Research ArticleAir Gauge Characteristics Linearity Improvement

Cz J Jermak M Jakubowicz J DerehyNski and M Rucki

Institute of Mechanical Technology Poznan University of Technology Piotrowo Street 3 60-965 Poznan Poland

Correspondence should be addressed to M Rucki miroslawruckigmailcom

Received 23 November 2015 Revised 14 March 2016 Accepted 20 March 2016

Academic Editor Carlos Andres Garcia

Copyright copy 2016 Cz J Jermak et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper discusses calibration uncertainty and linearity issues of the typical back-pressure air gauge In this sort of air gaugethe correlation between the measured dimension (represented by the slot width) and the air pressure in the measuring chamberis used in a proportional range However when high linearity is required (eg nonlinearity less than 1) the measuring rangeshould be shortened In the proposed method based on knowledge of the static characteristics of air gauges the measuring rangeis kept unchanged but the nonlinearity is decreased The static characteristics may be separated into two sections each of themapproximated with a different linear function As a result the nonlinearity is reduced from 5 down to 1 and even below

1 Introduction

Air gauges are well-known precise measuring devices [1]which have recently regained the interest of engineers [2]Even though the definition of the precise machining anddemands on the precise measurement are changing due tothe development of new methods [3] air gauges are stillconsidered to be high-accuracy measuring devices [4] Theyare especially useful in automatic measurement and selectionsystems [5] and in in-process control [6] It is assumed thatthe measurement accuracy of an air gauge is ca 2 120583m in therange of 0001mm [7] but in some applications accuracybelow 1 120583m is achievable [8] Due to their merits air gaugesmay replace other measuring devices [9]

The air gauging principle has been known for almost acentury The earliest known patent of this device was regis-tered in the USA in 1922 but the first marketed air gauge wasa back-pressure gauge which Solex in Germany introducedin 1926 and Sheffield in the USA in 1935 [10] The mainair gauging methods are flow (velocity) and pressure (back-pressure) ones [11] which are in turn divided into high-pressure and low-pressure devices In any case the measureddimension represented by the flapper surface works as arestriction for the air outflow which influences an air flowparameter For instance if the clearance between the nozzleand measured detail surface becomes wider the mass flow(or velocity) through the air gauge becomes larger while

the back-pressure gets smaller The magnification of back-pressure varies from 1000 1 to over 5000 1 depending onthe range while a flow gauge can amplify to over 500000 1without accessories [12]

Nowadays the dimensional accuracy of any manufac-turing process became critical because of increased qualitydemands That means the constant need for development ofmore accurate measuring methods and devices and mini-mization of expenses (the price of the equipment as well asoperation time and exploitation costs) Air gauges generallymeet those requirements and they can be improved withsmall additional costs

Since there is still some room for improvement [13]investigations on air gauges are being performed continu-ously The most recently published article gives informationconcerning the application of back-pressure air gauges inroundness assessment [14] where the calculations and simu-lations of the static characteristics are based on second criticalparameters However in typical devices the problem is withthe initial adjustment [15] which is performed usually aftereach exchange of the jet plug (measuring head) with oneor two master rings [16] Thus two points are set for thelinear approximation of static characteristics used furtherin the measurement Obviously shorter segments of thecharacteristics are more linear but the proper measuringrange should be kept More calibration points would requiremore respective master rings which would increase expenses

Hindawi Publishing CorporationJournal of Control Science and EngineeringVolume 2016 Article ID 8701238 7 pageshttpdxdoiorg10115520168701238

2 Journal of Control Science and Engineering

1 4 2 3 5

Figure 1 Investigation model of the air gauge 1 replaceable mea-suring nozzle 2 measuring chamber 3 replaceable inlet nozzle 4joint for back-pressure sensor 5 feeding joint

significantly deleting low costs as the main merit of airgauging

Hence the state of the art is as follows the static charac-teristics of the back-pressure air gauge can be calculated andsimulated with high accuracy but its nonlinearity in a largermeasuring range may affect the measurement results Theadjustment process requires expensive master rings so thenumber of calibration points should be minimal (typicallytwo) The proposed method improves the measurementaccuracy using two approximation lines and reducing theoverall nonlinearity calculated as a difference between thenominal point on the theoretical line and the actual pointregistered by the device

2 Investigation Apparatus

A group of high-pressure air gauges with the feeding pressure150 kPa has been investigated for many years in PoznanUniversity of Technology [17]The investigation model of theair gauge is presented in Figure 1 which enables the changingof the main parameters of an air gauge in order to check itsmetrological properties experimentally There are measuringchambers of different dimensions with two or more jointsfor back-pressure 119901119896 measurement replaceable measuringnozzles with various diameters 119889119901 and different geometry(eg conical inlet and corrected nozzle head) and replaceableinlet nozzles of diameters 119889119908

Main computerMicroBar

unit

Source ofpressuredand filtered air

Compressor

pz

pk

Model of air gauge

Moving tableFlapper surface

s

Control andmeasurement signal

Pressurestabilization

Figure 2 Scheme of the static characteristics investigation set [18]

To obtain the static characteristics of an air gauge theback-pressure signal 119901119896 is being compared with the displace-ment 119904 indication of measuring column TT 500 connectedwith the inductive sensor GT21HP and analyzed by dedicatedsoftware The laboratory set has been described in detailin [18] and its principle is shown in Figure 2 Additionaldevices could be included like aMicroBar unitwhich registersfluctuations of the back-pressure 119901119896 with high-frequencysampling (from 16Hz up to 4 kHz) [15] or temperaturesensors and flowmeter

The measuring slot 119904 is slowly changed in the range from0 up to themaximal value 119904max defined by the user dependenton the examined air gauge Typically 119904max does not exceed250 or 300 120583mThe registered functions of the back-pressure119901119896 volumetric flow 119902V and temperatures in the air gaugemeasuring chamber 1199051 and in the feeding chamber 1199052 couldbe presented in the following form

119901119896rarr = 119891 (119904)

119902Vrarr = 119891 (119904)

1199051119901rarr = 119891 (119904)

1199052119901rarr = 119891 (119904)

119904 isin ⟨0 119911⟩

(1)

119901119896larr = 119891 (119904)

119902Vlarr = 119891 (119904)

1199051119901larr = 119891 (119904)

1199052119901larr = 119891 (119904)

119904 isin ⟨119911 0⟩

(2)

The first set of (1) represents the results obtained from theincreasing values of s (the moving table is displacing air

Journal of Control Science and Engineering 3

00

02

04

06

08

10

12

0

25

50

75

100

125

150

0 25 50 75 100 150125s (120583m)

|K|

(kPa

120583m

)

Multiplication|K| = g(s)

Staticcharacteristic

pk

(kPa

)

pk = f(s)

(a)

0

25

50

75

100

125

150

00

02

04

06

08

10

12

|K|

(kPa

120583m

)

0 25 50 75 100 175150125s (120583m)

Staticcharacteristic

Multiplication|K| = g(s)

pk

(kPa

)

pk = f(s)

(b)

Figure 3 Examples of the experimentally obtained static characteristics and the multiplication graphs of air gauges

gauge away from the flapper surface) and (2) for decreasingones respectively It is obvious that the collected data containsome noise so the range of the mathematical functionsshould be applied to filter metrologically significant infor-mation Thus the data processing consists of the followingsteps

(i) Data smoothing

(ii) Interpolation

(iii) Calculation of the multiplication

(iv) Linearization of the experimentally obtained function119901119896 = 119891(119904)

After the data is processed the result may be presented bothfor average values and for separate increasing and decreasingfunctions The latter enables the possibility of revealing ahysteresis

From the numerous smoothing methods (see eg [19])the one based on the least squares has been chosen On thebasis of the subsequent 2119899 + 1 values of the variable (see (3))the polynomial of 119895 degree (see (4)) is fitted to achieve theminimal differences between the calculated values 119910(119909119894) andmeasured ones 119910119894

119910119894minus119899 119910119894minus119899 119910119894 119910119894+119899minus1 119910119894+119899 (3)

119910 (119909) = 1198880 + 1198881119909 + 11988821199092+ sdot sdot sdot + 119888119895119909

119895 (4)

119899

sum

119896=minus119899

[119910119894+119896 minus 119910 (119909119894+119896)2] = min (5)

The values 119910(119909119894) obtained in this way are assumed to bethe values of the smoothened function 1199101015840

119894= 119910(119909119894) In the

experiments a quadratic polynomial has been used based on

7measured points (see (6)) and the third-degree polynomialbased on 9 measured points (see (7))

119910119894(27) (119909) =1

21(minus2119910119894minus3 + 3119910119894minus2 + 6119910119894minus1 + 7119910119894 + 6119910119894+1

+ 3119910119894+2 minus 2119910119894minus3)

(6)

119910119894(39) (119909) =1

231(minus21119910119894minus4 + 14119910119894minus3 + 39119910119894minus2 + 54119910119894minus1

+ 59119910119894 + 54119910119894+1 + 39119910119894+2 + 14119910119894+3 minus 21119910119894+4)

(7)

It should be noted that for a higher degree of polynomialmore points should be considered and the obtained functionis less smoothened The procedure could be repeated severaltimes for the same data and the number of repetitionscould be chosen after the empirical analysis of a series ofcalculations

Among many known methods linear interpolation [20]has been chosen to achieve a steady distribution of themeasurement data It is described by the following formula

119871 (119909) = 1199100 +1199101 minus 1199100

1199091 minus 1199090

(119909 minus 1199090) (8)

which has appeared sufficient in order to achieve the desiredresults from the collected data

To evaluate the linearity of the obtained static character-istics the multiplication was calculated for each point andthe function |119870| = 119891(119904) was derived The function presentedgraphically gives quick information on the linearity of theanalyzed static characteristics119901119896 = 119891(119904) themultiplication ofthe linear part of the characteristics keeps at the same level forsome time For example in Figure 3 one can compare graphsof two experimentally achieved multiplication functions Itis seen that in one case (a) a linear range from 45 to75 120583m could be extracted and in the other case (b) thereis no horizontal part of the multiplication graph hencethe characteristics reveal worse linearity though the rangebetween 80 and 120 120583m may be considered satisfactorilylinear

4 Journal of Control Science and Engineering

Since multiplication is defined as a tangent of the staticcharacteristics declination angle the local multiplicationcould be calculated as follows

119870 (119904) =119889119891 (119904)

119889119904asympΔ119901119896

Δ119904

10038161003816100381610038161003816100381610038161003816119904isin(119904119904+Δ119904) (9)

In a real dataset however one deals with discrete values andthen the multiplication should be determined between thepoints 119899 + 1 and 119899

119870119899 = 119891 (119899 + 1) minus 119891 (119899)1003816100381610038161003816119899isin(0119911) (10)

3 Calibration Uncertainty

Thecalibrationmethods are described in the standard [21] Toperform the analysis of the air gauge calibration uncertaintyit is useful to present its static characteristics in the followingform

119901119896 = 119891 (119904) + 120578 = 119901119896(119904=0) + 119870119904 + 120578 (11)

where 119901119896(119904=0) is the starting point of the characteristics whenthe measuring nozzle is touching the flapper surface (slot 119904 =0) 119870 is multiplication and 120578 is the uncertainty

Estimators of those parameters could be calculated fromthe following equations

119896(119904=0)

