17h Word onference on Nondesrucive Tesing, 5-8 Oc 008, Shanghai, hina Simuaion of Scaering Acousic Fied in Rod and Idenify of Urasonic Faw Deecing Signa Ke-Yi YUAN 1, Wen-Ai SONG 1, Yi-Fang HEN 1 1 Deparmen of Mechanica Engineering, Tsinghua Universiy Beijing 10008, hina; Phone: +86-10-6773857, Fax: +86-10-677386 Emai: yky@mais.singhua.edu.cn, songwenai@nuc.edu.cn, chenyifang@mai.singhua.edu.cn Absrac A mehod of acousic fied simuaing was proposed, in his paper, he auhors simuaed he scaering acousic fied generaed by impusive ine source in a gass rod, and compared he resus wih he dynamic phooeasic experimens, expained he forming mechanism of he scaering wave (e.g. he boundary wave of urasonic faw deecion in rod. Based on his, he seria echo signa of he faw deecion in rod by singe ransducer was idenified, and a signa processing mehod was suggesed. According o hese, using singe ransducer, esing one ime, os of mechanica propery coud be anayzed. Key words: simuaion, scaering acousic fied, faw deecion, rod 1. Inroducion Rod is one of he mos basic shapes of boh raw maeria and indusria producs, accordingy, sudy abou he evauaion of mechanica properies and defec esing of a rod using urasonic is very significan. Los of work had been done abou he rod defec esing, bu ony a ie porion of he signa received from he rod coud be idenified and used [1][]. I is because ha he puse acousic fied in a rod is no very ceary o us, his paper means o improve his. Based on he numerica simuaion and dynamic phooesic experimen, he auhors researched on he ransien acousic fied and wave in an opic gass rod, anayzed he mechanism of he urasonic ransmiion in a rod, and hen idenified he signa received by he emiing ransducer. Using he idenified signa, he auhors cacuaed he veociy of ongiudina wave, ransverse wave and rayeigh wave in he rod, aso did he easic moduus of he rod.. Numerica simuaion of he acousic fied in rod and phooeasic experimen Whie simuaing he acousic fied, deaing wih he medium ha acousic parameer and bound condiion is aready knew, he medium can be reaed as a signa ransaing
sysem. The inpu of i is emiing signa of he ransducer, and he oupu is he acousic fied as a funcion of ime and space. Then, he simuaion of he acousic fied can be divided o wo seps: firs, go he impuse response of he sysem; second, do he ime convouion wih he impuse response and he inpu signa, and ge he rea acousic fied. Go he impuse response of he sysem using sne aw and Huygens principe, i.e. he acousic fied of he emiing source is erminaed a he scaering poin, and he scaering poin coninued as a sub-source, he energy and direcion of he sub-source are decided by sne aw, and he enire acousic fied is a he source s fied (emiing source and sub-source adding ogeher. Figure 1 is he comparison of he numerica simuaion resu and he dynamic phooeasic phoo, in figure 1(b, R indicaed o he rayeigh wave, T is he ransverse wave, L is he ongiudina wave, and L-T is he refeced ransverse wave from he ongiudina wave on he cyinder boundary. As showed in figure1, he resu of he numerica simuaion accorded we wih he phooeasic phoo, so we coud expain he forming mechanism of he acousic fied as he addiion of emiing source acousic fied and he sub-source acousic fied. 3. Idenificaion of urasonic echo signa of he defec esing in rod The rod in figure 1(b, is diameer is 80 mm, hickness is 0 mm. A ongiudina wave ransducer is used in phooeasic experimen and faw deecing, which frequency is1.8mhz, diameer is 0 mm. Figure shows he signa received by ha ransducer in period from 0 µ s o100 µ s, in he figure, using number o index he wave packes ha are going o be idenified. We wi idenify he signa wih he hep of he phooeasic experimen and numerica simuaion.
3.1 Firs boom echo Easy o know, in he figure, he wave packe 1 is he firs boom echo of he ongiudina wave, is ransmiing disance and figh ime can be expressed as formua (1: R + τ = = 1 7.3 (1 And, R is he radii of he rod, uni is mm ; is he veociy of ongiudina in he rod, uni is mm / µ s,τ is he deay of he sysem, uni is µ s, 1 is he firs zero poin of he wave packe 1, uni is µ s 3. Equiaera riange of he urasonic ransmiing pah: In figure, he wave packe, is firs zero poin is = 35.µ s, he forming 3
mechanism of i is shown in figure 3(a. The hree arrows composing he equiaera riange indicaes he ransmiing pah of he ongiudina wave ha came ino being he wave packe. I.e. emied from poin A; a poin B refeced o a ongiudina wave ha ransmied aong he horizona ine (in figure 3(a, L indicaes he wave fron of he refec wave; hen a poin, refeced o be a ongiudina wave ransmiing in a symmerica pah wih he emiing wave, and received by he ransducer a. Simiary, in he phooeasic experimen we can observe he equiaera riange ransverse wave ha ransmis in he same pah. I is show in figure3 (b, T indicaes he wave fron of he equiaera riange ransverse wave, ha was going o reurn o he ransducer. In figure, he equiaera riange ransverse wave corresponds o he wave packe 7, is firs zero poin is = 58.99µ s. Because using a ongiudina wave ransducer, 7 he ampiude of wave packe 7 is smaer. Deaing wih he wave packe and he wave packe 7 he same as he wave packe 1: is he veociy of ransverse wave in he rod. 3 3R + τ = = 35. ( 3 3R + τ = 7 = 58.99 (7 omparing wih he phooeasic experimen, we can obain ha in figure he wave packe 3 is he ransverse wave which is refeced by he emiing ongiudina wave on he boom. For i is mixed wih wave packe, we can ge is firs zero poin, bu si regiser i as convenion: 3 Is he firs zero poin of wave packe 3. R R + + τ = 3 (3 3.3 Isocees riange of he urasonic ransmiing pah: In figure, he firs zero poin of he wave packe is = 3.6µ s, is ransmiing pah is shown in figure (a, AB: ransmis wih he veociy of ongiudina wave; B: ransmis wih he veociy of ransverse wave; A: ransmis wih he veociy of ongiudina wave, and A=AB. A he wave fron ha ransmi in his hree pahs, no maer he enire pah is AB->B->A, or B->A->AB or oher ese, he signa of hem woud be received by he ransducer a ime. In figure (a, L T indicaes he wave fron of he ransverse wave refeced from he ongiudina wave. Simiary, he ransverse wave has a simiar ransmi pah, shown in figure (b, T L indicaes he wave fron of he ongiudina wave refeced from he ransverse wave.
