The Preliminary Study Of Machinability During Milling Of Titanium Alloy

(Ti-6Al-4V)

Claudia Serboi1,a, Stefan Velicu2,b, Philippe Darnis3,c, Raynald Laheurte4,d

and Cristian Ionescu5,e 1,2University Politehnica Of Bucharest, Romania

3,4,University Bordeaux 1, France

5S.C. HESPER S.A., Romania

aclaoodya@yahoo.com,

bvelstefan@hotmail.com,

cphilippe.darnis@u-bordeaux1.fr,

draynald.laheurte@u-bordeaux1.fr,

ekristy_ionescu@yahoo.com

corresponding author: claoodya@yahoo.com; tel: +40 (727) 845 868

Keywords: titanium alloys, machinability, cutting forces, machining parameters.

Abstract. Titanium and its alloys have found wide application in the aerospace, biomedical and

automotive industries owing to their good strength-to weight ratio and high corrosion resistance.

However, these alloys have very poor machinability, which is attributed to their inherent high

strength maintained at elevated temperature and low thermal conductivity leading to high cutting

temperatures. This paper presents the findings of an experimental investigation into the effects of

cutting speed, feed rate and depth of cut when milling titanium alloy Ti-6Al-4V. The cutting forces

were the response variables investigated. This experimental investigation is translated into a

mathematical model of cutting forces designed on the basis of the results obtained from this

research.

Introduction

Titanium alloys are widely used in many areas because of their superior mechanical properties, heat

resistance and corrosion resistance. Though the initial application of titanium alloys have been in

aerospace industries, there is a growing trend in their applications also in the industrial sector,

which includes petroleum refining, chemical and food processing, surgical implantation, nuclear

waste storage, automotive and marine applications. One of the very popular titanium alloys for these

applications is Ti–6Al–4V, which compromises about 45–60% of the total titanium products in

practical use [1, 2]. However, these materials are regarded as difficult to machine because of their

low thermal conductivity and high chemical reactivity with cutting tool materials [3, 4].

Machinability means "easiness of machining" [5]. The general criteria are: tool life, surface

roughness, surface integrity, magnitude of cutting forces or energy (power) consumption, etc.

Which criterion or criteria will be chosen for determining machinability varies in accordance

with the requirements of the particular operation or task to be performed [5]. In this paper we chose

for analysis the criterion of cutting efforts.

Research and Means of Methodology

Research Methodology. A process that is on within a certain technological system, can be defined

by variables connected through relation as:

Y = Γ(x1, x2,..., xj ,..., xn ) (1)

called process function;

where:

Applied Mechanics and Materials Vol. 186 (2012) pp 200-207Online available since 2012/Jun/14 at www.scientific.net© (2012) Trans Tech Publications, Switzerlanddoi:10.4028/www.scientific.net/AMM.186.200

All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP,www.ttp.net. (ID: 147.210.94.20, Université de Bordeaux, Talence, France-26/03/15,13:56:39)

xj , j = 1, 2, …., k represents the independent process variables (controllable inputs);

Y – the dependent process variable (output);

Γ – the type of dependence relation.

There were studied the controllable inputs, xj: cutting speed (v), feed (f) and depth of cut (ap).

The output, Y, was considered the cutting force.

Process functions can be theoretical or regressional. Theoretical functions are introduced by

definition or deducted by physic-mechanical or geometrical considerations and regression functions

are established by experimental relations [6].

The independent process variables. In order to study the machinability of titanium alloys during

milling, the independent process variables are the following: the workpiece material, the cutting tool

and the cutting parameters.

The characteristics of workpiece material. The workpiece used for tests is a massive piece of

titanium alloy Ti6Al4V, dimensions 100x100x10 [mm], in which were milled two parallel grooves,

and their width is equal to the diameter of cutting tool. The trajectory of one tool's tooth point is a

cycloidal curve, and the tool has two teeth (fig. 2).

The nominal chemical composition of the titanium alloy Ti6Al4V is presented in the table below.

Table 1. Nominal chemical composition of the titanium alloys

Work material Chemical composition (wt.%)

V Al N O H C Fe

Ti–6% Al–4% V 4 6 0.05 0.2 0.0125 0.1 0.3

Fig.1. Massive piece of titanium alloy Ti6Al4V - after processing

Fig. 2. The trajectory and the direction of cutting tool for the first test

Applied Mechanics and Materials Vol. 186 201

The characteristics of cutting tool. The cutting tool used for these tests is an end milling cutter

with the following characteristics: Φ = 25 mm, Z = 2, Re = 4 mm, with replaceable carbide plates,

type ISCAR ADKT 150540 HR- HM IC928 (fig. 3).

Fig. 3. The cutting tool

The machine tool. Cutting tests were conducted on a Horizontal Machining Centre model

VERNIER CH500 with 3, ½ axes (fig. 4).

Fig.4. The machine tool VERNIER CH500

Dependent process variables. Based on the aspects resulted from the research made on

machinability of milling we will establish the following dependent variables (outputs): the

components of the cutting force - Fx [N], Fy [N], Fz [N];

The machining functions. The machining functions are given by the relations:

Fx = f(v, f, ap), in [N]; (2)

Fy = f(v, f, ap), in [N]; (3)

Fz = f(v, f, ap), in [N]; (4)

202 Optimization of the Mechanical Engineering, Manufacturing Systems,Robotics and Aerospace

Experimental procedure. Figure 5 shows the block diagram of the experimental setup.

Fig. 5. Block diagram of the experimental setup [7]

The real and coded values of the inputs are presented in table 2 [6].

Table 2. Coded and real values of the controllable inputs, xj

Variables level

X1=Vc

[m/min]

X2=f [mm/cut edge]

X3=ap

[mm]

(-1) (0) (1) (-1) (0) (1) (-1) (0) (1)

40 45 50 0,1 0,12 0,14 0,2 0,3 0,4

The structure of the experimental procedure is presented in table 3. The experimental program

considered was Full Factorial three level design (8 runs) [8].

Table 3. The experiment setup parameters and measured values of the forces. Titanium alloy: Ti6Al4V

Process: end milling THE STRUCTURE OF THE EXPERIMENTAL PROCEDURE

i/xj Levels – coded values

Levels – natural values

Force components [N]

X1 X2 X3 X1=Vc X2=f X3=ap Fx Fy Fz 1 -1 -1 -1 40 0.1 0.2 112.6557469 120.7835198 204.719418 2 -1 -1 +1 40 0.1 0.4 50.7503474 298.6706468 311.122028 3 -1 +1 -1 40 0.14 0.2 190.0244529 39.6668258 302.968053 4 -1 +1 +1 40 0.14 0.4 167.5743058 183.4845234 243.00673 5 +1 -1 -1 50 0.1 0.2 116.2555688 100.8136365 262.302975 6 +1 -1 +1 50 0.1 0.4 174.6237274 86.553117 309.002775 7 +1 +1 -1 50 0.14 0.2 133.9338963 72.822443 275.221346 8 +1 +1 +1 50 0.14 0.4 181.5195166 85.285124 294.293877

Dynamometer Workpiece Cutting tool

X�

Z�

Y�

Spindle

The machine tool’s table

( ZYX���

,, ) The machine tool’s coordinate

system

Data

acq

uisitio

n sy

stem

The transmitted signals of the

angular positions:

d4

Amplifiers

The transmitted signals by the

piezoelectric transducers

u1, ... ,u9

The linear position encoders signals

d1, d2, d3

di : signals nr. i

ui : tensions nr. i

Exploitable data files :

*.txt

Computer for

data

acquisition:

Dewesoft®

Pc Devetron®

Applied Mechanics and Materials Vol. 186 203

There have been made 8 tests of end milling process of a titanium alloy. There have been

established the values of the 3 components of milling force: Fx , Fy , Fz.

For example, the parameters for the test no. 1 are:

• Cutting speed Vc = 40 [m/min];

• Cutting depth ap=0.1 [mm];

• Feed f=0.2 [mm/edge].

The table below shows a part of measured values of the cutting forces on the x, y, z directions,

resulted from the test no.1.

Table 4. Measured values of the cutting forces

No.

Crt.

Time [s] Fx [N] Fy [N] Fz [N]

1 42,706650 19,747030 75,778664 183,228043

2 42,706699 20,188637 76,744614 181,988968

3 42,706749 19,988848 77,880257 180,394501

4 42,706799 19,909733 78,460495 179,145340

5 42,706848 20,177361 78,029556 177,944214

6 42,706902 20,934538 76,546089 175,633713

7 42,706951 22,159609 74,218147 172,793015

8 42,707001 23,750845 71,666145 170,854080

9 42,707050 24,610144 69,811295 170,412247

10 42,707100 24,360050 68,941376 170,156693

11 42,707150 23,068424 69,295143 169,024307

12 42,707199 22,000189 70,579086 166,810074

13 42,707249 21,444885 71,848564 165,568817

14 42,707298 21,222368 72,305733 166,201736

15 42,707352 21,312218 71,921791 168,231400

16 42,707401 21,108643 70,984344 166,450882

17 42,707451 20,744854 70,463531 163,293869

18 42,707500 20,507149 70,200218 161,463959

19 42,707550 21,655825 70,918182 163,696747

20 42,707600 23,281101 72,161659 166,422195

Fig.6. The forces measured in test no.1

204 Optimization of the Mechanical Engineering, Manufacturing Systems,Robotics and Aerospace

Development of mathematical model. The processing of experimental results was performed using

the program for the multivariable regression functions determination, DataFit, version 9.0. DataFit

(fig. 7) is a science and engineering tool that solve the tasks of data plotting, regression analysis

(curve fitting) and statistical analysis.

