AE04.pdf

Acoustic emission source location f igure 9 result of

This preview shows page 12 - 14 out of 31 pages.

Acoustic Emission Source Location F IGURE 9. Result of source location with two transducers on an infinite plane. Legend D = distance (meter) between transducers R = distance (meter) from transducer 1 to source r 1 = distance (meter) from transducer 2 to source Z = distance from transducer plane to source X s , Y s = cartesian coordinates for the source θ = angle (radian) R r 1 = constant Transducer 2 r 1 Source X s , Y s R Transducer 1 Z D θ
Image of page 12

Subscribe to view the full document.

improve the situation. The input data now include a sequence of three hits and two time difference measurements (between the first and second hit transducers and the first and third hit transducers). Figure 10 illustrates the general situation. (14) now: (15) which yields: (16) and: (17) Equations 16 and 17 can be solved simultaneously to provide the location of a source in two dimensions as illustrated in Fig. 11 (this diagram shows an equilateral triangular array but solutions to Eqs. 16 and 17 do not require one). Source Location in Three Dimensions Most applications of acoustic emission source location techniques are directed at the problem of locating a source in a practically two-dimensional shell structure. However, when the wall is too thick or when the area of interest lies internally to the shell, then locating a source in three dimensions becomes important. In addition, there are now cases of liquid filled structures where internal sources can be located in three dimensions by using transducers mounted on the outside surface of the structure. One approach is to extrapolate the two-dimensional technique into three dimensions. Each transducer location is defined in full spatial coordinates ( X, Y and Z ) and the hyperbolae of Eqs. 16 and 17 become surfaces. The solution is more involved than in two dimensions and mapping onto a two-dimensional surface presents its own set of problems. 4 Three-Dimensional Source Location in Cylindrical Test Objects The following approach is applicable for an intermediate (thick walled) cylindrical vessel. If the outside diameter of the cylinder is not too large, then a distribution of four transducers, as shown in Fig. 12, is sufficient for volumetrically R D t V t V D = + ( ) 1 2 2 2 2 2 2 2 2 3 Δ Δ cos θ θ R D t V t V D = + ( ) 1 2 1 2 1 2 2 1 1 1 Δ Δ cos θ θ Δ t V r R 2 2 = Δ t V r R 1 1 = 128 Acoustic Emission Testing F IGURE 10. Three-transducer array with detection sequence 1, 2, 3. Transducer 1 ( X 1 , Y 1 ) Transducer 3 ( X 3 , Y 3 ) Transducer 2 ( X 2 , Y 2 ) Source 3 ( X s , Y s ) D 1 Z 1 θ Reference θ 3 r 2 Legend D = distance (meter) between transducers R = distance (meter) from transducer 1 to source r 1 = distance (meter) from transducer 2 to source z = distance from transducer plane to source X s , Y s = cartesian coordinates θ = angle (radian) R θ 1 D 2 r 1 F IGURE 11. Intersection of hyperbolae as used for defining source position.
Image of page 13
Image of page 14

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern