Non-Intrusive Measurement of Inner Bore Temperature of Small Arms Using Integrated Ultrasonic Transducers

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1 Nn-Intrusive Measurement f Inner Bre Temperature f Small Arms Using Integrated Ultrasnic Transducers D. Lévesque 1, a), R. Pimentel, M. Lrd 1, A. Beauchesne 1, S.E. Kruger 1, R. Stwe, F. Wng and J-P. Mnchalin 1 1 Natinal Research Cuncil Canada, 75 de Mrtagne Blvd., Bucherville (Qc), J4B 6Y4, Canada Defence Research and Develpment Canada, 459 de la Bravure Rad, Quebec (Qc), G3J 1X5, Canada a) Crrespnding authr: daniel.levesque@cnrc-nrc.gc.ca Abstract. Management f thermal input t a small arms weapns system is a significant design and peratinal cnstraint. A cllabrative prject was initiated with the bjective t measure nn-intrusively the inner bre barrel temperature f a small arm during actual firing. The apprach uses integrated ultrasnic transducers (IUTs) and the velcity temperature dependence f the lngitudinal wave prpagating thrugh thickness. IUT was successfully implemented n a small arm at 3 lcatins and results frm several firing tests are presented. The small but systematic increase in ultrasnic time delay f less than 1 ns after each firing sht is reliably measured, in agreement with a simple 1D mdel f heat cnductin, and measured temperature rises are cnsistent with the thicknesses at the different lcatins. The evaluatin f the peak inner bre temperatures using IUT and their validatin using erding surface thermcuples at the same lcatins in the barrel are discussed. INTRODUCTION The management f thermal input t a small arms weapns system is a significant design and peratinal cnstraint. Thermal input is a functin f firing rate and its subsequent effect is very much a functin f weapn system design and envirnmental cnditins. The peratinal effects f pr thermal management can be serius including reduced accuracy f fire, reduced barrel life, melting f essential electrnic system cmpnents, ammunitin ck-ff, burning f the sldier s skin and increased visible and IR signature and thus increase detectability. A cllabrative prject was recently initiated with the bjective t measure nn-intrusively the inner bre barrel temperature f a small arm during an actual firing. The apprach uses integrated ultrasnic transducers (IUTs) and the velcity temperature dependence f the lngitudinal wave prpagating thrugh thickness. The use f ultrasund t measure average temperature within a structure has a lng histry [1]. Hwever ultrasnic measurement in transient heat flux cnditins is mre recent. Amng thse, a recent wrk used a cnventinal transducer fr the measurement f inner bre temperature in large caliber guns []. This wrk explited the structure f the rifled regin f a gun barrel t measure internal temperature based n an ech dublet. Fr a small arm, n temperature difference exists in the rifled regin and determinatin f internal surface temperature using the back wall ech requires the use f an inverse methd using a simple mdel [3]. In the present wrk, a small arm is instrumented with paint-n integrated ultrasnic transducers (IUT) installed at different lcatins fr actual firing tests. The ultrasnic perfrmance f IUT has been demnstrated and its ptential applicatins fr the nn-intrusive real-time temperature and engine cnditin mnitring have been reprted [4]. Her Majesty the Queen in Right f Canada, as represented by the Minister f Natinal Defence, [015] Sa Majesté la Reine (en drit du Canada), telle que représentée par le ministre de la Défense natinale, [015] DRDC-RDDC-015-N10

Fr IUT measurement in small arms, simple 1D mdels f heat cnductin are first cnsidered t predict the temperature histry and determine the required precisin fr measuring ultrasnic time delay after each

Als, the evaluatin f the peak inner bre temperature and the validatin using erding surface thermcuples at the same lcatins in the barrel are discussed.

