Calculation of the Acoustic Field of a Direct Transducer with Piezoelectric Plates of Different Shapes

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The directivity characteristic of a normal probe with a circular piezoelectric plate has been calculated with allowance for pressure (elastic stress) oscillations within both the excitation region (the surface of the electrodes applied to the piezoelectric plate) and the plate itself, whose dimensions exceed those of the excitation region. It is established that, in the first and second cases, the directivity characteristics are somewhat wider and narrower, respectively, than those used in the conventional stepwise approximation of the pressure applied from a transmitting probe to the surface of a tested article. The effective piezoelectric-plate size is estimated.The conventional theory of the acoustic field of a normal probe implies that all of the points of the radiating surface create a pressure with the same amplitude over the contact area on the surface of a test object (TO), and the pressure is equal to zero at all other points of the TO surface [1]. However, the results of a computer simulation that considers actual boundary conditions at the piezoelectric-plate (PP) surfaces that are in contact with the damper and the wear face, as well as the finite dimensions of the excited area (electrodes), indicate an oscillatory behavior of the normal component of the elastic stress over the PP surface [2].This circumstance can to a certain degree affect the effective (actually working) PP surface and, as a result, the directivity characteristic and the amplitude of the transmitted signal; this should evidently be taken into consideration when using the well-known engineering formulas for calculating acoustic channels [1,3]. It should also be noted that the effective PP size sometimes appears to be unknown because the electrodes cover only a part of the PP surface; it is unclear whether the PP area that must be taken for calculations is the total area or the area covered with the electrodes [3,4].Following [4], the effective PP size can be estimated from the directivity characteristic if the following parameters are known: the operating frequency, the velocity of longitudinal waves in the medium being tested, and the directivity characteristic's experimentally determined opening angle that corresponds to an amplitude attenuation of 3 dB relative to its peak value. In this paper, the effective PP size for a normal probe is estimated on the basis of a computer simulation of the elastic-stress distribution similar to that found in the results that were published in [2].In the transmission mode, we calculated the magnitude of the stress-tensor component on the surface of a PP of radius a pl with an excitation area of radius a ex that was in contact with a wear face [2, 5] as a function of r measured from the PP center:(1)In formula (1), C 33 and C 13 are the PP (piezoceramic) elastic constants, e 33 is the piezoelectric constant, E z is the electric-field strength component along the OZ axis orthogonal to the plane of the PP of thickness ∆ z , V is the potential difference at the electrodes [5], andT zz i ( ) r z , ( )...

Section: Acoustic Methodsmentioning

confidence: 99%

An Estimate of the Effective Size of a Normal Probe's Piezoelectric Plate

Danilov

2005

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“…According to [5] pressure P produced by the normal probe with surface Σ, which is applied to surface z = z 1 = 0 ( Fig. 9), can be written in cylindrical coordinates (r, ϕ, z) in the form (7) where the following representation of expression is used [6]:…”

Section: Acoustic Methodsmentioning

confidence: 99%

Estimating the Parameters of Signals Observed during Ultrasonic Testing of a Cylindrical Article with a Normal Probe on the End Surface

