Method for computer analysis of as-programmed surface quality of composite structure

Abstract

To provide a method and a computer system for computer analysis of quality of an as-programmed surface of a composite laminate.SOLUTION: A method comprises: generating a first data set representing a first as-programmed top surface on the basis of, as-programmed ply definitions and a tool surface definition; generating a second data set representing coordinates of points of a first mesh on the as-programmed top surface, where the points form a first mesh; generating a third data set representing coordinates of points of a second mesh on the defined tool surface; calculating each angle of each mesh element of the first mesh relative to a corresponding mesh element of the second mesh; comparing each angle with an acceptable angle threshold; and, in response to the acceptable number of angles exceeding the acceptable angle threshold, programming a tow placement machine to fabricate a composite structure using the as-programmed ply definitions.SELECTED DRAWING: Figure 8A

Description

Technical Field

[0001] The present disclosure relates to methods for designing and manufacturing composite structures and components, and more particularly, to computer analysis of the surface quality of composite laminates.

Background Art

[0002] Composite structures and components are widely used in aircraft, aerospace, and other applications where materials with a high strength-to-weight ratio are required. Composite structures may be manufactured either manually or using automated equipment by progressively building a structure having multiple layers of thin composite tapes or tows (i.e., untwisted bundles of continuous filaments such as carbon or graphite fibers pre-impregnated with a thermosetting resin material such as epoxy) laid and laminated together layer by layer. These layers are often referred to as partial or full plies. In large structures that exceed the width of available materials, or in designs that can benefit from large unidirectional stress paths, each ply layer is typically made from multiple tape strips (hereinafter "tows") of material arranged such that they are close to each other or have edges that abut or overlap to some extent. Fiber reinforced composite laminates are typically constructed from plies having a constant fiber orientation. The stiffness of the laminate varies from panel to panel by reducing or increasing the plies.

[0003] Advanced fiber placement (also known as "tow placement technology") is a fully automated process for the production of composite laminates, combining the differential feeding function of filament winding with the compaction and cut-restart functions of automated tape laying. Various machines exist that can deposit different types of materials, namely fiber-reinforced thermosetting prepregs (pre-impregnated materials), fiber-reinforced thermoplastics, or dry fibers. Carbon fibers pre-impregnated with thermosetting resins are most commonly used in the aerospace industry; therefore, the fiber placement process described herein (hereinafter referred to as the "tow placement process") assumes a thermosetting material system.

[0004] Most tow placement systems have seven axes of motion and are computer-controlled. The axes of motion—three position axes, three rotation axes, and the axis that rotates the working mandrel—provide the flexibility of the tow placement machine in positioning the tow placement head over the part surface, enabling the production of complex composite parts. During the tow placement process, the tows of the slit prepreg tape are placed on the surface as bands of parallel fibers called courses (i.e., each course consists of multiple parallel tows). This technique allows the fibers to be curved and the tows to be cut and restarted individually, enabling the production of parts closer to their final shape and thus reducing scrap rates. The tow cutting and restarting function of the tow placement machine also allows for variations in course width. This can be used to eliminate gaps or overlaps between adjacent courses resulting from the geometric dimensions and the induced fiber courses.

[0005] Advanced tow placement has improved the ability to manufacture composite laminates, but some limitations remain. For example, the precise location of tow cuts / restarts relative to adjacent course or ply boundaries is determined by the coverage parameter. Tows are cut perpendicular to the fiber direction, resulting in non-smooth course boundaries and small triangular overlaps or gaps.

[0006] One process for designing, manufacturing, and inspecting composite parts lacks a robust method or tool for predicting the precise placement of materials. When the desired material form is a wide tape, the tape is cut in situ by a robotic material placement device. The resulting material has cut locations that are not fully defined by the engineering part definition. Often, many of these cut locations are close together. In the manufactured part, there are so many places where these cut locations are too close together that the resulting laminate has a significantly steeper inclination angle than indicated in the engineering part definition. [Overview of the project]

[0007] The subject matter disclosed below concerns methods for constructing composite parts using a wide range of tape materials, resulting in a bag-side surface smoother than the smoothness available using state-of-the-art methods. Analytical methods that may be used to predict the undulation of the bag-side (upper) surface before manufacturing are also disclosed. By applying these construction and analytical techniques, it becomes possible to produce parts such as aircraft wing skins. In such cases, the surface quality of the composite laminate can be more easily verified, thereby reducing the inspection time of the parts.