2 Fr IUT measurement in small arms, simple 1D mdels f heat cnductin are first cnsidered t predict the temperature histry and determine the required precisin fr measuring ultrasnic time delay after each firing sht. Then, results frm firing tests with IUTs implemented at 3 lcatins are presented. Als, the evaluatin f the peak inner bre temperature and the validatin using erding surface thermcuples at the same lcatins in the barrel are discussed. ULTRASONIC APPROACH Figure 1 shws a simplified representatin f the small arm t be instrumented with the barrel thickness varying frm 5 t 8 mm. Als in the figure, the typical pressure pulse inside the barrel induced by a single sht firing is shwn with a pulse duratin f less than 0.5 ms. Such pulse duratin is used in the calculatin examples f heat cnductinn t fllw. FIGURE 1. Schematic representatin f the small arm barrel and typical chamber pressure pulse (nrmalized) inside the barrel. Figure shws the ultrasnic velcity temperature dependence f the lngitudinal wave prpagating thrugh thickness previusly measured fr lw carbn steel typically usedd as the material fr a smalll arm. Such velcity variatins include the change f material stiffness and thermal expansin. At lwer temperature, the behavir is nearly linear with a slpe f abut m/s / C, but the nn-linear behavir bserved is taken int accunt in the calculatins and temperature estimatin using a fitted plynmial equatin v(t). FIGURE. Ultrasnic velcity temperaturee dependence f lngitudinal wave fr lw carbn steel.

Different 1D mdels f transient heat cnductin frm the literature are fund useful t predict the temperature histry and

Let us cnsider a finite slab f thickness L at a unifrm temperature T subject t a sudden heat flux pulse q(t) due t chamber

Neglecting cnvectin r thermal cntact resistance, the half space slutin T(x,t) fr a Dirac pulse f amplitude q m (J/m ) att t=0

In the calculatins, = 11.7 mm /s is used fr lw carbn steel and q m /k is assumed input.

) F () kl n1 with the nn-dimensina al numbers X= =x/l and F=t/L. One immediate resultt frm Eq.

mdel cnsidering a pulse f finite duratin finitee was recently btained fr studying laser heating f materials is [7]: t L X 1 T

pulse functin is chsen t be q q( t) m te t m t / t t t dq( t ) (n ) ) t exp( 0 )dt dt L m ; 0 q ( t) dt q m (5) (6) which is

3 Different 1D mdels f transient heat cnductin frm the literature are fund useful t predict the temperature histry and determine the required precisin fr measuring ultrasnic time delay after each firing sht [5-7]. Let us cnsider a finite slab f thickness L at a unifrm temperature T subject t a sudden heat flux pulse q(t) due t chamber pressure at x=0 while the slab is insulated at x=l (see Figure 3a). Neglecting cnvectin r thermal cntact resistance, the half space slutin T(x,t) fr a Dirac pulse f amplitude q m (J/m ) att t=0 valid fr shrt time is: qm x T (xx, t) T exp k t 4 (1) t where is the thermal diffusivity, k is the thermal cnductivity. In the calculatins, = 11.7 mm /s is used fr lw carbn steel and q m /k is assumed input. When the heat reaches the ther bundary, the slutin fr the slab subject t a Dirac pulse is: q T ( x, t) T m 1 cs( nx ) exp ( n ) F () kl n1 with the nn-dimensina al numbers X= =x/l and F=t/L. One immediate resultt frm Eq. () is that the thrugh- thickness average temperature at all time is a cnstantt given by: q T T m (3) kl Finally a third 1D mdel cnsidering a pulse f finite duratin finitee was recently btained fr studying laser heating f materials is [7]: t L X 1 T ( x, t ) T q( t) dt q( t) kl 0 k X L ( t)cs( nx ) (4) 3 k n1 ( n ) where the functin (t) is given by: (n ) (t) exp( L and the pulse functin is chsen t be q q( t) m te t m t / t t t dq( t ) (n ) ) t exp( 0 )dt dt L m ; 0 q ( t) dt q m (5) (6) which is maximum at t= =t m. An example f the pulse functin is shwn in Fig.. 3b fr t m =0.5 ms. An analytical expressin can be btained inserting Eq. (6) int Eq. (5) t calculatee the series in Eq. (4). FIGURE 3. Basic gemetry f the prblem and typical heat flux pulse inside the barrel used fr calculatins.

