Terence P. Lerch

Ultrasonic beam models: An edge element approach

A new method, the edge element method, has been developed to numerically evaluate a variety of ultrasonic transducer beam models. The edge element technique divides the transducer surface into a web of sources consisting of radiating straight line elements whose individual contributions can be evaluated analytically. When all of these edge elements are summed, the wave field of the transducer can be obtained at any field point in the surrounding medium for a given ultrasonic frequency. To demonstrate the versatility of this approach, it is shown that edge elements can accurately model the wave fields radiated into a fluid by focused and unfocused transducers of circular and noncircular apertures.

A boundary diffraction wave model for a spherically focused ultrasonic transducer

A model of a spherically focused piston transducer is developed in terms of boundary diffraction waves. The model represents the radiated pressure in terms of a direct wave and a one-dimensional edge wave integral. This decomposition allows the efficient calculation of the transducer beam in a form previously available only for a planar transducer. Numerical results for the simulation of the entire wave field of a transducer are given to illustrate the effectiveness of the formulation.

THE PARAXIAL APPROXIMATION FOR RADIATION OF A PLANAR ULTRASONIC TRANSDUCER AT OBLIQUE INCIDENCE THROUGH AN INTERFACE

The inspection of welds in structural plates with ultrasonic contact transducers is an important application of ultrasonic NDE [1]. Models that completely describe transducer/flaw interactions can help to make reliable, quantitative measurements on the welds in question. Thus, recently we have begun development of an ultrasonic weld inspection simulator and will present the preliminary work for the simulator in this paper.

Characterization of Spherically Focused Transducers Using an Ultrasonic Measurement Model Approach

A new and computationally efficient method is developed for characterizing a spherically focused, ultrasonic transducer (and its accompanying test system). Procedures for determining the probes effective radius, effective focal length, and system efficiency factor are described. Predicted responses that make use of these effective parameters are shown to correspond very well to measured responses for a number of different transducers.

Modeling the ultrasonic radiation of a planar transducer through a plane fluid-solid interface

Abstract. Three types of transducer beam models are developed for obtaining the bulk waves generated by a plane piston transducer radiating through a planar fluid—solid interface. The first type, called the surface integral model, is based on a Rayleigh—Sommerfeld-like integral that requires a two-dimensional surface integral to be evaluated. The second model, called the boundary diffraction wave (BDW) paraxial model, simplifies the two-dimensional integration of the surface integral model to a one-dimensional line integration. The third type of model, called the edge element model, is shown to be a novel way of efficiently evaluating the two-dimensional surface integration of the surface integral model. The limitations of these models for simulating inspections near critical refracted angles and near the interface are discussed. It is shown that the introduction of the paraxial approximation in the BDW model allows that model to be computed with a very large (300—1) speed advantage over the surface integral while retaining the same accuracy in most cases. The edge element model, while having a smaller (5—1) advantage over the direct numerical integration of the surface integral model, retains the accuracy of the surface integral model in cases where the paraxial approximation fails and can be easily generalized to more complex testing situations (focused probes, curved interfaces, etc.).

Ultrasonic Transducer Radiation through a Curved Fluid-Solid Interface

A number of typical ultrasonic immersion inspections require the transducer radiation to propagate through components with non-planar surfaces. As the complexity of the component’s surface increases in terms of shape and curvature, the effects of the part’s curvature on the transmitted wavefield become difficult, if not impossible, to predict by simple heuristic approaches. The development of accurate transducer beam models that can handle these types of fluid-solid interfaces, therefore, becomes essential.

The Wavefield of an Ultrasonic Angle Beam Shear Wave Transducer: An Elastodynamic Approach

Inspection of welded plate and pipe assemblies with ultrasonic angle beam shear wave transducers is an important and common application of ultrasonic NDE. With the advent of the Thompson and Gray measurement model [1], many practical ultrasonic testing configurations such as angle beam inspections can now be analytically modeled. An important component of the measurement model for any UT testing configuration is the calculation of the incident wavefields radiated by the transmitting transducer, commonly known as the transducer beam model.

Modeling the Propagation of Bounded Beams Through Curved Interfaces

In modeling ultrasonic immersion inspections involving complex geometries, one of the more difficult tasks is to predict the effect that a curved surface has on a beam of sound as it propagates from the fluid into the solid. In this paper, we will consider a hierarchy of models for this problem (see Fig. 1).

Modeling the Ultrasonic Radiation of Shear Wave Angle Beam Transducers

Weld inspections of fabricated plate and pipe assemblies made with shear wave angle beam transducers are a common and important application of ultrasonic NDE. It is now possible to develop complete models of such angle beam inspections (see, for example, the measurement model of Thompson and Gray [1]) for many practical configurations. One important element in these models is the calculation of the fields generated by the angle beam transducer, i.e. the transducer beam model. To date, three different beam models have been derived and studied. They are the Surface Integral model [2], the Boundary Diffraction Wave (BDW) Paraxial model [2], and the Edge Element model. Each has certain advantages and disadvantages associated with it, as will be seen in later sections of this paper.

Characterization of ultrasonic contact transducers using a Michelson interferometer

Accurate measurements of velocity, attenuation, and other ultrasonic properties of materials involve diffraction corrections that can significantly alter the measured values. Although diffraction calculations require knowledge of the transducer’s effective radius, this parameter is difficult to determine precisely for contact transducers. Here, an experimental method to quantitatively characterize longitudinal contact transducers is presented. Narrowband (toneburst) electronics excite the transducer, and a Michelson interferometer measures the out‐of‐plane displacements on the sample’s opposite side. With a resolution of approximately 10 μm, this optical technique allows transverse spatial scans of the displacement field to be obtained. Furthermore, the on‐axis position may be located with the interferometer and the transducer excitation frequency varied. The frequency dependence of the on‐axis amplitude is measured using a sample whose thickness is approximately half the nearfield distance at the transducer’s center frequency. The shape of the transverse scans and the observed minimum in the frequency dependence permit the transducer’s effective radius to be calculated. Measurements are presented for transducers in the 1‐ to 10‐MHz range with nominal radii between 2.5 and 6.4 mm. The results are compared to a numerical diffraction model to evaluate the accuracy and precision of this approach.