[0008] The construction methods disclosed herein seek to improve composite laminates, particularly in steep slope (ply drop-off) regions, by reducing the large angles that become apparent to be closer to the nominal angles defined by the engineering part specifications. Using the tools presented herein, it is possible to (1) incorporate engineering and manufacturing part specifications, (2) simulate placements that can be performed by robotic placement equipment, and (3) generate the resulting simulated bag-side (upper) surface and analyze the simulated surface for local undulations.

[0009] Any issues arising during part inspection due to manufacturing details appear to affect subsequent parts in the production sequence. Reworking according to engineering or manufacturing specifications is expensive and time-consuming. Without analytical methods, there is no way to demonstrate that any engineering rework improves inspection quality. The analytical methods described in this disclosure predict local surface undulations. The results can then be used to iterate on part designs before and independently of manufacturing, and to verify the resulting surface quality.

[0010] As used herein, the terms “bag-side surface” and “top surface” of a composite laminate are used synonymously to mean the surface of the composite laminate opposite to the tool-side surface that contacts the tool surface. For example, assuming a fixed coordinate system relative to a flat tool surface, a pair of points on the bag-side and tool-side surfaces having the same X and Y coordinates are separated by a distance in the Z direction equal to the thickness of the laminate. If the tool surface is not flat, the orientation and position of the X-Y-Z coordinate system may be changed to accommodate the undulations of the tool surface, for example, by aligning the Z axis perpendicular to the tool surface at each point. As used herein, the term “as-designed top surface” means data representing a simulated top surface defined by engineering part specifications (without assuming crenulated ply edges at ply boundaries). Furthermore, as used herein, the term “as-programmed top surface” means data representing a simulated top surface defined by manufacturing part specifications (with assuming crenulated ply edges at ply boundaries).

[0011] Various embodiments of methods for computer analysis of programmed surface quality of composite structures will be described in some detail below, one or more of these embodiments may be characterized by one or more of the following aspects.

[0012] One aspect of the subject matter disclosed in detail below is a method for computer analysis of the quality of programmed surfaces of composite structures. The method includes (a) generating a first dataset representing a first programmed top surface of a composite structure based on a plurality of initial programmed ply specifications and a tool surface specification representing a defined tool surface; (b) generating a second dataset representing the coordinates of a plurality of points on the first programmed top surface, which are arranged to form a first mesh containing a plurality of mesh elements; (c) generating a third dataset representing the coordinates of a plurality of points on a defined tool surface, which are arranged to form a second mesh containing a plurality of mesh elements; (d) calculating the respective angles of each mesh element of the first mesh with respect to the corresponding mesh elements of the second mesh; and (e) comparing each angle calculated in step (d) with an acceptable angle threshold. According to one embodiment, the method further includes controlling a display screen to display a symbol indicating an angle that exceeds the acceptable angle threshold. According to another embodiment, the method further includes programming a tow-positioning machine to fabricate a composite structure according to a plurality of initial programmed ply specifications in response to a number of acceptable angles exceeding an acceptable angle threshold in step (e).

[0013] Another aspect of the subject disclosed in detail below is a computer system comprising a processor and a non-transient, tangible, computer-readable storage medium. The non-transient, tangible, computer-readable storage medium stores executable code, which is configured to enable the processor to perform data processing operations that carry out steps (a) through (e) of the method described in the preceding paragraph.

[0014] A further aspect of the subject matter disclosed in detail below is a method for computer analysis of the programmed surface quality of composite structures. The method includes (a) obtaining data representing a defined tool surface; (b) obtaining a designed geometric ply specification for a composite structure from an engineering source, wherein each ply specification includes fiber orientation data and ply edge data; (c) using the designed geometric ply specification to generate a tool path specification and a shape specification including centerline data for each tow of each ply; (d) using the tool path specification and a shape specification to generate a plurality of initial programmed ply specifications for each ply; (e) generating a first dataset representing a first programmed top surface of a composite structure based on the plurality of initial programmed ply specifications and the tool surface specification; (f) generating a second dataset representing the coordinates of a plurality of points on the first programmed top surface, which are arranged to form a first mesh including a plurality of mesh elements; (g) calculating the respective angles of each mesh element of the first mesh with respect to the defined tool surface; and (h) comparing each angle calculated in step (g) with an acceptable angle threshold.

