Patent Publication Number: US-11644444-B2

Title: Ultrasonic inspection margin check for design and manufacturing

Description:
RELATED PATENT APPLICATION 
     This application claims the benefit, under Title 35, United States Code, Section 119(e), of U.S. Provisional Application No. 63/152,473 filed on Feb. 23, 2021. 
    
    
     BACKGROUND 
     The present disclosure relates generally to non-destructive inspection of structures made of composite material. As used herein, the term “composite material” means a laminate consisting of a stack of adhesively bonded plies, each ply consisting of parallel fibers embedded in an epoxy resin (hereinafter “epoxy”) matrix. The plies in a stack typically have different fiber orientations. 
     In the design of aircraft structure, there are structural requirements. A part that does not meet the structural requirements is not a valid design. Ultrasound is a non-destructive inspection (NDI) method used in the inspection of structures, including composite structures. In accordance with a typical ultrasonic inspection technique, an ultrasonic transducer transmits ultrasound into the structure to be inspected and then detects return ultrasound containing information concerning the integrity of the interrogated structure. The data acquired during an ultrasonic inspection may be used to determine whether the inspected structure satisfies strength and integrity requirements. For example, one strength check method may rely on a laminate-based material allowable database generated from coupon testing. 
     Ultrasound is the predominant NDI method for composites. However, certain geometries create challenges for ultrasonic inspection. For example, ultrasound is sensitive to the angle of incidence at any interface. In particular, on many aerospace structures, there are non-parallel surfaces, such as ramps. Non-parallel surfaces create angled interfaces which cause impinging ultrasonic waves to scatter. If the ultrasonic inspection is performed in the pulse echo mode (wherein the same ultrasonic transducer array is used to transmit and receive), the ultrasound will be scattered far enough away so that the return ultrasound cannot be received by the ultrasonic transducer array. In this case, the part design cannot be inspected using pulse echo ultrasonic inspection. 
     In the example case of ramps, the existing solutions to the problem of non-inspectable ramped structures are the following: (1) to limit the ramp angles, but there are no clear rules for allowable ramp angles; (2) to allow the ramp angles, but not require inspection (this adds weight to the aircraft); or (3) to allow certain ramp angles, but change the inspection procedure just for those ramps (this increases the cost and time incurred by the inspection process). 
     SUMMARY 
     A part design that results in a part which cannot be inspected should not be a valid design. The subject matter disclosed herein is directed to a method for quantitatively evaluating the expected ultrasonic inspectability of a part having a particular design with two non-parallel surfaces (hereinafter “interfaces”). During an ultrasonic inspection, the ultrasonic transducer array transmits an interrogating ray of ultrasound that is refracted at a first interface (e.g., an acoustic couplant—part interface) and then reflected at a second interface (e.g., a part—air interface) before returning to the ultrasonic transducer array. 
     More specifically, a process for calculating the risk of a non-inspectability condition during part design is proposed. An “NDI margin check” is created which is similar to a structural margin check. The process is based on definition and calculation of an ultrasonic inspectability metric that measures the distance separating a receive location on the ultrasonic transducer array from the center of the receive aperture due to scattering effects at the non-parallel reflecting interface. The benefits of this metric are the following: (1) the metric can be easily interpreted by engineers other than inspection experts; and (2) the metric can be incorporated into design and manufacturing tools as another constraint in the design space 
     Although various embodiments of methods for quantitatively evaluating the expected ultrasonic inspectability of a designed part will be described in some detail below, one or more of those embodiments may be characterized by one or more of the following aspects. 
     One aspect of the subject matter disclosed in detail below is a method for quantitatively evaluating the expected ultrasonic inspectability of a designed part, the method comprising: importing a model of a part; selecting a material of the part having a first index of refraction; selecting a material of an acoustic coupling medium having a second index of refraction different than the first index of refraction; defining an ultrasonic transducer array comprising a plurality of elements; defining a position of the acoustic coupling medium between the ultrasonic transducer array and the part; and defining a plurality of positions of a transmit aperture of the ultrasonic transducer array relative to the part. For each defined position of the transmit aperture, the method further comprises: tracing a path of a respective ray from a center of the transmit aperture of the ultrasonic transducer array, into and out of the part, and then to a respective receive location on the ultrasonic transducer array; calculating a respective value of an inspectability margin based at least in part on a respective distance between a center of the receive aperture and the respective receive location on the ultrasonic transducer array; and comparing each value of the inspectability margin to a threshold value. The method may further comprise rejecting the part for manufacture if the values of the inspectability margin indicate that a portion of the part is not ultrasonically inspectable and accepting the part for manufacture if the values of the inspectability margin indicate that the part is ultrasonically inspectable. 
