ESTIMATION OF PARAMETERS IN INDUSTRIAL PROCESSES
IMPROVING THE CUTTING OPERATION IN AUTOMOTIVE BELTS1
TOLEDO, Marcelo, [email protected]
Department of Mechanical Engineering
Zip code 12060-440 - Taubate-SP - Brazil - University of Taubate
Doutor NETO, Antonio Faria, [email protected]
Department of Mechanical Engineering
Zip code 12060-440 - Taubate-SP - Brazil - University of Taubate
Abstract
This article aims to demonstrate the application of factorial experiments designed
to estimate the parameters and to improve the industrial processes. The purpose of this
study was to reduce the rate of non-conforming parts in the cutting process manufacturing
industry of automotive belts and consequently reduce the environmental impact caused by
the disposal of vulcanized rubber in the environment besides to increase the
manufacturing productivity. The application of the techniques of design of experiments
determined the variables that affecting the process and the values that should be applied
in these variables to approach the values found in the process of the nominal specification
for the studied quality characteristic and reduce process variability.
Key words: Design of experiments, Parameters estimation, Process improvement,
Automotive belts.
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ISBN 978-85-62326-96-7
1 INTRODUCTION
With the development competitiveness in various industrial sectors, the
companies, independent of the market in which they operate, can only remain healthy,
economically viable, through continuous improvement of its processes and products. This
is even more pronounced in the automotive industry, which is increasingly demanding
consumers with quality products at affordable prices.
Within this scenario, the design of experiments techniques can be used in process
improvement, as in the development of processes and products. The aim of this study was
to determine the significant parameters in the cutting operation of automotive belts for the
belt width response and spread the use of better tools for experimentation within the
Brazilian industries, because, according to (ROSS 1991) [1], the largest part of the
engineers are familiar with the development of tests in order to model the real operating
conditions of a process and cause-effect relationship to project performance. However,
knowledge related to appropriate testing strategy is often limited. And yet, as (SCHWAAB
and PINTO 2011) [2], most cases of frustration related to use of designed experiments is a
result of misunderstanding about the use of planning techniques and experimental results,
in fact, can be obtained with the aid of these tools.
2 MATERIAL AND METHODS
Applying the concept of design of experiments was conducted in an industry
manufacturer of industrial, automotive and agricultural belts in São Paulo, Brazil. The cell
chosen for the experiments was automotive belts that have divided the process into the
following steps:





Building a slab at the builder, applying on a tooling steel, rubber and cord;
Slab vulcanization;
Grinding to fix the thickness of the slab;
Slab cutting to define the width of the belt;
Making of ribs (teeth) belt.
The experiments were performed in the step of slab cutting, where is defined width
of the belts to be obtained from slab. Basically, in this step, the slab is placed between two
axes to stretch it down and then a cutting knife falls on the surface of the tensioned slab,
which is already aligned to a reference flange, cutting it into various belts, depending on
the amount and the specified width.
The project goal was to find the combination of parameters that reduce variation in
quality characteristic cutting width (main defect caused the cutting operation) and,
consequently, reduce the formation of scrap and increase productivity in this operation.
The main control parameters in the cutting machine are:
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ISBN 978-85-62326-96-7







Upper axle speed;
Cutting profundity;
Belt length (perimeter);
Polyurethane sleeve condition (polyurethane sleeve covers the upper axle);
Tension applied on the slab between the two axles;
Pressure roller (pressure applied on the slab against the belt);
Slab alignment (relative to the flange reference).
The choice of control factors (parameters), levels adjustment (experimental region)
and the response variable was done joining with the areas of Production, Quality and
Process Engineering and it was decided that initially the factors studied are: upper axle
speed, cutting profundity, belt length and the polyurethane sleeve condition. These factors
were chosen because they had more rapid changes in the response variable studied.
Adjustment levels for the control factors are shown in table 1. An important
observation is related to levels of adjustment for polyurethane sleeve and belt length. For
the low level (-), old polyurethane sleeve means it was used for approximately 240
cutting slabs and already has your surface damaged and new polyurethane sleeve, high
level (+), is the sleeve with the surface intact. For the factor the belt length, the low level () lower, means the belt length minus 100 mm and high level (+) nominal, means
establishing this parameter with the nominal belt length (perimeter) in cutting machine.
