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Statistical quality control through overall vibration analysis

Ma Carmen Carnero a,, Rafael González-Palma b, David Almorza b, Pedro Mayorga b,Carlos López-Escobar c,d,e

a University of Castilla-La Mancha, Technical School of Industrial Engineering, Avda. Camilo José Cela s/n, 13071 Ciudad Real, Spainb University of Cádiz, Technical School of Industrial Engineering, Calle Chile 1, 11002 Cádiz, Spainc University of Cádiz, School of Work Sciences, Calle Duque de Ná jera 6, 1002 Cádiz, Spaind Electrical Technology Institute (ITE), Avenida de Juan de la Cierva 24, parque tecnoló gico de Valencia, 46980 Valencia, Spaine Aluminum Company of America (ALCOA), Paseo de la Castellana 95, Edificio Torre Europa, 28046 Madrid, Spain

a r t i c l e i n f o

Article history:

Received 24 October 2008

Received in revised form

4 September 2009

Accepted 11 September 2009Available online 25 September 2009

Keywords:

Machine tool

Vibration analysis

Quality

ANOVA

a b s t r a c t

The present study introduces the concept of statistical quality control in automotive

wheel bearings manufacturing processes. Defects on products under analysis can have a

direct influence on passengers’ safety and comfort. At present, the use of vibration

analysis on machine tools for quality control purposes is not very extensive in

manufacturing facilities.

Noise and vibration are common quality problems in bearings. These failure modes

likely occur under certain operating conditions and do not require high vibration

amplitudes but relate to certain vibration frequencies. The vibration frequencies are

affected by the type of surface problems (chattering) of ball races that are generated

through grinding processes.

The purpose of this paper is to identify grinding process variables that affect thequality of bearings by using statistical principles in the field of machine tools. In

addition, an evaluation of the quality results of the finished parts under different

combinations of process variables is assessed. This paper intends to establish the

foundations to predict the quality of the products through the analysis of self-induced

vibrations during the contact between the grinding wheel and the parts. To achieve this

goal, the overall self-induced vibration readings under different combinations of process

variables are analysed using statistical tools. The analysis of data and design of

experiments follows a classical approach, considering all potential interactions between

variables. The analysis of data is conducted through analysis of variance (ANOVA) for

data sets that meet normality and homoscedasticity criteria. This paper utilizes different

statistical tools to support the conclusions such as chi squared, Shapiro–Wilks,

symmetry, Kurtosis, Cochran, Hartlett, and Hartley and Krushal–Wallis.

The analysis presented is the starting point t o extend the use of predictive techniques

(vibration analysis) for quality control. This paper demonstrates the existence of

predictive variables (high-frequency vibration displacements) that are sensible to the

processes setup and the quality of the products obtained. Based on the result of this

overall vibration analysis, a second paper will analyse self-induced vibration spectrums

in order to define limit vibration bands, controllable every cycle or connected to

permanent vibration-monitoring systems able to adjust sensible process variables

identified by ANOVA, once the vibration readings exceed established quality limits.

& 2009 Elsevier Ltd. All rights reserved.

Contents lists available at ScienceDirect

journal homepage: www.elsevier.com/locate/jnlabr/ymssp

Mechanical Systems and Signal Processing

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0888-3270/$ - see front matter & 2009 Elsevier Ltd. All rights reserved.doi:10.1016/j.ymssp.2009.09.007

Corresponding author. Tel.: þ34 926 295300x3863; fax: þ34 926 295361.

E-mail address: [email protected] (M.C. Carnero).

Mechanical Systems and Signal Processing 24 (2010) 1138–1160

http://-/?-http://www.elsevier.com/locate/jnlabr/ymssphttp://localhost/var/www/apps/conversion/tmp/scratch_4/dx.doi.org/10.1016/j.ymssp.2009.09.007mailto:[email protected]:[email protected]://localhost/var/www/apps/conversion/tmp/scratch_4/dx.doi.org/10.1016/j.ymssp.2009.09.007http://www.elsevier.com/locate/jnlabr/ymssphttp://-/?-


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1. Introduction

Periodically, the mass media report on the appearance of defective lots not detected during the manufacturing process

and that therefore have come to the market. On occasions, the announced quantities are extremely high and the

manufacturers face high losses in expenses of review and substitution of elements. This type of problem is usual in the

automotive market, where volumes manufactured are high.

The appearance of this type of situation persists in spite of the existence of agreements of quality coordinated betweenmanufacturers and suppliers, as well as rigorous statistical systems of internal quality control, which assure the

maintenance of processes within the quality levels established. In some cases, the nature of the quality problems makes

their control complex, especially when the product specifications are tight.

In this paper, condition monitoring-technologies are applied to the study of the mechanical behaviour of high-precision

processes and then extend the concept of predictive maintenance to quality control. The aim is to discover the nature of

vibrations generated by the process itself to detect early symptoms that indicate a separation from the quality zone

objective, as well as to determine which are the variables that induce the vibration most suitable for predicting quality

problems.

It must be considered that at the moment there are very few companies that apply vibration analysis to machine tools in

the periodical control of quality insurance. At present, the study of vibration analysis induced by the process is a subject

that is almost unexplored.

Specifically, one of the major quality problems in the bearings industry is the occurrence of noises when bearings are in

certain functioning conditions. The existence of this fault does not need very big amplitudes but it conditions the frequencyof the vibration, which has been determined by the type of chattering obtained in the manufacturing processes of their

tracks of tread.

Harris [17] defines that the roundness of a part on a certain section is correct when a point exists in this section from

which all the points of the periphery are halfway, this point being the center of the circle. When the section is not totally

circular, the part is considered to be out of roundness and this is specified as the difference in distance between the

outlying points and the center. In Fig. 1, the degree of deviation of the roundness is the value r 2r 1, that is, the difference

between the maximum and minimum radii.

When a part is manufactured by a machine tool, the profile obtained is of an irregular type in the rolling tracks and in

the rolling elements (see Fig. 2); this will affect the durability and operation of the bearing.

Chattering has a decisive influence on the final vibration of the bearing; its importance depends on the number of

existing lobes and their depth. Besides, the problem is greater when taking into account that the final vibration is the result

of the combined effect of roundness of rolling tracks, balls, superficial finishes of all surfaces and assembly conditions. This

may lead to the manufacturing of noisy bearings if certain natural frequencies are excited, which is especiallyuncomfortable in automotive wheel bearings.

ARTICLE IN PRESS

r 2

r 1

Fig. 1. Examples of profiles. Circular profile r 2r 1=0 Profile with chattering of order 3 (3 lobes).

Acronyms

mm-H high-frequency displacements

mm-L low-frequency displacements

cpm cycles per minute

ED experimental design

g unit of acceleration caused by the force of gravity (9.8 m/s2)

H0 null hypothesis

H1 research hypothesis

Hz hertz

Lob A high-frequency chattering (very-fast move-

ments of the dial indicator on turning the

part).

Lob B low-frequency chattering (slow movements of

the hands of the dial indicator on turning the

part).

P values the significance level of a statistical testRMS root mean square

rpm revolutions per minute

SQC statistical quality control

W Shapiro–Wilks test

M a.C. Carnero et al. / Mechanical Systems and Signal Processing 24 (2010) 1138–1160 1139


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The final consequences of a certain chattering of tracks are difficult to predict by means of theoretical models, due to the

fact that in the final response of the mechanical system many variables related with the suspension system, tyres, etc.

intervene; As a result what generally occurs is that, the frequencies of noxious chattering are evaluated rather than the final

response of the vehicle.

The chattering of surfaces is a phenomenon that is impossible to fully eradicate, although it can be controlled. These

problems are more serious as requirements of roundness of pieces are more demanding.