     In accordance with one embodiment of the method described in the immediately preceding paragraph, tracing comprises: (a) tracing a first path of the first ray through the acoustic coupling medium; (b) simulating refraction of the first ray at a first interface between the acoustic coupling medium and the part at a point of entry into the part; (c) tracing a second path of the first ray through the part from the point of entry to a second interface opposing the first interface; (d) simulating reflection of the first ray at the second interface; (e) tracing a third path of the first ray through the part from the second interface to a point of exit; (f) simulating refraction of the first ray at the first interface at the point of exit; and (g) tracing a fourth path of the first ray through the acoustic coupling medium, which fourth path terminates at the receive location on the ultrasonic transducer array. 
     Another aspect of the subject matter disclosed in detail below is a system for quantitatively evaluating the expected ultrasonic inspectability of a designed part, which system comprises a computer configured (e.g., programmed) to perform operations corresponding to the steps of the above-described method. 
     Other aspects of methods for quantitatively evaluating the expected ultrasonic inspectability of a designed part are disclosed below. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The features, functions and advantages discussed in the preceding section can be achieved independently in various embodiments or may be combined in yet other embodiments. Various embodiments will be hereinafter described with reference to drawings for the purpose of illustrating the above-described and other aspects. None of the diagrams briefly described in this section are drawn to scale. 
         FIG.  1 A  is a diagram representing an ultrasonic transducer transmitting ultrasonic waves into a part. An acoustic coupling medium between the transducer and the part is not shown. 
         FIG.  1 B  is a diagram representing an ultrasonic transducer receiving ultrasonic waves which have been reflected from an interface at the back of a part, which interface opposes the interface between the part and an acoustic coupling medium (not shown). 
         FIG.  2    is a diagram representing a ray of ultrasound impinging on an interface of two materials having differing indices of refraction. The diagram shows a scenario in which one part of the incident ray is reflected (in accordance with the law of reflection) and another part of the incident ray is refracted (in accordance with Snell&#39;s law) at the interface. 
         FIGS.  3 A- 3 C  are diagrams showing a path of a ray of ultrasound which is scattered away from a transmitting location by an inner mold line (IML) ramp with increasing ramp angles of: 30:1 ramp=1.9 degrees ( FIG.  3 A ); 20:1 ramp=2.86 degrees ( FIG.  3 B ); and 10:1 ramp=5.71 degrees ( FIG.  3 C ). The upper material is water; the lower material is carbon fiber-reinforced plastic (CFRP). 
         FIGS.  4 A and  4 B  are diagrams showing a path of a ray of ultrasound which is scattered away from a transmitting location by outer mold line (OML) pad-ups ( FIG.  4 A ) or by OML and IML ramps ( FIG.  4 B ) of a wing panel. 
         FIG.  5    is a diagram showing a path of a ray of ultrasound transmitted from a transmit aperture of width w A , scattered at a ramp, and received at a location which is separated from a center of the transmit aperture by a distance d R . 
         FIG.  6 A  is a diagram showing positional relationships of an ultrasonic transducer array, an acoustic coupling medium, and a part to be inspected, which positional relationships are defined before tracing the path of a ray of ultrasound transmitted by elements of a transmit aperture. 
         FIG.  6 B  a diagram showing a path of a ray (e.g., a centerline of a beam) of ultrasound propagating through the acoustic coupling medium depicted in  FIG.  6 A  after being transmitted by a first transmit aperture consisting of first and second elements. (The ramp in  FIG.  6 A  is the mirror image of the ramp in  FIGS.  6 B- 6 E .) 
         FIG.  6 C  a diagram showing a path of a ray of ultrasound propagating through the part after the ray depicted in  FIG.  6 B  has been refracted at an interface of the acoustic coupling medium and part. 
         FIG.  6 D  a diagram showing a path of a ray of ultrasound propagating through the part after the ray depicted in  FIG.  6 C  has been reflected by an IML ramp of the part. 
         FIG.  6 E  a diagram showing a path of a ray of ultrasound propagating through the acoustic coupling medium after the ray depicted in  FIG.  6 D  has been refracted at the interface of the acoustic coupling medium and part. 
         FIG.  7 A  is a diagram showing a path of a ray of ultrasound propagating through the acoustic coupling medium depicted in  FIG.  6 A  after being transmitted by a second transmit aperture consisting of second and third elements. 
         FIG.  7 B  is a diagram showing the path of the ray depicted in  FIG.  7 A  following refraction at the interface of the acoustic coupling medium and part, reflection at the IML ramp, and refraction at the interface of the acoustic coupling medium and part. 
         FIG.  8 A  is a graph the profile of a wing panel having a structure including ramps that scatter ultrasound. 
         FIG.  8 B  is a graph showing the NDI margin versus location for the wing panel whose profile is shown in  FIG.  8 A . 
         FIG.  9    is a diagram showing respective paths of three rays of ultrasound propagating through the acoustic coupling medium depicted in  FIG.  6 A  after being transmitted by a first transmit aperture consisting of first and second elements. 
         FIG.  10    is a flowchart identifying steps of a method for quantitatively evaluating the expected ultrasonic inspectability of a designed part in accordance with one embodiment. 
         FIG.  11    is a block diagram identifying components of a computer system suitable for executing automated data processing functions such as ray tracing and metric calculation. 
     
    
    
     Reference will hereinafter be made to the drawings in which similar elements in different drawings bear the same reference numerals. 
     DETAILED DESCRIPTION 
     For the purpose of illustration, methods for quantitatively evaluating the expected ultrasonic inspectability of a designed part will now be described in detail. However, not all features of an actual implementation are described in this specification. A person skilled in the art will appreciate that in the development of any such embodiment, numerous implementation-specific decisions must be made to achieve the developer&#39;s specific goals, such as compliance with system-related and business-related constraints, which will vary from one implementation to another. Moreover, it will be appreciated that such a development effort might be complex and time-consuming, but would nevertheless be a routine undertaking for those of ordinary skill in the art having the benefit of this disclosure. 
     The methods for quantitatively evaluating the expected ultrasonic inspectability of a designed part proposed herein are enabled by definition and calculation of an ultrasonic inspectability metric using computer simulation. In accordance with the embodiments disclosed herein, the computer simulation employs ray tracing. The ray tracing method used herein calculates the path of ultrasonic waves through a system with regions of varying propagation velocity, refracting interfaces, and reflecting interfaces. An interface may be linear (e.g., a ramp) or curved. Under these circumstances, wavefronts may bend, change direction, or reflect at an interface. Ray tracing solves the problem by propagating simulated narrow beams called rays through the medium. 
     For the purpose of illustration, various embodiments of a system for evaluating the inspectability of composite structures will be described in the context of aircraft manufacturing. However, it should be appreciated that the technology disclosed herein is equally applicable to manufacturing composite structure other than fuselages, wings, and stabilizers of an aircraft. 
     The baseline inspection for a wing panel made of composite material is pulse echo ultrasound. Ultrasound is transmitted from a transducer, travels through the part, and is received by the same transducer. For example,  FIG.  1 A  is a diagram representing an ultrasonic transducer  11  transmitting ultrasonic waves  6  into a part  14 . An acoustic coupling medium between the ultrasonic transducer  11  and the part  14  is not shown. The part  14  has an interface  20  (e.g., a part—air interface) which reflects the ultrasonic waves  6  back toward the ultrasonic transducer  11 .  FIG.  1 B  is a diagram representing the ultrasonic transducer  11  receiving ultrasonic waves  8  which have been reflected from the interface  20 . The ultrasonic transducer  11  converts impinging ultrasound into electrical signals which carry information indicative of the structural integrity of the part  14 . 
     As previously mentioned, the ray tracing method used herein calculates the path of ultrasonic waves through a system with regions of varying propagation velocity and interfaces which refract and/or reflect.  FIG.  2    is a diagram including arrows representing a ray of ultrasound which is partially reflected and partially refracted. The arrow R 1  represents the path (hereinafter “path R 1 ”) of an incident ray of ultrasound propagating through a first material  22  at a velocity V L1 . In the example scenario depicted in  FIG.  2   , the incident ray having the path R 1  impinges on an interface  26  where the first material contacts a second material  24 . One portion of the incident ray is reflected at the interface  26  and continues to propagate at velocity V L1  in the first material  22  along a path represented by arrow R 2  (hereinafter “path R 2 ”). Because the first and second materials  22  and  24  have different indices of refraction, another portion of the incident ray is refracted at the interface and then propagates at velocity V L2  (V L1 ≠V L2 ) in the second material  24  along a path represented by arrow R 3  (hereinafter “path R 3 ”). 
     In accordance with the law of reflection, the angle between path R 1  of the incident ray and a line N normal to interface  26  and the angle between path R 2  of the reflected ray and line N normal to interface  26  are equal (θ 1 ). In accordance with Snell&#39;s law, the angle θ 2  between path R 3  of the refracted ray and line N normal to interface  26  may be calculated using the equation: 
     