Frm any f these mdels, the ultrasnic time delay can be estimated at given time t using the exact expressin: 0 L L dx v ( T ( x, t)) where and v are the reference

Als, a gd apprximatin is btained when cnsidering the average temperature fr thrugh-thickness prpagatin as: ( v( T ) v ) ( v( T ) v ) L (8) v v As a calculatin example,

5 mm thick slab and an arbitrary heat flux amplitude q m with t m =0.5 ms.

Als the ultrasnic delay and thrugh-thickness average temperature are fund nearly cnstant after 10 t m.

Mst imprtantly, the ultrasnic delay fr a 100 C temperature rise is expected t be ff less than 1 ns.

delay measurements. v (7) FIGURE 4. Temperature histry at the inner wall and averaged thrughh thickness and ultrasnic delay fr a 7.

4 Frm any f these mdels, the ultrasnic time delay can be estimated at given time t using the exact expressin: 0 L L dx v ( T ( x, t)) where and v are the reference prpagatin time and crrespnding ultrasnic velcity (e.g. at rm temperature). Als, a gd apprximatin is btained when cnsidering the average temperature fr thrugh-thickness prpagatin as: ( v( T ) v ) ( v( T ) v ) L (8) v v As a calculatin example, Figure 4 shws the temperature histry (time in lg scale) at the inner wall and the expected ultrasnic delay (with respect t the reference) fr a 7.5 mm thick slab and an arbitrary heat flux amplitude q m with t m =0.5 ms. One first ntes thatt a time lag f abut t m is fund between maximum pressure and maximum inner bre temperature. Als the ultrasnic delay and thrugh-thickness average temperature are fund nearly cnstant after 10 t m. The inner temperature reaches the average temperature (unifrm final ne) in abut 1 s. Mst imprtantly, the ultrasnic delay fr a 100 C temperature rise is expected t be ff less than 1 ns. Therefre, a signal prcessing technique using precise crss-crrelatin with a reference signal at lw temperature and interplated maximum shuld be used [8, 9] fr ultrasnic delay measurements. v (7) FIGURE 4. Temperature histry at the inner wall and averaged thrughh thickness and ultrasnic delay fr a 7.5 mmm thick slab and an arbitrary heat flux amplitude with t m =0.5 ms. Therefre, functin: ne culd determine the average temperature frm measured ultrasnic delay using the rt f the v( T ) v v 0 Als, the inner bre temperature can be estimated frm the average temperature and a multiplicative factr using the abve equatins r the fllwing apprximatin valid fr time larger than t m : (9) T in T ( t) T T where T is the unifrm temperature, typically in abut 1 sec. L 1 t (10) SHOT FIRING TESTS A first test series with actual sht firing using the small arm instrumented with IUTs was perfrmed t verify the validity f the apprach in view f the required precisin. The IUT fabricatin prcess and the implementatin at

each lcatin n the small arm is similar t the descriptin fund in Ref. [10].

The frequency cntent is frm t 5 MHz and is nearly the same fr the three lcatins.

reference signal at rm temperature fr a ttal f 00 firing shts in 7 sequences.

delays t clearly see the stepss f abut 0.

firing shts at the beginning in Fig. 6b. Accrding t the equatins abve, the 10.

unifrm thrugh the thickness f the barrel.

shws steps f abut 1 ns and the 7 ns increase after the first sequence crrespnds t

Typical IUT signal at lcatinn 1 n the smalll arm. FIGURE 6.

a ttal f 00 firing shts in 7 sequences, and zm f the first few firing shts at the

Frm these prmising results, a secnd test series was perfrmed using the small arm

made flush at the inner wall after drilling and installed at the 3 lcatins at 90

Figure 7 shws the average temperaturee determined frm thrugh-thickness and then

Als superimpsed is ultrasnic delay in the thinnest prtin at lcatin 3 fr a ttal f

wall at this lcatin shwing a similar trend but with a sharp peak after each sht

As predicted frm mdelling, the thrugh- bre thickness average temperature given by

given by the thermcuplee reaches the average temperature in abutt 1 s.