= 119901119896(119904=0)119904119903

minus 119904 119904119903

=sum119873

119894=1(119904119894 minus 119904 119904119903) (119901119896

119894

119904119903 minus 119901119896 119904119903)

sum119873

119894=1(119904119894 minus 119904 119904119903)

2

(12)

where 119901119896 119904119903 and 119904 119904119903 correspond to the mean values

119904 119904119903 =1

119873

119873

sum

119894=1

119904119894

119901119896 119904119903 =1

119873

119873

sum

119894=1

119901119896119894

(13)

Thus the estimation formula will be presented as follows

119896= 119896(119904=0)

+ 119904 = 119901119896 119904119903 + (119904 minus 119904 119904119903) (14)

And the calibration characteristics are described by

lowast= 1198880 + 1198881119896 = 1198880 + 1198881 (119896(119904=0) + 119904) (15)

where

1198880 = minus119896(119904=0)

1198881 =1

(16)

The assumptions for the calibration procedure were as fol-lows

70 90 110 130 150 170

15

10

05

00

minus05

minus10

minus15

ΔgΔ

d(120583

m)

Δd (M= 1)

Δg (M= 1)

Δd (M= 15)

Δg (M= 15)

slowast0 (120583m)

Figure 4 Calibration uncertainties for air gauges with measuringnozzle 119889119901 = 1208mm and inlet nozzle 119889119908 = 0830mm [22]

35 55 75 95

20

15

10

05

00

minus05

minus10

minus15

minus20

ΔgΔ

d(120583

m)

Δd (M= 1)

Δg (M= 1)

Δd (M= 15)

Δg (M= 15)

slowast0 (120583m)

Figure 5 Calibration uncertainties for air gauges with measuringnozzle 119889119901 = 1810mm and outer inlet nozzle 119889119908 = 0720mm [22]

(i) Expected value of 120578 is zero (119864120578 = 0)

(ii) Variation of 120578 is constant and independent of 119904(var120578 = 1205902

120578)

(iii) The probability distribution of the random errors isGaussian (119901(120578) = 119873(0 1205902

120578))

(iv) Errors are not correlated with the measured value 119904(cov120578 119904 = 0)

(v) The errors of the set masters are negligibly small

When the same value of 1199040 in the process 1205780 is measured119872 times the uncertainty of the calibrated system could bedetermined as the confidence interval Δ = 119904

lowastminus 119904 The

examples of upper (Δ119892) and lower (Δ119889) confidence intervalsfor119872 = 1 and119872 = 15 are presented in the graphs (Figures 4and 5)

Journal of Control Science and Engineering 5

Table 1 Results of the calibration

Parameter 119904119901 = 40120583m 119904119901 = 50 120583m 119904119901 = 60 120583m 119904119901 = 70 120583m 119904119901 = 80 120583m 119904119901 = 90 120583m 119904119901 = 100 120583m119904119896[120583m] 916 1135 1395 1655 1915 2215 2495

Measuring range 119911119901 [120583m] 521 639 799 960 1119 1340 14981198772 09978 09991 09984 09969 09953 09922 09902119903 09989 09995 09992 09984 09976 09961 09951120575max [] 29 20 36 42 54 65 48

s (120583m)

140

130

120

110

100

90

80

70

60

pk

(kPa

)

sp = 40120583msp = 70120583msp = 100120583msp = 50120583m

sp = 80120583msp = 60120583msp = 90120583m

22520518516514512510585654525

Figure 6 Linear approximation of the air gauge characteristics inthe pressure range between 120 and 60 kPa

4 Linearity Improvement

Earlier investigations had proved that it is possible to achievebetter linearity by applying more setting masters [23] Morerecent investigations were made in Poznan University ofTechnology to improve linearity in the air gauging systemPneusmart The system includes a mechanical unit (gaugingheads etc) a pneumatic unit and a control unit [24] andlinearity is improved digitally by dividing the measuringrange into two parts

In fact the approximation of the static characteristics inthe required measuring range could give too poor linearityTable 1 contains the results of measurement and calculationswhich correspond to graphs in Figure 6 Here 119904119901 is the slotwidth at which the measuring range 119911119901 begins and 119904119896 is theone it ends with 1198772 is the determination factor which givenin percentage shows how many points are determined by theregression [25] 1198772 is corresponding to the correlation factor119903

119903 = radic1198772 (17)

It is assumed that when the correlation factor 119903 lies between09 and 1 the correlation is almost complete which is the caseshown in Table 1

120115110

95908580757065605550

sp (120583m)pk

(kPa

)25023021019017015013011090

Section A approximationSection B approximation

y = minus05131x + 16527

R2 = 09987

y = minus03118x + 12974

R2 = 09915

105100

Figure 7 Example of the characteristics approximated with twofunctions

However the linearity error from 2 to 65 is highlyunsatisfactory To reduce the linearity error the measuringrange 119911119901 should be shortened In Figure 7 the static charac-teristics are presented which reveal the nonlinearity as morethan 2 in the range 119911119901 from 100 to 240 120583m A reducedmeasuring range from 100 to 170 120583m (section A in Figure 7)has the linearity error 120575max = 08

Thus in order to keep the longer measuring range theapproximation with two functions is proposed The staticcharacteristics are then divided into two sections (A and Bin the example shown in Figure 7) each approximated withits own function The maximal linearity error for the entiremeasuring range 119911119901 from 100 to 240120583m is reduced down to120575max = 08

The Pneusmart device enables the collection of exper-imental data on the static characteristics of the particularmeasuring head (gauge plug) and to keep it in memoryTo calibrate it later it is enough to recall the appropriatecharacteristics ascribed to this plug and to check just onepoint with the setting master

5 Discussion

The air flow through the nozzles measuring chamber andthe flapper-nozzle area itself generates some phenomenaimpossible to omit which has been described decades ago[26] Although some improvement could be made [27] onthe curve function 119901119896 = 119891(119904) to prolong its proportional(linear) range the problem stays basically the same in a

6 Journal of Control Science and Engineering

wider range the linearity of the functions gets worse Anadditional problem is the need of adjustment any time thejet plug (measuring head) is changed to perform a differentmeasuring task It has been found that the adjustment withmore than two master rings can improve the measurementresults but the expenses rise disproportionately

In the previous investigations due to the electronic con-version of the pneumatic signal and then digital processingof the measured data it appeared possible to store the once-adjusted function and then to recall it after the exchange ofthe jet plug In that case to calibrate the new jet plug it isenough to use one setting master to check just one point onthe recorded linear characteristics

The results presented above prove that the next step couldbe done to reduce the final measurement uncertainty whichis affected by the nonlinearity of the 119901119896 = 119891(119904) functionThe laboratory equipment (Figure 2) enabled the collectionof scores of measuring points to check the difference betweenthe actual measurement result and the theoretical linearfunction obtained in the adjustment process The obtainedresults confirmed the well-known rule that better linearitycould be achieved in a smaller measuring range In the caseof Figure 7 only the range ca 70 120583m is able to provide theacceptable nonlinearity 120575max = 08 which however appearsunacceptably short for many applications

The Pneusmart device makes it possible to join togethertwo sections of the 119901119896 = 119891(119904) function each of themapproximated with a different line and each of them ofacceptable nonlinearity 120575max = 08 The overall measuringrange is kept the same ca 140 120583m Then in an industrialenvironment the adjustment could be performed with twomaster rings as usual but the finalmeasurement result will bemuch less affected by the nonlinearity error of approximation

6 Conclusion

The investigation results led to the following conclusionnew programmable air gauging devices may increase mea-surement accuracy keeping long measuring range after theappropriate calibration and the approximation with twofunctions The linearity error which appears to be as large as6 for long measuring ranges could be reduced down to 1which is a satisfactory result In this way nonlinearity is notthe main factor affecting the measurement uncertainty of anair gauge

Competing Interests

The authors declare that there are no competing interestsrelated to this paper

References

[1] C J Tanner ldquoAir gaugingmdashhistory and future developmentsrdquoInstitution of Production Engineers Journal vol 37 no 7 pp448ndash462 1958

[2] G Schuetz ldquoPushing the limits of air gagingmdashandkeeping themthererdquo Quality Magazine vol 54 no 7 pp 22ndash26 2015

[3] N Taniguchi ldquoCurrent status in and future trends of ultra-precision machining and ultrafine materials processingrdquo CIRPAnnals-Manufacturing Technology vol 32 no 2 pp 573ndash5821983

[4] J Destefani ldquoAir gagingrdquo Manufacturing Engineering vol 131no 4 pp 5ndash9 2003

[5] Y H Wang S Q Hu and Y Hu ldquoAn automatic sorting systembased on pneumatic measurementrdquo Key Engineering Materialsvol 295-296 pp 563ndash568 2005

[6] Ch Koehn ldquoIn-process air gagingrdquo Quality Magazine vol 53no 5 pp 22ndash23 2014

[7] W Gopel J Hesse and J N Zemel Sensors A ComprehensiveSurvey vol 8 VCH Press Weinheim Germany 1995

[8] T Thomas C Hamaker J Martyniuk and G MirroldquoNanometer-level autofocus air gaugerdquo Precision Engineeringvol 22 no 4 pp 233ndash242 1998

[9] G Schuetz ldquoWhen air blows mechanical gaging awayrdquo QualityMagazine vol 53 no 1 pp 28ndash32 2014

[10] J A Bosch Coordinate Measuring Machines and Systems Mar-cel Dekker Inc New York 1995

[11] M Curtis and F Farago Handbook of Dimensional Measure-ment Industrial Press New York NY USA 2014

[12] H FWalker A K Elshennawy B C Gupta andMMVaughnThe Certified Quality Inspector Handbook ASQ Quality PressMilwaukee Wis USA 2013

[13] Cz J Jermak and M Rucki ldquoAir gauging still some room fordevelopmentrdquoAASCIT Communication vol 2 no 2 pp 29ndash342015

[14] C J Jermak and M Rucki ldquoStatic characteristics of air gaugesapplied in the roundness assessmentrdquo Metrology and Measure-ment Systems vol 23 no 1 pp 85ndash96 2016

[15] M Rucki ldquoReduction of uncertainty in air gauge adjustmentprocessrdquo IEEE Transactions on Instrumentation and Measure-ment vol 58 no 1 pp 52ndash57 2009

[16] J Liu X Pan G Wang and A Chen ldquoDesign and accuracyanalysis of pneumatic gauging for form error of spool valveinner holerdquo FlowMeasurement and Instrumentation vol 23 no1 pp 26ndash32 2012

[17] Cz J Jermak and M Rucki Air Gauging Static and DynamicCharacteristics IFSA Barcelona Spain 2012

[18] M Rucki B Barisic and T Szalay ldquoAnalysis of air gageinaccuracy caused by flow instabilityrdquoMeasurement vol 41 no6 pp 655ndash661 2008

[19] J S Simonoff Smoothing Methods in Statistics Springer Seriesin Statistics Springer New York NY USA 1996

[20] W Dos PassosNumerical Methods Algorithms and Tools in CCRC Press Boca Raton Fla USA 2010

[21] International Organization for Standardization ldquoLinear cali-bration using reference materialsrdquo International Standard ISO110951996 International Organization for Standardization1996

[22] M Jakubowicz and Cz J Jermak ldquoMeasurement uncertainty ofair guages for length measurementrdquo Machine Engineering vol18 no 3 pp 48ndash59 2013 (Polish)

[23] M Rucki B Barisic and G Varga ldquoAir gauges as a part of thedimensional inspection systemsrdquo Measurement vol 43 no 1pp 83ndash91 2010