       
         
           
             
               
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                 ⁢ 
                 
                   θ 
                   1 
                 
               
               
                 sin 
                 ⁢ 
                 
                   θ 
                   2 
                 
               
             
             = 
             
               
                 V 
                 
                   L 
                   ⁢ 
                   1 
                 
               
               
                 V 
                 
                   L 
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       FIGS.  3 A- 3 C  are diagrams showing a path of a ray of ultrasound which is scattered away from a transmitting location by an inner mold line (IML) ramp with increasing ramp angles of: 30:1 ramp=1.9 degrees ( FIG.  3 A ); 20:1 ramp=2.86 degrees ( FIG.  3 B ); and 10:1 ramp=5.71 degrees ( FIG.  3 C ). The upper material  22  is water; the lower material  24  is carbon fiber-reinforced plastic (CFRP). The water contacts the CFRP part at an interface  26 . The simulation results presented in  FIGS.  3 A- 3 C  were derived assuming that height h 1  of the water is 1.4″, whereas the height h 2  of the CFRP is 1.2″. 
     Each of  FIGS.  3 A- 3 C  depicts a scenario in which a ray of ultrasound propagates along a series of paths R 1  through R 4 . In each instance, the ray of ultrasound is transmitted from and returned to an ultrasonic transducer array not shown in  FIGS.  3 A- 3 C . More specifically, the ray propagates: through the water along path R 1  from a point of entry P 1  to the interface  26 ; through the CFRP along path R 2  from the interface  26  to an IML ramp  16 ; through the CFRP along path R 3  after reflection at the IML ramp  16 ; and through the water along path R 4  from the interface  26  to a point of exit P 2 . 
     The ellipse A in each of  FIGS.  3 A- 3 C  surrounds the point of entry P 1  and the point of exit P 2 . The point of entry P 1  is collocated at the center of the transmit aperture of the ultrasonic transducer array, which is in contact with the water; the point of exit P 2  is collocated at a receive location on the ultrasonic transducer array. As seen in  FIGS.  3 A and  3 B , the separation distance between points P 1  and P 2  when the ramp angle is 2.86 degrees (see  FIG.  3 B ) is greater than the separation distance when the ramp angle is 1.90 degrees (see  FIG.  3 A ). Analogously, the separation distance between points P 1  and P 2  when the ramp angle is 5.71 degrees (see  FIG.  3 C ) is greater than the separation distance when the ramp angle is 2.86 degrees (see  FIG.  3 B ). Thus, the simulation results confirmed that ultrasound scatters farther away from the ultrasound source (the center of the transmit aperture) with increasing ramp angle. 
       FIGS.  3 A- 3 C  show scattering of ultrasound away from the center of the transmit aperture due the presence of an IML ramp  16  in the material  24 . Undesirable scattering may also be caused by other structures in a wing panel configuration. 
     For example,  FIG.  4 A  shows a path of a ray of ultrasound which is scattered away from the center of a transmit aperture of an ultrasound transducer array  10  by an OML pad-up  34  of a part  14  (e.g., of a wing panel) having an OML skin  32 . The acoustic couplant between ultrasound transducer array  10  and part  14  is not shown in  FIG.  4 A . The ray of ultrasound propagates through the acoustic couplant along a path R 1 . At the interface of the acoustic couplant and OML pad-up  34 , the ray is refracted and then propagates through the part  14  and to an interface  20  along a path R 2 . Following reflection at the interface  20 , the ray propagates through the part  14  along a path R 3  and does not impinge on the ultrasound transducer array  10 . 
       FIG.  4 B  shows a path of a ray of ultrasound which is scattered away from the center of a transmit aperture of an ultrasound transducer array  10  by an OML ramp  36  and an IML ramp  16  of a part  14  (e.g., of a wing panel) having an OML skin  32 . The acoustic couplant between ultrasound transducer array  10  and part  14  is not shown in  FIG.  4 B . The ray of ultrasound propagates through the acoustic couplant along a path R 1 . At the interface of the acoustic couplant and OML ramp  36 , the ray is refracted and then propagates through the part  14  and to the IML ramp  16  along a path R 2 . Following reflection at the IML ramp  16 , the ray propagates through the part  14  along a path R 3  and does not impinge on the ultrasound transducer array  10 . 
     As previously mentioned, the methods for evaluating part inspectability proposed herein are enabled by definition and calculation of an ultrasonic inspectability metric.  FIG.  5    is a diagram showing the geometry involved in defining an inspectability metric named “NDI margin”. The downward arrow in  FIG.  5    represents a path R 1  of a ray of ultrasound transmitted from an ultrasound transducer array toward a reflective interface (not shown). After reflection, the ultrasound ray propagates along path R 2  and impinges at a receive location having coordinates (x r , y r ). The dashed line in  FIG.  5    indicates a distance d R , which is the separation distance between the center of receive aperture  15  and the receive location (x r , y r ). The receive aperture  15  has an aperture width w A . In a linear transducer array, the aperture width w A  equals the product of the number of elements being used multiplied by the size of one element (assuming each element has the same size). 
     In accordance with one pulse echo ultrasonic inspection technique, assume that the transmit aperture includes the same elements used to form the receive aperture. As seen in  FIG.  5   , if the separation distance d R  is greater than one-half of the aperture width w A , then the reflected ray will miss the receive aperture  15  and not be detected. Any deviation of the measured separation distance d R  from the allowed distance w A /2 may be measured using an ultrasonic inspectability metric. 
     In accordance with one proposed implementation, the ultrasonic inspectability metric is expressed by the following equation: 
                     NDI   ⁢         margin     =           w   A     /   2       d   R       -   1             (   1   )               
This formula has the advantage that the NDI margin is a negative number when the simulated return ray from the inspected part misses (does not impinge upon) the receive aperture  15  of the ultrasound transducer array due to ray scattering effects.
 
