Acoustic emission source location f igure 9 result of

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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
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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.
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