-rate dependence at high

temperatures. Johnson-cook model gives the following equation (1) for the flow stress

, , = + + [ ()] (1) Where is the equivalent plastic strain, is the plastic strain-rate, and A, B, C, n, and m are

material constants. The strain-rate and temperature are normalized for simplicity in representing the

model. The normalized strain-rate and temperature in equation (1) are defined as

=

, = ()() (2)

Where is the effective plastic strain-rate of the quasi-static test. is a reference temperature, and

is a reference melt temperature.

A simplified illustration of the plastic deformation for the formation of a continuous chip when

machining a ductile material is given in Figure 1.1.

Figure 2.1: Deformation zones in Orthogonal cutting

Where V is the cutting speed, is the rake angle, VS is the shear velocity, is the shear angle, is

the length of AB, is the undeformed thickness, is the chip thickness.

There are two deformation zones [2] in this simplified model a primary zone and a

secondary zone. The primary plastic deformation takes place in a finitely sized shear zone. The work

material begins to deform when it enters the primary zone from lower boundary CD, and it continues

to deform until it reaches the upper boundary EF. Even after exiting from the primary deformation

zone, some material experiences further plastic deformation in the secondary deformation zone only

on a smaller scale.

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The average value for shear strain rate along AB is,

= (3) The shear angle is expressed as,

=

(4)

The average shear strain in the primary deformation zone is given by

= () (5) 2.2. THERMAL MODEL

In a thermo-mechanically coupled model, a huge amount of heat energy will be generated due to

large deformations and temperature of the model will increase during the process. The rate of

specific volumetric flux due to plastic work is given by the following equation,

=

(6)

Where, f is the fraction of plastic work converted into heat, and is the rate of plastic work. Heat

generated due to friction is given by the equation,

= (7) Where, Ffr is the friction force, Vr is the relative sliding velocity between tool and chip. Due to the

change in temperature, thermal material laws are needed to be defined to adapt the elastic-plastic

model to the new temperature conditions. Convective heat transfer at the tool-work piece interface,

thermal expansion, and heat capacity is defined for range of temperatures.

3. BOUNDARY CONDITIONS 3.1. FRICTION BETWEEN TOOL AND WORK PIECE

The dependence of friction parameter on the cutting conditions can be explained by considering

the distribution of frictional shear stress on the rake face of the tool. Over the length h1, the normal

stress is very high and the metal adheres to the rake face, the friction stress is independent of the

normal. This region is called sticking region. On the length h2, smaller normal stresses exist and the

usual condition of sliding friction applies. This region is called sliding region. Based on this, two

types of friction models were developed called Coulomb type and Shear type.

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Figure 2.2: Frictional Shear stress

The shear friction model is given by

=

(8)

Where m is the shear friction factor needs to be estimated and given as input, is the

shear flow stress of the chip at the primary zone and is the frictional stress.

The coulomb friction model is given by

=

(9)

Where is the coulomb friction factor needs to be estimated and given as input, is the normal stress at the shear plane.

3.2. SELF CONTACT

The chip formed from the work piece will contact the work piece after a curl, therefore a constraint is

deployed to avoid contact between work piece and its chip.

3.3. MOVEMENT

In actual turning process, the work piece is rotated at a specific rpm, and the tool is moved along

the axis of the work piece at a constant feed rate. In simulation, work piece is fixed and tool is moved

along the surface of the work piece. The tool is being driven at respective cutting velocity along the

surface of the work piece.

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4. RESULTS

AISI 1045 has been taken as the elastic-plastic work piece and Tungsten carbide (WC) is used as the

rigid cutting tool. The cutting parameters used for the simulation are

1) Depth of cut (d) 0.5 mm

2) Feed rate (f) 0.3 mm

3) Environment Temperature 20

4) Shear friction factor 0.6

5) Heat transfer coefficient at tool-work piece interface 0.2 N/s/mm/.

4.1. EFFECT OF CUTTING SPEED ON EFFECTIVE STRESS

When the cutting speed increases the generated temperature on chip also increases, due to increase of

required energy at high cutting speed. More heat will be generated as cutting speed increases,

consequently the maximum temperature on the tool and work piece surface increase at higher cutting

speed. Figure 4.2. shows maximum effective stress vs. time for different cutting speeds.

Figure 4.1: Effective stress vs. Time under different cutting speeds

To find an average effective stress value over varying cutting speed, a constant stroke length is

taken as a reference. A stroke length of 0.35 mm is taken to average the stress values. The cutting

time to reach this stroke length is also noted. Table 1 shows the average Effective stress values over

different cutting speed.

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Table 1:

4.2. EFFECT OF CUTTING SPEED ON TEMPERATURE

As the cutting speed increases, the temperature rises rapidly in the initial conditions, and keeps

increasing gradually and stabilizes in a small temperature region when steady state is reached.

Figure 4.2: Temperature vs. time under different cutting speed.

To find an average temperature values over varying cutting speed a small time interval of

2.0e-4 sec to 3.5e-4 sec is taken so that the initial gradient in the transient state will not be accounted

for calculations. Stroke length covered in each cutting speed is also noted. Table 2 showing average

temperature vs. cutting speed.

Cutting Speed

(m/min)

Average Effective Stress

(MPa)

Cutting time

( e-5 sec)

100 1432.12 20.6

150 1346.57 13.7

250 1404.84 8.0

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Table 2:

4.3. EFFECT OF CHANGE IN RAKE ANGLE

According to Gunay et al [6] when rake angle decreases to negative values, high cutting forces

act on the material and therefore high heat will be generated. Figure 4.7. shows temperature vs.

cutting time for different rake angles. Table 3 shows maximum cutting force along the cutting

direction and maximum temperature reached for different rake angles. The results are agreeable with

findings from Gunay et al [6].

Figure 4.3: Temperature vs. time for different rake angles

Cutting Speed

(m/min) Average Temperature () Stroke Length (mm)

100 734.36 0.277

150 750.25 0.376

250 771.50 0.605

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Rake angle(), Clearance angle() Maximum Temperature (0C) Maximum Cutting force (kN)

50 , 70 585 0.925

00, 70 514 1.178

-50, 70 724 1.462

Table 3:

5. TOOL EDGE RADIUS EFFECT ON MICRO-TURNING

Micro turning is one type of micromachining process which uses a solid tool and its material

removal process is almost similar to conventional turning operation. In recent years, researchers have

explored a number of ways to improve the micro turning process performance by analyzing the

different factors that affect the quality characteristics. Unlike conventional macro-machining

processes, micro-machining displays different characteristics due to its significant size reduction.

Therefore size effect [6] is defined as the effect due to the small ratio of the depth of cut to the tool

edge radius. Often, the edge radius of the tools is relatively larger than the chip thickness to prevent

plastic deformations or breakage of the micro-tools. In contrast to the conventional sharp-edge

cutting model, chip shear in micro-machining occurs along the rounded tool edge.

Tool edge radius is an important parameter for surface quality in micromachining. Under

certain machining practices, cutting tip of the tool is strengthened with an edge radius for higher tool

life. Assumption of famous shear plane model in conventional machining is acceptable only when

undeformed chip thickness a is very much larger than the tool edge radius r, by at least three

orders of magnitude. This study is mainly focused on the behavior of chip formation in the transient

stages of several micro seconds where tool deformation is not accounted for.

In this study, the analysis of micro machining with FEM is performed under plane strain

condition using the explicit dynamic algorithm and the ALE as the solution method similar to that

macro turning process we have done already. The work piece used here is AISI 4340 and tool is

Tungsten Carbide. The tool radius varies from 1m to 5 m to illustrate the tool edge radius effect. The depth of cut is kept constant at 2 m. Cutting speed is also kept constant at 1666.67 mm/s.

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6. RESULTS ON MICRO TURNING 6.1. CHIP FORMATION

Figure 6.1 shows the mesh distortion initially when tool starts to deform the work piece for different

tool radius. For radius r = 0,1 m, chip is formed directly on the rake face of the tool. As the radius increases material begins to flow around the tool edge more gradually. At r = 4,5 m, material takes the shape of the tool edge and begins to shear much later than for r = 1,2 m.

Figure 6.1: Initial mesh distortion for different tool radii.