The corresponding wave packe in figure is wave packe 5, is firs zero poin is = 51.5µ s, because in his pah, he ransducer can receive some ongiudina wave, he 5 ampiude of he wave packe 5 is bigger. According o he sne aw, he wave packe can be regisered as: R cosθ Rsin(θ sin θ cos(θ τ + + = = 3.6, = ( θ is he ongiudina wave s inciden ange. And he Isocees riange ransverse wave is he same: R cosθ Rsin(θ sin θ cos(θ τ + + = 5 = 51.5 = (5 θ is he ransverse wave s inciden ange. 3. Ohers The wave packe 6 in figure is he second boom echo ongiudina wave of he emiing ongiudina wave, is firs zero poins can be accuraey measured for i s compound wih he wave packe 5, si regiser i as: 8R +τ = 6 (6 In figure he wave packe 7 is idenified before. The wave packe 8 is more compex, i 5
incuded some boom echo wave compounded wih ongiudina wave and ransverse wave, and a ongiudina wave wih sar-shape pah, and a ransverse wave wih equiaera penagon pah, for a he wave signa mixed ogeher, can ge accurae firs zero ime, i s no regisered. The wave packe 9 is wice figh ime of he ongiudina equiaera riange wave, so regisered as: 6 3R + τ = 9 = 70.7 (9 The wave packe 10 and 1 are aso compound wave packes, so hey are no regisered. The wave packe 11 is he rayeigh wave ransmied around he cyinder surface, i is usefu in evauaing he surface quaiy, he firs zero ime of i is = 76. 11 8, regisered as: πr + τ = R 11 = 76.8 (11 6
R is he veociy of he rayeigh wave,figure 5 shows he ransmiing of he rayeigh wave. The signa in figure is from opic gass rod, he posiion of he wave packes a he ime axis is deermined by he raio beween he veociy of ongiudina wave and ransverse waver. In differen maeria, ha may be differen, bu if we can ge some wave packes firs zero poin, using he formua(1((3((5(6(7(9(11, he corresponding veociy can be measured. Accordingy, for differen maeria, creaing he signa modes ike he signa shown in figure, i is hepfu for he urasonic NDE of he rods. Experimens and easic moduus cacuaion In homogeneous maeria, he easic moduus can be cacuaed using hese formuas [3] : The shear moduus: 3 G = ρ ; The Young s moduus: E = ρ ; The buk moduus: K 3 = ρ ρ ; The poisson s raio: 1 σ =. abe. ρ is he densiy of he maeria. The experimen resus are shown in figure 6, abe1 and 7
Tabe1 experimen daa (in he abe / means can ge accurae firs zero poin. maeria Diameer 1 3 5 6 7 9 11 (mm Gass1 80.18 7.3 35. / 3.6 55.8 / 58.99 70.7 76.8 Gass 60.8 0.01 5.91 / 3.7 39.83 1.3 5.3 / 60.3 See 60. 18.8.1 / 3.09 0.01 38.30 / / 57.76 Auminum 90.0 8.33 36.8.50 9.56 66.9 55.93 / 73.16 95.57 Tabe cacuaion of veociy an easic moduus maeria diameer R τ ρ G E (mm ( m / s ( m / s ( m / s ( g / cm 3 (10 10 N / m (10 10 N / m Gass1 80.18 5905 3531 386 0.16.3 3.01 7.381 Gass 60.8 5681 3366 308-1.1.3.75 6.751 See 60. 605 338 350-0.66 7.905 9.05 3.33 Auminum 90.0 606 35 965 0.8.800.91 7.78 5 oncusions Using numerica simuaion and dynamic phooesic experimen, he auhors expained he forming mechanism of he puse acousic fied in rods; and creaed signa modes and veociy cacuaing formuas for rods, in he siuaion ha uses singe ongiudina wave ransducer. Then he veociy of differen ype urasonic wave and he easic moduus of differen maerias were measured, so using ony one ransducer, he mechanica propery of rods coud be anayzed compeey. Reference: [1] SAE AMS 631B. Urasonic Inspecion Tianium and Tianium Aoy Bar and Bie [] ML-T-907G Tianium and Tianium Aoy Bars (Roed or Forged and Reforging Sock, Aircraf Quaiy [3] hen Yifang, Zhang Jiajun. A Research on Tesing Easic Modui of Workpiece Maerias. Proceedings 8
of 1 Word onf. on NDT.1996, India 9