     In practice, the receive aperture  15  is usually the same size as the transmit aperture. However, for the NDI margin check proposed herein, the receive aperture  15  may be any size. The NDI margin check may be performed with different receive apertures to identify which receive aperture provides the optimal NDI results. Thus, the actual NDI procedure could be altered based on the results of the NDI margin check calculations. 
     The NDI margin may be calculated in accordance with Eq. (1) at a multiplicity of equally spaced positions along an X or Y axis of a composite part. In the case where the part is a wing panel having a particular design, the X axis is aligned with the spanwise direction and the Y axis is aligned with the chordwise direction. If the NDI margin is negative at multiple locations in a region, that region may be classified as being un-inspectable, in which case that particular design of the wing panel may be rejected for manufacture. 
     One example of a method for quantitatively evaluating the expected ultrasonic inspectability of a designed part having a ramp will now be described for the purpose of illustration. The proposed methodology is equally applicable to designed parts having curved interfaces. The ray tracing and NDI margin check calculations may be performed by a computer system that is communicatively coupled to a database server in which CAD (or other geometric) models of designed parts are stored. To quantitatively evaluate the inspectability of a particular part design, the corresponding model is imported into the computer system from the database. For example, the designed part may include one or more ramps or other ultrasound-scattering structures. The system operator then interacts with an input interface of the computer system to select a material (e.g., CFRP) of the part having a first index of refraction. This will determine the speed of ultrasound propagation (hereinafter “ultrasound velocity”) through the part. In addition, the system operator selects a material (e.g., water or plastic) of an acoustic coupling medium having a second index of refraction. The second index of refraction is different than the first index of refraction; 
     Thereafter, the system operator defines an ultrasonic transducer array comprising a plurality of elements (e.g., individual piezoelectric transducers). Such definition includes: (a) the frequency of the transmitted ultrasound (e.g., 3.5 MHz); (b) the number of elements in the array (e.g., 64 elements); and (c) the size and spacing (pitch) of the elements in the array (e.g., a pitch equal to 0.08 inch). The pitch is the distance between the centers of two adjacent elements. 
     Next the system operator defines a position of the ultrasonic transducer array relative to the part, with the acoustic coupling medium disposed between the array and the part.  FIG.  6 A  is a diagram showing positional relationships of an ultrasonic transducer array  10 , an acoustic coupling medium  12 , and a part  14  to be inspected, which positional relationships are defined before tracing the path of a virtual ray of ultrasound transmitted by virtual elements of a transmit aperture during simulation. The example array depicted in  FIG.  6 A  has four elements  1 - 4  arranged along a line with constant pitch. The part  14  has an IML ramp  16 . The acoustic coupling medium  12  is in contact with the OML surface of part  14  at an interface  13 . 
     In accordance with one proposed implementation, a ray tracing algorithm is performed by a computer system using information input by a system operator. For example, the system operator selects the number of elements to be included in the transmit aperture. For a given ray of ultrasound, the center of the transmit aperture is treated as the point of origin of the ray. The ray tracing function is further configured to calculate the point at which a ray intersects an interface, such as the interface between an acoustic coupling medium and a part. At the intersection point, the ray tracing function also calculates the direction in which the ray of ultrasound will travel after crossing the interface using Snell&#39;s law. 
     Initially, the respective positions of ultrasonic transducer array  10 , acoustic coupling medium  12 , and part  14  are defined as shown in  FIG.  6 A . Thereafter, a first position of a transmit aperture of the ultrasonic transducer array  10  relative to part  14  is defined. This process includes the step of selecting the number of elements to be included in the transmit aperture. For the purpose of illustration, an example will now be described in which the transmit aperture includes two mutually adjacent elements. It should be appreciated that the position of the transmit aperture relative to the part during scanning may be changed either of two ways: (A) by including different pairs of elements in the transmit aperture for successive ray tracings while not moving the array relative to the part; or (B) by including the same pair of elements in the transmit aperture for successive ray tracings while moving the array relative to the part. In the following example described with reference to  FIGS.  6 B- 6 E,  7 A, and  7 B , the transmit aperture is scanned across the transducer array. 