6.2. VON MISES EFFECTIVE STRESS DISTRIBUTION

Plastic deformation behavior of the work at different tool radius is reflected from the Von Mises

flow stress as shown in figure . For radius r=1,2 m plastic deformation is intense at the chip root and extending towards the turning point of the chip free boundary, which is known as the primary

deformation zone in the conventional turning model. But as the radius increases the deformation

zone gets larger, and material in the vicinity of the rounded tool edge undergoes severe plastic

deformation. The increase in size and thickness of the plastic zone is due to the merger of the

primary and secondary deformation zone. Critically at r=5m, the deformation zone is highly

a) R= 0m

d) R= 3m e) R= 4m

b) R= 1m c) R= 2m

f) R= 5m

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localized in front of the rounded tool edge which could lead to the changes in chip formation

behavior.

Figure 6.2: Von-Mises Effective stress distribution for various tool radii.

6.3. CUTTING FORCES

As the radius of the tool edge increases, the effective rake angle deviates from the tool rake angle

because the chip growth doesnt happen under rake face, it happens in front of the rounded tool edge

due to the changes in the chip formation. This leads to a effective negative rake angle eff in micro-

turning as shown in Figure 6.3 .Due to this increase in negative rake angle, the cutting forces

increases as the tool radius increases. Figures 6.4 and 6.5 showing cutting forces and thrust forces for

tool radii r=1,3,5 m.

Figure 6.3: Formation of negative rake angle at the rounded tool edge.

a) R= 0

d) R= 3

e) R= 4

b) R= 1

c) R= 2

f) R= 5

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Figure 6.4: Thrust force vs. time for tools with different edge radius

Figure 6.5: Cutting force vs. time for tools with different edge radius

7. CONCLUSION

7.1. TURNING SIMULATION

The simulation of the chip formation, temperature distributions and stress distributions in chip

and on the machined surface are successfully achieved. This study establishes a framework to further

study the turning process conditions and optimization of cutting parameters. Extending this

framework can be done to attain deeper insight of the process characteristics.

From the results, the following can be concluded:

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1) As cutting speed increases, the effective stress on the chip formed decreases momentarily and

then increases, indicating i.e. in a allowable cutting speed range for which the effective stress

can attain a minimum value.

2) The temperature of the chip formed in turning of AISI 1045 increases with increase in cutting

speed. Therefore higher the cutting speed, larger the coolant flow to maintain the

temperature.

3) Machining with a negative rake angle tool results in higher cutting force and temperature, but

than positive rake angle.

7.2. TOOL EDGE RADIUS EFFECT

As the tool edge radius r approaches the depth of cut a, the chip formation behavior and the

associated stress states are greatly affected by rounded tool edge. This study has shown that the

assumption of perfect tool sharpness is invalid in micromachining.

1) The ratio of undeformed chip thickness to tool edge radius is a deciding parameter in micro

machining in which chip formation, material deformation and stress distribution are greatly

influenced.

2) When tool radius becomes more than depth of cut primary and secondary deformation zone

merges together, and a single concentrated shear zone arises at the tool edge.

3) Beyond certain radius size, effective rake angle is no longer the tool rake angle and it

becomes negative influencing in cutting forces and surface roughness.

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8. REFERENCES

[1] G.R.JOHNSON, W.H. COOK, 1983, A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures, Proceedings of the 7th International Symposium on Ballistics, The Hague, The Netherlands, 541- 547.

[2] OXLEY, P.L.B., 1989, Mechanics of Machining, An Analytical Approach to Assessing Machinability, Halsted Press, John Wiley & Sons Limited, New York, 1989. [3] SHAW, M.C. and MAMIN, P.A., Friction characteristics of Sliding Surfaces undergoing sub-surface plastic flow, Journal of Basic Engineering, 1960. [4] ERNST, H., Machining of Metals, American Society for Metals, 1938. [5] K.S.WOON, M.RAHMAN, F.Z.FANG, K.S.NEO, K.LIU, Investigations of tool edge radius effect in micromachining: A FEM simulation approach, Journal of materials processing technology, 2008.

[6] J.CHAE, S.S.PARK, T.FREIHEIT, Investigation of micro-cutting operations, International journal of Machine tools and manufacture, 2006.