Therefore, the purposes of this paper are to identify important design variables affecting the quality of the bearings by

using statistical tools in the field of machine tools, to evaluate quality results of the parts corresponding to the variation of

process parameters, and to evaluate the quality of components by means of a cross-vibration analysis. In a bearing there are

different sources of vibration, whose repercussion on its functioning will depend on the amplitude and frequency of

occurrence.The condition-monitoring techniques have been applied with success in different systems and machinery; in DC motors

[45], helicopters [22], turbine driving a centrifugal compressor [31], rolling element bearings [39] or railway systems [30].

However, their application to the motor vehicle industry is more limited, though some interesting contribution in this

sector has been developed (see [25] but more related to warranty claims.

In the literature related to the diagnosis of machinery, there are a great number of contributions (generally applied to

bearings and gear boxes) that use vibration analysis together with statistical concepts; among them, the following can be

outlined: [2,6,20,23,24,26,34,36,38,40,41,43,47].

The diagnosis specifically applied to machine tools has been extensively analysed in literature too; in [35] a sum of

condition-monitoring techniques applied to machine tools can be checked. In [42] autocorrelation analysis is used in

conjunction with windowing capability to isolate causes for subsequent remedial actions. In [8] the Taguchi method and

analysis of variance (ANOVA) were used to analyse the effect of the process of self-induced vibration.

Snoeys [37] and Biera et al. [4,5] justify instability in the behaviour of self-induced vibrations of the grinding process.

Ref. [11] presents experimental results from the in-process measurement of d under chatter conditions on a cylindricalgrinding machine.Ref. [12] describes the tests conducted to measure the variation in force caused by oscillation in part

speed and its significant effect on chatter in grinding. In [46] a non-linear dynamic model is developed so that numerical

simulations can provide a view of the stability of this grinding process for the design, analysis and verification of

manufacturer roll grinding measurements.

In spite of the work of Hahn [16], where different input variables are selected in the grinding process to improve the

production grinding performance, the application to the follow-up and control of the quality processes by means of the

application of these condition-monitoring techniques is a field that is practically unexplored at present. As explained in [3],

less attention is devoted to developments in integrated condition-monitoring systems with data collected from

maintenance, quality, production, etc., though the necessity to identify and eliminate quality deviations and causes of

failure at early stages, thus assuring high-quality products, is widely recognised [1].

Nevertheless, the few papers and existing research that might be applied to quality control in machine tools are of a very

general type. Neither process tolerances nor critical frequencies of vibration are considered, because the quantity of data

produced would turn out to be impossible to handle [7,27].This paper applies vibration analysis technology to a high-volume production line, composed of a group of similar high-

precision grinding machines. The problem analysed is the sporadic appearance of chattered surfaces. This problem may

cause quality defects to the extent of 106 m in parts due to the lobes resulting to any machining process. Thus, an effort

must be made to control these small deviations that may, however, generate quality problems or otherwise seriously affect

the behaviour of the vehicle and passengers’ comfort; the part analysed has significant influence on the safety of the

vehicle, and therefore, control of potential failures is critical.

During their normal cyclical functioning, the machine tools cross zones of insufficient quality, which suggests the

existence of vibrations induced by the process itself. This aspect depends on the natural response of the mechanical system

faced with the stimulation caused by the process. These deviations happen even when all the process parameters under

control are within tolerance.

The object of this paper is to reach conclusions about the relation between the mechanics of the process and the

resulting quality, and thereby to establish a generic protocol of analysis. In order to do this, it is first necessary to evaluate

the behaviour of global values of the different vibration units during work cycles, as well as analysing the influence of process variables in different mechanical vibration units in order to discover which mechanical variables show greater

ARTICLE IN PRESS

r 1

r 2r 4 AB

r 3

Fig. 2. Chattered profile on part processed in a machine tool.

M a.C. Carnero et al. / Mechanical Systems and Signal Processing 24 (2010) 1138–11601140


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sensitivity against failure occurrence; this will be the starting point of the spectral analysis that will be developed in later

contributions. For the attainment of these aims, an experimental design and variance analysis of the mechanical response

of the process (alert variables) has been chosen, expressed as global values of displacements, velocities and accelerations,

depending on the variation of entry parameters (cause variables). The number of variables that influence the quality of the

part or mechanical behaviour of the process is high. The present protocol establishes criteria for selecting the most

influential variables.

Preliminary experiments were developed by altering different process variables; these experiences were evaluated

along with other considerations to determine the most appropriate experimental design methodology for the analysis.Hereby, the set of variables effect, reason and alert with influence on the problem will be determined and included in the

statistical analyses (see Fig. 3 for the process description followed in this paper).

In the global experimentation, the quality outcome of parts manufactured (effect variables) during the sequence of

experiments is also assessed in order to be able to detect the possible relation of the overall vibration value with the quality

obtained. During the tests, the profiles of changes in magnitudes in different work cycles are also assessed, including the load

and unload cycles of parts, the grinding wheel to part distance and the machining phases (rough, finishing). The aim of ANOVA

of overall vibration values is to distinguish which of them or their interactions must be the basis for a later spectral analysis.

The study is applied to interior and exterior rectified machines in a bearings factory of an important company that

manufactures automotive components. The experimental phase of the protocol required the placement of vibration sensors

in strategic places in machines, near the grinding wheel–part contact, so that vibrations caused during the elimination of

material processes could be registered. The analysis carried out in this paper, applied to bearings, controls potential

catastrophic failures in the bearings that could risk safety and comfort of the vehicle passengers.

The paper layout is as follows. Section 2 explains the characteristics of the behaviour of the machine tools. In Section 3,the measurement system used for data acquisition is explained. In Section 4, the selection process of the variables to be

included in the research is described. In Section 5, the hypotheses of the statistical quality control (SQC) model are shown.

In Section 6, the overall vibration analysis carried out by means of ANOVA and quality results from the process to the

product (automotive bearings) are described. Section 7 gives the conclusions and finally the bibliography.

2. Cyclical behaviour of machine tools

The vibratory behaviour of machinery that operates in conditions of invariable load is well known [15]; the spectral

vibratory is simple, and the acquisition of information does not cause any limitation exempting the transitory periods

(start-ups, stops, opening valves, etc.). The behaviour of the machine tool analysed is cyclical, the cycle time lasting, in

many cases, of only a few seconds [14]. Besides, the cycles are divided into sub-processes in which work parameters

change, so the requirements of the mechanical components are modified, and consequently the dynamic behaviour of thesystem is altered.

ARTICLE IN PRESS

INPUT VARIABLES

The machine

The diameter of life of the grinding wheel

The speed of the grinding wheel

The rotational speed of the part

The magnetism or grip on the part

OUT VARIABLES

High frequency displacements (10-6m)

Low frequency displacements (10-3m)

Velocity of vibration (10-3m/s)

Acceleration (g)

High frequency chattering (Lob A)

Low frequency chattering (Lob B)

Alert variables(Mechanical behaviour

of the process (vibration))

Effect variables

(Quality of the process)

EXPERIMENTAL DESIGN

(ANOVA)

PRELIMINARY

EXPERIMENTS

Influence of the advance speed of the grinding wheel on the final chattering of the part.

Influence of the variable rotational speed of the part on chattering.

Influence of the relationship between the variable rotational speed of the part and the speed of the

grinding wheel in non-quality. Lack of roundness due to incorrect relation of the rotational speeds.

Spectral change alert. Bad finishing due to vibrations on the diamond roll.

Influence of the rotational speeds relation. Lack of roundness due

to incorrect relation of the rotational speeds.

Influence of the imbalance in the lack of roundness. Low frequency effects.

Influence of the variable rotational speed of the grinding wheel on chattering.

EVALUATION OF INTERACTIONS

THE MACHINE VARIABLE

PRELIMINARY

EXPERIMENTS

Influence of the relationship between the variable rotational speed of the part and the speed of the

grinding wheel in non-quality. Lack of roundness due to incorrect relation of the rotational speeds.

Spectral change alert. Bad finishing due to vibrations on the diamond roll.

