olerai

u 3, Ia

Keywords:Residual stress measurementAccuracy

hole

tendency of the strain gages. Although the drilling tool is optically aligned, the eccentricity

to obtain a so small eccentricity, the drilling tool is opti-cally aligned so that its drilling axis is precisely positionedover the target at the center of the strain-gage rosette. But,

strain-gages area. The case of the through hole is studied.

2. Description of the actual methods

Rendler and Vigness [5] observed for the rst time thatthe accuracy of the method. . . will be directly related tothe operators ability to position the milling cutter

0263-2241/$ - see front matter 2008 Elsevier Ltd. All rights reserved.

* Corresponding author. Tel.: +40 232 275070; fax: +40 232 260650.E-mail addresses: paulbarsanescu@yahoo.com (P. Barsanescu), pcarlescu

2004@yahoo.com (P. Carlescu).1 Tel./fax: +40 232 232337.

Measurement 42 (2009) 474477

Contents lists available at ScienceDirect

Measure

journal homepage: www.elsevidoi:10.1016/j.measurement.2008.09.002A predominant factor contributing to structural failureof machine parts may be the residual stresses. Hole drillingis the most widely used method for residual stress mea-surement [1,2]. ASTM E837-01 is the accepted standardfor residual stress measurement by the hole-drilling meth-od [3]. A detailed explanation of this ASTM standard is pre-sented in the Technical Note TN 503 by the MeasurementGroup [4]. The accuracy of this technique is directly relatedto the precision with which the hole is drilled through thecenter of strain-gage rosette. In practice, the requiredalignment precision is to within 0.025 mm [3]. In order

affecting the accuracy of this technique [57]. An equationfor correction of the data affected by hole eccentricity hasbeen proposed by Ajovalasit [8], but it is not precise en-ough, because it is founded on the wrong hypothesis: inthe strain-gage area there is a uni-axial state of stress, in-stead bi-axial one.

The paper presents a new analytical method for exper-imental data correction, in order to diminish the errorsintroduced by the hole eccentricity and to improve theaccuracy of the hole-drilling technique. This method takeaccount of the plane (bi-axial) state of stress in the1. Introductionalways cannot be zero and it is a source of error, affecting the accuracy of this technique. Anequation for correction of the data affected by hole eccentricity has been proposed by A.Ajovalasit, but it is not precise enough, because it is founded on the wrong hypothesis thatin the strain gage area there is a uni-axial state of stress, instead bi-axial one. The paperpresents a new equation for data correction, which take account of the plane (bi-axial)state of stress in the strain gages area. After the hole-drilling and data acquisition, the holeeccentricity will be measured, using an optical microscope. Knowing the eccentricity, thedata will be corrected using the proposed equation. This equation is more precise, becauseit is founded on a realistic hypothesis (bi-axial state of stress in the strain gages area).

2008 Elsevier Ltd. All rights reserved.

although the tool is optically aligned, the eccentricity can-not be zero and eccentricity of the hole is a source of error,Received 29 April 2008Accepted 7 September 2008Available online 18 September 2008

residual stress measurement, is directly related to: (1) the eccentricity between the holecenter and rosette center, respectively, and (2) the accuracy of corrections for integrationCorrection of errors introduced by hmeasurement by the hole-drilling st

Paul Barsanescu a,1, Petru Carlescu b,*a Technical University Gh. Asachi, Blvd. Mangeron 59, Iasi 700050, RomaniabUniversity of Agricultural Sciences and Veterinary Medicine, Aleea Sadovean

a r t i c l e i n f o

Article history:

a b s t r a c t

The accuracy of theeccentricity in residual stressn-gage method

si 700490, Romania

-drilling strain-gage technique, the most widely used method forment

er .com/ locate /measurement

precisely in the center of the strain gage rosette. More re-cent works have quantied the error in calculated stressdue to eccentricity of the hole [9,10]. In the conditions ofa non-uniform stresses distribution around the hole, theintegration tendency of the strain gages is an importantsource of error [9]. This error can be corrected using theaverage theorem from the integral calculus.

The output of the strain gage is proportional with theaverage strain on the grid area [11].

In the non-uniform axial state of stress, the W. Soetteand R. Van Crombrugge method [11] can be used in orderto correct the experimental data affected by errors. Theoutput of the strain gage will be

e 1x2 x1

Z x2x1

exxdx 1

where x2 x1 = GL is the length of the strain gage grid; ex(x)is the strain in the direction of the strain grid laments.

In the non-uniform bi-axial state of stress, the R.G. Boi-ten and Ten Cate method [11] can be used in order to cor-

its own system of axis is presented. The average value ofthe strain gage output can be determined using the R.G.Boiten and Ten Cate method

e 1S

Z x2x1

dxZ y2y1

exx; ydy 3

e 1S

Z x2x1

dxZ 0y1

exx; ydyZ x2x1

dxZ y20

exx; ydy" #

4

For a symmetric function (as ex in the area near a hole in aplate in tensile), we ca writeZ 0y1

exx; ydy Z y10

exx; ydy 5

From Eqs. (4) and (5) we can write

e 1S

S00

S00

Z x2x1

dxZ y10

exx; ydy S0

S0

Z x2x1

dxZ y20

exx; ydy

6and

e 1S

S00e00 S0e0 7where the grid surface is

S S0 S00 8The main residual stresses are calculated for a plate in aplane state of stress, with a through hole in it, function of

P. Barsanescu, P. Carlescu /Measurement 42 (2009) 474477 475rect the experimental data

e 1S

ZSexx; ydS 2

where S is the strain gage grid surface.In the paper [8], Ajovalasit presented an analytical

method that can be used in order to correct the experimen-tal data affected by the hole eccentricity. Because themathematical problem is complex one, he used Eq. (1) in-stead of Eq. (2). Using this way, we must do only a usualintegral, instead a double one but, of course, the precisionof obtained equations is affected. The present paper use Eq.(2) in order to obtain a better formula for experimentaldata correction (affected by the hole eccentricity).