Table 1. Control factors and adjustments levels of factors - 01/24/2012
Factors
A. Polyurethane sleeve
B. Axle speed
C. Cutting profundity
D. Belt length
Source: Author
Adjustments levels
-1
Old
300 (rpm)
101 (mm)
Lower
+1
New
600 (rpm)
105 (mm)
Nominal
For the four control factors and their two levels was made the choice of the
experimental design and decided to use a fractional factorial 2k-1 (k = 4), ie half fraction of
experiment 24 with resolution IV. Whereas the thickness of the slab entering the cutting
machine has a small variation, and that such variation is not significant in the cutting
process, all belt obtained in a given setting of the process may be regarded as a replica of
the experiment. Thus, we chose to measure 30 belts in each experiment, divide them into
groups of 5 belts and the mean response of each group was considered to be a replica of
the experiment. Due to the difficulty of working with the same kind of belt in all experiments
(cut eight consecutive belts of the same width and stop processes running), we chose to
evaluate like response of the experiments the standard deviation of the width, so
independent the width of the cut belt, evaluates the results on the same optical, which is
precisely the change we want to reduce in the process.
With all these considerations it was possible to perform an experiment fractional
factorial 2 (4-1) with eight different combinations of factors and with six replicates each. This
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approach allowed us to reduce the number of experiments, the execution time and obtain
the results and the probability of damaging belts, if one of the combinations provide belts
outside of customer specifications and all experiments were performed in a single block in
one day.
3 THEORY
In accordance with (RODRIGUES and IEMMA 2009) [3], factorial experiments
designed are those which evolve combinations between levels of two or more factors. For
(MONTGOMERY, 2009) [5], a designed experiment is a test or series of tests in which
purposeful changes are made on the input variables of a process, which you can see and
identify corresponding changes in the output response. As a process, defines the activities
that use resources and transform raw material into a product output.
According (MONTGOMERY, RUNGER and HUBELE 2001) [4], most processes
can be described in terms of several controllable variables, such as temperature, pressure
and feed rate. By the use of designed experiments, engineers can determine which subset
of process variables have the greatest influence on process performance.
According (MONTGOMERY 2009) [5], some of the process variables are
controllable, while others are not controllable (although they may be controllable for the
purpose of testing). Sometimes these uncontrollable factors are called noise factors.
The main objectives of the design of experiments are:




Define which variables are most influential in the response studied
y, being that the type of experiment aim for this determination is the
characterization;
Setting the value to be given the variables that influence the response y, so
that it is near the specified value;
Define the value of influential variables (x's) that make the variation in the
response y, smaller;
Define the value of influential variables (x's) which minimize the effect of
noise on the response y.
The choice of the experimental design will depend on the choice of factors and
levels. A factorial experiment using all possible combinations of factors and their levels are
defined as full factorial. However, with the increased number of factors and levels, the
number of runs required to perform the experiment becomes excessively high. In order to
reduce the number of runs in experiments 2k, especially within the industry and the
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consequent cost linked thereto, can be used replica of fractionated experiments 2k-1 or
fractions even smaller 2k-p.
As is generally the main effects and second order interactions are responsible for
significant variations in the studied response y, the interactions of third order and higher
are commonly neglected. Considering that in the initial stages of studying a particular
process seeks to perform a scan by adding various factors to experiments to identify which
of them have significant effects on the response of interest and then can be studied in
detail, using fractional factorial experiments is a good alternative to be used to obtain
information on main effects and interactions of second order.
In the use of fractional factorial experiments as a result of the decrease of the
degrees of freedom by reducing the number of runs, the effect of the major factors are now
estimated with the effects of the interactions in linear combinations, i.e. having an estimate
of the sum two or more effects, depending on the number of studied factors and the
fraction chosen.
Another possibility to reduce the number of runs in factorial experiments planned
is to perform experiments 2k without repetitions or replicas. However, this practice do not
provides degrees of freedom to the residue and consequently to calculate the standard
error. Still considering the interactions of higher orders are not significant variation in the
response y, we can combine these interactions as an estimate of the error, but for
experiments without repetition, this device is not appropriate. As an estimate of error is
needed so that one can make inferences about the studied response and obtain
predictions of the process, a lot strategy used in this case is a normal probability plot for
evaluate the significance of the effects. According to (MONTGOMERY, RUNGER e
HUBELE 2001) [4], the effects are negligible are normally distributed with mean zero and
tend to fall along a straight line in the graph, while no significant effects have not null mean
and not to lie down along the line. Other ways of estimating errors are adding points to the
central experimental design and adding axial points.