5 each lcatin n the small arm is similar t the descriptin fund in Ref. [10]. Figure 5 shws a typical IUT signal btained at lcatin 1 n the small arm. The frequency cntent is frm t 5 MHz and is nearly the same fr the three lcatins. Figure 6 shws measured thrugh-thickness ultrasnic delay at lcatin 1 with a reference signal at rm temperature fr a ttal f 00 firing shts in 7 sequences. The time reslutin f IUT measurements is 1 ms which allws averaging f the small delays t clearly see the stepss f abut 0. ns denting temperature rise after each sht as seen in the zm f the first few firing shts at the beginning in Fig. 6b. Accrding t the equatins abve, the 10.5 ns increase after the first sequence crrespnds t a 35 C temperature rise mstly unifrm thrugh the thickness f the barrel. Similar results (nt shwn here) btained in the thinner prtin f the arm at lcatin 3 shws steps f abut 1 ns and the 7 ns increase after the first sequence crrespnds t a 130 C unifrm temperature rise. FIGURE 5. Typical IUT signal at lcatinn 1 n the smalll arm. FIGURE 6. Measured ultrasnic delay at lcatin 1 with a reference signal at rm temperature fr a ttal f 00 firing shts in 7 sequences, and zm f the first few firing shts at the beginning. Frm these prmising results, a secnd test series was perfrmed using the small arm instrumented with IUTs and thermcuples (TCS-10-J caxial surface prbe, MEDTHERM) made flush at the inner wall after drilling and installed at the 3 lcatins at 90 n the barrel circumference with respect t IUT depsitin fr temperature validatin. Figure 7 shws the average temperaturee determined frm thrugh-thickness and then cling. Als superimpsed is ultrasnic delay in the thinnest prtin at lcatin 3 fr a ttal f 00 firing shts in 10 sequences the temperature frm the thermcuplee at the inner wall at this lcatin shwing a similar trend but with a sharp peak after each sht as seen in the first few firing shts in Fig. 7b. As predicted frm mdelling, the thrugh- bre thickness average temperature given by the ultrasnic delay is nearly cnstant after each sht, and the inner temperature given by the thermcuplee reaches the average temperature in abutt 1 s. It is nted that n adjustable parameter is needed t get such a gd agreement f the temperature rise during firing and final temperaturee drp. Similarly, Fig. 8 shws the average temperature determined frm thrugh-thickness ultrasnic delay at lcatin 5 f intermediate thickness near the muzzle and the temperature frm the thermcuple at the inner wall shwing a similar trend but with sharp peaks this time lking mre erratic. Part f this behaviur may be explained by the

6 finite time reslutin f 1 ms during measurements. Als Fig. 9 shws bth temperature measurements in the thicker prtin at lcatin 1 near the chamber with sme unexplained deviatin after the third sht sequence. It is wrth mentining that the temperature rises bserved are cnsistent with the thicknesses at the three lcatins. FIGURE 7. Temperatures frm IUT and frm thermcuple at the inner wall at lcatin 3, fr 000 firing shts in 10 sequences and then cling, and zm f the first few firing shts at the beginning. FIGURE 8. Temperatures frm IUT and frm thermcuple at the inner wall at lcatin 5, fr 000 firing shts in 10 sequences and then cling, and zm f the first few firing shts at the beginning. FIGURE 9. Temperatures frm IUT and frm thermcuple at the inner wall at lcatin 1, fr 000 firing shts in 10 sequences and then cling, and zm f the first few firing shts at the beginning.

T investigate the effect f time reslutin n the sharp

nly with thermcuples were perfrmed with a time reslutin

Figure 10 shws the temperature at the inner wall at

A large variability is still bserved in the peak

Frm measurements at the three lcatins, the peak

muzzle with respect t the backgrund unifrm temperature,

140 400 10 Temperature ( C) 100 80 60 40 Thermcuple 1

150 00 Time (s) 0 50 300 350 0 50 1000 150 00 50 300

Temperature frm thermcuple at the inner wall with a

abve 1D mdels can be used t relate the stepping average

sht using a multiplicative factr as in Eq. (10).

fairly gd cnsidering the variability f such measurement.

the inner wall t make the apprach mre reliable.