Influence of the advance speed of the grinding wheel on the final chattering of the part.

Influence of the variable rotational speed of the part on chattering.

Influence of the rotational speeds relation. Lack of roundness due

to incorrect relation of the rotational speeds.

Influence of the imbalance in the lack of roundness. Low frequency effects.

Influence of the variable rotational speed of the grinding wheel on chattering.

EVALUATION OF INTERACTIONS

THE MACHINE VARIABLE

Fig. 3. Experimental process applied.



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In machine tool, on many occasions, very low vibration levels are measured in empty conditions (without grinding

wheel–part contact), that do not justify the deficient quality results of the products manufactured. The explanation of this

phenomenon is due to vibrations induced by the process itself. The evolution of the overall vibration value throughout the

work cycle of a machine tool presents the form that is shown in Fig. 4. Vibration peaks can be observed at the beginning

and end of the cycle, due to rapid movements of sliding panels of the machine. The points indicated in the first cycle

correspond to the beginning of the refine transition, refine finished and end of cycle. In Fig. 4, the vibration dependence

with time can be appreciated, obtaining very different values depending on the instant chosen for data acquisition.

3. Measurement system

The research is applied to interior and exterior rectified machines in a bearings factory of an industrial firm that

manufactures automotive components. The experimental phase required the placement of vibration sensors in strategic

places in machines, near the grinding wheel–part contact, so that the vibrations caused during the elimination of material

processes could be registered. The devices used to acquire vibration data and quality measurements are calibrated by

independent entities.

The tests undertaken during the experimental phase were carried out with the following devices:

1. Vibration analyser IRD 890 Mechanalysis. The selection range of maximum frequencies is between 1500 and1,500,000cpm; it has the capacity to measure displacement, velocity and acceleration in global values and spectral

charts (fast Fourier transform) as well as wave forms. The resolution depends on the maximum selected frequency

(F max), the number of resolution lines and on the number of averages that are established during the gathering/data

acquisition process to eliminate the influence of transitory vibrations. The time of data acquisition depends on the

aforementioned parameters. Therefore, once the F max optimum is fixed, the large number of averages and large number

of resolution lines increase the time considerably of data acquisition, as a result, these parameters were chosen so that

the time of data acquisition remained inferior to the time of contact grinding of the wheel–part (around 15 s in the

phase of experimental design). The conditioning signal is carried out by means of root mean square (RMS) of the peak

values of velocity and acceleration and peak–peak in displacement readings.

The analysis of relative influence between variables will be developed by means of overall vibration values in RMS. RMS

amplitude is the square root of the average of the squared values of the waveform. In the case of vibration waves, the

RMS value is 0.707 times the peak value. The RMS value of a vibration signal is an important measure of its amplitude.

To calculate this value, the instantaneous amplitude values of the vibration waveform must be squared, and these valuesmust be averaged over a certain length of time. This time interval must be at least one period of the wave in order to

obtain the correct value. The squared values are all positive, and therefore, so is their average. Then the square root of

this average value is extracted to get the RMS value. The overall vibration values in RMS give values for vibration

changes in the RMS value of the velocity amplitude from 10 to 1000 Hz; this system has been used in the study due that

these measurements are used in international standards [18].

The electric characteristics of the analyser mean that the vibration readings below 300 cpm (5 Hz) are not reliable when an

accelerometer is used due to the fact that single or double integration is required to obtain velocity and displacement data.

2. Accelerometer 970 from Mechanalysis. It has a range from 100 cpm to 600 kcpm of lineal behaviour. The anchorage type

used for the sensor is by means of an magnet of great power that limits the resolution of data acquisition up to

240 kcpm. This maximum frequency is far beyond the range in which the spectral data will appear; and therefore is

suitable for the measurement system.

3. The databases for the storage and manipulation of vibration data are the 7090 system of IRD Mechanalysis and ODYSSEY

system from Entek-IRD. In both cases, multiple graphic tools are included, as well as determination of vibration values inbands defined by the user and presentation of historical data.

ARTICLE IN PRESS

Vibration Beginning of data acquisition

level 1st cycle 2nd cycle 3rd cycle

Time

Fig. 4. Expected overall vibration trend during three consecutive cycles.



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To evaluate the quality of the parts, measurement devices available in the production areas were used. These devices are

able to detect if the chattering is in low frequency (slow movements of the needle of the clock comparer when the piece is

rotating), or high frequency (very quick movements of the clock comparer). Besides, three levels of chattering were

established for low and high frequency, according to the width of the displacements of the needle of the clock comparer.

These levels are established in a qualitative way as follows:

level 0—null or practically imperceptible chattering;

level 1—

movement of the sensitive indicator and level 2—severe chattering, significant widths of displacement.

Both the establishment of the types of chattering (low and high frequency) and the definition of different levels of

chattering severity were carried out so that the quality dataset of the parts obtained was governable; in so doing it is

possible to guarantee the correct treatment of data. Although a different definition of chattering types or levels could also

have been valid, it should be pointed out that the quality specifications of components, which cannot be detailed for

reasons of confidentiality, have validated the classification developed as suitable. The quality classification defined enables

the quantity of information to process to be controlled.

4. Determination of variables

Before the variables to be included in the analysis were determined, a previous study was developed to analyse realcases of quality problems motivated by vibration in machine tools in the manufacturing plant. These preliminary

experiments indicate the existence of a relation between the vibrations of machines and processes with the quality of parts.

The experiments that appear later are original and do not come from any bibliographical reference.

The set of experiments is carried out in two identical machines with the aim of applying the concept of global inter-

comparison. The selected machines are of the exterior rectified type, and the part is clamped by means of magnetism

combined with mechanical skates. The part is manufactured by the abrasive action of a grinding wheel that has a large

diameter and a long life. It is therefore an application without centers, selected by the high requirements of final roundness

(chattering) demanded of the product.

The following are among the cases that were analysed:

1. Influence of the relationship between the variable rotational speed of the part and the speed of the grinding wheel in

non-quality. Lack of roundness due to incorrect relation of the rotational speeds.

This case illustrates the importance of the correct choice for the turn speed of the part and the speed of the grindingwheel to prevent any components of the system from being in resonance. In this case, the quality audits showed a

persistent chattering of order eight (see Fig. 5) that was not responding to habitual treatments applied by qualified

personnel, such as modification of the rotational speed of the grinding wheel, adjustment of slide skates of the part,

modification of the grasp magnetic force, etc.

Speed controllers showed that the rotational speeds were correct, and it was not possible to find any difference with a

similar machine tool; therefore, vibration data acquisition was developed to compare it with others that had similar

characteristics (spectral comparison between machines). It was observed that the vibration peak of rotational speed of

the part work-head was shifted (300 cpm) compared with other identical machine tools (which were located near

700 cpm). This displacement in the spectrum of the imbalances indicated that the speed controller of the machine was

badly adjusted and showed a value far from the real one, which made the speed relation grinding wheel–part in the

process approach a resonance situation, causing the lobes to amplify considerably, and getting near to roundness values

of 6106 m, which is absolutely prohibitive in this application.

Fig. 5 shows the part before and after the adjustment of the rotational speed.

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Fig. 5. Roundness of tread track before and after changing the relative rotational speeds of the part and grinding wheel. Differences in quality results(chattering) are apparent. Both rotational speeds are within tolerance.



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2. Spectral change alert. Bad finishing due to vibrations on the diamond roll.

This case describes superficial bad finishing problems on the exterior grinder. In the machine tool there is a light

spectral degeneration at a point near the bearing of the dressing wheel shaft that regenerates the profile of the grinding

wheel. The overall vibration data show an increasing trend (see Fig. 6).

As quality problems arose and supplies were very expensive, it was decided not to take any type of action until new data

were obtained. However, the machine tool was required by the production process, and then a problem arose regarding

the superficial finishing of the parts. The spectral change in the problem is shown in Fig. 7.

3. Influence of the rotational speeds relation. Lack of roundness due to incorrect relation of the rotational speeds.

In the next experiment, the machine tool has a regulator for the peripheral speed of the grinding wheel, that is, the

rotational speed increases as the diameter of the grinding wheel diminishes, as well as rotational speeds of carries-partand wheel-dressing constants.

When the diameter of the grinding wheel reached 0.6 m, chattering of level five was generated on the part (see Fig. 8).

It was observed that the angular speed of the axis wheel dressing was exactly five times the value of the rotational speed

of draft of the axis carries-part and coincident with the rotational speed of the grinding wheel to this diameter; in these

conditions, the grinding wheel caused the part to include the mistake made in the dressing process. The problem was

solved by looking for a constant value of the rotational speed of the grinding wheel that did not cause any problems

throughout its useful life.

This test demonstrates the importance of the rotational relations between the different elements of a machine tool

when very small tolerances are allowed; thus, it is critical to reach a relation of prohibited speeds that stimulates one of

the frequencies of the system itself. This problem arises in all machines, though the relations of problematic speeds are

different in each case; however, the experience allows generating ranges of non-permissible functioning areas. These

ranges and the number of predictable lobes dependent on speed relations do not always provide coherent results. The

application of the numbers of lobes provided by Miller [27] has been effective only in very specific cases of the pointsanalysed in this paper. This is due to a lack of consideration of other random vibrations, not directly related to the

ARTICLE IN PRESS

O V

E R A L L V I B R A T I O N

V E L O C I T Y ( 1 0 - 3

m / s )

2.54

0

J F M A M J J A S O N D J F M A

MONTH

Fig. 6. Monthly trend of overall vibration speed in four measurement points located close to the wheel-dressing roller. The horizontal line is a reference

value set at 2.54103 m/s.

g e

o r a r y c

h a n

Result after repair

T e m p Quality problems

Degradations starts

mpck06)mpc(ycneuqer F0 kcpm

Initial spectra

Fig. 7. Spectral changes during development of bad surface finishing problems due to vibrations in the dressing wheel. The initial spectrum corresponds

to a situation with no quality problems. The increase of spectral activity at high frequencies observed in spectrums 2–4 is not shown due to a significant

increase of the overall vibration value but relates to surface quality problems.



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different combinations of speeds, which determine the final behaviour in quality. The aim of the SQC is precisely to

consider any possible influence that the contact grinding wheel–part by itself could cause.4. Influence of the imbalance in the lack of roundness—low-frequency effects.

The relation between vibration and chattering is very complex, because although high-amplitude vibrations were

registered, this need not cause chattering. This aspect must be considered by means a spectral analysis.

The next test shows the influence of low-frequency vibration on the chattering of the product. The aim of this

experiment was to determine if there is a direct relation between the imbalance of the carries-grinding wheel and the

appearance of defective pieces. This is often the first intuitive explanation for chattering, but as will be observed later,

though very high values of imbalance are obtained by means of the addition of counterweights, chattering may remain

the same or reach high values of vibration corresponding to the rotational speed of the screw.

In the test results shown in Table 1, the grinding wheel speed was kept at 21,500 rpm, and for every value of imbalance

there was the development of a rotational speed sweep of the head carries-part; the parts were mechanized to 90%,

100% and 110% of their nominal value, set at 760 rpm. In no case did any significant chattering appear, although light

fluctuations were observed in the frequency of the tiny existing lobes. Even in the test with an imbalance of

0.33103

kg, there was some very noisy functioning but no valuable chattering was obtained.5. Influence of the advance speed of the grinding wheel on the final chattering of the part.

In this test, the spectra obtained during the finishing and refining processes have similar characteristics, which can be

observed in Fig. 9. The results of chattering in the mechanized parts do not show any significant differences, as can be

appreciated in Fig. 10.

6. Influence of the variable rotational speed of the part on chattering.

One of the variables with most influence on the quality of parts is the rotational speed of the part. In the next test, all

variables except the rotational speed of the part are kept constant. In the test carried out, it can be appreciated that

there are values of this variable that transform the final profile of the part and its behaviour on the final product. Fig. 11

shows the sensitivity of the rectified surface, and a chattering frequency of level 29 is shown in profile B.

7. Influence of the variable rotational speed of grinding wheel on chattering.

Another critical variable is the rotational speed of grinding wheel, due that this parameter may cause some harmonics

depending on the values of the process variables. On the shop floor, the modification of the rotational speed of the

grinding wheel is the first parameter that the operator carries out to remove the non-quality condition of the machine. Areal example of this affirmation appears in Fig. 12.

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Table 1

Influence of low-frequency vibrations on chattering of parts.

Imbalance (103 kg) Vibration (103 m/s) Functioning Chattering

0 0.6 Normal Not important

0.11 0.8 Normal Not important

0.33 1.3 Very noisy Not important

The vibration registered was mainly in the rotational frequency of 21,500 rpm. Although vibration was present in the rotational speed frequency, it did not

obtain the expected chattering.

Fig. 8. Roundness problem. Chattering level 5.


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The set of previous experiments offered a preliminary vision of the problem treated and it allowed a pre-selection of

influential variables that will be integrated in the protocol. The rotational speeds of the grinding wheel and the part, as well

as their relative values influence the problem analysed, and so they are included as cause variables in the later analysis.

Alterations in machine vibration spectrums related to a decrease in the quality obtained and affected by the condition of the wheel-dressing device were identified. The dressing cycles in the machine tool studied are produced every 15

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Fig. 9. Spectrums taken during rough and finish grinding sub-processes. The similar frequencies and vibration amplitudes can be appreciated. Main

vibration frequencies occur at 60, 7000 and 14,400 cpm. In spite of the grinding wheel feed rate difference between the rough and finish phases, the

frequencies of self-induced vibrations are similar.

Fig. 10. Dominant level 28 lobes are obtained keeping all process variables at constant level with the exception of the grinding wheel feed. The feed

difference is 10 times between both parts shown above; however, the type of chattering found is very similar in both cases.

Fig. 11. The only difference between these three parts is their rotational speed during the grinding process. Level 29 chattering appears at an intermediate

rotational speed (profile B), combined with a level 2–3 harmonic that is present in the three ground profiles (oval and triangular shapes).



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machining cycles, the current analysis being focused on the evolution of the quality between consecutive machining cycles.

In spite of the possible influence of the dressing parameters on the problem analysed, different levels of this variable arenot considered in the later experimental design, the analysis focusing on the consideration of the wheel dressing through

the reduction of the diameter of the grinding wheel. The introduction of the set of dressing variables in the development of

chattered surfaces supposes an interesting field for future research.

Previous experiences alerted the need to include the vibration spectral distribution as well as the overall vibration values as

variables in the experiments. The results obtained from the spectral vibration distributions will be presented in later papers.

The effect non-quality variables are measured by means of the profile of chattering of the parts. The profiles of chattering

quantifying in module and frequency of the out of roundness lobes are sensitive to the modification of cause variables.

The feed speeds of the grinding wheel bench do not greatly concern the spectral profile of the vibration process. The

chattering phenomenon of rectified parts is not related, in this study, to the feed speeds of the grinding wheel, this being a

process parameter that is kept constant during the experimentation phase. Certain previous experiences illustrated the

conservation of the profile of chattering before the variation of the speed of advance keeping the rest of the process

variables constant; nevertheless, future developments of this analysis with vibration devices during the fastest cycle can

affect this possible cause variable and, more precisely, its variations during the contact between grinding wheel and part.For the subsequent experimental design, different grinding wheel feed speeds are not considered, however, the influence of

this variable should be analysed in dedicated studies.

4.1. Variables from previous experiences

The analyses of different levels of rotational speeds of the processed part and the grinding wheel are considered possible

cause variables. As for alert variables it is decided that it is necessary to gather both the profiles of overall vibration and the

spectral profile of the process for each of the experiments carried out, without assuming that both variables provide

equivalent information about the quality process.

The effect variable or final quality obtained is quantified by means of the measurement of the real chattering profile of

the manufactured parts. Thereby, it will be possible to know the nature of the fault both in amplitude and frequency, and

later, to establish the level of severity of the fault found.

4.2. Evaluation of interactions

The previous experiences detect the importance of interactions between the cause variables. The enormous influence of

the relationships between speeds in the final quality was detected. The importance of interactions between cause variables

is one of the hypotheses that this analysis claims to validate and to determine the type of experimental design (ED) to be

considered, that is to say, it induces the selection of the ED methodology that best adapts to the detection of influences due

to the interaction between cause variables. Therefore, in the analysis the existence of possible interactions between all the

cause variables will be considered.

4.3. Incorporation of new cause variables—Final set of variables to consider

The diameter of the grinding wheel is an uncontrollable factor during the process since it is in agreement with what isobserved in the quality records in production lines, the parameter that determines the zone or zones of functioning outside

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Fig. 12. Chattering profiles of two parts. Although there is a difference in chattering between the two parts (levels 7 and 39), the only difference is a 10%

variation of the grinding wheel rotational speed. This variation is within the allowed tolerance for this variable.



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quality specification. The grinding wheel diameters that present work problems always depend on values adopted by the

other parameters, hence the importance of interactions in the problem studied. Machine tools settle this limitation

by means of rotational speed controllers, which minimize the problem provoked by the variation of the grinding

wheel diameter, keeping the peripheral speed constant or increasing the rotational speed when the radius of the grinding

wheel diminishes.

The magnetism or force with which the machine holds the manufactured part is also an important parameter in the

process. The power with which the piece is fixed to the magnetic gyratory plate determines its rotational speed, and so this

cause variable must also be included in the analysis. Previous experiments support the incorporation of magnetism insidethe set to be studied, and in them, the appearance of 12 lobes can be observed, with up to 6 107 m of amplitude when

the magnetic force changes from 50 to 60 G, from a situation of absence of chattering.

To give validity to the results, it becomes necessary to compare the same ones in different types of mechanized

equipment. Therefore, the machine variable is considered to be a cause variable. The influence of this variable will be

contemplated in the spectral analysis and will be of great importance for the demonstration of the existence of spectral

identity of the processes in later contributions.

Considering the previous aspects, the following variables are included for the development of the research:

1. cause variables:

diameter of the grinding wheel (103 m);

rotational speed of the grinding wheel (rpm);

rotational speed of the part (rpm);

magnetism or force of grasp on the part (Gs);

machine, interactions between all the previous variables;

2. alert variables:

overall vibration values during the process (displacement (m), velocity (m/s) and acceleration (9.8 m/s2 habitually

called g ));

spectra of process vibration;

3. effect variable:

level of quality obtained (frequency and amplitude of rectified lobes)

5. Statistical quality control model—Hypothesis

The statistical quality control by means of overall vibration analysis looks for links between two variables with

harmonic behaviour to control the quality of the processes by monitoring the vibration bands induced by the process. The

relationships between the variables included in the previous section will be formalised through the ED and statistical

relationships.

This is intended to determine the process variables and interactions that have the maximum influence on overall

vibration variables measured in the processes.

The first analysis to measure the influence of process variables and noises is carried out on the control base of the overall

vibrations. Most of the process variables may affect the vibration level induced, the quality results or both, although

previous experience indicates that there is a combination of these whose influence is critical.

The following controllable cause variables are considered as components of the matrix of control process variables:

rotational speed of the grinding wheel (rpm);

rotational speed of the part (rpm) and

magnetism or grip on the part (Gs).

Each of these variables is assigned two levels of possible variation: the maximum and minimum permitted according to

the specification of the process. The time limitations for data gathering of the equipment used oblige us to keep the

advance speed constant without distinction between the sub-processes of refining and finishing traditionally applied in

rectified technology.

The diameter of the grinding wheel (103 m) is considered as noise or an uncontrolled factor during the process but

controllable during the experimental phase. Four different variation levels are considered for the diameter in the matrix of

experiments.

There are other variables such as the rotational speed of the dressing device, quality and quantity of process coolant,

quantity of material to be mechanized, feed speed distribution, external vibrations, etc., which experiences of quality

obtained during production consider to be less influential in the problem analysed, although later investigations may help

to quantify their exact relative influence.

As far as interactions between variables are concerned, it is considered that they can exist between all the control andnoise variables selected, which again suggests the use of ANOVA rather than Taguchi. For each of the tests defined

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according to the experimental design approach the data related to the global value of the displacement vibration variables,

vibration speed and process vibration acceleration and the results of the chattering of parts are obtained and stored.

The previous set of experiments gives us the information necessary to validate the following set of hypotheses:

1. The overall vibration profiles, measured in all their variables, present a tendency associated with the type of process and

dependent on its control variables. This tendency is repeated cycle by cycle if the process conditions are maintained.

2. There are sensitive overall vibration magnitudes, whose behaviour during the contact of the grinding wheel with the

part reflects a demonstrable dependency with regard to the process variables and which must be used for futurespectral analysis.

3. Rotational speeds of the part and the grinding wheel influence their overall vibration value.

4. Interactions between variables have an important effect on the process vibrations.

5. Influential interactions must correspond to the experimental observations, that is, the action of the operator on

accessible process variables due to the appearance of quality problems (for example, in the normal operation of the

equipment, the operators usually resolve the apparition of chattering by modifying the value of the grinding wheel’s

rotational speed. The grinding wheel’s wear and tear value and its diameter are not modifiable, unless great cost was

incurred to carry out a substantial variation).

6. Overall analysis of vibration tendencies during the grinding wheel–part contact is insufficient for the detection of quality

problems in the development phase. The SQC cannot be supported only by the analysis of overall values. The SQC by means

of vibration analysis determines only the sensitive variables for their development in the spectral SQC (in a latter paper).

6. Overall vibration analysis— Transfer of quality to the product

6.1. Fundaments of overall vibration analysis

Now conclusions about the relationship between the mechanics of the process and the resulting quality will be

presented. In order to do this, it is necessary to evaluate the behaviour of the overall displacement values, speeds and

accelerations during the work cycles, as well as to analyse the influence of the process variables on the different mechanical

units of vibration to, in this way, focus the spectral study in later contributions applied to the units sensitive to the process.

The set of input variables considered are:

the machine;

the diameter of life of the grinding wheel;

the speed of the grinding wheel;

the rotational speed of the part and

the magnetism or grip on the part.

In the experimentation previous to the application of the ANOVA methodology results were gathered of the quality of the

parts made during the sequence of experiments in order to be able to detect the possible relationship between the overall

vibration value and the quality obtained. These quality results not only tell us whether the part was chattered or not, but

also whether the type of chattering defect was of high or low frequency. The measurement of the defect was carried out on

manual measurement devices due to the fact that the large quantity of experiments carried out impeded inspection of all

parts in the machine of profile inspection.

During tests the profiles of evolution of magnitudes during the work cycles were gathered, including the loading and

unloading cycles of the parts, the grinding wheel–part approximation, the rough removal phase, the final finishing and

turning off of sparks. In this last phase of the process the grinding wheel and the part are in contact but with no relative

advance, an aspect considered in some studies to be important in the final chattering profile of the part.

6.2. Description of the experiments: optimization and reading problems— profiles of mechanical process variables

For each of the machines the process parameters are altered during the life of the grinding wheel since this is one of the

most influential parameters in the problem studied. Four grinding wheel diameters are chosen, from new to its final minimum

diameter, to evaluate the differences. For a certain machine and diameter all the possible combinations of the three diameters

are carried out; grinding wheel speed, part speed and magnetism with two levels of variation for each (23=8 combinations).

grinding wheel diameter: fmax, f4fmedium, fofmedium, fmin;

rotational speed of the part: maximum and minimum values permitted;

part rotational speed: maximum and minimum values permitted and magnetism: maximum and minimum values permitted.

