NDT.net - Sep 2001, Vol. 6 No. 9 |
Pipeline girth weld ultrasonic inspection is now well established. Although the introduction of phased array technology into this venue is fast being recognised for its advantages there are those who seem to think that the sound field made by a phased array probe is different and inferior to single element probes.
In a conference in Houston a couple years ago one of the competing companies' representatives stood up to state that the lateral beam size of a phased array probe was significantly disadvantaged because it was not focused in that plane.
Not only does this sort of statement shows poor judgement since all of the major players have been attempting to prepare their own phased array systems, but those holding this view have not even bothered to do the simple math to calculate the beam size.
This little description is intended to show that lateral beam extent is not a detracting factor for phased array systems and phased array probes may even prove to have an advantage in this regard.
In Canada we have qualified 4 systems for use on pipeline construction. Although all use similar principles there are differences in the details. Transducer design is in fact one of the details different in each of the four systems. The qualified systems are identified here by their company names in Canada.
1. RTD Quality Services | Lens focused |
2. Shaw Pipeline Service | Shaped Element focusing |
3. Weldsonix | Unfocused (for original qualification they used shaped elements) |
4. Canspec | Phased Array focusing |
One of the requirements for zonal discrimination is a small beam spot size to ensure that the flaw position can be correctly assessed.
Options 1 and 2 usually provide a spherical focus, which when measured perpendicular to the beam axis indicates a fairly round focal spot. But even these systems resort to an elliptical element or apodised spherical shape to achieve the required spot size on long sound path lengths.
Option 3 more recently has resorted to " the natural focus" of a flat element. If the wedge is correctly machined to provide the focus at the exact distance to the fusion line the results can be close to acceptable to ASTM-E1961 requirements for a minimum of 6dB separation between zones. However, for thick wall examination the overlap between zones can be such that it is difficult to determine which zone the flaw is located in.
Option 4 uses a linear phased array. The array permits focusing in the vertical plane but natural divergence occurs in the lateral plane. This, like the apodised spherical or elliptical elements, forms an elliptical spot.
Although the individual that posed the question in the Houston conference also had some zones that used elliptical spots in his system, he worded the question as though it was a unique shortcoming of phased array systems. It would appear that this individual (and others that seem to have repeated his question when assessing system performances) did not bother to do the math.
Although it would have been a simple matter to compare the lateral beam extents by measuring the probe displacement on a calibration block with the standard 2mm diameter flat bottom hole, this too was not done prior to making the statement at the conference.
To illustrate how trivial the matter is a few simple calculations can be made.
Three conditions will be examined:
For the natural focus we can use the basics for beam divergence and spot size calculations. (see web reference http://www.panametrics-ndt.com/)
For the focused conditions we will use the software programme Beam (Dr. D. Mair) which has proven to be effective as a representative presentation previously (see web reference http://www.ndt.net/article/ginzel/hotchkis/hotchkis.htm). Calculations will be for the ideal 6dB boundary (which equates to the 3dB boundary in the one-way transmission calculated by Dr. Mair).
Three parameters will be compared for the three conditions;
For inspection of 10 to 15mm wall the probe used most often has been the 0.375" or 0.5" diameter 5MHz. For the sake of uniformity the inch units will be converted to mm.
0.375" = 9.5mm and 0.5" = 12.5mm
An assumed acoustic velocity of 3250m/s for the shear mode will be used and 2730m/s for compression mode in Perspex.
Near zone
The formula for Near Zone is
For the 9.5mm diameter
N=(9.5)^{2}/4(0.65) |
=34.7mm |
For the 12.5mm diameter
N=(12.5)^{2}/4(0.65) |
=60.1mm |
Spot Size
The formula for spot size (BD=beam diameter) is;
For the 9.5mm diameter
BD= 0.2568(9.5)*1 |
= 2.4mm |
For the 12.5mm diameter
BD= 0.2568(12.5)*1 |
= 3.21mm |
Focal length = Radius of Curvature = F
Normalised focal length S_{F}=F/N
Flat element _{}S_{F} = 1
Divergence
The formula for divergence is
For the 9.5mm diameter
Sin(a/2) = 0.514(3250)/5,000,000*0.0095 |
= 0.035168 |
(a/2) = 2.0° |
a = 4° |
For the 12.5mm diameter
= 0.026728 |
(a/2) = 1.5° |
a = 3° |
A near zone calculation does not apply to focused probes. However, in order for a true focusing effect to occur the intended focal distance of a focused probe must be less than the natural focus or near zone.
We will assume that the lens focused probes and element shaped probes provide a similar spot size. The standard equations for focusing apply to the element shaped focusing.
For this demonstration we will use a 12.5mm diameter 7.5 MHz element with a radius of curvature that provides for a focal spot at about 75mm.
Spot Size
The near zone for a flat element with 12.5mm diameter and 7.5MHz nominal frequency would be:
N=D^{2}/4l |
=(12.5)^{2}/4(0.43) |
=90.8mm |
The natural spot size would be BD= 0.2568(12.5)*1 or 3.21mm
To provide a focusing effect the new focal length must be less than the near field. The 75mm radius of curvature we have selected meets this requirement.
The formula for spot size (BD=beam diameter) is;
For a focused element
BD =1.02Fc/fD |
=1.02(75)(3250)/7,500,000(0.0125) |
=2.65mm |
Divergence
Beam divergence in a focused probe's beam is rarely considered. It is assumed that the user has selected the optimum position of the focus to coincide with the point of interest. A more graphic presentation will be required to investigate this aspect for focused beams.
For a phased array probe we need to treat the phasing part of the focal plane similarly to a shaped element and the un-phased lateral plane as a flat rectangular element.