[24] J Derezynski ldquoPNEUSMARTmdashpneumatic system for geomet-rical measurementsrdquoMachine Engineering vol 18 no 3 pp 88ndash99 2013 (Polish)

Journal of Control Science and Engineering 7

[25] M Ezekiel Methods of Correlation Analysis Wiley New YorkNY USA 1945

[26] R Breitinger Fehlerquellen beim pneumatischen Langenmessen[PhD thesis] TU Stuttgart 1969

[27] C Crnojevic G Roy A Bettahar and P Florent ldquoThe influenceof the regulator diameter and injection nozzle geometry onthe flow structure in pneumatic dimensional control systemsrdquoJournal of Fluids Engineering vol 119 no 3 pp 609ndash615 1997

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International Journal of

2 Journal of Control Science and Engineering

1 4 2 3 5

Figure 1 Investigation model of the air gauge 1 replaceable mea-suring nozzle 2 measuring chamber 3 replaceable inlet nozzle 4joint for back-pressure sensor 5 feeding joint

significantly deleting low costs as the main merit of airgauging

Hence the state of the art is as follows the static charac-teristics of the back-pressure air gauge can be calculated andsimulated with high accuracy but its nonlinearity in a largermeasuring range may affect the measurement results Theadjustment process requires expensive master rings so thenumber of calibration points should be minimal (typicallytwo) The proposed method improves the measurementaccuracy using two approximation lines and reducing theoverall nonlinearity calculated as a difference between thenominal point on the theoretical line and the actual pointregistered by the device

2 Investigation Apparatus

A group of high-pressure air gauges with the feeding pressure150 kPa has been investigated for many years in PoznanUniversity of Technology [17]The investigation model of theair gauge is presented in Figure 1 which enables the changingof the main parameters of an air gauge in order to check itsmetrological properties experimentally There are measuringchambers of different dimensions with two or more jointsfor back-pressure 119901119896 measurement replaceable measuringnozzles with various diameters 119889119901 and different geometry(eg conical inlet and corrected nozzle head) and replaceableinlet nozzles of diameters 119889119908

Main computerMicroBar

unit

Source ofpressuredand filtered air

Compressor

pz

pk

Model of air gauge

Moving tableFlapper surface

s

Control andmeasurement signal

Pressurestabilization

Figure 2 Scheme of the static characteristics investigation set [18]

To obtain the static characteristics of an air gauge theback-pressure signal 119901119896 is being compared with the displace-ment 119904 indication of measuring column TT 500 connectedwith the inductive sensor GT21HP and analyzed by dedicatedsoftware The laboratory set has been described in detailin [18] and its principle is shown in Figure 2 Additionaldevices could be included like aMicroBar unitwhich registersfluctuations of the back-pressure 119901119896 with high-frequencysampling (from 16Hz up to 4 kHz) [15] or temperaturesensors and flowmeter

The measuring slot 119904 is slowly changed in the range from0 up to themaximal value 119904max defined by the user dependenton the examined air gauge Typically 119904max does not exceed250 or 300 120583mThe registered functions of the back-pressure119901119896 volumetric flow 119902V and temperatures in the air gaugemeasuring chamber 1199051 and in the feeding chamber 1199052 couldbe presented in the following form

119901119896rarr = 119891 (119904)

119902Vrarr = 119891 (119904)

1199051119901rarr = 119891 (119904)

1199052119901rarr = 119891 (119904)

119904 isin ⟨0 119911⟩

(1)

119901119896larr = 119891 (119904)

119902Vlarr = 119891 (119904)

1199051119901larr = 119891 (119904)

1199052119901larr = 119891 (119904)

119904 isin ⟨119911 0⟩

(2)

The first set of (1) represents the results obtained from theincreasing values of s (the moving table is displacing air

Journal of Control Science and Engineering 3

00

02

04

06

08

10

12

0

25

50

75

100

125

150

0 25 50 75 100 150125s (120583m)

|K|

(kPa

120583m

)

Multiplication|K| = g(s)

Staticcharacteristic

pk

(kPa

)

pk = f(s)

(a)

0

25

50

75

100

125

150

00

02

04

06

08

10

12

|K|

(kPa

120583m

)

0 25 50 75 100 175150125s (120583m)

Staticcharacteristic

Multiplication|K| = g(s)

pk

(kPa

)

pk = f(s)

(b)

Figure 3 Examples of the experimentally obtained static characteristics and the multiplication graphs of air gauges

gauge away from the flapper surface) and (2) for decreasingones respectively It is obvious that the collected data containsome noise so the range of the mathematical functionsshould be applied to filter metrologically significant infor-mation Thus the data processing consists of the followingsteps

(i) Data smoothing

(ii) Interpolation

(iii) Calculation of the multiplication

(iv) Linearization of the experimentally obtained function119901119896 = 119891(119904)

After the data is processed the result may be presented bothfor average values and for separate increasing and decreasingfunctions The latter enables the possibility of revealing ahysteresis

From the numerous smoothing methods (see eg [19])the one based on the least squares has been chosen On thebasis of the subsequent 2119899 + 1 values of the variable (see (3))the polynomial of 119895 degree (see (4)) is fitted to achieve theminimal differences between the calculated values 119910(119909119894) andmeasured ones 119910119894

119910119894minus119899 119910119894minus119899 119910119894 119910119894+119899minus1 119910119894+119899 (3)

119910 (119909) = 1198880 + 1198881119909 + 11988821199092+ sdot sdot sdot + 119888119895119909

119895 (4)

119899

sum

119896=minus119899

[119910119894+119896 minus 119910 (119909119894+119896)2] = min (5)

The values 119910(119909119894) obtained in this way are assumed to bethe values of the smoothened function 1199101015840

119894= 119910(119909119894) In the

experiments a quadratic polynomial has been used based on

7measured points (see (6)) and the third-degree polynomialbased on 9 measured points (see (7))

119910119894(27) (119909) =1

21(minus2119910119894minus3 + 3119910119894minus2 + 6119910119894minus1 + 7119910119894 + 6119910119894+1

+ 3119910119894+2 minus 2119910119894minus3)

(6)

119910119894(39) (119909) =1

231(minus21119910119894minus4 + 14119910119894minus3 + 39119910119894minus2 + 54119910119894minus1

+ 59119910119894 + 54119910119894+1 + 39119910119894+2 + 14119910119894+3 minus 21119910119894+4)

(7)

It should be noted that for a higher degree of polynomialmore points should be considered and the obtained functionis less smoothened The procedure could be repeated severaltimes for the same data and the number of repetitionscould be chosen after the empirical analysis of a series ofcalculations

Among many known methods linear interpolation [20]has been chosen to achieve a steady distribution of themeasurement data It is described by the following formula

119871 (119909) = 1199100 +1199101 minus 1199100

1199091 minus 1199090

(119909 minus 1199090) (8)

which has appeared sufficient in order to achieve the desiredresults from the collected data

To evaluate the linearity of the obtained static character-istics the multiplication was calculated for each point andthe function |119870| = 119891(119904) was derived The function presentedgraphically gives quick information on the linearity of theanalyzed static characteristics119901119896 = 119891(119904) themultiplication ofthe linear part of the characteristics keeps at the same level forsome time For example in Figure 3 one can compare graphsof two experimentally achieved multiplication functions Itis seen that in one case (a) a linear range from 45 to75 120583m could be extracted and in the other case (b) thereis no horizontal part of the multiplication graph hencethe characteristics reveal worse linearity though the rangebetween 80 and 120 120583m may be considered satisfactorilylinear

4 Journal of Control Science and Engineering

Since multiplication is defined as a tangent of the staticcharacteristics declination angle the local multiplicationcould be calculated as follows

119870 (119904) =119889119891 (119904)

119889119904asympΔ119901119896

Δ119904

10038161003816100381610038161003816100381610038161003816119904isin(119904119904+Δ119904) (9)

In a real dataset however one deals with discrete values andthen the multiplication should be determined between thepoints 119899 + 1 and 119899

119870119899 = 119891 (119899 + 1) minus 119891 (119899)1003816100381610038161003816119899isin(0119911) (10)

3 Calibration Uncertainty

Thecalibrationmethods are described in the standard [21] Toperform the analysis of the air gauge calibration uncertaintyit is useful to present its static characteristics in the followingform

119901119896 = 119891 (119904) + 120578 = 119901119896(119904=0) + 119870119904 + 120578 (11)

where 119901119896(119904=0) is the starting point of the characteristics whenthe measuring nozzle is touching the flapper surface (slot 119904 =0) 119870 is multiplication and 120578 is the uncertainty

Estimators of those parameters could be calculated fromthe following equations

119896(119904=0)

= 119901119896(119904=0)119904119903

minus 119904 119904119903

=sum119873

119894=1(119904119894 minus 119904 119904119903) (119901119896

119894

119904119903 minus 119901119896 119904119903)

sum119873

119894=1(119904119894 minus 119904 119904119903)

2

(12)

where 119901119896 119904119903 and 119904 119904119903 correspond to the mean values

119904 119904119903 =1

119873

119873

sum

119894=1

119904119894

119901119896 119904119903 =1

119873

119873

sum

119894=1

119901119896119894

(13)

Thus the estimation formula will be presented as follows

119896= 119896(119904=0)

+ 119904 = 119901119896 119904119903 + (119904 minus 119904 119904119903) (14)

And the calibration characteristics are described by

lowast= 1198880 + 1198881119896 = 1198880 + 1198881 (119896(119904=0) + 119904) (15)

where

1198880 = minus119896(119904=0)

1198881 =1

(16)

The assumptions for the calibration procedure were as fol-lows

70 90 110 130 150 170

15

10

05

00

minus05

minus10

minus15

ΔgΔ

d(120583

m)

Δd (M= 1)

Δg (M= 1)

Δd (M= 15)

Δg (M= 15)

slowast0 (120583m)

Figure 4 Calibration uncertainties for air gauges with measuringnozzle 119889119901 = 1208mm and inlet nozzle 119889119908 = 0830mm [22]

35 55 75 95

20

15

10

05

00

minus05

minus10

minus15

minus20

ΔgΔ

d(120583

m)

Δd (M= 1)

Δg (M= 1)

Δd (M= 15)

Δg (M= 15)

slowast0 (120583m)

Figure 5 Calibration uncertainties for air gauges with measuringnozzle 119889119901 = 1810mm and outer inlet nozzle 119889119908 = 0720mm [22]

(i) Expected value of 120578 is zero (119864120578 = 0)

(ii) Variation of 120578 is constant and independent of 119904(var120578 = 1205902

120578)

(iii) The probability distribution of the random errors isGaussian (119901(120578) = 119873(0 1205902

120578))

(iv) Errors are not correlated with the measured value 119904(cov120578 119904 = 0)

(v) The errors of the set masters are negligibly small

When the same value of 1199040 in the process 1205780 is measured119872 times the uncertainty of the calibrated system could bedetermined as the confidence interval Δ = 119904

lowastminus 119904 The

examples of upper (Δ119892) and lower (Δ119889) confidence intervalsfor119872 = 1 and119872 = 15 are presented in the graphs (Figures 4and 5)

Journal of Control Science and Engineering 5

Table 1 Results of the calibration

Parameter 119904119901 = 40120583m 119904119901 = 50 120583m 119904119901 = 60 120583m 119904119901 = 70 120583m 119904119901 = 80 120583m 119904119901 = 90 120583m 119904119901 = 100 120583m119904119896[120583m] 916 1135 1395 1655 1915 2215 2495

