OPTIMIZATION OF PARAMETERS OF TURNING PROCESS
Dražen Bajić
Ivan Majce
Prof. dr. sc. D. Bajić, University of Split, FESB, R. Boškovića bb, 21000 Split
I. Majce, University of Split, FESB, R. Boškovića bb, 21000 Split
Key words: longitudinal turning process, surface roughness, cutting parameters,
mathematical modelling, optimization
ABSTRACT
The objective of this study was to investigate influence of cutting parameters on the
surface roughness, during the longitudinal turning process. Detailed experiments according
to the factors test plan and regression analysis, gave the extend equation for mean
arithmetical roughness, as one of the most useful signs of the surface roughness. In other to
get a minimum values of the surface roughness, optimization of the mathematical model is
done by and optimal values of the examined factors are determined.
The obtained results are, according to the experiment plan, valid for the testing of
material Č5431 (DIN 34CrNiMo6). The test results are to be probably applied to other
materials, however, has to be proved for each separate case.
1. INTRODUCTION
The development of new technologies, building and introduction of numerically
controlled machine tools i.e. machine systems have significantly changed conditions and
relation within production. The lack of reliable technological bases, necessary for machining
systems programming, causes significant troubles for the successful exploitation of the
present machining systems. There exists a misconception that in the present time of
electronic computers it is not necessary to be well familiar with chip-forming machining,
considering it obsolete. However, just under new conditions it is necessary to obtain new
knowledge about regularities in chip forming machining, about cutting features of new,
highly-productive tools, about machinability of workpiece material and so on. High reliability
and efficiency which is required from modern machining systems directly depend upon the
reliability of input data such as: material machinability, patterns of tool wear, optimal
operating parameters, finished surface unevenness, chip formation of adequate size and so
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on. Due to this, research in this field is of great importance and highly developed countries
invest lot o money in it.
Surface roughness has a significant influence on exploitation characteristics of the
part that carries the above-mentioned surface. Surface finish defined as average of mean
deviation of the profile from the mean line, is important for tribologic behavior of workpieces
in working conditions. On the other hand, an increased depth of surface roughness has a
negative effect on dynamically loaded parts because of their notch impact that can cause a
rupture of the part. Thus a knowledge of interdependence between depth of surface
roughness and an average of mean deviation of the profile from the line is needed.
2. FACTORS THAT INFLUENCE SURFACE ROUGHNESS
The roughness of the machined surface is seen through micro-geometrical
irregularities of the surface. The evaluation of the quality of machined surface is based on the
judgment of its roughness. Theoretical roughness depends exclusively on tools geometry
and applied process of machining whereas a real roughness appears as the result of
theoretical roughness though with bigger or lesser occasional roughness provoked by the
many factors. The surface roughness is influenced by the most important factors such as:








cutting parameters,
tool geometry,
build-up edge,
process time,
workpiece and tool material,
tool wear,
dynamical behavior of cutting system,
appliance of coolants and lubricants.
Cutting speed influence is associated to generation of build-up edge i.e. build-up
edge’s influence on surface roughness of processed surface. At lower cutting speed (0,160,6 [m/s]), generation of build-up edge results with grater surface roughness.
Increment of cutting speed results causes decrement of build-up edge influence that
induces as reduction of surface roughness. With further increment of cutting speed, nature of
particles separation changes, what results as decrement of plastic deformation causing
surface roughness reduction. Unlimited increment of cutting speed doesn’t influence
roughness because it causes greater tool wear that keeps surface roughness approximately
on the same level.
Feed influences surface roughness directly proportional. Feed increment results as
increment of surface roughness. However feed influence is related to cutting tool nose radius
influence. Unlimited reduction of feed does not result with reduction of surface roughness. At
some level, value of cutting tool nose radius prevents further reduction of surface roughness
causing it to stay at minimum possible level.
Cutting tool nose radius influences surface roughness inversely proportional.
Increment of cutting tool nose radius value causes reduction of surface roughness.
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Reduction of surface roughness is limited with some minimal value. Further increment of
cutting tool nose radius value causes vibrations that have negative influence in surface
roughness.
From geometrical perspective, the depth of cut doesn’t influence surface roughness
because it has no influence on size and form of bumps. However, influence of depth of cut is
indirect trough generation of build-up edge, deformation of separated particles, cutting
temperature, cutting forces, vibrations etc.
Figure 1 shows influential factors on surface roughness regarding chip-forming
machining.
Process
kinematics
Machining
Parameters
Cooling
fluid
Cutting tool
Properties
Tool
material
Depth
of cut
Stepover
Tool
shape
Runout
errors
Nose
radius
Surface
Roughness
Cutting
speed
Workpiece
diameter
Workpiece
length
Feed
rate
Tool
angle
Accelerations
Workpiece
hardness
Chip
formations
Vibrations
Friction in the
cutting zone
Workpiece
Properties
Cutting
Phenomena
Cutting force
variation
Figure 1. – Fishbone diagram with the factors that affect surface roughness
3. THE AIM, METHODOLOGY AND CONDITIONS OF EXPERIMENT
Experiment aim is to define adequate mathematical model that is used to determine
the influence of independent factors and cutting data, at surface roughness. The following
independent factors are selected: cutting speed (vc), depth of cut (ap), and feed (f). For a
concrete case, that means determination of criteria:
– surface roughness: Ra = f(vc, ap, f).
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Experiments are performed on lathe machine “PRVOMAJSKA” D-420/1500.
Workpiece material is steel 34CrNiMo6 (DIN). The experiments are carried out by the tool for
external machining, which consists of toolholder mark PTGNR 2020K 16 and insert mark
TNMG 160408-PF4015. The “SURTRONIC 3” instrument, produced by Rank Taylor Hobsen,
has done the measurements of surface roughness. The multifactor design of the second
degree has been used to carry out this experiment. Actually, in order to learn more about the
maximum or minimum of the process or its function it is necessary to approximate it by the
polynomial of the second rather than the polynomial of the first degree.
The selected values of the cutting parameters are the following:
– cutting speed:
vc,max = 2,0525 [m/s]
vc,min = 0,821 [m/s]
– depth of cutt:
ap,max = 1,2 [mm]
ap,min = 0,6 [mm]
– feed:
fmax = 0,28 [mm/r]
fmin = 0,16 [mm/r].
Central composite design with empiric polynomial model of the second degree is
taken:
k
k
k
i 0
1 i  j
i 1
y  b0   bi  xi   bij  xi  x j   bii  xi2
(1)
–- b0, bi, bij, bii – regression coefficient,
– x
– coded values of input parameters.
In order to get regression equation determined by polynomial of the second degree
using the statistics analysis, it is necessary to expand the design matrix with some other
physic factor values or rather to increase the number of experimental points which is to get
by rotatability character. Rotatability can be selected by an appropriate choice of coefficient,
marked by  value of which depends upon the number of the points of factorial design. For
k=3 the given value of  = 1,682. The needed experimental points number, as far as the
design of the second degree is concerned, figure out the following:
N  2 k  n0  n  20
2k – the design number within the basic points
n0 – the repeated design number of the average level, n0 = 6
n – the design number on the central axes, n = 6
Adding the points to the central axes where xi = ± , and  = 1,682, the 3-factorial
design can be presented in Table 1.
(2)
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Table 1. – Physic values and coded indexes of input factors
Coded values of input factors
x-i
x-i,min
x-i0
xi,max
x+i
-1,682
-1
0
+1
+1,682
x1 = vc [m/s]
0,401
0,821
1,4367
2,0525
2,4724
x2 = ap [mm]
0,4
0,6
0,9
1,2
1,4
x3 = f [mm/r]
0,12
0,16
0,22
0,28
0,32
Input factors
4. EXPERIMENTAL RESULTS, STATISTICS ANALYSIS AND OPTIMIZATION
Measured values of surface roughness, as the results of testing twenty experimental
points defined by experiment plan matrix, are shown in Table 2. The mentioned values of
surface roughness are input data for mathematical modeling of results, which was made by
multiple regression analysis and by using program package “Design Expert 6”.
Table 2. – Given results of the surface roughness measurements
TEST
NUMBER
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
INPUT
Measured
values
Calculated
values
vc [m/s
ap [mm]
f mm/r
Ra m
Ra m
0,8210
2,0525
0,8210
2,0525
0,8210
2,0525
0,8210
2,0525
1,4367
1,4367
1,4367
1,4367
1,4367
1,4367
0,4010
2,4724
1,4367
1,4367
1,4367
1,4367
0,6
0,6
1,2
1,2
0,6
0,6
1,2
1,2
0,9
0,9
0,9
0,9
0,9
0,9
0,9
0,9
0,4
1,4
0,9
0,9
0,16
0,16
0,16
0,16
0,28
0,28
0,28
0,28
0,22
0,22
0,22
0,22
0,22
0,22
0,22
0,22
0,22
0,22
0,12
0,32
4,10
2,70
3,55
2,10
5,10
3,77
5,30
3,92
3,78
3,80
3,81
3,79
3,78
3,79
5,87
3,30
3,55
3,30
2,49
4,78
4,16
2,71
3,58
2,13
5,16
3,71
5,37
3,92
3,78
3,78
3,78
3,78
3,78
3,78
5,75
3,32
3,55
3,25
2,42
4,75
Regression analysis has shown which factors and interactions have had an important
impact on the value of surface roughness. Applying repeated regression analysis the
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Optimization of parameters of turning process
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coefficient of regression, multi-regression factor, standard false evaluation and the value of ttest have been determined. Significant factors and interactions are as follows: vc, f, ap·f, vc2,
ap2, f2, whereas non-significant ones are: ap, vcap, vcf.
On the basis of the applied regression analysis, the dependence of an average
arithmetic roughness Ra and examined factors can be expressed as:
Ra  4.66  3.202  vc  10.257  f  11.012  a p  f  0.705  vc2  1.515  a 2p  19.412  f 2
(3)
with regression coefficient: r2 = 0,9963.
The analysis of obtained mathematical models and cutting data influence at surface
roughness has been made using diagrams shown in Figures 2, 3, 4, 5, 6, and 7.
Figure 2.- Surface roughness in dependence of
cutting depth ap and cutting speed vc
(fmin= 0,12 [mm/r])
Figure 3.- Surface roughness in dependence of
cutting depth ap and cutting speed vc
(fmx= 0,32 [mm/r])
Figure 4.- Surface roughness in dependence of
cutting depth ap and feed f
(vc, min= 0,4 [m/s])
Figure 5.- Surface roughness in dependence of
cutting depth ap and feed f
(vc, max= 2,47 [m/s])
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Optimization of parameters of turning process
Figure 6.- Surface roughness in dependence of
cutting speed vc and feed f
(ap,min= 0,4 [mm])
7
Figure 7.- Surface roughness in dependence of
cutting speed vc and feed f
(ap,max= 1,4 [mm])
Given mathematical model (3), due to the applied regression analysis, is optimised
the way that the model parameters such as: cutting speed, depth of cut and feed, assume
the optimum values whereas the aim function, figured out through the average arithmetic
roughness, gain the minimum value. The minimum aim function has been found out for the
following cutting parameters:
vc,opt = 2,2697 [m/s];
ap,opt = 1,4 [mm];
fopt = 0,12 [mm/r]
for which the aim function or rather minimal value of the average arithmetic roughness is
expressed as: Ra,min = 0,858 [µm] .
Figure 8.- Surface roughness in dependence of cutting depth ap and feed f
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(vc, opt= 2,2697 [m/s])
5. CONCLUSION
Mathematical model presents quite well the performance of the average arithmetic
roughness. However, it can be used as well for the evaluation of the surface roughness value
in longitudinal turning work, whilst applying specific cutting parameters or as a useful model
in selection of appropriate cutting parameters in order to achieve a specific demanding
roughness.
Relating to the given equation and diagrams it is worth to point out the following
conclusions:

