NDT.net September 2003, Vol. 9 No.09 |
Keywords: nondestructive testing; ultrasonic waves, waveguiding extensions, transducers
It is necessary to note that the UT methods are well developed and presented by a wide variety of tools and instrumentation. Still, there are several problems connected with application of ultrasonic methods for testing of nonmetallic or nonmagnetic materials. One of them is related to the design of ultrasonic transducers. Traditionally applicable transducers have plate contact with the testing material surface and require usage of a special couplant for creation of acoustic contact. These Couplant Plate Contract (CPC) transducers have several disadvantages: couplant is responsible for instability of test measurements repetition; application of CPC transducers is hindered on rough and curved surfaces; there is a possibility of an error (commensurable with their contact area) connected with determination of distance between two CPC transducers for surface testing. Couplant free DPC transducers could allow avoiding these problems and increasing a number of ultrasonic NDT applications.
Theoretical and experimental studies of waveguiding extensions for UT testing in [1, 2] demonstrated results and formulae for calculations of transmission of acoustic waves from one medium to another on the base of solution of the problem of wave propagation in finite medium. A group of researchers, who received the first positive results, rushed into practical application of DPC transducers for laboratory and field testing of composite materials and structures [3]. Dependency of measurements of velocity of ultrasonic wave propagation on the angle of the waveguiding exte inclination to the testing material surface was also investigated.
Fig 1: Waveguiding extensions for DPC transducers (from left to right): exponential, conic, cylindrical, and needle shapes. |
Extensions are made of a hard metal alloy. They represent an acoustic transformer for better matching of acoustic impedence between testing medium and transducer. Experimental tests showed that shape and design of waveguiding extensions affect measurement results considerably, making them impossible in some cases. An attempt to find an explanation of this phenomenon on the base of analysis of AF characteristics of DPC transducers is made here. Application of the elements of the wave theory to the analysis of exponential waveguiding extension gives the following formulae for the extension with a variable section:
(1)
Where p - excess pressure, k - wave number, S(x) - function of the cross section, x - coordinate. The variable waveguiding extension section is accepted in the shape of exponent (Figure 2).
Fig 2: Scheme for calculation of exponential waveguiding extension, where: L - length of waveguiding extension, S_{0} - area of the base, a - shape coefficient. |
S(x) = S_{0} exp( - ax) (2)
where: a - shape coefficient.
After differentiation of (2) and substitution into (1) receive
(3)
This is a differential equation with partial derivatives, constant coefficient , and characteristic equation, where _{ }is a characteristic parameter.
(4)
Taking into account that wave number k
(5)
Where: V - velocity of longitudinal wave propagation, w - cyclic frequency, receive the following roots of the equation (4)
(6)
The form of the solution (6) depends on the determinant D sing and, thus, on the shape coefficient a :
(7)
For frequencies w (12 ÷ 120)·10^{4} rad^{-1} and velocities V = 2000 ÷ 5000 m/s determinant D ≤, and roots (6) are of complex character. General solution will take the form
(8)
Assuming that waveguiding extension is excited by the excessive pressure from the side of the section S_{0} and loaded on an immovable and absolutely elastic body from the side of acoustic contact with material S(L) , boundary conditions will be of the following form: p(0) = p'(x,w), p'(L) = 0 .
After differentiation and substitution into (8) receive values of arbitrary constants A_{1} and A_{2} . The following designation is used
(9)
and
(10)
where V - ultrasonic velocity, E - Young module, r - density of the material utilized for waveguiding extensions, K - coefficient of velocity dispersion depending on the relation of wave length l to the cross section S_{x} , receive the following formula
It is necessary to point out that for different combinations of a and V there is a number of critical frequencies w_{CRIT} , below which waves are not propagating. The values w_{CRIT} can be calculated: w_{CRIT} ~ V · a p ÷ 2 r. Exponential waveguiding extensions have parametric high frequency resonance on frequency w_{0}. The plots of the AF characteristics of waveguiding extension calculated according to (12) for V = 5000 m/s, L = 0.05 m and a = 0.025, 0.0125, and 0.225 are shown in the Figure 3. These plots demonstrate that exponential waveguiding extensions could be looked upon as high frequency filters (HFF) with resonance frequency w_{0} higher that 300 kHz and critical block frequency w_{CRIT} in the low frequency band (Figure. 3).
Fig 3: Ampletude-frequency characteristics of waveguiding extensions with the following shape coefficients: 1- a = 0.025; 2- a = 0.125; 3- a = 0.225 |
Fig 4: DPC transducer set-up. |
Fig 5: Experimental set-up: 1 - plastic box; 2, 3 - DPC transducers; 4 - probe frame; 5 - ice specimen; 6 - rubber protector; 7 - preamplifier; 8 - adaptive amplifier; 9 - ultrasonic measurement equipment UK-14PM; 10 - digital oscilloscope. |
Measurements were carried out using surface testing by the DPC transducers on different parts of the specimen with repeated contact conditions. The probe was manipulated by hand with load force about 1 kg. Three types of experiments were carried out with a) ice specimens on rubber protector; b) ice specimens in plastic box with water; c) water in plastic box. The experiment type (a) is shown in the Figure 6.
Fig 6: Ultrasonic measurements of an ice specimen on rubber protector. |
(13)
There are experimental data of the three types of experiments a) ice specimens on rubber protector; b) ice specimens in plastic box with water; c) water in plastic box are given in the corresponding Table 1.
Measurement ## | WATER | ICE | ICE & WATER | |||||
1 | 1.4981 | 3.7974 | 3.5087 | |||||
2 | 1.517 | 3.7151 | 3.519 | |||||
3 | 1.5444 | 3.6923 | 3.519 | |||||
4 | 1.5503 | 3.7267 | 3.5398 | |||||
5 | 1.5463 | 3.8095 | 3.4985 | |||||
6 | 1.5604 | 3.7037 | 3.5087 | |||||
7 | 1.2834 | 3.7383 | 3.5294 | |||||
8 | 1.517 | 3.6253 | 3.5398 | |||||
9 | 1.5075 | 3.7037 | 3.4782 | |||||
10 | 1.2834 | 3.5294 | 3.409 | |||||
11 | 1.3808 | 3.6253 | 3.3898 | |||||
12 | 1.4101 | 3.6585 | 3.3707 | |||||
13 | 1.4117 | 3.6585 | 3.3802 | |||||
14 | 1.4388 | 3.5928 | 3.5928 | |||||
15 | 1.4251 | 3.4985 | 3.4985 | |||||
16 | 1.5189 | 3.6474 | 3.3898 | |||||
Table 1: ULTRASONIC MEASUREMENTS |
Basic statistical analysis of testing results for ice specimen, ice and water, and just water is presented in Table 2.
STATISTICAL PARAMETERS | WATER | ICE | ICE & WATER | |||||
MEAN, km/c | 1.46 | 3.67 | 3.48 | |||||
STANDARD DEVIATION, km/c | 0.09 | 0.08 | 0.06 | |||||
VARIANCE, % | O.81 | O.7 | 0.5 | |||||
Table 2: |
The ultrasonic velocity distributions for ice and ice & water are presented in the Figure 7:
Fig 7: Ultrasonic velocity distributions: 1- ice and water; 2- ice. |
Fig 8: Surface coating testing |
Fig 9: Robotic ultrasonic testing bench |
Theoretical analysis and experimental data of acoustical properties of waveguiding extensions show that their type, shape, as well as the material that they are made of, determine their acoustic characteristics and respectively their field of applications.
It is posible to speculate that DPC transducers with modified waveguiding extensions could be used for:
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