Measuring range 119911119901 [120583m] 521 639 799 960 1119 1340 14981198772 09978 09991 09984 09969 09953 09922 09902119903 09989 09995 09992 09984 09976 09961 09951120575max [] 29 20 36 42 54 65 48

s (120583m)

140

130

120

110

100

90

80

70

60

pk

(kPa

)

sp = 40120583msp = 70120583msp = 100120583msp = 50120583m

sp = 80120583msp = 60120583msp = 90120583m

22520518516514512510585654525

Figure 6 Linear approximation of the air gauge characteristics inthe pressure range between 120 and 60 kPa

4 Linearity Improvement

Earlier investigations had proved that it is possible to achievebetter linearity by applying more setting masters [23] Morerecent investigations were made in Poznan University ofTechnology to improve linearity in the air gauging systemPneusmart The system includes a mechanical unit (gaugingheads etc) a pneumatic unit and a control unit [24] andlinearity is improved digitally by dividing the measuringrange into two parts

In fact the approximation of the static characteristics inthe required measuring range could give too poor linearityTable 1 contains the results of measurement and calculationswhich correspond to graphs in Figure 6 Here 119904119901 is the slotwidth at which the measuring range 119911119901 begins and 119904119896 is theone it ends with 1198772 is the determination factor which givenin percentage shows how many points are determined by theregression [25] 1198772 is corresponding to the correlation factor119903

119903 = radic1198772 (17)

It is assumed that when the correlation factor 119903 lies between09 and 1 the correlation is almost complete which is the caseshown in Table 1

120115110

95908580757065605550

sp (120583m)pk

(kPa

)25023021019017015013011090

Section A approximationSection B approximation

y = minus05131x + 16527

R2 = 09987

y = minus03118x + 12974

R2 = 09915

105100

Figure 7 Example of the characteristics approximated with twofunctions

However the linearity error from 2 to 65 is highlyunsatisfactory To reduce the linearity error the measuringrange 119911119901 should be shortened In Figure 7 the static charac-teristics are presented which reveal the nonlinearity as morethan 2 in the range 119911119901 from 100 to 240 120583m A reducedmeasuring range from 100 to 170 120583m (section A in Figure 7)has the linearity error 120575max = 08

Thus in order to keep the longer measuring range theapproximation with two functions is proposed The staticcharacteristics are then divided into two sections (A and Bin the example shown in Figure 7) each approximated withits own function The maximal linearity error for the entiremeasuring range 119911119901 from 100 to 240120583m is reduced down to120575max = 08

The Pneusmart device enables the collection of exper-imental data on the static characteristics of the particularmeasuring head (gauge plug) and to keep it in memoryTo calibrate it later it is enough to recall the appropriatecharacteristics ascribed to this plug and to check just onepoint with the setting master

5 Discussion

The air flow through the nozzles measuring chamber andthe flapper-nozzle area itself generates some phenomenaimpossible to omit which has been described decades ago[26] Although some improvement could be made [27] onthe curve function 119901119896 = 119891(119904) to prolong its proportional(linear) range the problem stays basically the same in a

6 Journal of Control Science and Engineering

wider range the linearity of the functions gets worse Anadditional problem is the need of adjustment any time thejet plug (measuring head) is changed to perform a differentmeasuring task It has been found that the adjustment withmore than two master rings can improve the measurementresults but the expenses rise disproportionately

In the previous investigations due to the electronic con-version of the pneumatic signal and then digital processingof the measured data it appeared possible to store the once-adjusted function and then to recall it after the exchange ofthe jet plug In that case to calibrate the new jet plug it isenough to use one setting master to check just one point onthe recorded linear characteristics

The results presented above prove that the next step couldbe done to reduce the final measurement uncertainty whichis affected by the nonlinearity of the 119901119896 = 119891(119904) functionThe laboratory equipment (Figure 2) enabled the collectionof scores of measuring points to check the difference betweenthe actual measurement result and the theoretical linearfunction obtained in the adjustment process The obtainedresults confirmed the well-known rule that better linearitycould be achieved in a smaller measuring range In the caseof Figure 7 only the range ca 70 120583m is able to provide theacceptable nonlinearity 120575max = 08 which however appearsunacceptably short for many applications

The Pneusmart device makes it possible to join togethertwo sections of the 119901119896 = 119891(119904) function each of themapproximated with a different line and each of them ofacceptable nonlinearity 120575max = 08 The overall measuringrange is kept the same ca 140 120583m Then in an industrialenvironment the adjustment could be performed with twomaster rings as usual but the finalmeasurement result will bemuch less affected by the nonlinearity error of approximation

6 Conclusion

The investigation results led to the following conclusionnew programmable air gauging devices may increase mea-surement accuracy keeping long measuring range after theappropriate calibration and the approximation with twofunctions The linearity error which appears to be as large as6 for long measuring ranges could be reduced down to 1which is a satisfactory result In this way nonlinearity is notthe main factor affecting the measurement uncertainty of anair gauge

Competing Interests

The authors declare that there are no competing interestsrelated to this paper

References

[1] C J Tanner ldquoAir gaugingmdashhistory and future developmentsrdquoInstitution of Production Engineers Journal vol 37 no 7 pp448ndash462 1958

[2] G Schuetz ldquoPushing the limits of air gagingmdashandkeeping themthererdquo Quality Magazine vol 54 no 7 pp 22ndash26 2015

[3] N Taniguchi ldquoCurrent status in and future trends of ultra-precision machining and ultrafine materials processingrdquo CIRPAnnals-Manufacturing Technology vol 32 no 2 pp 573ndash5821983

[4] J Destefani ldquoAir gagingrdquo Manufacturing Engineering vol 131no 4 pp 5ndash9 2003

[5] Y H Wang S Q Hu and Y Hu ldquoAn automatic sorting systembased on pneumatic measurementrdquo Key Engineering Materialsvol 295-296 pp 563ndash568 2005

[6] Ch Koehn ldquoIn-process air gagingrdquo Quality Magazine vol 53no 5 pp 22ndash23 2014

[7] W Gopel J Hesse and J N Zemel Sensors A ComprehensiveSurvey vol 8 VCH Press Weinheim Germany 1995

[8] T Thomas C Hamaker J Martyniuk and G MirroldquoNanometer-level autofocus air gaugerdquo Precision Engineeringvol 22 no 4 pp 233ndash242 1998

[9] G Schuetz ldquoWhen air blows mechanical gaging awayrdquo QualityMagazine vol 53 no 1 pp 28ndash32 2014

[10] J A Bosch Coordinate Measuring Machines and Systems Mar-cel Dekker Inc New York 1995

[11] M Curtis and F Farago Handbook of Dimensional Measure-ment Industrial Press New York NY USA 2014

[12] H FWalker A K Elshennawy B C Gupta andMMVaughnThe Certified Quality Inspector Handbook ASQ Quality PressMilwaukee Wis USA 2013

[13] Cz J Jermak and M Rucki ldquoAir gauging still some room fordevelopmentrdquoAASCIT Communication vol 2 no 2 pp 29ndash342015

[14] C J Jermak and M Rucki ldquoStatic characteristics of air gaugesapplied in the roundness assessmentrdquo Metrology and Measure-ment Systems vol 23 no 1 pp 85ndash96 2016

[15] M Rucki ldquoReduction of uncertainty in air gauge adjustmentprocessrdquo IEEE Transactions on Instrumentation and Measure-ment vol 58 no 1 pp 52ndash57 2009

[16] J Liu X Pan G Wang and A Chen ldquoDesign and accuracyanalysis of pneumatic gauging for form error of spool valveinner holerdquo FlowMeasurement and Instrumentation vol 23 no1 pp 26ndash32 2012

[17] Cz J Jermak and M Rucki Air Gauging Static and DynamicCharacteristics IFSA Barcelona Spain 2012

[18] M Rucki B Barisic and T Szalay ldquoAnalysis of air gageinaccuracy caused by flow instabilityrdquoMeasurement vol 41 no6 pp 655ndash661 2008

[19] J S Simonoff Smoothing Methods in Statistics Springer Seriesin Statistics Springer New York NY USA 1996

[20] W Dos PassosNumerical Methods Algorithms and Tools in CCRC Press Boca Raton Fla USA 2010

[21] International Organization for Standardization ldquoLinear cali-bration using reference materialsrdquo International Standard ISO110951996 International Organization for Standardization1996

[22] M Jakubowicz and Cz J Jermak ldquoMeasurement uncertainty ofair guages for length measurementrdquo Machine Engineering vol18 no 3 pp 48ndash59 2013 (Polish)

[23] M Rucki B Barisic and G Varga ldquoAir gauges as a part of thedimensional inspection systemsrdquo Measurement vol 43 no 1pp 83ndash91 2010

[24] J Derezynski ldquoPNEUSMARTmdashpneumatic system for geomet-rical measurementsrdquoMachine Engineering vol 18 no 3 pp 88ndash99 2013 (Polish)

Journal of Control Science and Engineering 7

[25] M Ezekiel Methods of Correlation Analysis Wiley New YorkNY USA 1945

[26] R Breitinger Fehlerquellen beim pneumatischen Langenmessen[PhD thesis] TU Stuttgart 1969

[27] C Crnojevic G Roy A Bettahar and P Florent ldquoThe influenceof the regulator diameter and injection nozzle geometry onthe flow structure in pneumatic dimensional control systemsrdquoJournal of Fluids Engineering vol 119 no 3 pp 609ndash615 1997

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Shock and Vibration

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Civil EngineeringAdvances in

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Chemical EngineeringInternational Journal of Antennas and

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International Journal of

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Navigation and Observation

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DistributedSensor Networks

International Journal of

Journal of Control Science and Engineering 3

00

02

04

06

08

10

12

0

25

50

75

100

125

150

0 25 50 75 100 150125s (120583m)

|K|

(kPa

120583m

)

Multiplication|K| = g(s)

Staticcharacteristic

pk

(kPa

)

pk = f(s)

(a)

0

25

50

75

100

125

150

00

02

04

06

08

10

12

|K|

(kPa

120583m

)

0 25 50 75 100 175150125s (120583m)

Staticcharacteristic

Multiplication|K| = g(s)

pk

(kPa

)

pk = f(s)

(b)

Figure 3 Examples of the experimentally obtained static characteristics and the multiplication graphs of air gauges

gauge away from the flapper surface) and (2) for decreasingones respectively It is obvious that the collected data containsome noise so the range of the mathematical functionsshould be applied to filter metrologically significant infor-mation Thus the data processing consists of the followingsteps

(i) Data smoothing

(ii) Interpolation

(iii) Calculation of the multiplication

(iv) Linearization of the experimentally obtained function119901119896 = 119891(119904)

After the data is processed the result may be presented bothfor average values and for separate increasing and decreasingfunctions The latter enables the possibility of revealing ahysteresis

From the numerous smoothing methods (see eg [19])the one based on the least squares has been chosen On thebasis of the subsequent 2119899 + 1 values of the variable (see (3))the polynomial of 119895 degree (see (4)) is fitted to achieve theminimal differences between the calculated values 119910(119909119894) andmeasured ones 119910119894

119910119894minus119899 119910119894minus119899 119910119894 119910119894+119899minus1 119910119894+119899 (3)

119910 (119909) = 1198880 + 1198881119909 + 11988821199092+ sdot sdot sdot + 119888119895119909