Danilov

2005

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The first and second signals observed during ultrasonic testing of a cylindrical article with a normal probe set on the article's end surface are studied. The amplitude of the second pulse caused by a reflection from a lateral wall with transformation of elastic waves is estimated relative to the amplitude of the first (ordinary bottom-reflected) pulse. It is ascertained that, under certain conditions, the amplitude of the second pulse can be comparable to or even exceed the amplitude of the first pulse. The effect of a change in the specimen radius-to-length ratio on the amplitude of the bottom signal is estimated.The necessity of testing cylindrical articles from ends using normal probes is encountered during ultrasonic testing of appropriately shaped forged pieces, axles of rolling-stock wheel pairs, etc.[1]. In acceptance tests of axles according to the regulatory document RD 32.144-2000 [2], a method of testing their sounding is used, which consists in determining the difference (in decibels) between bottom echo signals obtained from a face of a standard specimen CO-2 (at a distance of 59 mm) and from the opposite end of an axle. This axle is considered inconsistent with the requirements of the acceptance test if this difference exceeds 46 dB.It is known that, in the far-field zone of a normal probe, the amplitude of the bottom signal falls (without allowance for a decrease due to the absorption and scattering by microinhomogeneities) as a result of a divergence of the wave front of a longitudinal wave in inverse proportion to the increasing distance to the reflecting surface; this decrease in the bottom signal occurs more slowly than a decrease with the distance of echo signals from cylindrical, spherical, flat-bottomed, and other reflectors [1,3]. However, when cylindrical articles are tested from their ends, signal reflections from lateral surfaces can be observed. This leads to the appearance of additionally detected pulses (false signals), the amplitude of which, owing to a certain focusing effect of these surfaces, can be comparable with the amplitudes of signals reflected directly from the ends (bottom signals). This may complicate the discrimination of bottom signals since their selection by the time of arrival becomes obligatory. The author of this paper has performed studies of the first two echo pulses observed during ultrasonic testing from the ends of cylindrical specimens. The corresponding results are presented below.The specimens used in this study were steel cylinders no. 1 of radius b = 35 mm and length h = 142 mm and steel cylinders no. 2 with b = 45 mm and h = 210 mm. Elastic waves were emitted and received by a èêàá -Ñ 11 normal probe at a frequency of 2.5 MHz ( è 111-2.5-K12-002). Figure 1 shows (in arbitrary units) the first and second pulses observed on the screen of the AVGUR computer apparatus upon excitation and reception of elastic waves by the probe located axisymmetrically at the end of specimen no. 1. Fig. 1, pulse 1 corresponds to a bottom signal (from the opposite end). The d...

“…The formula for the distribution of pressure P created by a discshaped normal probe along axis z to a semiinfinite medium has been refined [24]:…”

Section: The Acoustic Field Of a Probe And Controlling Such A Fieldmentioning

confidence: 99%

Progress in the theory of ultrasonic flaw detection. Problems and prospects

Ermolov¹

2004

This paper was prepared upon request from the organizers of the XVIII St. Petersburg conference "Ultrasonic Flaw Detection in Metal Structures. UZDM 2004." The progress made in the theoretical issues of ultrasonic flaw detection over the past 20 years is briefly considered, and some practical issues are discussed. Specific problems that are waiting to be solved are formulated, and the author's opinions about the prospects of developments in ultrasonic flaw detection are presented. The preparation of the paper was much facilitated by book [1], which was published recently. WAVES AND THEIR PROPERTIES New or Rarely Used Types of WavesHead waves are presently well known, but this topic involves concepts that need to be discussed. Longitudinal head waves are waves that propagate along a surface. They are also called surface-longitudinal waves. The term head wave is only widespread among defectoscopists in Russia. Acousticians consider it to be a type of leaky surface waves [2]. Foreign seismoacousticians and defectoscopists call it a creep wave or lateral wave. There are differences between these waves. For example, when these waves propagate near the surface of a convex cylinder, a wave propagating along the surface is called a creep wave, whereas a wave propagating along a bisecant is called a lateral wave. The utilization of head waves for flaw detection was proposed by N.P. Razygraev (TsNIITMASh) in 1974 [3]. Figure 1 shows a system of waves that appear when a longitudinal wave falls from the plastic wedge of a probe to the interface of a metal, e.g., steel, at the first critical angle [4, p. 649]. A longitudinal wave with wavefront P has the highest velocity. From the angle probe, this wave, which may be a head wave creeping along the surface, propagates as a diverging bundle of rays. This explains the dependence shown in Fig. 2 for the amplitude of the echo signal obtained from flat-bottomed holes that have different depths h and probe-reflector distances. Rays at an angle of about 80 ° have the maximum amplitude.When a longitudinal wave propagates along the surface, this wave alone cannot satisfy the boundary condition on the free surface of a test object (TO) since the stresses are equal to zero. At each point of the surface, it generates transverse wave S that propagates at an angle to a surface normal. This angle equals the third critical angle. The condition at the free surface is satisfied due to this transverse wave. The transverse wave carries away energy; as a result, wave C rapidly decays. The wavefront of transverse waves H is an inclined plane. It is this wave H that is called the head wave in acoustics and in the foreign literature on flaw detection, whereas Russian defectoscopists call it a shear side wave. The transverse wave generates longitudinal wave P , which is delayed in time with respect to wave P mentioned above; however, some theoreticians doubt the existence of wave P .The head wave is usually excited and received by means of angle-type send/receive probes with an incidence angle equal t...