An important step that precedes the design of experiments is the definition of the
problem to be studied, the expectations with respect thereto and what results are intended
to be achieved with the experimental design. MONTGOMERY (2009) [5] provides some
guidelines for the design of experiments:
1.
2.
3.
4.
5.
6.
7.
Recognition and reporting of the problem;
Choice of factors and levels;
Selection of the response variable;
Choice of experimental design;
Conducting the experiment;
Analysis of the data;
Conclusions and recommendations.
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An important consideration that should be made is also about getting
unsatisfactory results. As the experimentalist performs assumptions about the system,
such as which factors will be studied and which area of experimentation, many classified
as poor results are the result of wrong choice of factors, levels and experimental technique
used and should not be construed as such. These results should be used to define new
variables of study hypotheses and experimental conditions and provide the basis for all
other knowledge that will be obtained in the process. Moreover, as every design of
experiments is conducted on the basis of prior knowledge, whenever undesirable results
are obtained, new hypotheses must be made and new experiments conducted, seeking
the combination of factors that lead levels in the process to optimal performance.
4 RESULTS AND DISCUSSION
Table 2 shows the experimental matrix used in this project and the responses for
each run.
4-1
Table 2. Fractional factorial experiment 2
Runs
Polyurethane sleeve
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
new
old
old
old
new
new
old
new
new
old
new
old
new
old
old
new
new
new
old
old
old
old
new
Axle speed
(rpm)
600
600
300
600
600
600
600
600
300
300
600
300
300
300
600
300
600
600
600
300
300
300
600
Cutting profundity
(mm)
105
105
105
101
105
101
101
101
105
101
105
105
101
105
101
105
105
101
105
105
101
105
101
Belt length
(mm)
nominal
lower
nominal
nominal
nominal
lower
nominal
lower
lower
lower
nominal
nominal
nominal
nominal
nominal
lower
nominal
lower
lower
nominal
lower
nominal
lower
Response, y
(deviation in inches)
0,010
0,010
0,015
0,010
0,009
0,007
0,012
0,011
0,010
0,008
0,009
0,015
0,009
0,015
0,008
0,010
0,008
0,010
0,007
0,010
0,011
0,013
0,011
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24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
Source: Author
600
300
600
600
300
600
600
300
600
300
300
300
300
600
600
300
600
300
300
300
300
600
300
600
300
new
new
old
new
old
old
old
new
old
old
new
new
old
old
old
new
new
new
old
new
new
old
new
new
old
101
105
101
105
101
101
105
101
105
105
105
101
101
105
105
105
105
101
101
101
101
101
105
101
101
lower
lower
nominal
nominal
lower
nominal
lower
nominal
lower
nominal
lower
nominal
lower
lower
lower
lower
nominal
nominal
lower
nominal
nominal
nominal
lower
lower
lower
0,008
0,007
0,013
0,012
0,010
0,009
0,007
0,009
0,006
0,009
0,009
0,009
0,010
0,008
0,010
0,010
0,008
0,007
0,012
0,009
0,008
0,008
0,012
0,010
0,010
Table 3 presents the effects and coefficients for the factors and their interactions
that were estimated for the response y (variation cutting width). In this table, it appears that
the most significant main effects are: B and A. And the interactions that have the most
significant effects are: AD and AB, but their effects are confounded with other second
order interactions (AB = CD, AC = BD and AD = BC), making it difficult to determine the
combination of the most important parameters in cutting process of automotive belts.
Table 3. Effects and estimated coefficients for the response y (coded units).
Terms
Effect
Coefficient SE Coef
T
P
-
0,00975
0,000253
38,47
0,000
A. Polyurethane sleeve
-0,0010
-0,00050
0,000253
-1,97
0,055
B. Axle speed
-0,0011
-0,00054
0,000253
-2,14
0,039
C. Cutting profundity
0,0004
0,00021
0,000253
0,82
0,416
D. Belt length
0,0008
0,00042
0,000253
1,64
0,108
AB = CD
0,0014
0,00071
0,000253
2,79
0,008
AC = BD
0,0001
0,00004
0,000253
0,16
0,870
AD = BC
Source: Author
-0,0015
-0,00075
0,000253
-2,96
0,005
Constant
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Figure 1 shows the normal probability plot of the experiment, in this graph, the
non-significant effects are normally distributed and have zero mean, resting on the line.