119895 (4)

119899

sum

119896=minus119899

[119910119894+119896 minus 119910 (119909119894+119896)2] = min (5)

The values 119910(119909119894) obtained in this way are assumed to bethe values of the smoothened function 1199101015840

119894= 119910(119909119894) In the

experiments a quadratic polynomial has been used based on

7measured points (see (6)) and the third-degree polynomialbased on 9 measured points (see (7))

119910119894(27) (119909) =1

21(minus2119910119894minus3 + 3119910119894minus2 + 6119910119894minus1 + 7119910119894 + 6119910119894+1

+ 3119910119894+2 minus 2119910119894minus3)

(6)

119910119894(39) (119909) =1

231(minus21119910119894minus4 + 14119910119894minus3 + 39119910119894minus2 + 54119910119894minus1

+ 59119910119894 + 54119910119894+1 + 39119910119894+2 + 14119910119894+3 minus 21119910119894+4)

(7)

It should be noted that for a higher degree of polynomialmore points should be considered and the obtained functionis less smoothened The procedure could be repeated severaltimes for the same data and the number of repetitionscould be chosen after the empirical analysis of a series ofcalculations

Among many known methods linear interpolation [20]has been chosen to achieve a steady distribution of themeasurement data It is described by the following formula

119871 (119909) = 1199100 +1199101 minus 1199100

1199091 minus 1199090

(119909 minus 1199090) (8)

which has appeared sufficient in order to achieve the desiredresults from the collected data

To evaluate the linearity of the obtained static character-istics the multiplication was calculated for each point andthe function |119870| = 119891(119904) was derived The function presentedgraphically gives quick information on the linearity of theanalyzed static characteristics119901119896 = 119891(119904) themultiplication ofthe linear part of the characteristics keeps at the same level forsome time For example in Figure 3 one can compare graphsof two experimentally achieved multiplication functions Itis seen that in one case (a) a linear range from 45 to75 120583m could be extracted and in the other case (b) thereis no horizontal part of the multiplication graph hencethe characteristics reveal worse linearity though the rangebetween 80 and 120 120583m may be considered satisfactorilylinear

4 Journal of Control Science and Engineering

Since multiplication is defined as a tangent of the staticcharacteristics declination angle the local multiplicationcould be calculated as follows

119870 (119904) =119889119891 (119904)

119889119904asympΔ119901119896

Δ119904

10038161003816100381610038161003816100381610038161003816119904isin(119904119904+Δ119904) (9)

In a real dataset however one deals with discrete values andthen the multiplication should be determined between thepoints 119899 + 1 and 119899

119870119899 = 119891 (119899 + 1) minus 119891 (119899)1003816100381610038161003816119899isin(0119911) (10)

3 Calibration Uncertainty

Thecalibrationmethods are described in the standard [21] Toperform the analysis of the air gauge calibration uncertaintyit is useful to present its static characteristics in the followingform

119901119896 = 119891 (119904) + 120578 = 119901119896(119904=0) + 119870119904 + 120578 (11)

where 119901119896(119904=0) is the starting point of the characteristics whenthe measuring nozzle is touching the flapper surface (slot 119904 =0) 119870 is multiplication and 120578 is the uncertainty

Estimators of those parameters could be calculated fromthe following equations

119896(119904=0)

= 119901119896(119904=0)119904119903

minus 119904 119904119903

=sum119873

119894=1(119904119894 minus 119904 119904119903) (119901119896

119894

119904119903 minus 119901119896 119904119903)

sum119873

119894=1(119904119894 minus 119904 119904119903)

2

(12)

where 119901119896 119904119903 and 119904 119904119903 correspond to the mean values

119904 119904119903 =1

119873

119873

sum

119894=1

119904119894

119901119896 119904119903 =1

119873

119873

sum

119894=1

119901119896119894

(13)

Thus the estimation formula will be presented as follows

119896= 119896(119904=0)

+ 119904 = 119901119896 119904119903 + (119904 minus 119904 119904119903) (14)

And the calibration characteristics are described by

lowast= 1198880 + 1198881119896 = 1198880 + 1198881 (119896(119904=0) + 119904) (15)

where

1198880 = minus119896(119904=0)

1198881 =1

(16)

The assumptions for the calibration procedure were as fol-lows

70 90 110 130 150 170

15

10

05

00

minus05

minus10

minus15

ΔgΔ

d(120583

m)

Δd (M= 1)

Δg (M= 1)

Δd (M= 15)

Δg (M= 15)

slowast0 (120583m)

Figure 4 Calibration uncertainties for air gauges with measuringnozzle 119889119901 = 1208mm and inlet nozzle 119889119908 = 0830mm [22]

35 55 75 95

20

15

10

05

00

minus05

minus10

minus15

minus20

ΔgΔ

d(120583

m)

Δd (M= 1)

Δg (M= 1)

Δd (M= 15)

Δg (M= 15)

slowast0 (120583m)

Figure 5 Calibration uncertainties for air gauges with measuringnozzle 119889119901 = 1810mm and outer inlet nozzle 119889119908 = 0720mm [22]

(i) Expected value of 120578 is zero (119864120578 = 0)

(ii) Variation of 120578 is constant and independent of 119904(var120578 = 1205902

120578)

(iii) The probability distribution of the random errors isGaussian (119901(120578) = 119873(0 1205902

120578))

(iv) Errors are not correlated with the measured value 119904(cov120578 119904 = 0)

(v) The errors of the set masters are negligibly small

When the same value of 1199040 in the process 1205780 is measured119872 times the uncertainty of the calibrated system could bedetermined as the confidence interval Δ = 119904

lowastminus 119904 The

examples of upper (Δ119892) and lower (Δ119889) confidence intervalsfor119872 = 1 and119872 = 15 are presented in the graphs (Figures 4and 5)

Journal of Control Science and Engineering 5

Table 1 Results of the calibration

Parameter 119904119901 = 40120583m 119904119901 = 50 120583m 119904119901 = 60 120583m 119904119901 = 70 120583m 119904119901 = 80 120583m 119904119901 = 90 120583m 119904119901 = 100 120583m119904119896[120583m] 916 1135 1395 1655 1915 2215 2495

Measuring range 119911119901 [120583m] 521 639 799 960 1119 1340 14981198772 09978 09991 09984 09969 09953 09922 09902119903 09989 09995 09992 09984 09976 09961 09951120575max [] 29 20 36 42 54 65 48

s (120583m)

140

130

120

110

100

90

80

70

60

pk

(kPa

)

sp = 40120583msp = 70120583msp = 100120583msp = 50120583m

sp = 80120583msp = 60120583msp = 90120583m

22520518516514512510585654525

Figure 6 Linear approximation of the air gauge characteristics inthe pressure range between 120 and 60 kPa

4 Linearity Improvement

Earlier investigations had proved that it is possible to achievebetter linearity by applying more setting masters [23] Morerecent investigations were made in Poznan University ofTechnology to improve linearity in the air gauging systemPneusmart The system includes a mechanical unit (gaugingheads etc) a pneumatic unit and a control unit [24] andlinearity is improved digitally by dividing the measuringrange into two parts

In fact the approximation of the static characteristics inthe required measuring range could give too poor linearityTable 1 contains the results of measurement and calculationswhich correspond to graphs in Figure 6 Here 119904119901 is the slotwidth at which the measuring range 119911119901 begins and 119904119896 is theone it ends with 1198772 is the determination factor which givenin percentage shows how many points are determined by theregression [25] 1198772 is corresponding to the correlation factor119903

119903 = radic1198772 (17)

It is assumed that when the correlation factor 119903 lies between09 and 1 the correlation is almost complete which is the caseshown in Table 1

120115110

95908580757065605550

sp (120583m)pk

(kPa

)25023021019017015013011090

Section A approximationSection B approximation

y = minus05131x + 16527

R2 = 09987

y = minus03118x + 12974

R2 = 09915

105100

Figure 7 Example of the characteristics approximated with twofunctions

However the linearity error from 2 to 65 is highlyunsatisfactory To reduce the linearity error the measuringrange 119911119901 should be shortened In Figure 7 the static charac-teristics are presented which reveal the nonlinearity as morethan 2 in the range 119911119901 from 100 to 240 120583m A reducedmeasuring range from 100 to 170 120583m (section A in Figure 7)has the linearity error 120575max = 08

Thus in order to keep the longer measuring range theapproximation with two functions is proposed The staticcharacteristics are then divided into two sections (A and Bin the example shown in Figure 7) each approximated withits own function The maximal linearity error for the entiremeasuring range 119911119901 from 100 to 240120583m is reduced down to120575max = 08

The Pneusmart device enables the collection of exper-imental data on the static characteristics of the particularmeasuring head (gauge plug) and to keep it in memoryTo calibrate it later it is enough to recall the appropriatecharacteristics ascribed to this plug and to check just onepoint with the setting master

5 Discussion

The air flow through the nozzles measuring chamber andthe flapper-nozzle area itself generates some phenomenaimpossible to omit which has been described decades ago[26] Although some improvement could be made [27] onthe curve function 119901119896 = 119891(119904) to prolong its proportional(linear) range the problem stays basically the same in a

6 Journal of Control Science and Engineering

wider range the linearity of the functions gets worse Anadditional problem is the need of adjustment any time thejet plug (measuring head) is changed to perform a differentmeasuring task It has been found that the adjustment withmore than two master rings can improve the measurementresults but the expenses rise disproportionately

In the previous investigations due to the electronic con-version of the pneumatic signal and then digital processingof the measured data it appeared possible to store the once-adjusted function and then to recall it after the exchange ofthe jet plug In that case to calibrate the new jet plug it isenough to use one setting master to check just one point onthe recorded linear characteristics

The results presented above prove that the next step couldbe done to reduce the final measurement uncertainty whichis affected by the nonlinearity of the 119901119896 = 119891(119904) functionThe laboratory equipment (Figure 2) enabled the collectionof scores of measuring points to check the difference betweenthe actual measurement result and the theoretical linearfunction obtained in the adjustment process The obtainedresults confirmed the well-known rule that better linearitycould be achieved in a smaller measuring range In the caseof Figure 7 only the range ca 70 120583m is able to provide theacceptable nonlinearity 120575max = 08 which however appearsunacceptably short for many applications

The Pneusmart device makes it possible to join togethertwo sections of the 119901119896 = 119891(119904) function each of themapproximated with a different line and each of them ofacceptable nonlinearity 120575max = 08 The overall measuringrange is kept the same ca 140 120583m Then in an industrialenvironment the adjustment could be performed with twomaster rings as usual but the finalmeasurement result will bemuch less affected by the nonlinearity error of approximation

6 Conclusion

The investigation results led to the following conclusionnew programmable air gauging devices may increase mea-surement accuracy keeping long measuring range after theappropriate calibration and the approximation with twofunctions The linearity error which appears to be as large as6 for long measuring ranges could be reduced down to 1which is a satisfactory result In this way nonlinearity is notthe main factor affecting the measurement uncertainty of anair gauge

Competing Interests

The authors declare that there are no competing interestsrelated to this paper

References

[1] C J Tanner ldquoAir gaugingmdashhistory and future developmentsrdquoInstitution of Production Engineers Journal vol 37 no 7 pp448ndash462 1958

[2] G Schuetz ldquoPushing the limits of air gagingmdashandkeeping themthererdquo Quality Magazine vol 54 no 7 pp 22ndash26 2015