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The set of values measured is given in Table 2 (input data) and Table 3 (output data), all of them being within the

tolerance of process parameters allowed. The sample size is 32. Although we are aware that the sample size is small the

difficulties in carrying out each experiment in a normal operating plant must be taken into account. The experiments

developed are original.

During the tests, it has been found that each of the mechanical vibration magnitudes shows a characteristic change

profile throughout the cycle and a different sensitivity to the changes in parameters produced. The characteristic forms

found are shown in Figs. 13–15.

The mechanical magnitude of the vibration speed is shown to be sensitive to the blows produced in the loading and

unloading of the part that is manifested in a brusque rise and fall of the overall value. These alterations are not big enough

to go off the scale of the measuring equipment.

During the mechanization there is a gradual increase of 103 m/s measured, a maximum value in the mechanized cycle

is produced and this is the value we have collected to carry out the variance analysis study ( Fig. 13).The tendency of overall acceleration during the process (Fig. 14), is presented as a very stable indicator in the behaviour

of the mechanized process, thanks to the scarce influence on this magnitude of the movements necessary to change the

part. The pronounced aspect of the profile of accelerations during this mechanized cycle indicates the appearance of high

vibration frequencies, although at this stage of analysis it is not known whether these frequencies are harmful to the final

chattering of the part processed; for this reason, during the data collection for the ANOVA analysis the type of chattering

(high and/or low frequency), as well as the vibration values, was registered, to establish the possible relationship between

vibration of a certain frequency and chattering profiles with a high or low frequency. During the sequence of experiments it

was found that this parameter is especially sensitive to the grinding wheel-dressing cycles, which in practice are not

related to the appearance of the type of chattering analysed; this observation leads us to suspect that it is not the most

reliable indicator for our purpose. The phenomenon can be explained taking into account the amplifying effect that the

acceleration variable has on high-frequency variables generated by the erosive action of infinite grains of the grinding

wheel. This strong dependence on acceleration with regard to the state of the surface makes the acceleration less sensitive

to the variation of parameters described than the rest of the magnitudes, although this is a hypothesis that the varianceanalysis must validate.

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Table 2

Input data.

Machine Diameter (103m) Rotational speed of the

grinding wheel (rpm)

Rotational speed of the

part (rpm)

Magnetism (G)

1 595 45 100 50

1 595 45 100 60

1 595 45 120 50

1 595 45 120 601 595 60 100 50

1 595 60 100 60

1 595 60 120 50

1 595 60 120 60

1 575 45 100 50

1 575 45 100 60

1 575 45 120 50

1 575 45 120 60

1 575 60 100 50

1 575 60 100 60

1 575 60 120 50

1 575 60 120 60

1 529 45 100 50

1 529 45 100 60

1 529 45 120 50

1 529 45 120 60

1 529 60 100 50

1 529 60 100 60

1 529 60 120 50

1 529 60 120 60

1 495 45 100 50

1 495 45 100 60

1 495 45 120 50

1 495 45 120 60

1 495 60 100 50

1 495 60 100 60

1 495 60 120 50

1 495 60 120 60


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As far as the displacement profiles obtained are concerned, these present very different characteristics according to the

filter used to collect the data in microns. The use of a high-frequency (mm-H) or low-frequency (mm-L) filter is due to

technical limitations of the equipment used and obliges us to consider the displacement spectrums in a special way,

accepting that according to the unit chosen (mm-L or mm-H) the apparatus will be considered the band included between 0

and 1500 cpm (mm-H) or between 1500 cpm and the maximum frequency chosen (mm-L).

The profiles obtained during the sequence of experiments were of a very even or stable type for high-frequency

displacements and highly fluctuating in the case of low-frequency displacements. The level of variation of the latter made it

complicated to determine the maximum value to be considered in the ANOVA. In Fig. 15 this aspect is demonstrated; it can

be observed that the collection of the maximum value of process vibration displacement occurring in the high-frequency

range is easily identifiable in the evolution profile of the variable, and we can see slight tendencies cycle by cycle during the

experimental phase. The measurement of the low-frequency displacements presented the opposite behaviour, where anyexterior disruption (movement of machine elements not involved in the process, the starting of cooling devices, opening/

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Table 3

Ouput data.

High-frequency

displacement (106 m)

Low-frequency

displacement (106m)

Velocity of vibration

(103m/s)

Acceleration ( g ) Lob A Lob B

1.5 6 0.37 0.26 1 0

1.5 7 0.32 0.21 0 0

2.0 6 0.34 0.23 0 0

1.4 5 0.29 0.21 0 02.0 6 0.44 0.24 1 0

2.0 10 0.36 0.20 0 0

2.0 7 0.43 0.22 1 0

2.2 6 0.36 0.18 0 0

1.7 7 0.43 0.27 2 2

1.7 7 0.4 0.23 2 2

1.7 7 0.44 0.23 2 2

1.4 7 0.32 0.19 0 0

2.5 6 0.32 0.13 0 0

2.5 6 0.33 0.17 1 1

3.0 7 0.35 0.19 0 0

2.6 7 0.46 0.15 1 0

2.9 7 0.35 0.24 0 1

2.7 18 0.32 0.27 0 2

2.6 12 0.37 0.25 0 2

2.7 9 0.42 0.18 0 2

3.8 7 0.52 0.19 0 0

3.5 8 0.41 0.14 1 0

3.1 8 0.38 0.14 0 0

3.5 7 0.35 0.14 0 0

2.6 10 0.34 0.19 0 0

2.6 7 0.33 0.18 0 0

2.3 6 0.32 0.21 0 0

2.5 9 0.32 0.22 1 0

2.2 6 0.38 0.2 1 0

2.3 10 0.41 0.17 0 0

2.4 8 0.37 0.17 0 0

2.2 7 0.37 0.16 0 0

i o n

m / s )

Load

Approxi-

mation Contact tool-part Unload

e r a l l v i b r a t i

o c i t y ( 1 0 - 3 m

0.5Maximum value

O v e

v e l o

0

0 s 20 sTime (s)

Fig. 13. Speed self-induced vibration profile during a complete work cycle, including the automatic loading of the part, grinding wheel approach, material

removal and unloading. The trend rises steadily to the maximum value (this is the value that has been recorded for statistical analysis).



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closing of valves, fairing movements of the machine, etc.) directly affected the reading of the apparatus. The choice of the

maximum value mm-L is considerably complicated for this reason.

The profiles of the overall magnitudes measured in the temporary tendencies shown in Figs. 13–15 show the same typeof evolution throughout the experimentation. The maximum values collected during the tests carried out are shown in

Tables 1 and 2.

This characteristic enables each mechanized process to be associated with a certain overall tendency of vibration

variables. The relation between process parameters and the vibrations they cause will later be subject to a more detailed

study in a spectral sense.

6.3. Evaluation of the quality of the processes

Apart from the vibration magnitudes previously described, quality results of the parts corresponding to the variation of

the process parameters were also gathered. The way of evaluating the quality of the resulting parts was carried out on

measurement devices existing in the specific operation. These pieces of equipment are capable of detecting whether the

chattering is of low frequency (slow movements of hands of the dial indicator on turning the part=Lob B), or high frequency(very-fast movements of the dial indicator on turning the part=Lob A). Three levels of low- and high-frequency chattering

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Fig. 14. Acceleration profile of the vibration self-induced during the grinding process. The acceleration is not affected by the loading and unloading

processes (low-frequency displacements). However, it is sensitive to changes in the feed speed of the grinding wheel.

Fig.15. Profiles of low-frequency vibration displacements (106 m) and high-frequency vibration displacements (106 m) during the work cycle. There are

very uniform high-frequency displacement readings and fluctuating low-frequency vibrations during the cycle.