       FIG.  6 B  is a diagram showing a path R 1  of a first ray (e.g., a centerline of a beam) of ultrasound propagating through acoustic coupling medium  12  after being transmitted by a first transmit aperture consisting of elements  1  and  2 . The center of the first transmit aperture is the mid-point between the centers of elements  1  and  2 . The path R 1  begins at the center of the first transmit aperture and terminates at the interface  13  where acoustic coupling medium  12  is in contact with the OML surface of part  14 . The ray tracing function (module) is configured to trace the path R 1  of the first ray through the acoustic coupling medium  12  based on the location of the center of the first transmit aperture and the steering angle. The ray tracing function is also configured to simulate refraction of the first ray at interface  13  as the first ray propagates from acoustic coupling medium  12  into part  14  at a point of entry. 
       FIG.  6 C  is a diagram showing a path R 2  of the first ray of ultrasound propagating through part  14  after the first ray has been refracted at interface  13 . Path R 2  begins at the point of entry into part  14  and terminates at the IML ramp  16 . The ray tracing function is further configured to trace the path R 2  of the first ray through the part  14  based on a first angle of refraction at interface  13 . The ray tracing function is also configured to simulate reflection of the first ray at IML ramp  16 . 
       FIG.  6 D  is a diagram showing a path R 3  of the first ray of ultrasound propagating through part  14  after the first ray has been reflected by IML ramp  16 . The path R 3  begins at the IML ramp  16  and terminates at the interface  13  at a point of exit from part  14 . The ray tracing function is configured to trace the path R 3  of the first ray through the part  14  based on the angle of reflection at IML ramp  16 . The ray tracing function is further configured to simulate refraction of the first ray at interface  13  as the first ray propagates from part  14  into acoustic coupling medium  12  at the point of exit. 
       FIG.  6 E  is a diagram showing a path R 4  of the first ray of ultrasound propagating through the acoustic coupling medium  12  after the first ray has been refracted at interface  13 . The path R 4  begins at the point of exit from part  14  and terminates at a receive location on the ultrasound transducer array  10 . The ray tracing function is configured to trace the path R 4  of the first ray through the acoustic coupling medium  12  based on a second angle of refraction at interface  13 . The ray tracing function is further configured to calculate the coordinates (x r , y r ) of the receive location. 
     The ray tracing process described with reference to  FIGS.  6 B- 6 E  may be repeated for each subsequent ray to be traced. For example,  FIG.  7 A  is a diagram showing a path R 1  of a second ray of ultrasound propagating through the acoustic coupling medium  12  after being transmitted by a second transmit aperture consisting of elements  2  and  3 . The center of the second transmit aperture is the mid-point between the centers of elements  2  and  3 . The path R 1  begins at the center of the second transmit aperture and terminates at the interface  13  where acoustic coupling medium  12  is in contact with the OML surface of part  14 . The ray tracing function is configured to trace the path R 1  of the second ray through the acoustic coupling medium  12  based on the location of the center of the second transmit aperture and the steering angle. The ray tracing function is also configured to simulate refraction of the second ray of ultrasound at interface  13  as the second ray propagates from acoustic coupling medium  12  into part  14  at a point of entry. 
       FIG.  7 B  is a diagram showing the path of the second ray depicted in  FIG.  7 A  following refraction at the interface  13 , reflection at IML ramp  16 , and refraction at interface  13 .  FIG.  7 B  shows paths R 2 , R 3 , and R 4  as the second ray propagates into and out of the part  14 . More specifically, the second ray propagates in succession along: (a) path R 2  in part  14  after the second ray has been refracted at interface  13 ; (b) path R 3  in part  14  after the second ray has been reflected by IML ramp  16 ; and (c) path R 4  in acoustic coupling medium  12  after the second ray has been refracted at interface  13 . 
     Path R 2  begins at the point of entry into part  14  and terminates at the IML ramp  16 . Path R 3  begins at the IML ramp  16  and terminates at the interface  13  at the point of exit from part  14 . The path R 4  begins at the point of exit from part  14  and terminates at a receive location on the ultrasound transducer array  10 . The ray tracing function is configured to perform the same steps previously described with reference to  FIGS.  6 C,  6 D, and  6 E . 