Default focal laws for the phasing system used by Canspec provide for optimum performance when using 16 elements in the array for a beam. For the typical phased array probe now used in pipeline inspections a 7.5MHz nominal frequency is used and the elements are about 1mm long and 10mm wide. Selecting 16 elements for the focusing allows us to use the spot size formula used in Case 2. We will again calculate to achieve a 75mm focus in steel.
Spot Size
The formula for spot size (BD=beam diameter) is;
For a focused element
BD =1.02Fc/fD |
=1.02(75)(3250)/7,500,000(0.016) |
=2.07mm |
But in the lateral direction we must rely on the natural focus as provided by the near field effect.
Using the equations seen above for the unfocused elements, we get for the 10mm element width, a near zone effect at 57.6mm and so the spot dimension at that position is about 2.7mm. Krautkramer (Ultrasonic Testing of Materials) cautions that for a square element the near field is pushed further away. For a square element the near field is 1.35 times further that would be calculated for a circular oscillator with diameter " D" equal to the sides (length and width) of the square element. This would place the actual near field in the phased beam to a point closer to 70-75mm.
Divergence
Krautkramer (Ultrasonic Testing of Materials) points out that the divergence of a rectangle is slightly different from a round element.
The formula for divergence in the rectangle is
Sin(a/2) = 0.44(3250)/5,000,000*0.01 |
= 0.0286 |
(a/2) = 1.6° |
a = 3.2° |
Tabulated Results
Parameter | 5MHz Flat | %MHz Flat | 7.5 Spherical focused | 7.5 Phased array |
Element dimensions used | 9.5mm diameter | 12.5mm diameter | 12.5mm diameter | 16mm (focused) X 10mm (unfocused) |
Near field/Focal length | 34.7mm in steel | 60.1mm in steel | 75mm in steel | 75mm in steel |
Spot Size | 2.4mm | 3.21mm | 2.65mm | 2.07mm X 2.7 |
Divergence (twice the half angle of divergence) | 4.0° | 3.0° | Estimated at 2.04° | 3.2° in lateral plane and vertical estimated 1.52° |
Divergence in the focused beams is noted in the plotted information below. A trendline extrapolated to the origin from points beyond the focal distance at 75mm were used to estimate divergence.
PA divergence after focus as calculated by trendline to zero is 1.52°.
Spherical focused divergence after focus as calculated by trendline to zero is 2.04°.
The above table indicates calculated values. Note that for the calculations we have used the shear wave velocity in steel (assumed to be 3250m/s). Because all applications for weld inspection use angled beams the delay effects of the refracting wedge are not allowed for. Wedge delays will be different for each configuration adding typically from about 8 to 16mm of travel in Perspex (equivalent to about 6.7-13.4mm in steel at shear velocity).
Graphed Calculations
Fig 1: |
Fig 2: |
Fig 3: |
Fig 4: |
An " approximate" beam divergence for the phased array probe in the lateral direction is indicated using a " natural focus" of 2.7mm at 70mm along the beam axis. The figure below is a " hybrid" of the divergence calculated for the rectangular piston and the near zone distance as described in Krautkramer.
Fig 5: |
Fig 6: |
Graphs of the unfocused calculations (i.e. 9.5mm flat, 12.5mm flat and 10mm rectangular side of Phased array) were all made using the calculated divergence angle for points past the near zone. The calculated near zone spot size was used for the end point of the near zone and the lines from the probe face are merely the element extremities.
Graphs for the focused elements (i.e. the 12.5mm spherical and the 16mm phased array) were derived from the modelled beams seen below.
On the left is the spherical focus and on the right the phased array modelled beams.
The amplitude curves along the vertical axes indicate the peak amplitudes configured for about 75mm and the amplitude curves above the beam images indicate the lateral extents at the focal distances.
From the graphed values it is seen that flat elements have the largest spot sizes and divergence causes the beam to spread quickly especially in the critical vertical direction. Optimum use of such elements would require precise machining of wedges to ensure that the natural focus is occurring very near to the intended area of concern.
Spherically focused elements can improve spot size and the reduced divergence would indicate that the " working range" based on the focal spot size can be increased over that available by unfocused probes. Wedge path lengths will also present limits of accuracy in placing the focal spot at the desired position along the beam axis.
Phased array focusing in the vertical plane can provide similar or improved spot sizes to that attained by spherical focusing but phased arrays have the advantage that the wedge need not limit the ability to optimise the performance of the focalisation. Phased arrays can be " tuned" to provide the focus where desired and are not at the mercy of the pre-designed element shape or size.
The lateral extents of the phased array modelled beam in this demonstration are superior to both the 9.5mm and 12.5mm flat elements. At the focal length designed for the spherically focused element and phased array element (about 75mm) the lateral extent of the phased array beam is essentially the same as the spherically focused beam (2.7mm versus 2.65mm). The divergence from the trendline information derived from the spherically focused indicates a 2.02° divergence after focused and this compares to 3.2° in the lateral plane for the phased array beam.
Recent calibration scans using a phased array probe on 2mm diameter flat bottom holes in a 15mm wall thickness indicate that beam widths consistently between 4mm to 5mm. This is slightly better that the graph of the " hybrid" of the divergence calculated for the rectangular element and the modified near zone distance as described in Krautkramer.
In conclusion, the lateral divergent effects of a phased array sound beam are not the great concern alluded to by critics of the system. The 1 or 2 millmetre differences between phased array and spherically focused systems would be insignificant. In fact in some cases (especially when the wedge delay is not optimal for spherical focusing) it may be seen that phased array beam widths are smaller.
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