Method and apparatus for focusing propagating wave paths of a phased array in spherically-bounded materials

A method for focusing ultrasonic waves emitted from a plurality of elements of a phased array mechanism and directed toward a spherical nuclear reactor pressure vessel head, having a surface and a center, to arrive at a pre-selected focal point at the same time and in phase, comprising the steps of:

• calculating the location of at least one of a plurality of preferred refraction points on a surface of the spherical vessel head using an iterative process, each of said preferred refraction points corresponding to one of the elements of the phased array mechanism and each of said preferred refraction points being uniquely defined relative to the location of the center of the spherical vessel head by a first angle, θp, representing a rotation about a first spatial axis, and a second angle, φp, representing a rotation about a second spatial axis;
• and
• calculating a pulse firing time for each element of the phased array mechanism that relates to the relative timing of the emitted waves from the elements.

An apparatus for focusing ultrasonic waves emitted from a plurality of elements of a phased array mechanism and directed toward a spherical work piece, having a surface and a center, to arrive at a pre-selected focal point at the same time and in phase, comprising:

• location calculating means for calculating the location of at least one of a plurality of preferred refraction points on a surface of the spherical work piece using an iterative process, each of said preferred refraction points corresponding to one of the elements of the phased array mechanism and each of said preferred refraction points being uniquely defined relative to the location of the center of the spherical work piece by a first angle, θp, representing a rotation about a first spatial axis, and a second angle, φp, representing a rotation about a second spatial axis;
• and
• pulse firing time means for calculating a pulse firing time for each element of the phased array mechanism that relates to the relative timing of the emitted waves from the elements.

An apparatus for focusing ultrasonic waves emitted from a plurality of elements of a phased array mechanism and directed toward a spherical nuclear reactor pressure vessel head, having a surface and a center, to arrive at a pre-selected focal point at the same time and in phase, comprising:

• means for calculating the location of at least one of a plurality of preferred refraction points on a surface of the spherical vessel head using an iterative process, each of said preferred refraction points corresponding to one of the elements of the phased array mechanism and each of said preferred refraction points being uniquely defined relative to the location of the center of the spherical vessel head by a first angle, θp, representing a rotation about a first spatial axis, and a second angle, φp, representing a rotation about a second spatial axis;
• and
• means for calculating a pulse firing time for each element of the phased array mechanism that relates to the relative timing of the emitted waves from the elements.