     In summary,  FIGS.  6 B- 6 E,  7 A, and  7 B  show tracing a ray that propagates from a center of a transmit aperture of an ultrasonic transducer array  10 , to the IML ramp  16 , and then to a receive location on the ultrasonic transducer array  10 . The computer system is further configured to calculate a respective value of an inspectability margin for each ray tracing based at least in part on the estimated distance between a center of the transmit aperture and the receive location. The computer system is further configured (e.g., programmed) to analyze all inspectability metric data generated by the simulations. This analysis includes comparing the values of the inspectability margin to a threshold value and then determining whether the comparison results indicate that the designed part is not inspectable. On the one hand, if a determination is made that the designed part is not inspectable, then the designed part is rejected for manufacture. On the other hand, if a determination is made that the designed part is inspectable, then the designed part is accepted for manufacture 
     For example,  FIG.  8 A  is a graph showing a profile of a wing panel having structure that scatters ultrasound. For example, the X axis may be parallel to the spanwise direction in the frame of reference of the wing panel. The above-described ray tracing method may be applied with respect to as many points along the X axis as are needed to cover the entire wing panel. The inspectability margin values calculated from the ray tracing data are stored in list format in association with respective X locations along the wing panel. (All data is stored in a non-transitory tangible computer-readable storage medium.) 
     The list of inspectability (NDI) margin values may be plotted to easily identify problem areas along the wing panel. For example,  FIG.  8 B  is a graph showing the NDI margin versus location for the wing panel whose profile is shown in  FIG.  8 A . The negative NDI margin values in the section that extends from x=4 to x=6 indicate that this section of the wing panel may be difficult to inspect and may need redesign. 
     In accordance with an alternative embodiment, instead of representing the ultrasound as a single ray emanating from the center of the transmit aperture, the simulation could create three rays: one ray at the center of the transmit aperture and two rays that bound the ultrasound beam. An NDI margin value could be calculated for each ray. A resulting NDI margin value could be calculated such as by taking the average, minimum or maximum of the three values. For example,  FIG.  9    shows respective paths R 1 -R 3  of three rays of ultrasound propagating through the acoustic coupling medium  12  after being transmitted by a transmit aperture consisting of elements  1  and  2 . 
       FIG.  10    is a flowchart identifying steps of a method  100  for quantitatively evaluating the expected ultrasonic inspectability of a designed part in accordance with one embodiment. A model of a part is imported into the computer system (step  102 ). Then the system operator selects a material of the part having a first index of refraction (step  104 ). In addition, the system operator selects a material of an acoustic coupling medium having a second index of refraction different than the first index of refraction (step  106 ). Then the system operator defines an ultrasonic transducer array comprising a plurality of elements (step  108 ); defines a position of the acoustic coupling medium between the ultrasonic transducer array and the part (step  110 ); and defines a plurality of positions of a transmit aperture of the ultrasonic transducer array relative to the part (step  112 ). 
     For each defined position of the transmit aperture, the method  100  further comprises: tracing a path of a respective ray from a center of the transmit aperture of the ultrasonic transducer array, into and out of the part, and then to a respective receive location on the ultrasonic transducer array (step  114 ). Also, the computer system calculates a respective value of an inspectability margin based at least in part on a respective distance between a center of the receive aperture and the respective receive location on the ultrasonic transducer array (step  116 ). Each value of the inspectability margin is compared to a threshold value (step  118 ). In alternative embodiments, step  118  may be performed for all ray tracings after all rays have been traced rather than after each respective ray is traced. 
     Following completion of step  118 , a determination is made whether all rays for different positions of the transmit aperture have been traced or not (step  120 ). On the one hand, if a determination is made that not all rays for different positions of the transmit aperture have been traced, the method  100  returns to step  112  and the next ray is traced. On the other hand, if a determination is made that all rays for different positions of the transmit aperture have been traced, the method  100  proceeds to step  122 . 
     In step  122 , a determination is made whether the NDI margin values indicate that the part is not ultrasonically inspectable or not. On the one hand, if a determination is made that the NDI margin values indicate that the part is ultrasonically inspectable, the part design is accepted for manufacture (step  124 ). On the other hand, if a determination is made that the NDI margin values indicate that the part is not ultrasonically inspectable, the part design is rejected for manufacture (step  126 ). 