[3] N Taniguchi ldquoCurrent status in and future trends of ultra-precision machining and ultrafine materials processingrdquo CIRPAnnals-Manufacturing Technology vol 32 no 2 pp 573ndash5821983

[4] J Destefani ldquoAir gagingrdquo Manufacturing Engineering vol 131no 4 pp 5ndash9 2003

[5] Y H Wang S Q Hu and Y Hu ldquoAn automatic sorting systembased on pneumatic measurementrdquo Key Engineering Materialsvol 295-296 pp 563ndash568 2005

[6] Ch Koehn ldquoIn-process air gagingrdquo Quality Magazine vol 53no 5 pp 22ndash23 2014

[7] W Gopel J Hesse and J N Zemel Sensors A ComprehensiveSurvey vol 8 VCH Press Weinheim Germany 1995

[8] T Thomas C Hamaker J Martyniuk and G MirroldquoNanometer-level autofocus air gaugerdquo Precision Engineeringvol 22 no 4 pp 233ndash242 1998

[9] G Schuetz ldquoWhen air blows mechanical gaging awayrdquo QualityMagazine vol 53 no 1 pp 28ndash32 2014

[10] J A Bosch Coordinate Measuring Machines and Systems Mar-cel Dekker Inc New York 1995

[11] M Curtis and F Farago Handbook of Dimensional Measure-ment Industrial Press New York NY USA 2014

[12] H FWalker A K Elshennawy B C Gupta andMMVaughnThe Certified Quality Inspector Handbook ASQ Quality PressMilwaukee Wis USA 2013

[13] Cz J Jermak and M Rucki ldquoAir gauging still some room fordevelopmentrdquoAASCIT Communication vol 2 no 2 pp 29ndash342015

[14] C J Jermak and M Rucki ldquoStatic characteristics of air gaugesapplied in the roundness assessmentrdquo Metrology and Measure-ment Systems vol 23 no 1 pp 85ndash96 2016

[15] M Rucki ldquoReduction of uncertainty in air gauge adjustmentprocessrdquo IEEE Transactions on Instrumentation and Measure-ment vol 58 no 1 pp 52ndash57 2009

[16] J Liu X Pan G Wang and A Chen ldquoDesign and accuracyanalysis of pneumatic gauging for form error of spool valveinner holerdquo FlowMeasurement and Instrumentation vol 23 no1 pp 26ndash32 2012

[17] Cz J Jermak and M Rucki Air Gauging Static and DynamicCharacteristics IFSA Barcelona Spain 2012

[18] M Rucki B Barisic and T Szalay ldquoAnalysis of air gageinaccuracy caused by flow instabilityrdquoMeasurement vol 41 no6 pp 655ndash661 2008

[19] J S Simonoff Smoothing Methods in Statistics Springer Seriesin Statistics Springer New York NY USA 1996

[20] W Dos PassosNumerical Methods Algorithms and Tools in CCRC Press Boca Raton Fla USA 2010

[21] International Organization for Standardization ldquoLinear cali-bration using reference materialsrdquo International Standard ISO110951996 International Organization for Standardization1996

[22] M Jakubowicz and Cz J Jermak ldquoMeasurement uncertainty ofair guages for length measurementrdquo Machine Engineering vol18 no 3 pp 48ndash59 2013 (Polish)

[23] M Rucki B Barisic and G Varga ldquoAir gauges as a part of thedimensional inspection systemsrdquo Measurement vol 43 no 1pp 83ndash91 2010

[24] J Derezynski ldquoPNEUSMARTmdashpneumatic system for geomet-rical measurementsrdquoMachine Engineering vol 18 no 3 pp 88ndash99 2013 (Polish)

Journal of Control Science and Engineering 7

[25] M Ezekiel Methods of Correlation Analysis Wiley New YorkNY USA 1945

[26] R Breitinger Fehlerquellen beim pneumatischen Langenmessen[PhD thesis] TU Stuttgart 1969

[27] C Crnojevic G Roy A Bettahar and P Florent ldquoThe influenceof the regulator diameter and injection nozzle geometry onthe flow structure in pneumatic dimensional control systemsrdquoJournal of Fluids Engineering vol 119 no 3 pp 609ndash615 1997

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

4 Journal of Control Science and Engineering

Since multiplication is defined as a tangent of the staticcharacteristics declination angle the local multiplicationcould be calculated as follows

119870 (119904) =119889119891 (119904)

119889119904asympΔ119901119896

Δ119904

10038161003816100381610038161003816100381610038161003816119904isin(119904119904+Δ119904) (9)

In a real dataset however one deals with discrete values andthen the multiplication should be determined between thepoints 119899 + 1 and 119899

119870119899 = 119891 (119899 + 1) minus 119891 (119899)1003816100381610038161003816119899isin(0119911) (10)

3 Calibration Uncertainty

Thecalibrationmethods are described in the standard [21] Toperform the analysis of the air gauge calibration uncertaintyit is useful to present its static characteristics in the followingform

119901119896 = 119891 (119904) + 120578 = 119901119896(119904=0) + 119870119904 + 120578 (11)

where 119901119896(119904=0) is the starting point of the characteristics whenthe measuring nozzle is touching the flapper surface (slot 119904 =0) 119870 is multiplication and 120578 is the uncertainty

Estimators of those parameters could be calculated fromthe following equations

119896(119904=0)

= 119901119896(119904=0)119904119903

minus 119904 119904119903

=sum119873

119894=1(119904119894 minus 119904 119904119903) (119901119896

119894

119904119903 minus 119901119896 119904119903)

sum119873

119894=1(119904119894 minus 119904 119904119903)

2

(12)

where 119901119896 119904119903 and 119904 119904119903 correspond to the mean values

119904 119904119903 =1

119873

119873

sum

119894=1

119904119894

119901119896 119904119903 =1

119873

119873

sum

119894=1

119901119896119894

(13)

Thus the estimation formula will be presented as follows

119896= 119896(119904=0)

+ 119904 = 119901119896 119904119903 + (119904 minus 119904 119904119903) (14)

And the calibration characteristics are described by

lowast= 1198880 + 1198881119896 = 1198880 + 1198881 (119896(119904=0) + 119904) (15)

where

1198880 = minus119896(119904=0)

1198881 =1

(16)

The assumptions for the calibration procedure were as fol-lows

70 90 110 130 150 170

15

10

05

00

minus05

minus10

minus15

ΔgΔ

d(120583

m)

Δd (M= 1)

Δg (M= 1)

Δd (M= 15)

Δg (M= 15)

slowast0 (120583m)

Figure 4 Calibration uncertainties for air gauges with measuringnozzle 119889119901 = 1208mm and inlet nozzle 119889119908 = 0830mm [22]

35 55 75 95

20

15

10

05

00

minus05

minus10

minus15

minus20

ΔgΔ

d(120583

m)

Δd (M= 1)

Δg (M= 1)

Δd (M= 15)

Δg (M= 15)

slowast0 (120583m)

Figure 5 Calibration uncertainties for air gauges with measuringnozzle 119889119901 = 1810mm and outer inlet nozzle 119889119908 = 0720mm [22]

(i) Expected value of 120578 is zero (119864120578 = 0)

(ii) Variation of 120578 is constant and independent of 119904(var120578 = 1205902

120578)

(iii) The probability distribution of the random errors isGaussian (119901(120578) = 119873(0 1205902

120578))

(iv) Errors are not correlated with the measured value 119904(cov120578 119904 = 0)

(v) The errors of the set masters are negligibly small

When the same value of 1199040 in the process 1205780 is measured119872 times the uncertainty of the calibrated system could bedetermined as the confidence interval Δ = 119904

lowastminus 119904 The

examples of upper (Δ119892) and lower (Δ119889) confidence intervalsfor119872 = 1 and119872 = 15 are presented in the graphs (Figures 4and 5)

Journal of Control Science and Engineering 5

Table 1 Results of the calibration

Parameter 119904119901 = 40120583m 119904119901 = 50 120583m 119904119901 = 60 120583m 119904119901 = 70 120583m 119904119901 = 80 120583m 119904119901 = 90 120583m 119904119901 = 100 120583m119904119896[120583m] 916 1135 1395 1655 1915 2215 2495

Measuring range 119911119901 [120583m] 521 639 799 960 1119 1340 14981198772 09978 09991 09984 09969 09953 09922 09902119903 09989 09995 09992 09984 09976 09961 09951120575max [] 29 20 36 42 54 65 48

s (120583m)

140

130

120

110

100

90

80

70

60

pk

(kPa

)

sp = 40120583msp = 70120583msp = 100120583msp = 50120583m

sp = 80120583msp = 60120583msp = 90120583m

22520518516514512510585654525

Figure 6 Linear approximation of the air gauge characteristics inthe pressure range between 120 and 60 kPa

4 Linearity Improvement

Earlier investigations had proved that it is possible to achievebetter linearity by applying more setting masters [23] Morerecent investigations were made in Poznan University ofTechnology to improve linearity in the air gauging systemPneusmart The system includes a mechanical unit (gaugingheads etc) a pneumatic unit and a control unit [24] andlinearity is improved digitally by dividing the measuringrange into two parts

In fact the approximation of the static characteristics inthe required measuring range could give too poor linearityTable 1 contains the results of measurement and calculationswhich correspond to graphs in Figure 6 Here 119904119901 is the slotwidth at which the measuring range 119911119901 begins and 119904119896 is theone it ends with 1198772 is the determination factor which givenin percentage shows how many points are determined by theregression [25] 1198772 is corresponding to the correlation factor119903

119903 = radic1198772 (17)

It is assumed that when the correlation factor 119903 lies between09 and 1 the correlation is almost complete which is the caseshown in Table 1

120115110

95908580757065605550

sp (120583m)pk

(kPa

)25023021019017015013011090

Section A approximationSection B approximation

y = minus05131x + 16527

R2 = 09987

y = minus03118x + 12974

R2 = 09915

105100

Figure 7 Example of the characteristics approximated with twofunctions

However the linearity error from 2 to 65 is highlyunsatisfactory To reduce the linearity error the measuringrange 119911119901 should be shortened In Figure 7 the static charac-teristics are presented which reveal the nonlinearity as morethan 2 in the range 119911119901 from 100 to 240 120583m A reducedmeasuring range from 100 to 170 120583m (section A in Figure 7)has the linearity error 120575max = 08

Thus in order to keep the longer measuring range theapproximation with two functions is proposed The staticcharacteristics are then divided into two sections (A and Bin the example shown in Figure 7) each approximated withits own function The maximal linearity error for the entiremeasuring range 119911119901 from 100 to 240120583m is reduced down to120575max = 08

The Pneusmart device enables the collection of exper-imental data on the static characteristics of the particularmeasuring head (gauge plug) and to keep it in memoryTo calibrate it later it is enough to recall the appropriatecharacteristics ascribed to this plug and to check just onepoint with the setting master

5 Discussion

The air flow through the nozzles measuring chamber andthe flapper-nozzle area itself generates some phenomenaimpossible to omit which has been described decades ago[26] Although some improvement could be made [27] onthe curve function 119901119896 = 119891(119904) to prolong its proportional(linear) range the problem stays basically the same in a

6 Journal of Control Science and Engineering

wider range the linearity of the functions gets worse Anadditional problem is the need of adjustment any time thejet plug (measuring head) is changed to perform a differentmeasuring task It has been found that the adjustment withmore than two master rings can improve the measurementresults but the expenses rise disproportionately

