The Ideal Angle Beam Probes for DGS Evaluation Wolf Kleinert, York Oberdoerfer, Gerhard Splitt, GE Sensing & Inspection Technologies GmbH, Huerth, Germany

2 May 5, 2015 Wolf Kleinert The Discussion About the Near Field Length of Angle Beam Probes With Rectangular Transducers Is Quite Old. Source:

3 May 5, 2015 Wolf Kleinert The DGS Method Was Developed for Straight Beam Probes With Circular Flat Transducers Normalized DGS Diagram Distance s/N Gain [dB]

4 May 5, 2015 Wolf Kleinert Existing Tools at the Time of the Development of the DGS Method

5 May 5, 2015 Wolf Kleinert Sound Pressure on the Acoustic Axis of a Circular Transducer by Continuous Sound (Algebraic Solution)

6 May 5, 2015 Wolf Kleinert Sound Pressure on the Acoustic Axis of a Circular Transducer by Continuous Sound (Algebraic Solution) The sine has maxima for z under the following condition: With this for the last maximum on the acoustic axis follows: D: Transducer diameter N: Near field length : Wave length

7 May 5, 2015 Wolf Kleinert Conversion of the Near Field Length From a Rectangular Transducer to an Equivalent Circular Transducer State of the Art The near field length of a rectangular transducer is calculated by: Refer to: J. und H. Krautkrämer, Werkstoffprüfung mit Ultraschall, 5. Editon, page 82 For a 8 times 9 mm 2 rectangular transducer follows: N = 15,4 mm With: a: half of the longer side b: half of the shorter side h: correction value (refer to the table) l: wave length in the test material

8 May 5, 2015 Wolf Kleinert Sound Pressure on the Acoustic Axis by Continuous Sound Good match between the calculation of the near field length according to the state of the art with the numeric solution. Circular transducer (algebraic)Rectangular transducer (numeric) 9 times 8 mm 2, N = 14.8 mm Sound Pressure p(z) Distance z [mm]

9 May 5, 2015 Wolf Kleinert Comparison Between the Rectangular Transducer and the Equivalent Circular Transducer Rectangular transducer 9 times 8 mm 2 Circular transducer Depth [mm]

10 May 5, 2015 Wolf Kleinert Recent Measurements With Angle Beam Probes Show Significant Deviation Evaluation using the equivalent circular transducer

11 May 5, 2015 Wolf Kleinert Problem to Be Solved f = 4 MHz, c = m/s, D = 12,2 mm How does the transducer look like? Sound field contour in 2 dB steps Distance x [mm] Depth z [mm]

12 May 5, 2015 Wolf Kleinert Just Two Preconditions Are Used. At the end of the near field the difference between the central beam and a perimeter beam equals half the wave length. Fermat-Principle: The fastest path from a point A in a first medium to a point B in a second medium follows Snell‘s Law. Not only valid in the 2D plane but as well in the 3D space.

13 May 5, 2015 Wolf Kleinert Constructing an Angle Beam Probe With Predefined Angle of Refraction  and Pre-defined Delay Line v w Transferring the sound path for each angle g from a given straight beam probe to the angle beam probe to be modeled. (Not only in the 2D plane, but as well in the 3D space) MW M‘ W‘

14 May 5, 2015 Wolf Kleinert Result (Probe Similar to the MWB 60-4) Transducer Shape Cross Section Longitudinal Section Longitudinal Section after coordinate transformation

15 May 5, 2015 Wolf Kleinert True DGS Technology Drives Accuracy DGS software in our instruments will support both probes Current Technology OVER Sizing NEW Technology PRECISE Sizing

16 May 5, 2015 Wolf Kleinert Curved Coupling Surfaces For concave test surfaces the Standard EN requests matching of the delay line of the probe to the surface of the test piece in all cases unless the diameter is large enough to ensure good coupling. (The following figure is taken from the European Standard EN 583-2) For convex surfaces matching is required when: In these cases the EN does not allow the use of the DGS method. The model described above can nevertheless be easily expanded to curved coupling surfaces to ensure even in these cases the validity of the DGS method.

17 May 5, 2015 Wolf Kleinert Positive Phasing Angles The delay laws can be calculated directly when positive phasing angles are used, by comparing the position and orientation of the original transducer with those of the virtual transducer. The delay laws follow then from the distances between the transducer elements of the original and the virtual transducer:

18 May 5, 2015 Wolf Kleinert Necessary Additional Matching Using Negative Phasing Angles

19 May 5, 2015 Wolf Kleinert Phased Array Angle Beam Probe MWB 56-4 trueDGS, 45° Phasing

20 May 5, 2015 Wolf Kleinert Phased Array Angle Beam Probe MWB 56-4 trueDGS, 60° Phasing

21 May 5, 2015 Wolf Kleinert Phased Array Angle Beam Probe MWB 56-4 trueDGS, 70° Phasing

22 May 5, 2015 Wolf Kleinert Summary of the Evaluation Significantly improved DGS accuracy can be achieved with this new trueDGS technology without any „Focus Pocus“, if the angle beam probe is designed according to the trueDGS technology: „Focus Physics“ Phasing angle in steel [°] Sound path to the near field end Sound path [mm] Single ElementPhased Array All measurements were done manually