Fig. 7. DataFit software

The regression function representing the cutting forces components is polynomial type expressed

as [6]:

∑ ∑= <=

++=k

i

k

jlj

ijjijj xxaxaay1 1,1,

0

(5)

where jij aaa ,,0 , i, j = 1…3, are regression coefficients;

Considering the variables used to express the cutting force equation, the regression equation will

be expressed as:

3113322321123322110 xxaxxaxxaxaxaxaaY ++++++=

(6)

meaning,

pcpcpc avaafafvaaafavaaY ⋅⋅+⋅⋅+⋅⋅+⋅+⋅+⋅+= 1323123210 (7)

The results of regression analysis are given in table 5.

Table 5. Modeled values of axial, tangential and radial forces

Exp.

point

s

Fx [N] Fy [N] Fz [N]

Modeled

values

Error

%

Modeled

values

Error

%

Modeled

values

Error

%

1 106,376 5,57 128,382 -6,29 222,061 -8,47

2 57,030 -12,37 291,071 2,54 293,779 5,57

3 196,304 -3,30 32,067 19,15 285,625 5,72

4 161,294 3,74 191,083 -4,14 260,348 -7,13

5 122,535 -5,40 93,214 7,53 244,960 6,61

6 168,344 3,59 94,152 -8,77 326,344 -5,61

7 127,654 4,68 80,421 -10,43 292,563 -6,30

8 187,799 -3,45 77,686 8,91 276,951 5,89

The final mathematical model as determined by the analysis described above, is given below:

Tangential cutting force

][57.4704.179202.21203.232972.1030730.1336.565 NpacvpaffcvpafcvxF ⋅⋅+⋅⋅+⋅⋅−⋅−⋅+⋅+−=

(8)

Radial cutting force

][87.8014.45981.20838.409422.1066822.818.526 NpacvpaffcvpafcvyF ⋅⋅−⋅⋅−⋅⋅+⋅+⋅−⋅−=

(9)

Axial Cutting force

][83.445.1212491.3972.137719.561031.561.463 NpacvpaffcvpafcvzF ⋅⋅+⋅⋅−⋅⋅−⋅+⋅+⋅+−=

(10)

Applied Mechanics and Materials Vol. 186 205

The cutting force is often used as an indication of the machinability of a metal. A higher cutting

force usually indicates a poorer machinability.

The graphics for the measured and modeled values of axial, tangential and radial forces are given

in the figures below.

a) x component of the cutting force (Fx)

b) y component of the cutting force (Fy)

c) z component of the cutting force (Fz)

Fig. 8. Measured and modeled values of axial, tangential and radial forces

Conclusion

In accordance to the considerations presented in this paper, we may draw the following

conclusions on the milling experimental procedures of Ti-6Al-4V titanium alloy: the processing of

experimental results was performed using the program for the multivariable regression functions

determination DataFit.

206 Optimization of the Mechanical Engineering, Manufacturing Systems,Robotics and Aerospace

From the study of data obtained by running the program, there are noted the followings:

• The models determined for the cutting force components in titanium alloy milling are

appropriate, having the coefficient of multiple determination (R2) close to 1 (0.9796 for Fx,

0.9902 for Fy and 0.7529 for Fz), which is the ideal value;

• Relative errors between measured values and those predicted by the model are maximum

12,37% for Fx, 19,15% for Fy, 8,47% for Fz;

• The coefficients have been determinated for a confidence interval of 95%.

For every single coefficient, DataFit indicates a t-ratio value as it is shown in the table 6.

Table.6. The t-ratio values for the significant coefficients.

The significant

coefficients

t-ratio for Fx t-ratio for Fy t-ratio for Fz

a1 1,561 -0,797 0,225

a2 3,462 -2,943 0,678

a3 -3,414 4,960 0,731

T-ratio is the ratio of the estimated parameter value to the estimated parameter standard

deviation. The larger the ratio is, the more significant the parameter is in the regression model. For

Fx component of the cutting force, the most important parameter is feed rate (f) and for the

components Fy and Fz, the significant parameter is cutting depth (ap).

Acknowledgement

The work has been funded by the Sectoral Operational Program Human Resources Development

2007-2013 of the Romanian Ministry of Labour, Family and Social Protection through the Financial

Agreement POSDRU/88/1.5/S/60203.

The authors would like to thank prof. Olivier Cahuc, Philippe Darnis and Raynald Laheurte from

the Matériaux Procédés Interactions Laboratory, University Bordeaux 1, Talence, France for their

help with the experiments

References

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Applied Mechanics and Materials Vol. 186 207

Optimization of the Mechanical Engineering, Manufacturing Systems, Robotics and Aerospace 10.4028/www.scientific.net/AMM.186 The Preliminary Study of Machinability during Milling of Titanium Alloy (Ti-6Al-4V) 10.4028/www.scientific.net/AMM.186.200

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