Regression coefficient r2 which determines quality and reliability of model is 0,9963,
what means that 99,63 % of variability is caused by impact of variables, meaning that
mathematical model quite well describes correlation of surface roughness Ra, to
selected input factors vc, ap, f .

The increase of the cutting speed in a certain interval effects the improvement of the
surface roughness but soon after, due to the layer on the cutting edge and vibrations,
it deteriorates.

The feed actually has the greatest impact on the surface roughness. The more it
decreases the more it improves the surface roughness.

The increase of depth of cut improves the surfaces roughness as well. This can be
taken as an advantage for the improvement of productivity.
6. LITERATURE
1
2
3
4
5
6
CEBALO, R.; BAJIĆ D.; BILIĆ, B.: Mathematical modelling of cutting forces in the
longitudinal turning process, 10th International Scientific Conference on Production
Engineering CIM 2005, Lumbarda, 2005., str. I 31-I 40.
BENARDOS, P.G.; VOSNIAKOS, G.-C..: Predicting surface roughness in machining: a
review, International Journal of Machine Tools & Manufacture, 43 (2003), 833-844.
BILIĆ, B.; BAJIĆ, D.; VEŽA, I.: Optimization of cutting parameters regarding surface
roughness during longitudinal turning, 15th International DAAAM Symposium:
Intelligent Manufacturing & Automation: Globalisation – Technology – Men - Nature,
Vienna, 2004., str. 039-040.
CEBALO, R.: Ovisnost dubine hrapavosti o srednjoj aritmetičkoj hrapavosti brušene
površine kod različitih postupaka brušenja, Strojarstvo 35(5,6) 231-235 (1993).
MONTGOMERY, D.C.: Design and Analysis of Experiments, John Wiley & Sons, Inc.,
New York, 1997.
CEBALO, R.: Prepoznavanje materijala i automatsko određivanje elemenata rezanja
kod tokarenja, Zbornik II, Suvremeni trendovi proizvodnog strojarstva, Zagreb, 1992.