       FIG.  11    is a block diagram identifying components of a computer system  200  suitable for executing automated data processing functions such as ray tracing and metric calculation. In accordance with one embodiment, computer system  200  comprises a memory device  202  (e.g., a non-transitory tangible computer-readable storage medium) and a processor  204  coupled to memory device  202  for use in executing instructions. More specifically, computer system  200  is configurable to perform one or more operations described herein by programming memory device  202  and/or processor  204 . For example, processor  204  may be programmed by encoding an operation as one or more executable instructions and by providing the executable instructions in memory device  202 . 
     Processor  204  may include one or more processing units (e.g., in a multi-core configuration). As used herein, the term “processor” is not limited to integrated circuits referred to in the art as a computer, but rather broadly refers to a controller, a microcontroller, a microcomputer, a programmable logic controller, an application specific integrated circuit, a field-programmable gate array, and other programmable circuits. 
     In the exemplary embodiment, memory device  202  includes one or more devices (not shown) that enable information such as executable instructions and/or other data to be selectively stored and retrieved. In the exemplary embodiment, such data may include, but is not limited to, material properties of metallic and composite materials, characteristics of ultrasonic waves, modeling data, imaging data, calibration curves, operational data, and/or control algorithms. In the exemplary embodiment, computer system  200  is configured to perform a ray tracing function as well inspectability metric calculations. Alternatively, computer system  200  may use any algorithm and/or method that enables the methods and systems to function as described herein. Memory device  202  may also include one or more non-transitory tangible computer-readable storage media, such as, without limitation, dynamic random access memory, static random access memory, a solid state disk, and/or a hard disk. 
     In the exemplary embodiment, computer system  200  further comprises a display interface  206  that is coupled to processor  204  for use in presenting information to a user. For example, display interface  206  may include a display adapter (not shown) that may couple to a display device  208 , such as, without limitation, a cathode ray tube, a liquid crystal display, a light-emitting diode (LED) display, an organic LED display, an “electronic ink” display, and/or a printer. 
     Computer system  200 , in the exemplary embodiment, further comprises an input interface  212  for receiving input from the user. For example, in the exemplary embodiment, input interface  212  receives information from an input device  210  suitable for use with the methods described herein. Input interface  212  is coupled to processor  204  and to input device  210 , which may include, for example, a joystick, a keyboard, a pointing device, a mouse, a stylus, a touch sensitive panel (e.g., a touch pad or a touch screen), and/or a position detector. 
     In the exemplary embodiment, computer system  200  further comprises a communication interface  214  that is coupled to processor  204 . In the exemplary embodiment, communication interface  214  communicates with at least one remote device, e.g., a transceiver  216 . For example, communication interface  214  may use, without limitation, a wired network adapter, a wireless network adapter, and/or a mobile telecommunications adapter. A network (not shown) used to couple computer system  200  to the remote device may include, without limitation, the Internet, a local area network (LAN), a wide area network, a wireless LAN, a mesh network, and/or a virtual private network or other suitable communication means. 
     In the exemplary embodiment, computer system  200  further comprises simulation software that enables at least some of the methods and systems to function as described herein. In one proposed implementation, the simulation software includes a modeling module  218 , a ray tracing module  220 , and an analysis module  222 . These modules may take the form of code executed by the processor  204 . In the exemplary embodiment, modeling module  218  is configured to generate models of composite parts having ramps or other ultrasound-scattering structures; ray tracing module  220  is configured to produce and process ray tracings as described hereinabove; and analysis module  222  is configured to perform inspectability metric calculations and analysis of the inspectability metric data to determine the degree of inspectability of various part designs. 
     While methods for quantitatively evaluating the expected ultrasonic inspectability of a designed part have been described with reference to various embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the scope of the teachings herein. In addition, many modifications may be made to adapt the teachings herein to a particular situation without departing from the scope thereof. Therefore it is intended that the claims not be limited to the particular embodiments disclosed herein. 
     In the method claims appended hereto, any alphabetic ordering of steps is for the sole purpose of enabling subsequent short-hand references to antecedent steps and not for the purpose of limiting the scope of the claim to require that the method steps be performed in alphabetic order.