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were also established according to the size of movements of hands of the dial indicator. These levels are established

qualitatively in the following way:

level 0—no or practically imperceptible chattering;

level 1—movement of the sensitive indicator and

level 2—severe chattering. Great amplitudes.

Both the establishing of low- and high-frequency types of chattering and the definition of different levels of severity werecarried out in such a way that the set of data related to the quality of the parts obtained was manageable, and in this way

the correct treatment of the data was guaranteed. It is evident that a different definition of types of chattering and levels

could have been valid, and so it must be indicated that the specifications of quality of the components, which cannot be

revealed due to motives of confidentiality, have indicated the choice of the classification indicated. The classification of

quality previously chosen allows us to keep the quantity of information to be processed, which is presented in this first

calculation, under control.

Fig. 12 shows two examples obtained during tests in which we can distinguish the concepts of high and low-frequency

chattering. Although the quality profiles look very different, the difference between the process parameters of the two parts

is minimal. Despite the difference in chattering (order 7 and 39 dominants, respectively), the only difference between them

is a variation of 10% in the grinding wheel speed, the rest of the parameters being constant. This variation is within the

tolerance permitted for this process variable.

6.4. Application of statistical methods to the vibration process values. Determination of sensitive variables

The purpose of applying the ANOVA technique is to determine the influence of input variables or operation parameters

and their interactions in output variables (alert and effect). The groups of variables are as follows:

alert variables—mechanical behaviour of the process (vibration): high-frequency displacement (106m), low-frequency

displacement (103 m), velocity of vibration (103 m/s) and acceleration ( g );

effect variables—quality of the process: Lob A and Lob B.

The first objective of the statistical analysis is to determine which variables selected produce the most important changes

in the mechanical behaviour of the processes. In the statistical analysis not only were the control variables considered

separately but a specific treatment was also carried out to find possible interactions between variables that could affect the

processes negatively.

The hypothesis that interactions between the process variables may have as much influence as or more influence

than the separate variable, is what determined the formulation of experiments chosen, in which all possible combinations

of variables are considered. This is the reason why we have not opted for other experimental design formulations

like Taguchi, since it does not give importance to interactions between variables that they have in the problem with

which we are concerned [32,44]. These circumstances oblige us to carry out a greater number of experiments,

but guarantee that none of the possible relationships between variables be subdued by an inadequate treatment

of the data. In previous sections the controllable variables or process parameters and the output variables were

defined, divided into mechanical process variables or influential variables and variables measuring the resultant

quality:

controllable cause variables—grinding wheel speed (rpm), part speed (rpm) and magnetism (gauss);

uncontrollable cause variables—grinding wheel diameter (103 m);

alert variables—high-frequency displacements (106m), low-frequency displacements (106 m), velocity (103 m/s) and

acceleration ( g );

quality or effect variables—Lob A and Lob B.

The set of data obtained during the experimentation corresponding to the previous variables is shown in Table 4.

One tool for statistical inference is test hypotheses, which evaluate the evidence of an affirmation on the population. In

statistics, an affirmation on the population is made in the form of work hypothesis. The complementary hypotheses are

called: null hypothesis (H0) and research hypothesis (H1).

The hypotheses are related to population parameters. A hypothesis test is a procedure that specifies:

for what values the decision will be not to push the null hypothesis back and

for what values the null hypothesis will be pushed back in favour of the research hypothesis.

P -value is defined as the exact significance level of a statistical test; that is, the probability of obtaining a value of the

test statistic that is at least as extreme as the one observed when the null hypothesis is true. The smaller the P -value thegreater the evidence in opposition to H0.

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The objective of the analysis that will now be developed is to determine the relationship between the quality of the

parts and the effect of the controllable variables on the influential variables.

6.4.1. Concurrent analysis of the variables

An analysis is carried out of the multi-factorial variance with the controllable variables and on their effect on the

influential variables or vibration values (see results in Table 4). The objective of this first study is to consider all factors in

order to determine which are the most important. From this study the following aspects are observed:

1. High-frequency displacement is affected by the diameter of the grinding wheel and the rotational speed of the grindingwheel. The P -value evaluates the effect of each of the factors and turns out to be less than 0.025 in the case of the

variables diameter and rotational speed of the grinding wheel; therefore it is concluded that the process is influenced by

these variables.

2. The overall vibration acceleration is affected by the grinding wheel speed and magnetism, although, following a

reasoning process similar to the previous one, such an influence is less since the P-values obtained are substantially

greater than those obtained in the previous case.

3. The rest of the vibration variables are not significantly influenced by the process variables.

6.4.2. Multi-factorial ANOVA

A confidence interval of C % can be defined for a parameter as an interval of values calculated from the information of the

sample and by using a method that has a probability C that the above-mentioned interval will contain the real value of the

parameter.Now a multi-factorial ANOVA is carried out with controllable variables and their effect on the quality variables is

analysed. It is found that both high-frequency chattering (Lob A) and low-frequency chattering (Lob B) are affected by the

grinding wheel diameter, Lob B being also affected by the grinding wheel speed. The previous conclusion is established

with 95% reliability, although the P-values obtained in these last two cases (Lob A and Lob B) do not indicate such a strong

dependency as was observed in high-frequency displacements.

The practical experience corroborates the preliminary statistical results obtained since in the normal operation of the

equipment, the operators usually resolve the appearance of chattering by modifying the value of the rotational speed of the

grinding wheel. The wear and tear value of the grinding wheel and its diameter are not modifiable, unless great cost was

incurred on a substantial variation.

The two sets of output variables previously analysed have in common the appearance of the same controllable variables,

which indicates not only the importance of these process parameters, but also the possible relationship between the two

sets of output variables, which would provide the base for our aim, which is the determination of links between the

mechanical behaviour of the process, expressed in terms of the vibrations it induces, and the resulting quality.The joint analysis of the variables determines which are the most influential of the total set of the variables studied. The

sensitivity observed in the high-frequency displacements faced with the alteration of the process parameters supports the

realization of a detailed study of this variable, which is now presented.

6.4.3. Effect of the controllable variables on the high-frequency process displacements

Now a variance analysis will be carried out exclusively on the high-frequency displacements, considering the

interactions between the principle controllable variables. Firstly we analyse the high-frequency displacement variance

according to the grinding wheel speed and diameter separately, obtaining in both cases the fact that the average

displacement value is different for the different values of these variables with a degree of reliability of 95% (see Table 5).

Next another analysis is carried out on the variance considering the separate controllable variables and their

interactions; in this supposition it can be seen that the influence of the diameter is maintained although the influence of

the grinding wheel speed is less in this case and is determined by its interaction with the diameter.

The overall high-frequency displacements generated by the process increase as the diameter decreases and decrease asthe rotational speed of the grinding wheel decreases. This result is very interesting if we take into account its possible

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Table 4

P -values of all the variables considered according to the multi-factorial variance analyses carried out.

High-frequency


Low-frequency


Velocity of vibration

(103 m/s)

Acceleration

( g )

Lob A Lob B

Diameter of the grinding wheel 0.0000 0.0553 0.4861 0.1240 0.0414 0.0045

Rotational speed of the grinding wheel 0.0002 0.2749 0.0559 0.0003 0.5714 0.0017

Rotational speed of the part 0.8271 0.4327 0.6206 0.1580 0.2622 0.5637

Magnetism 0.5860 0.2749 0.1858 0.0252 0.5714 1.0000

The cases in which there is a significant dependence between variables are those with P o0.025.


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agreement with real observations, since chattering problems tend to appear when the grinding wheel’s life is coming to an

end, that is to say, when the grinding wheel diameter is small. These conclusions will be reinforced in later statistical

analyses. Fig. 16 represents the behaviour of the high-frequency displacement variable according to the grinding wheel

diameter and the speed.

6.4.4. Normality and homoscedasticity of high-frequency displacement

The results of the ANOVA are subject to considerations of normality and homoscedasticity. In order to study normality

we use chi-squared, Shapiro–Wilks, symmetry and kurtosis tests (see [28]).