Normal Plot of the Standardized Effects
(response is Deviation, Alpha = 0,10)
99
Effect Ty pe
Not Significant
Significant
95
AB
90
Percent
80
70
60
50
40
30
F actor
A
B
C
D
N ame
P U sleev e
A xle speed
C utting profundity
Length belt
A
B
20
10
AD
5
1
-3
-2
-1
0
1
Standardized Effect
2
3
Figure 1. Normal probability plot
Source: Author
Figure 2 is a Pareto chart of the estimated effects of the main factors and their
interactions, which shows the significance of them based on the value of the statistic T, t (df;
α/2), where d.f. are degrees of freedom of the residue and α is the significance level
evaluated.
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Pareto Chart of the Standardized Effects
(response is Deviation, Alpha = 0,10)
1,684
F actor
A
B
C
D
AD
AB
N ame
P U sleev e
A xle speed
C utting profundity
Length belt
Term
B
A
D
C
AC
0,0
0,5
1,0
1,5
2,0
Standardized Effect
2,5
3,0
Figure 2. Pareto effects
Source: Author
A graphical interpretation of Figures 1 and 2 is the same as in Table 3, i.e. factors
and interactions have significant effects are: B, A, AD and AB. However, as previously
mentioned, the effects of interactions are confounded. Table 4 presents the analysis of
variance (ANOVA), which checks whether the statistical variation of the experimental
results is significant in the cutting process studied.
Table 4. Analysis of variance (ANOVA) - coded units
Source
DF
Main Effects
A. Polyurethane sleeve
B. Axle speed
C. Cutting profundity
D. Belt length
2-Way Interaction
AB = CD
AC = BD
AD = BC
Residual Error
Pure Error
Total
4
1
1
1
1
3
1
1
1
40
40
47
Sequential
sum of
squares
0,00003650
0,00001200
0,00001408
0,00000208
0,00000833
0,00005117
0,00002408
0,00000008
0,00002700
0,00012333
0,00012333
0,00021100
Adjusted sum
of squares
Adjusted mean
squares
0,00003650
0,00001200
0,00001408
0,00000208
0,00000833
0,00005117
0,00002408
0,00000008
0,00002700
0,00012333
0,00012333
0,00000913
0,00001200
0,00001408
0,00000208
0,00000833
0,00001706
0,00002408
0,00000008
0,00002700
0,00000308
0,00000308
F
p
Value
2,96
3,89
4,57
0,68
2,70
5,53
7,81
0,03
8,76
0,031
0,055
0,039
0,416
0,108
0,003
0,008
0,870
0,005
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Source: Author
Analysis of Variance (ANOVA) for the response variation of cutting width,
demonstrates, with 90% confidence that the factors that influence the cutting operation of
the company studied are: the condition of the polyurethane sleeve (PU sleeve), the upper
axle speed, the interaction length belt x PU sleeve that is confused with the interaction
axle speed x cutting profundity and the interaction PU sleeve x axle speed that is confused
with the interaction cutting profundity x length belt.
Figures 3 and 4 illustrate the main effects of the factors and the effects of the
interactions on the response y, respectively.
Main Effects Plot for Response Cutting Width Variation
Data Means
PU sleeve
0,0104
Axle speed
0,0100
Mean
0,0096
0,0092
old
new
300
Cutting profundity
0,0104
600
Length belt
0,0100
0,0096
0,0092
101
105
lower
nominal
Figure 3. Main effects factors
Source: Author
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Interaction Plot for Response Cutting Width Variation
Data Means
300
600
101
105
lower
nominal
0,011
0,010
PU sleeve
PU sleev e
old
new
0,009
0,011
0,010
Axle speed
0,009
0,011
0,010
Cutting profundity
0,009
A xle
speed
300
600
C utting
profundity
101
105
Length belt
Figure 4. Interactions between factors
Source: Author
With data and knowledge obtained so far on the process, it can be considered that
the effect of the interaction AC = BD it is not significant in the response cutting width
variation, however, the establishment of the levels of factor C = cutting profundity and D =
belt length, which are not significant, cannot be safely neglected, since the interaction AB
= CD has a significant effect on the response of interest and, according MONTGOMERY
(2009) [5], when the interaction is very large, the corresponding main effects have little
meaning. Thus, knowledge of the interaction CD is more useful than the knowledge of
main effect. A significant interaction may mask the significance of main effects.
