Fig. 7. Testing FBGs response. (a)

Fig. 7. Testing FBGs response. (a) Plug under press. (b) Strain linearity vs. compression force.The plug is inserted by compression at room temperature in awork roll hole that has been initially drilled (Fig. 4(a)). To obtaina strong fixation of the plug in the roll, the difference of diame-ter between plug and hole is 1 ‰(hole diameter smaller than plusdiameter by 1 ‰). Once the plug has been inserted in the work roll,the surface is re-ground to be flat (Fig. 8(a)) so that marks on stripsare limited. After this roll re-grinding, the Bragg gratings are locatedat 2.175 mm under the roll surface.Optical fibers signals are extracted from the roll center whereall the four FBG reflected spectra are gathered together on a sin-gle optical fiber using an optical coupler. Thus all the four FBGscan be interrogated simultaneously. Bragg wavelength of each FBGhas been determined with respect to the expected spectral rangeduring the roll tests, in order to prevent two spectra to overlap, itis then still possible to identify each optical fiber even if, for anyreason, only one reflected spectrum (instead of four expected) istransmitted through the optical coupler. This signal is then trans-mitted from the rotating roll to an external fixed data acquisitionstation through a Fiber Optic Rotary Joint (FORJ). One can see thisrotary joint and the out-coming optical fiber in Fig. 8(b).4. Sensor calibrationThe whole measurement system (composed of the work roll,the plug, the FBGs and the data acquisition system) has beencalibrated with two different data acquisition systems workingat two different frequencies: 960 Hz and 3378 Hz. Both systemsmust be calibrated separately. To get calibration test conditionsclose to rolling conditions, the instrumented work roll is motor-ized and rotates directly against the other work roll that rotatesfreely (no motorization or brace) as shown in Fig. 9(a). No slid-ing between both rolls occurred during calibration tests, and shearstress in the roll/roll contact can be neglected because most of tan-gential forces applied in the contact are used to spin the lowerroll and do not generate significant shear stress in the roll body.Thus, in these conditions, the classical Hertz contact formulasare applied in order to model calibration tests: Hertz formulasenable here to get a known contact stress distribution at roll sur-face to calibrate sub-surface optical fibers response. Three rollingforces, corresponding to 25 tons, 50 tons and 75 tons (or alterna-tively 833.3 N/mm, 1666.6 N/mm and 2500 N/mm since the workroll width is 300 mm) have been applied during calibration. How-ever since linearity is good, as detailed in Section 3, all three testshave the same conclusions. The Hertz cylinder/cylinder contact for-mulas are summarized in Table 1, where the exponent H refers toHertz. Contact pressures for the three rolling forces are presentedin Fig. 9(b).With the Hertz contact pressure H, a very simple elastic modelenables to compute strains in the roll body and especially at theinner radius Rm. Multiplicative calibration coefficients K45, KandKrrare obtained by matching computed strains (at the inner radiusRm) with measured strains. Matching process is done by minimizingFig