In the previous investigations due to the electronic con-version of the pneumatic signal and then digital processingof the measured data it appeared possible to store the once-adjusted function and then to recall it after the exchange ofthe jet plug In that case to calibrate the new jet plug it isenough to use one setting master to check just one point onthe recorded linear characteristics

The results presented above prove that the next step couldbe done to reduce the final measurement uncertainty whichis affected by the nonlinearity of the 119901119896 = 119891(119904) functionThe laboratory equipment (Figure 2) enabled the collectionof scores of measuring points to check the difference betweenthe actual measurement result and the theoretical linearfunction obtained in the adjustment process The obtainedresults confirmed the well-known rule that better linearitycould be achieved in a smaller measuring range In the caseof Figure 7 only the range ca 70 120583m is able to provide theacceptable nonlinearity 120575max = 08 which however appearsunacceptably short for many applications

The Pneusmart device makes it possible to join togethertwo sections of the 119901119896 = 119891(119904) function each of themapproximated with a different line and each of them ofacceptable nonlinearity 120575max = 08 The overall measuringrange is kept the same ca 140 120583m Then in an industrialenvironment the adjustment could be performed with twomaster rings as usual but the finalmeasurement result will bemuch less affected by the nonlinearity error of approximation

6 Conclusion

The investigation results led to the following conclusionnew programmable air gauging devices may increase mea-surement accuracy keeping long measuring range after theappropriate calibration and the approximation with twofunctions The linearity error which appears to be as large as6 for long measuring ranges could be reduced down to 1which is a satisfactory result In this way nonlinearity is notthe main factor affecting the measurement uncertainty of anair gauge

Competing Interests

The authors declare that there are no competing interestsrelated to this paper

References

[1] C J Tanner ldquoAir gaugingmdashhistory and future developmentsrdquoInstitution of Production Engineers Journal vol 37 no 7 pp448ndash462 1958

[2] G Schuetz ldquoPushing the limits of air gagingmdashandkeeping themthererdquo Quality Magazine vol 54 no 7 pp 22ndash26 2015

[3] N Taniguchi ldquoCurrent status in and future trends of ultra-precision machining and ultrafine materials processingrdquo CIRPAnnals-Manufacturing Technology vol 32 no 2 pp 573ndash5821983

[4] J Destefani ldquoAir gagingrdquo Manufacturing Engineering vol 131no 4 pp 5ndash9 2003

[5] Y H Wang S Q Hu and Y Hu ldquoAn automatic sorting systembased on pneumatic measurementrdquo Key Engineering Materialsvol 295-296 pp 563ndash568 2005

[6] Ch Koehn ldquoIn-process air gagingrdquo Quality Magazine vol 53no 5 pp 22ndash23 2014

[7] W Gopel J Hesse and J N Zemel Sensors A ComprehensiveSurvey vol 8 VCH Press Weinheim Germany 1995

[8] T Thomas C Hamaker J Martyniuk and G MirroldquoNanometer-level autofocus air gaugerdquo Precision Engineeringvol 22 no 4 pp 233ndash242 1998

[9] G Schuetz ldquoWhen air blows mechanical gaging awayrdquo QualityMagazine vol 53 no 1 pp 28ndash32 2014

[10] J A Bosch Coordinate Measuring Machines and Systems Mar-cel Dekker Inc New York 1995

[11] M Curtis and F Farago Handbook of Dimensional Measure-ment Industrial Press New York NY USA 2014

[12] H FWalker A K Elshennawy B C Gupta andMMVaughnThe Certified Quality Inspector Handbook ASQ Quality PressMilwaukee Wis USA 2013

[13] Cz J Jermak and M Rucki ldquoAir gauging still some room fordevelopmentrdquoAASCIT Communication vol 2 no 2 pp 29ndash342015

[14] C J Jermak and M Rucki ldquoStatic characteristics of air gaugesapplied in the roundness assessmentrdquo Metrology and Measure-ment Systems vol 23 no 1 pp 85ndash96 2016

[15] M Rucki ldquoReduction of uncertainty in air gauge adjustmentprocessrdquo IEEE Transactions on Instrumentation and Measure-ment vol 58 no 1 pp 52ndash57 2009

[16] J Liu X Pan G Wang and A Chen ldquoDesign and accuracyanalysis of pneumatic gauging for form error of spool valveinner holerdquo FlowMeasurement and Instrumentation vol 23 no1 pp 26ndash32 2012

[17] Cz J Jermak and M Rucki Air Gauging Static and DynamicCharacteristics IFSA Barcelona Spain 2012

[18] M Rucki B Barisic and T Szalay ldquoAnalysis of air gageinaccuracy caused by flow instabilityrdquoMeasurement vol 41 no6 pp 655ndash661 2008

[19] J S Simonoff Smoothing Methods in Statistics Springer Seriesin Statistics Springer New York NY USA 1996

[20] W Dos PassosNumerical Methods Algorithms and Tools in CCRC Press Boca Raton Fla USA 2010

[21] International Organization for Standardization ldquoLinear cali-bration using reference materialsrdquo International Standard ISO110951996 International Organization for Standardization1996

[22] M Jakubowicz and Cz J Jermak ldquoMeasurement uncertainty ofair guages for length measurementrdquo Machine Engineering vol18 no 3 pp 48ndash59 2013 (Polish)

[23] M Rucki B Barisic and G Varga ldquoAir gauges as a part of thedimensional inspection systemsrdquo Measurement vol 43 no 1pp 83ndash91 2010

[24] J Derezynski ldquoPNEUSMARTmdashpneumatic system for geomet-rical measurementsrdquoMachine Engineering vol 18 no 3 pp 88ndash99 2013 (Polish)

Journal of Control Science and Engineering 7

[25] M Ezekiel Methods of Correlation Analysis Wiley New YorkNY USA 1945

[26] R Breitinger Fehlerquellen beim pneumatischen Langenmessen[PhD thesis] TU Stuttgart 1969

[27] C Crnojevic G Roy A Bettahar and P Florent ldquoThe influenceof the regulator diameter and injection nozzle geometry onthe flow structure in pneumatic dimensional control systemsrdquoJournal of Fluids Engineering vol 119 no 3 pp 609ndash615 1997

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Control Science and Engineering 5

Table 1 Results of the calibration

Parameter 119904119901 = 40120583m 119904119901 = 50 120583m 119904119901 = 60 120583m 119904119901 = 70 120583m 119904119901 = 80 120583m 119904119901 = 90 120583m 119904119901 = 100 120583m119904119896[120583m] 916 1135 1395 1655 1915 2215 2495

Measuring range 119911119901 [120583m] 521 639 799 960 1119 1340 14981198772 09978 09991 09984 09969 09953 09922 09902119903 09989 09995 09992 09984 09976 09961 09951120575max [] 29 20 36 42 54 65 48

s (120583m)

140

130

120

110

100

90

80

70

60

pk

(kPa

)

sp = 40120583msp = 70120583msp = 100120583msp = 50120583m

sp = 80120583msp = 60120583msp = 90120583m

22520518516514512510585654525

Figure 6 Linear approximation of the air gauge characteristics inthe pressure range between 120 and 60 kPa

4 Linearity Improvement

Earlier investigations had proved that it is possible to achievebetter linearity by applying more setting masters [23] Morerecent investigations were made in Poznan University ofTechnology to improve linearity in the air gauging systemPneusmart The system includes a mechanical unit (gaugingheads etc) a pneumatic unit and a control unit [24] andlinearity is improved digitally by dividing the measuringrange into two parts

In fact the approximation of the static characteristics inthe required measuring range could give too poor linearityTable 1 contains the results of measurement and calculationswhich correspond to graphs in Figure 6 Here 119904119901 is the slotwidth at which the measuring range 119911119901 begins and 119904119896 is theone it ends with 1198772 is the determination factor which givenin percentage shows how many points are determined by theregression [25] 1198772 is corresponding to the correlation factor119903

119903 = radic1198772 (17)

It is assumed that when the correlation factor 119903 lies between09 and 1 the correlation is almost complete which is the caseshown in Table 1

120115110

95908580757065605550

sp (120583m)pk

(kPa

)25023021019017015013011090

Section A approximationSection B approximation

y = minus05131x + 16527

R2 = 09987

y = minus03118x + 12974

R2 = 09915

105100

Figure 7 Example of the characteristics approximated with twofunctions

However the linearity error from 2 to 65 is highlyunsatisfactory To reduce the linearity error the measuringrange 119911119901 should be shortened In Figure 7 the static charac-teristics are presented which reveal the nonlinearity as morethan 2 in the range 119911119901 from 100 to 240 120583m A reducedmeasuring range from 100 to 170 120583m (section A in Figure 7)has the linearity error 120575max = 08

Thus in order to keep the longer measuring range theapproximation with two functions is proposed The staticcharacteristics are then divided into two sections (A and Bin the example shown in Figure 7) each approximated withits own function The maximal linearity error for the entiremeasuring range 119911119901 from 100 to 240120583m is reduced down to120575max = 08

The Pneusmart device enables the collection of exper-imental data on the static characteristics of the particularmeasuring head (gauge plug) and to keep it in memoryTo calibrate it later it is enough to recall the appropriatecharacteristics ascribed to this plug and to check just onepoint with the setting master

5 Discussion

The air flow through the nozzles measuring chamber andthe flapper-nozzle area itself generates some phenomenaimpossible to omit which has been described decades ago[26] Although some improvement could be made [27] onthe curve function 119901119896 = 119891(119904) to prolong its proportional(linear) range the problem stays basically the same in a

6 Journal of Control Science and Engineering

wider range the linearity of the functions gets worse Anadditional problem is the need of adjustment any time thejet plug (measuring head) is changed to perform a differentmeasuring task It has been found that the adjustment withmore than two master rings can improve the measurementresults but the expenses rise disproportionately

In the previous investigations due to the electronic con-version of the pneumatic signal and then digital processingof the measured data it appeared possible to store the once-adjusted function and then to recall it after the exchange ofthe jet plug In that case to calibrate the new jet plug it isenough to use one setting master to check just one point onthe recorded linear characteristics

The results presented above prove that the next step couldbe done to reduce the final measurement uncertainty whichis affected by the nonlinearity of the 119901119896 = 119891(119904) functionThe laboratory equipment (Figure 2) enabled the collectionof scores of measuring points to check the difference betweenthe actual measurement result and the theoretical linearfunction obtained in the adjustment process The obtainedresults confirmed the well-known rule that better linearitycould be achieved in a smaller measuring range In the caseof Figure 7 only the range ca 70 120583m is able to provide theacceptable nonlinearity 120575max = 08 which however appearsunacceptably short for many applications

The Pneusmart device makes it possible to join togethertwo sections of the 119901119896 = 119891(119904) function each of themapproximated with a different line and each of them ofacceptable nonlinearity 120575max = 08 The overall measuringrange is kept the same ca 140 120583m Then in an industrialenvironment the adjustment could be performed with twomaster rings as usual but the finalmeasurement result will bemuch less affected by the nonlinearity error of approximation

6 Conclusion

The investigation results led to the following conclusionnew programmable air gauging devices may increase mea-surement accuracy keeping long measuring range after theappropriate calibration and the approximation with twofunctions The linearity error which appears to be as large as6 for long measuring ranges could be reduced down to 1which is a satisfactory result In this way nonlinearity is notthe main factor affecting the measurement uncertainty of anair gauge

Competing Interests

The authors declare that there are no competing interestsrelated to this paper

References

[1] C J Tanner ldquoAir gaugingmdashhistory and future developmentsrdquoInstitution of Production Engineers Journal vol 37 no 7 pp448ndash462 1958

[2] G Schuetz ldquoPushing the limits of air gagingmdashandkeeping themthererdquo Quality Magazine vol 54 no 7 pp 22ndash26 2015

[3] N Taniguchi ldquoCurrent status in and future trends of ultra-precision machining and ultrafine materials processingrdquo CIRPAnnals-Manufacturing Technology vol 32 no 2 pp 573ndash5821983

[4] J Destefani ldquoAir gagingrdquo Manufacturing Engineering vol 131no 4 pp 5ndash9 2003

[5] Y H Wang S Q Hu and Y Hu ldquoAn automatic sorting systembased on pneumatic measurementrdquo Key Engineering Materialsvol 295-296 pp 563ndash568 2005

[6] Ch Koehn ldquoIn-process air gagingrdquo Quality Magazine vol 53no 5 pp 22ndash23 2014

[7] W Gopel J Hesse and J N Zemel Sensors A ComprehensiveSurvey vol 8 VCH Press Weinheim Germany 1995

[8] T Thomas C Hamaker J Martyniuk and G MirroldquoNanometer-level autofocus air gaugerdquo Precision Engineeringvol 22 no 4 pp 233ndash242 1998

[9] G Schuetz ldquoWhen air blows mechanical gaging awayrdquo QualityMagazine vol 53 no 1 pp 28ndash32 2014

[10] J A Bosch Coordinate Measuring Machines and Systems Mar-cel Dekker Inc New York 1995

[11] M Curtis and F Farago Handbook of Dimensional Measure-ment Industrial Press New York NY USA 2014

[12] H FWalker A K Elshennawy B C Gupta andMMVaughnThe Certified Quality Inspector Handbook ASQ Quality PressMilwaukee Wis USA 2013

[13] Cz J Jermak and M Rucki ldquoAir gauging still some room fordevelopmentrdquoAASCIT Communication vol 2 no 2 pp 29ndash342015

[14] C J Jermak and M Rucki ldquoStatic characteristics of air gaugesapplied in the roundness assessmentrdquo Metrology and Measure-ment Systems vol 23 no 1 pp 85ndash96 2016

[15] M Rucki ldquoReduction of uncertainty in air gauge adjustmentprocessrdquo IEEE Transactions on Instrumentation and Measure-ment vol 58 no 1 pp 52ndash57 2009

[16] J Liu X Pan G Wang and A Chen ldquoDesign and accuracyanalysis of pneumatic gauging for form error of spool valveinner holerdquo FlowMeasurement and Instrumentation vol 23 no1 pp 26ndash32 2012

[17] Cz J Jermak and M Rucki Air Gauging Static and DynamicCharacteristics IFSA Barcelona Spain 2012

[18] M Rucki B Barisic and T Szalay ldquoAnalysis of air gageinaccuracy caused by flow instabilityrdquoMeasurement vol 41 no6 pp 655ndash661 2008

[19] J S Simonoff Smoothing Methods in Statistics Springer Seriesin Statistics Springer New York NY USA 1996

[20] W Dos PassosNumerical Methods Algorithms and Tools in CCRC Press Boca Raton Fla USA 2010

[21] International Organization for Standardization ldquoLinear cali-bration using reference materialsrdquo International Standard ISO110951996 International Organization for Standardization1996

[22] M Jakubowicz and Cz J Jermak ldquoMeasurement uncertainty ofair guages for length measurementrdquo Machine Engineering vol18 no 3 pp 48ndash59 2013 (Polish)

[23] M Rucki B Barisic and G Varga ldquoAir gauges as a part of thedimensional inspection systemsrdquo Measurement vol 43 no 1pp 83ndash91 2010

[24] J Derezynski ldquoPNEUSMARTmdashpneumatic system for geomet-rical measurementsrdquoMachine Engineering vol 18 no 3 pp 88ndash99 2013 (Polish)

Journal of Control Science and Engineering 7

[25] M Ezekiel Methods of Correlation Analysis Wiley New YorkNY USA 1945

[26] R Breitinger Fehlerquellen beim pneumatischen Langenmessen[PhD thesis] TU Stuttgart 1969

[27] C Crnojevic G Roy A Bettahar and P Florent ldquoThe influenceof the regulator diameter and injection nozzle geometry onthe flow structure in pneumatic dimensional control systemsrdquoJournal of Fluids Engineering vol 119 no 3 pp 609ndash615 1997

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

6 Journal of Control Science and Engineering

wider range the linearity of the functions gets worse Anadditional problem is the need of adjustment any time thejet plug (measuring head) is changed to perform a differentmeasuring task It has been found that the adjustment withmore than two master rings can improve the measurementresults but the expenses rise disproportionately

In the previous investigations due to the electronic con-version of the pneumatic signal and then digital processingof the measured data it appeared possible to store the once-adjusted function and then to recall it after the exchange ofthe jet plug In that case to calibrate the new jet plug it isenough to use one setting master to check just one point onthe recorded linear characteristics

The results presented above prove that the next step couldbe done to reduce the final measurement uncertainty whichis affected by the nonlinearity of the 119901119896 = 119891(119904) functionThe laboratory equipment (Figure 2) enabled the collectionof scores of measuring points to check the difference betweenthe actual measurement result and the theoretical linearfunction obtained in the adjustment process The obtainedresults confirmed the well-known rule that better linearitycould be achieved in a smaller measuring range In the caseof Figure 7 only the range ca 70 120583m is able to provide theacceptable nonlinearity 120575max = 08 which however appearsunacceptably short for many applications

The Pneusmart device makes it possible to join togethertwo sections of the 119901119896 = 119891(119904) function each of themapproximated with a different line and each of them ofacceptable nonlinearity 120575max = 08 The overall measuringrange is kept the same ca 140 120583m Then in an industrialenvironment the adjustment could be performed with twomaster rings as usual but the finalmeasurement result will bemuch less affected by the nonlinearity error of approximation

6 Conclusion

The investigation results led to the following conclusionnew programmable air gauging devices may increase mea-surement accuracy keeping long measuring range after theappropriate calibration and the approximation with twofunctions The linearity error which appears to be as large as6 for long measuring ranges could be reduced down to 1which is a satisfactory result In this way nonlinearity is notthe main factor affecting the measurement uncertainty of anair gauge

Competing Interests

The authors declare that there are no competing interestsrelated to this paper

References

[1] C J Tanner ldquoAir gaugingmdashhistory and future developmentsrdquoInstitution of Production Engineers Journal vol 37 no 7 pp448ndash462 1958

[2] G Schuetz ldquoPushing the limits of air gagingmdashandkeeping themthererdquo Quality Magazine vol 54 no 7 pp 22ndash26 2015

[3] N Taniguchi ldquoCurrent status in and future trends of ultra-precision machining and ultrafine materials processingrdquo CIRPAnnals-Manufacturing Technology vol 32 no 2 pp 573ndash5821983

[4] J Destefani ldquoAir gagingrdquo Manufacturing Engineering vol 131no 4 pp 5ndash9 2003

[5] Y H Wang S Q Hu and Y Hu ldquoAn automatic sorting systembased on pneumatic measurementrdquo Key Engineering Materialsvol 295-296 pp 563ndash568 2005

[6] Ch Koehn ldquoIn-process air gagingrdquo Quality Magazine vol 53no 5 pp 22ndash23 2014

[7] W Gopel J Hesse and J N Zemel Sensors A ComprehensiveSurvey vol 8 VCH Press Weinheim Germany 1995

[8] T Thomas C Hamaker J Martyniuk and G MirroldquoNanometer-level autofocus air gaugerdquo Precision Engineeringvol 22 no 4 pp 233ndash242 1998

[9] G Schuetz ldquoWhen air blows mechanical gaging awayrdquo QualityMagazine vol 53 no 1 pp 28ndash32 2014

[10] J A Bosch Coordinate Measuring Machines and Systems Mar-cel Dekker Inc New York 1995

[11] M Curtis and F Farago Handbook of Dimensional Measure-ment Industrial Press New York NY USA 2014

[12] H FWalker A K Elshennawy B C Gupta andMMVaughnThe Certified Quality Inspector Handbook ASQ Quality PressMilwaukee Wis USA 2013

[13] Cz J Jermak and M Rucki ldquoAir gauging still some room fordevelopmentrdquoAASCIT Communication vol 2 no 2 pp 29ndash342015

[14] C J Jermak and M Rucki ldquoStatic characteristics of air gaugesapplied in the roundness assessmentrdquo Metrology and Measure-ment Systems vol 23 no 1 pp 85ndash96 2016

[15] M Rucki ldquoReduction of uncertainty in air gauge adjustmentprocessrdquo IEEE Transactions on Instrumentation and Measure-ment vol 58 no 1 pp 52ndash57 2009

[16] J Liu X Pan G Wang and A Chen ldquoDesign and accuracyanalysis of pneumatic gauging for form error of spool valveinner holerdquo FlowMeasurement and Instrumentation vol 23 no1 pp 26ndash32 2012

[17] Cz J Jermak and M Rucki Air Gauging Static and DynamicCharacteristics IFSA Barcelona Spain 2012

[18] M Rucki B Barisic and T Szalay ldquoAnalysis of air gageinaccuracy caused by flow instabilityrdquoMeasurement vol 41 no6 pp 655ndash661 2008

[19] J S Simonoff Smoothing Methods in Statistics Springer Seriesin Statistics Springer New York NY USA 1996

[20] W Dos PassosNumerical Methods Algorithms and Tools in CCRC Press Boca Raton Fla USA 2010

[21] International Organization for Standardization ldquoLinear cali-bration using reference materialsrdquo International Standard ISO110951996 International Organization for Standardization1996

[22] M Jakubowicz and Cz J Jermak ldquoMeasurement uncertainty ofair guages for length measurementrdquo Machine Engineering vol18 no 3 pp 48ndash59 2013 (Polish)

[23] M Rucki B Barisic and G Varga ldquoAir gauges as a part of thedimensional inspection systemsrdquo Measurement vol 43 no 1pp 83ndash91 2010

[24] J Derezynski ldquoPNEUSMARTmdashpneumatic system for geomet-rical measurementsrdquoMachine Engineering vol 18 no 3 pp 88ndash99 2013 (Polish)

Journal of Control Science and Engineering 7

[25] M Ezekiel Methods of Correlation Analysis Wiley New YorkNY USA 1945

[26] R Breitinger Fehlerquellen beim pneumatischen Langenmessen[PhD thesis] TU Stuttgart 1969

[27] C Crnojevic G Roy A Bettahar and P Florent ldquoThe influenceof the regulator diameter and injection nozzle geometry onthe flow structure in pneumatic dimensional control systemsrdquoJournal of Fluids Engineering vol 119 no 3 pp 609ndash615 1997

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Control Science and Engineering 7

[25] M Ezekiel Methods of Correlation Analysis Wiley New YorkNY USA 1945

[26] R Breitinger Fehlerquellen beim pneumatischen Langenmessen[PhD thesis] TU Stuttgart 1969

[27] C Crnojevic G Roy A Bettahar and P Florent ldquoThe influenceof the regulator diameter and injection nozzle geometry onthe flow structure in pneumatic dimensional control systemsrdquoJournal of Fluids Engineering vol 119 no 3 pp 609ndash615 1997

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of