Cmparisn f the temperature given by the thermcuple at

IUT averagee temperature using the 1D mdel and zm f the

CONCLUSIONN Integrated ultrasnic transducers (IUTs)

7 T investigate the effect f time reslutin n the sharp temperature peak after each sht, additinal measurements nly with thermcuples were perfrmed with a time reslutin f 1 μs. Figure 10 shws the temperature at the inner wall at lcatins 1 and 5. A large variability is still bserved in the peak amplitude at lcatin 5. Frm measurements at the three lcatins, the peak amplitude is fund t increase frm the chamber t the muzzle with respect t the backgrund unifrm temperature, respectively f abut 5, 35 and 100 C Temperature ( C) Thermcuple 1 Temperature ( C) Thermcuple Time (s) Time (s) FIGURE 10. Temperature frm thermcuple at the inner wall with a time reslutin f 1 s at lcatins 1 and As already mentined, the abve 1D mdels can be used t relate the stepping average temperature rise t the inner temperature at each firing sht using a multiplicative factr as in Eq. (10). Figure 11 is a preliminary result in that directin fr the first sht sequence at lcatin 5. The peak amplitudes estimated are slightly lwer but fairly gd cnsidering the variability f such measurement. Mre wrk is needed in bth mdelling and measurement at the inner wall t make the apprach mre reliable. FIGURE 11. Cmparisn f the temperature given by the thermcuple at the inner wall at lcatin 5 and the estimatin frm the IUT averagee temperature using the 1D mdel and zm f the first sht. CONCLUSIONN Integrated ultrasnic transducers (IUTs) were successfully implemented n a small arm at 3 lcatins. The small but systematic increase in ultrasnic delay f less than 1 ns measured at different lcatins after each firing sht is clearly indicative f the temperature rise inside the barrel. Als measured temperature rises are cnsistent with the thickness at thse lcatins. IUT prvides the thrugh-thickness average temperature rise after each sht, that is nearly cnstant in agreement with a simple 1D mdel. The mdel can als be used t determine the inner bre

8 temperature essentially shwing f a sharp peak at each sht. Different time scales are invlved in the measurements. Fr each single sht, the bre temperature may be 100 C higher in 1 ms than the temperature mstly unifrm after 1 s. Several sht firing sequences prduce successive increase f temperature (with sme thermal lsses frm earlier shts) ver 100 s, mre r less unifrm thrugh thickness. Future wrk is t further test reprducibility with thermcuples and perfrm IUT testing n additinal small arms. REFERENCES 1. L. C. Lynnwrth, Ultrasnic measurements fr prcess cntrl, Academic Press Inc., San Dieg CA, 1989, pp D. E. Yukas, M. J. Muttn, J. R. Remiasz and C. L. Vrres, Ultrasnic measurements f bre temperature in large caliber guns, Review f Quantitative NDE Vl. 8, ed. by D.O. Thmpsn and D.E. Chimenti, AIP Cnf. Prc. 1096, New Yrk, pp (009). 3. M. R. Myers, D. G. Walker, D. E. Yuhas, and M. J. Muttn, Heat flux determinatin frm ultrasnic pulse measurements, in Prceedings f IMECE, ASME, Bstn MA, pp (009). 4. M. Kbayashi, K.-T. Wu, C.-K. Jen, J. Bird, B. Galete and N. Mrad, High temperature integrated ultrasnic transducers fr engine cnditin mnitring, in Prceedings f Cansmart Wrkshp, pp (009). 5. F. P. Incrpera, D. P. DeWitt, Intrductin t Heat Transfer, 4th Editin, Jhn Wiley and Sns, W. J. Parker, R. J. Jenkins, C. P. Butler and G. L. Abbtt, J. Appl. Phys. 3, (1961). 7. M. K. El-adawi, S. A. Shalaby, S. S. Mstafa and M. F. Ktkata, Opt. & Laser Technl. 39, (007). 8. J.-D. Aussel and J.-P. Mnchalin, Ultrasnics 7, (1989). 9. D. Lévesque, S. E. Kruger, G. Lamuche, R. Klarik, G. Jeskey, M. Chquet, J.-P. Mnchalin, NDT&E Intern. 39, 6-66 (006). 10. M. Kbayashi, C.K. Jen, Y. On and J.-F. Misan, CINDE Jurnal, March/April, 005, pp

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