ESTIMATION OF PARAMETERS IN INDUSTRIAL PROCESSES … · ESTIMATION OF PARAMETERS IN INDUSTRIAL...

The 4th International Congress on University-Industry Cooperation – Taubate, SP – Brazil – December 5th through 7th, 2012 ISBN 978-85-62326-96-7

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.

mailto:[email protected]


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:


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 Adjustments levels

-1 +1

A. Polyurethane sleeve Old New

B. Axle speed 300 (rpm) 600 (rpm)

C. Cutting profundity 101 (mm) 105 (mm)

D. Belt length Lower Nominal

Source: Author

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


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


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. Recognition and reporting of the problem; 2. Choice of factors and levels; 3. Selection of the response variable; 4. Choice of experimental design; 5. Conducting the experiment; 6. Analysis of the data; 7. Conclusions and recommendations.


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.

Table 2. Fractional factorial experiment 24-1

Runs Polyurethane sleeve Axle speed

(rpm) Cutting profundity

(mm) Belt length

(mm) Response, y

(deviation in inches)

1 new 600 105 nominal 0,010 2 old 600 105 lower 0,010 3 old 300 105 nominal 0,015 4 old 600 101 nominal 0,010 5 new 600 105 nominal 0,009 6 new 600 101 lower 0,007 7 old 600 101 nominal 0,012 8 new 600 101 lower 0,011 9 new 300 105 lower 0,010 10 old 300 101 lower 0,008 11 new 600 105 nominal 0,009 12 old 300 105 nominal 0,015 13 new 300 101 nominal 0,009 14 old 300 105 nominal 0,015 15 old 600 101 nominal 0,008 16 new 300 105 lower 0,010 17 new 600 105 nominal 0,008 18 new 600 101 lower 0,010 19 old 600 105 lower 0,007 20 old 300 105 nominal 0,010 21 old 300 101 lower 0,011 22 old 300 105 nominal 0,013 23 new 600 101 lower 0,011


24 new 600 101 lower 0,008 25 new 300 105 lower 0,007 26 old 600 101 nominal 0,013 27 new 600 105 nominal 0,012 28 old 300 101 lower 0,010 29 old 600 101 nominal 0,009 30 old 600 105 lower 0,007 31 new 300 101 nominal 0,009 32 old 600 105 lower 0,006 33 old 300 105 nominal 0,009 34 new 300 105 lower 0,009 35 new 300 101 nominal 0,009 36 old 300 101 lower 0,010 37 old 600 105 lower 0,008 38 old 600 105 lower 0,010 39 new 300 105 lower 0,010 40 new 600 105 nominal 0,008 41 new 300 101 nominal 0,007 42 old 300 101 lower 0,012 43 new 300 101 nominal 0,009 44 new 300 101 nominal 0,008 45 old 600 101 nominal 0,008 46 new 300 105 lower 0,012 47 new 600 101 lower 0,010 48 old 300 101 lower 0,010

Source: Author

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

Constant - 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 -0,0015 -0,00075 0,000253 -2,96 0,005

Source: Author


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.

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.

3210-1-2-3

99

95

90

80

70

60

50

40

30

20

10

5

1

Standardized Effect

Pe

rce

nt

A PU sleev e

B A xle speed

C C utting profundity

D Length belt

Factor Name

Not Significant

Significant

Effect Type

AD

AB

B

A

Normal Plot of the Standardized Effects(response is Deviation, Alpha = 0,10)


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 Sequential

sum of squares

Adjusted sum of squares

Adjusted mean squares

F p

Value

Main Effects 4 0,00003650 0,00003650 0,00000913 2,96 0,031 A. Polyurethane sleeve 1 0,00001200 0,00001200 0,00001200 3,89 0,055 B. Axle speed 1 0,00001408 0,00001408 0,00001408 4,57 0,039 C. Cutting profundity 1 0,00000208 0,00000208 0,00000208 0,68 0,416 D. Belt length 1 0,00000833 0,00000833 0,00000833 2,70 0,108 2-Way Interaction 3 0,00005117 0,00005117 0,00001706 5,53 0,003 AB = CD 1 0,00002408 0,00002408 0,00002408 7,81 0,008 AC = BD 1 0,00000008 0,00000008 0,00000008 0,03 0,870 AD = BC 1 0,00002700 0,00002700 0,00002700 8,76 0,005 Residual Error 40 0,00012333 0,00012333 0,00000308

Pure Error 40 0,00012333 0,00012333 0,00000308 Total 47 0,00021100

AC

C

D

A

B

AB

AD

3,02,52,01,51,00,50,0

Te

rm

Standardized Effect

1,684

A PU sleev e

B A xle speed

C C utting profundity

D Length belt

Factor Name

Pareto Chart of the Standardized Effects(response is Deviation, Alpha = 0,10)


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.

Figure 3. Main effects factors

Source: Author

newold

0,0104

0,0100

0,0096

0,0092

600300

105101

0,0104

0,0100

0,0096

0,0092

nominallower

PU sleeve

Me

an

Axle speed

Cutting profundity Length belt

Main Effects Plot for Response Cutting Width VariationData Means


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

600300 105101 nominallower

0,011

0,010

0,009

0,011

0,010

0,009

0,011

0,010

0,009

PU sleeve

Axle speed

Cutting profundity

Length belt

old

new

PU sleeve

300

600

speed

Axle

101

105

profundity

Cutting

Interaction Plot for Response Cutting Width VariationData Means


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


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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