3. Presentation of a new method

In Fig. 1, a strain gage grid near a hole with eccentricityis presented. The wrong position of hole has the center inO0, instead of O. In Figs. 2 and 3, the gage grid reported at

Fig. 1. Strain gage grid near an eccentric hole through a plate.Fig. 2. Strain gage grid in xy system of reference.

Fig. 3. Strain gage grid in x00y00 system of reference.

a and b coefcients, which take account of integration ten-dency of strain gages. The two coefcients are well knownfrom the literature [10] and are determined for a centrichole (with the center in O). For this particular situation,we have (Figs. 2 and 3)

y1 y2 GW2

9

S0 S00 S2

10e0 e00 e 11In order to calculate the residual stresses for a through cen-tered hole, a and b coefcients are used (Fig. 4):

a 2wr2 r1

1r2

h1 h2 12

b 21mwr2 r1

1r2 21m

1m h1h2sin2h1sin2h2

476 P. Barsanescu, P. Carlescu /Measurement 42 (2009) 474477 1r2

sin2h1 cos2 h12r21

sin2h2 cos2 h2

2r22

#13

where

w 2GWD

r1 2R1Dr2 2R2Dr D

D0 D2R0

D R1 R2

14

In order to correct the errors introducedbyhole eccentricity.For an eccentric hole, the correction can be made simply

using Eq. (7) and coefcients ae; be, instead of a and b. Theae; be coefcients are calculated for two strain gages near acentric hole, having the grid width 2(GW/2 + DGW) and2(GW/2 DGW), respectively

ae 1GWGW2

DGW

a0 GW2

DGW

a00

15

Fig. 4. Centered hole with a strain gage grid.be 1GWGW2

DGW

b0 GW2

DGW

b00

16

where a0; b0 and a00; b00 are determined using Eqs. (12) and(13), but applied for S0 and S00, respectively, surfaces.

Developing the equations we obtain

ae R20

GW GL Dh0 Dh00 17

be 21 mae R201 mGW GL

(sin 2h01 sin 2h02

sin 2h001 sin 2h002

R20

21R21e

sin 2h01 cos2 h01 sin 2h001 cos2 h001

"

1R22e

sin 2h02 cos2 h02 sin 2h002 cos2 h002

#) 18where

Dh0 h01 h02Dh00 h001 h002

19

The method presented above it is a very easy way to cor-rect the errors introduced by eccentricity. It is in the sametime more accurate, because Eq. (2), good for a plane stressof state, was used in this demonstration, instead of Eq. (1),good for axial state of stress and used by the actual meth-ods for error correction.

4. Conclusions

The hole eccentricity of is an important source of error,which affect the accuracy of residual stress measurementby the hole-drilling method. Although in practice the opti-cal alignment is used, the eccentricity cannot be zero.

A very easy and more accurate method for errors intro-duced by eccentricity correction has been presented in thispaper. It takes account of the plane (bi-axial) state of stressin the strain gages area reduces the case of the eccentrichole at the well known case of the centric hole.

Acknowledgements

The researches presented in this paper are partially sup-ported by Romanian Ministry of Education and Research,Contract No. 49/2006 (CEEX Rolight) and Contract No.7016/2007 (PN II Modis).

References

[1] F.A. Kandil, J.A. Lord, P. Mummery, G.A. Webster, UK needs forresidual stress measurement, N.P.L. Report, C.M.M.T., vol. 7,December 2001, p. 177.

[2] J. Lu (Ed.), Handbook of Measurement Residual Stresses, SEM-CETIM,Fairmont Press, 1996.

[3] ASTM E837-01, Standard Test Method for Determining ResidualStresses by the Hole-Drilling Strain Gage Method, Annual ASTM Bookof Standards. Available from: .

[4] Measurements Group, Technical Note TN 503, Measurement ofResidual Stresses by the Hole-Drilling Strain Gage Method. Availablefrom: .

[5] N.J. Rendler, I. Vigness, Hole drilling strain-gage method ofmeasuring residual stresses, in: Proceedings of the SESA XXIII, vol.2, 1966, pp. 577586.

[6] J.P. Sandifer, G.E. Bowie, Residual stress by blind-hole methodwith off-center hole, Experimental Mechanics 18 (1978) 173179.

[7] H.C. Wang, The alignment of the hole-drilling method, ExperimentalMechanics 17 (1979) 2327.

[8] A. Ajovalasit, Measurement of residual stresses by hole drillingmethod: inuence of hole eccentricity, Journal of Strain Analysis 14(4) (1979) 171178.

[9] E. Procter, E.M. Beaney, Recent developments in center-holetechnique for residual-stress measurement, ExperimentalTechniques 6 (1982) 1015.

[10] S. Redner, C.C. Perry, Factors affecting the accuracy of residual stressmeasurement using the blind-hole drilling method, in: Proceedingsof the 7th International Conference on Experimental Stress Analysis,Haifa, Technion, 1982.

[11] L. Pet, P. Barsanescu, O. Ciobanu, Analytical and Numerical MethodsUsed to Correct the Errors Introduced by Integrating Tendency of theStrain Gages, Bulletin of Technical Institute of Iasi, Tom XXXIX(XLIII), Fasc. 14, Sect. V, 1993, pp. 113124.

P. Barsanescu, P. Carlescu /Measurement 42 (2009) 474477 477

Correction of errors introduced by hole eccentricity in residual stress measurement by the hole-drilling strain-gage methodIntroductionDescription of the actual methodsPresentation of a new methodConclusionsAcknowledgementsReferences