The chi-squared test divides the level of high-frequency displacement into fifteen types and compares the number of

observations in each of the types to the quantity expected according to the normal distribution.

The Shapiro–Wilks test or W test carries out a comparison between the data obtained and that of a normal distribution.

W may be thought of as the correlation between given data and their corresponding normal scores, with W =1 when the

given data are perfectly normal in distribution. When W is significantly smaller than 1, the assumption of normality is not

met. That is, a significant W statistic causes the researcher to reject the assumption that the distribution is normal.

The skewness test focuses on the possible lack of symmetry in the data observed. Finally, the kurtosis test analyses the

form of distribution.

From all tests a minimum P-value of 0.32 is obtained, which allows us to assure with 90% reliability that the high-

frequency displacements behave according to a normal distribution. This result makes it possible to apply differentstatistical grinding wheels with a high level of reliability, an aspect that will be taken into account in some of the

hypotheses that are contrasted in later analyses.

The statistical methods based on variance analysis require the high-frequency displacement variable to meet the

condition of homoscedasticity with regard to the different controllable variables, whose effect we intend to analyse. In

order to contrast this condition the Cochran, Hartlett and Hartley tests [9,10,19,29] are used starting from the null

hypothesis, which consists of considering that the high-frequency displacement variance for each level of the controllable

variables is the same. By applying this hypothesis it is obtained that equality of variances hypothesis is fulfilled for high-

frequency displacement with respect to the grinding wheel speed.

In order to analyse the condition of homoscedasticity of high-frequency displacement with respect to the diameter of

the grinding wheel two possible levels are considered:

level 1 (end of the grinding wheel’s life)—from 495103 m to 529103 m and

level 2 (start of the grinding wheel’s life)—

from 575103 m to 595103 m.

With the previous levels of diameter, the influence of the diameter on high-frequency displacement is maintained, and the

hypothesis of homoscedasticity is verified with regard to the two levels of diameter considered. Fig. 17 shows this situation.

Now the effect of interaction of the diameter with grinding wheel speed on high-frequency displacements is analysed.

The interaction variable chosen adopts the following values:

1. diameter=level 2 and grinding wheel speed=45,

2. diameter=level 2 and grinding wheel speed=60,

3. diameter=level 1 and grinding wheel speed=45 and

4. diameter=level 1 and grinding wheel speed=60.

By applying ANOVA we can observe the influence of this new variable on high-frequency displacement with aconfidence degree of 95%. However, the hypothesis of necessary homoscedasticity is not verified and the graphical

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Table 5

P-values obtained in the high-frequency displacement variance analysis vs all variables and their possible interactions.

interactions

Diameter–rotational speed of the grinding wheel 0.0130

Diameter–rotational speed of the part 0.2957

Diameter–magnetism 0.5298

Rotational speed of the grinding wheel–rotational speed of the part 0.6431

Rotational speed of the grinding wheel–magnetism 0.7279

Rotational speed of the part–magnetism 0.9075

Independent variables

Diameter 0.0000

Rotational speed of the grinding wheel 0.0553

Rotational speed of the part 0.3776

Magnetism 0.7108

The interaction diameter–rotational speed of the grinding wheel is more important than rotational speed of the grinding wheel only.



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representation of the variation of high-frequency displacement with respect to variable interaction is very clear (see

Fig. 18). A progressive increase in the high-frequency displacement intervals can be appreciated.

As a consequence of the failure to fulfil the homoscedasticity hypothesis the Krushal–Wallis Test [13,28,29] is applied,and significant differences in the medians can be appreciated (95% reliability). To discover the relative values of the

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3.4

3.1

2.8

2.5

495

1.9

1.6

529 575 595 H i g h f r e q u e n c y d i s p l a c e m e n t ( 1 0 - 6

m )

Tool diameter (10-3 m)

2.2

2.9

2.7

2.5

2.1

1.9

45 60 H i g h f r e q u e n c y d i s p l a c e m e n t ( 1 0 - 6

m )

Tool speed (rpm)

2.3

Fig. 16. Intervals of high-frequency displacements (106 m) vs grinding wheel diameter and rotational speed of the part. Large grinding wheel diameters

relate to lower high-frequency displacements. High grinding wheel rotating speeds increase the high-frequency displacements measured during theworking cycles.

2.8

1.8

Level 1 Level 2

H i g h

f r e q u e n c y

d i s p l a c e m e n t ( 1 0 - 6

m )

2.2

Levels of diameter

495-529 (10-3 m) 575-595 (10-3 m)

Fig. 17. Variation of high-frequency displacements (106 m) in relation with the two levels of grinding wheel diameter considered. The two distributions

are separated with no overlap between them.



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medians between the groups we use a box and whisker type chart (see [21] for examples) representation (Fig. 19). It can be

observed that the median of the displacements is clearly less for interaction=1, that is, the groups in which the diameters

are great and the speeds low.

The Krushal–Wallis test (Fig. 20) also shows significant differences for the diameter variable, which does not verify the

homoscedasticity hypothesis either. For this, the null hypothesis consisting of considering that the variation in the medians

for the four levels is null, is verified. The degree of reliability of obtaining different medians for the different stages of thelife of the grinding wheel is higher than 95%.

6.4.5. Multi-factorial ANOVA with variable interaction

Once we have discovered the influence of the interaction variable on the mechanical behaviour of the process measured

in terms of displacements, this variable is incorporated into a new multi-factorial analysis to substitute the diameter and

speed variables, since it is a combination of these. In the same way the influence of this new variable on the quality

obtained is analysed.

The table of P-values obtained as a consequence of the series of variance analyses applied allows us to

establish conclusions in a similar way to the previous analysis. The most relevant results obtained in this study are the

following:

1. high-frequency displacement is affected by interaction;2. low-frequency displacement is affected by interaction;

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3.2

2.9

2.6

2.0

2.3

1.4

1 2

H i g h f r e q u e n c y d i s p l a c e m e n t ( 1 0 - 6

m )

3 4

1.7

Interaction

Fig. 18. Variation of high-frequency displacements (106 m) vs the interaction of the tool diameter with rotational speed. The increasing trend of high-

frequency displacements can be appreciated.

Fig. 19. Box and whisker representation, high-frequency displacements (106 m) vs interaction. It can be appreciated that the median of the

displacements is smaller for interaction=1 (larger diameters and lower speeds).



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The ANOVA also provides other interesting conclusions, although the three previous points are the starting point for the

search for a relationship between the quality of the processes and the predictive variables.

The analysis presented is the starting point to extend the use of predictive grinding wheels (vibration analysis) to

quality control once it demonstrated the sensitivity of predictive variables (high-frequency displacements) to the

behaviour of the processes. Future contributions about the previous conclusions will look in more detail at the spectral

character of the vibrations, in order to, once the maximum high-frequency vibration displacement values allowed are

known, be able to define the limit spectrums, controllable cycle by cycle and even connected to permanent motorization

controls of the machines so that they may modify their sensitive parameters, identified by ANOVA and according to thevibration readings. This feedback of the processes focused on quality control constitutes the principle contribution of the

current SQC by means of overall vibration analysis and later spectral SQC. In this first stage, the SQC is proposed as a new

technique for the determination of mechanical vibration variables for quality control of processes with high quality

requirements, through the application of existing predictive tools (vibration analysis) according to experimental design and

applying statistical tools to confirm the results. This conclusion validates the method presented and opens the doors for

spectral analysis based on high-frequency displacements, which will be developed later.

Future investigations consist of a spectral study that will allow us to establish which vibration frequencies are especially

harmful for the processes and which are the process variables that can restore the functioning conditions with quality

assured. The spectral focus will be made possible by the fact of knowing the different natures of the overall mechanical

variables measured, the high-frequency displacements being the variable chosen as a result of the SQC by means of

vibration analysis presented in this study.

References

[1] B. Al-Najjar, To

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