The Ideal Angle Beam Probes for DGS Evaluation

Wolf Kleinert, York Oberdoerfer, Gerhard Splitt,GE Sensing & Inspection Technologies GmbH,

Huerth, Germany

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April 18, 2023

Wolf Kleinert

The Discussion About the Near Field Length of Angle Beam Probes With Rectangular Transducers Is Quite Old.

Source: http://www.ndt.net/forum/thread.php?forenID=1&rootID=8596#

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April 18, 2023

Wolf Kleinert

The DGS Method Was Developed for Straight Beam Probes With Circular Flat Transducers

Normalized DGS Diagram

Distance s/N

Gai

n [

dB

]

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April 18, 2023

Wolf Kleinert

Existing Tools at the Time of the Developmentof the DGS Method

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April 18, 2023

Wolf Kleinert

Sound Pressure on the Acoustic Axis of a Circular Transducer by Continuous Sound (Algebraic Solution)

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April 18, 2023

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 diameterN: Near field length: Wave length

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April 18, 2023

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:

Ratiob/a

h

1,0 1,370,9 1,250,8 1,150,7 1,090,6 1,040,5 1,010,4 1,000,3 0,990,2 0,990,1 0,99

Refer to: J. und H. Krautkrämer, Werkstoffprüfung mit Ultraschall, 5. Editon, page 82

For a 8 times 9 mm2 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

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April 18, 2023

Wolf Kleinert

Sound Pressure on the Acoustic Axisby Continuous Sound

Good match between the calculation of the near field length accordingto the state of the art with the numeric solution.

Circular transducer (algebraic) Rectangular transducer (numeric)9 times 8 mm2, N = 14.8 mm

So

un

d P

ress

ure

p(z

)

So

un

d P

ress

ure

p(z

)

Distance z [mm] Distance z [mm]

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April 18, 2023

Wolf Kleinert

Comparison Between the Rectangular Transducerand the Equivalent Circular Transducer

Rectangular transducer 9 times 8 mm2 Circular transducer

Dep

th [

mm

]

Dep

th [

mm

]

Dep

th [

mm

]

Dep

th [

mm

]

Dep

th [

mm

]D

epth

[m

m]

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April 18, 2023

Wolf Kleinert

Recent Measurements With Angle Beam Probes Show Significant Deviation

Evaluation using the equivalent circular transducer

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April 18, 2023

Wolf Kleinert

Problem to Be Solved

f = 4 MHz, c = 3 255 m/s, D = 12,2 mm

How does thetransducer look like?

Sound field contour in 2 dB steps

Distance x [mm]

Dep

th z

[m

m]

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April 18, 2023

Wolf Kleinert

Just Two Preconditions Are Used.

At the end of the near field the difference betweenthe central beam and a perimeter beam equalshalf the wave length.

Fermat-Principle:The fastest path from a point A in a firstmedium to a point B in a second mediumfollows Snell‘s Law.

Not only valid in the 2D plane but as wellin the 3D space.

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April 18, 2023

Wolf Kleinert

Constructing an Angle Beam Probe WithPredefined Angle of Refraction and Pre-defined Delay Line vw

Transferring the sound path for each angle g from a given straight beamprobe to the angle beam probe to be modeled.(Not only in the 2D plane, but as well in the 3D space)

M W

M‘W‘

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April 18, 2023

Wolf Kleinert

Result (Probe Similar to the MWB 60-4)Transducer Shape Cross Section

Longitudinal Section Longitudinal Section after coordinate transformation

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April 18, 2023

Wolf Kleinert

True DGS Technology Drives Accuracy

DGS software in our instruments will support both probes

Current Technology

OVER Sizing

NEW Technology

PRECISE Sizing

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April 18, 2023

Wolf Kleinert

Curved Coupling SurfacesFor concave test surfaces the Standard EN 583-2 requests matching of the delay line ofthe probe to the surface of the test piece in all cases unless the diameter is large enoughto 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 583-2 does not allow the use of the DGS method. The modeldescribed above can nevertheless be easily expanded to curved coupling surfaces toensure even in these cases the validity of the DGS method.

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April 18, 2023

Wolf Kleinert

Positive Phasing Angles

The delay laws can be calculated directly when positive phasing angles are used , by comparingthe 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 theoriginal and the virtual transducer:

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April 18, 2023

Wolf Kleinert

Necessary Additional MatchingUsing Negative Phasing Angles

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April 18, 2023

Wolf Kleinert

Phased Array Angle Beam ProbeMWB 56-4 trueDGS, 45° Phasing

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April 18, 2023

Wolf Kleinert

Phased Array Angle Beam ProbeMWB 56-4 trueDGS, 60° Phasing

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April 18, 2023

Wolf Kleinert

Phased Array Angle Beam ProbeMWB 56-4 trueDGS, 70° Phasing

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April 18, 2023

Wolf Kleinert

Summary of the Evaluation

Significantly improved DGS accuracy can be achieved with this new trueDGS technologywithout any „Focus Pocus“, if the angle beam probe is designed according to thetrueDGS technology: „Focus Physics“

Phasing angle in steel [°]

Sound path to the near field end

So

un

d p

ath

[m

m]

Single Element Phased Array

Probe FBH [mm] ERS [mm] [%]

MWB 45-2 tD 3 0,10 3,3%MWB 60-2 tD 3 0,14 4,7%MWB 70-2 tD 3 0,10 3,3%MWB 45-4 tD 3 0,17 5,7%MWB 60-4 tD 3 0,16 5,3%MWB 70-4 tD 3 0,16 5,3%

All measurementswere done manually