A more satisfactory operating condition is shown in Table 5, for evaluating the
graphs of interaction (Figure 4), considering the AD interaction, the belt length should be
set at the low level, i.e. lower length of the belt, because even with wear of the PU sleeve
(old PU sleeve), the cutting width variation remains small. For BC interaction, we must
establish the axle speed at 600 rpm and cutting profundity at 101 mm because, although
the process with the axle speed at 600 rpm and cutting profundity at 105 mm generate
less variation, the wear of PU sleeve is larger, and it has high replacement cost. And
operate the cutting machine with low axle speed (300 rpm) and low cutting profundity (101
mm) is not feasible, due low productivity. Considering the AB interaction, we must work
with new PU sleeve (high level) and axle speed at 600 rpm, because with the wear of PU
sleeve, if the axle speed is low, the cutting width variation increases. Now, considering the
CD interaction, we have that, the factor`s levels that compose it already been established,
when settled the levels of the factors for the other interactions, i.e. cutting profundity at 101
mm and lower length of the belt.
Table 5. New operating condition
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Factors
Level
Value
A. Polyurethane sleeve
+1
New
B. Axle speed
+1
600 (rpm)
C. Cutting profundity
-1
101 (mm)
D. Belt length
-1
Lower
Source: Author
Despite being obtained an improved condition of operation, the fact that some
second-order interactions have shown significant effects on the response of interest and
determination of these effects are linear combinations of the sum of two interactions, the
real impact of the effect of these interactions on the cutting width variation cannot be
determined. Thus, during the presentation of results for management of process
engineering, production and quality team, was suggested the another half-fraction from
fractional factorial experiment 24-1, which is allowed for the estimation of independent
experimental effects (planning orthogonal matrix), and then, after the characterization of
the cutting process, which is conducted an experiment of optimization with techniques of
response surface planning to determine the set of conditions of the significant factors on
the width variation result in the best performance of the process.
5 CONCLUSIONS
Initially, through the experiments we were able to get interest for the company`s
people for the use of statistical methods for quality improvement of products and
processes. Another benefit achieved is the demonstration by data, which control the
characteristic cutting width, so only by establishing the desired width of the cutting
machine, is not sufficient to ensure the specified width, but it is necessary to implement
controls the other variables input. The scientific method used to seek the solution of the
problem also demonstrated that interactions between variables can only be evaluated with
the simultaneous variation of their levels and the technique of one factor at a time is
inefficient.
Another important point to be noted is that there is no single recipe for the
experimental design of all the problems, being necessary besides statistical knowledge, to
add knowledge about the process investigated and the availability of the company to
perform the experiments in pursuit of continuous improvement, a since, all the knowledge
to start on assumptions that, over time, with the advent of new technologies and the
expansion of knowledge, are being reviewed and improved based on the results obtained.
ACKNOWLEDGEMENTS
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Thanks to the managers of the company studied, believing that scientific
knowledge applied within the industry could bring significant results for the whole society
and the employees of the company for the conduct of this work.
REFERENCES
[1] ROSS, Phillip J. Aplicações das Técnicas de Taguchi na Engenharia da Qualidade. São Paulo:
McGraw-Hill Ltda, 1991.
[2] SCHWAAB, Marcio; PINTO, José C. Análise de dados experimentais, volume II: Planejamento
de experimentos. Rio de Janeiro: E-papers, 2011.
[3] RODRIGUES, Maria I. ; IEMMA, Antonio F. Planejamento de experimentos e otimização de
processos, 2ed. Campinas: Casa do espirito amigo fraternidade fé e amor, 2009.
[4] MONTGOMERY, Douglas C.; RUNGER, George C.; HUBELE, Norma F. Estatística aplicada a
engenharia, 2ed., Rio de Janeiro: LTC, 2001.
[5] MONTGOMERY, Douglas C. Introdução ao controle estatístico da qualidade, 4ed., reimpr. Rio
de Janeiro: LTC, 2009.
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