[0015] According to one embodiment, the method described in the preceding paragraph further includes (i) generating a plurality of revised programmed ply specifications in accordance with angles exceeding an acceptable angle threshold; (j) generating a third dataset representing a second programmed top surface of a composite structure based on the plurality of revised programmed ply specifications and tool surface specifications; (k) generating a fourth dataset representing the coordinates of a plurality of points on the second programmed top surface, which are arranged to form a second mesh comprising a plurality of mesh elements; (l) calculating the respective angles of each mesh element of the second mesh with respect to the defined tool surface; and (m) comparing each angle calculated in step (l) with an acceptable angle threshold.

[0016] Other aspects of methods for computer analysis of programmed surface quality of composite structures are disclosed below.

[0017] The features, functions, and advantages described above may be realized individually in various embodiments, or in combination in yet another embodiment. For the purpose of illustrating the above-described and other embodiments, various embodiments will now be described with reference to the drawings. [Brief explanation of the drawing]

[0018] [Figure 1] This figure illustrates the relationship between a designed ply drop-off schedule and a cross-sectional view of a composite laminate having an interior ply drop-off region consisting of ply drops positioned and spaced apart according to the slope on the exterior and the designed ply drop-off schedule. The figure shows the edges of the plies with fiber orientation (relative to the coordinate system) as follows: 0 degrees (---), 90 degrees (---), 45 degrees (---), and -45 degrees (----). [Figure 2] Figures 2 and 3 are parallel diagrams showing the relationship between the designed ply drop-off schedule shown in Figure 1 (see Figure 2) and the programmed ply drop-off schedule showing the small, toothed ply edges resulting from the material morphology and manufacturing equipment (see Figure 3). The fiber orientation of the edges of the plies depicted in Figures 2 and 3 is shown by the same dashed and solid line scheme used in Figure 1. [Figure 3] Figures 2 and 3 are parallel diagrams showing the relationship between the designed ply drop-off schedule shown in Figure 1 (see Figure 2) and the programmed ply drop-off schedule showing the small, toothed ply edges resulting from the material morphology and manufacturing equipment (see Figure 3). The fiber orientation of the edges of the plies depicted in Figures 2 and 3 is shown by the same dashed and solid line scheme used in Figure 1. [Figure 4]This figure shows a designed ply dropoff schedule for one embodiment of a slope in a composite laminate, transitioning in the manner of a ply dropoff region 24 from a first constant-thickness area 34a having N plies to a second constant-thickness area 34b having N-19 plies. That is, the ply dropoff region contains 19 ply drops. For example, the number of N plies may be equal to 81, as seen in the embodiment depicted in Figure 1. The fiber orientation of the plies with edges depicted in Figure 4 is shown by the same scheme as the dashed and solid lines used in Figure 1. In the embodiment depicted in Figure 4, the desired drop ratio is 20:1. If the thickness of each ply is 0.0076 inches, the designed spacing between edges is 20 × 0.0076 = 0.152 inches. [Figure 5] This diagram shows a top view of a single course consisting of 20 tows laid and cut by an automatic tow-laying machine (also known as a tape-laying machine). Cuts for each tow are made where the tow's centerline intersects an exemplary designed ply boundary. The virtual ply boundary has a straight edge, while the course includes two smaller toothed ply edges extending from both ends of the straight ply edge. [Figure 5A] This diagram shows the top surface of a portion of a ply consisting of a toe with cuts that define the excess (overfill) and insufficient (underfill) areas relative to the designed ply boundary, indicated by dashed rectangles. [Figure 6] This figure shows a more enlarged area of ​​the programmed ply dropoff schedule depicted in Figure 3. In this embodiment, the number of plies in one constant thickness area is N=81, and the slope includes 19 ply drops. [Figure 7] This diagram shows a programmed ply drop-off schedule. It is designed so that ply edges with small teeth are intentionally spaced apart from each other to avoid multiple ply edges intersecting in a proximity region. [Figure 8A]Figures 8A and 8B are respective portions of a flowchart identifying steps of a method of using a computer to analyze a pride drop-off region of a simulated composite material structure, according to one proposed embodiment. [Figure 8B] Figures 8A and 8B are respective portions of a flowchart identifying steps of a method of using a computer to analyze a pride drop-off region of a simulated composite material structure, according to one proposed embodiment. [Figure 9] A flowchart identifying steps of an algorithm executed by a computer to calculate respective angles of each mesh element of a first mesh with respect to corresponding mesh elements of a second mesh. The first mesh includes a plurality of points on a programmed upper surface, and the second mesh includes a plurality of points on a defined tool surface. [Figure 10] A figure representing a mesh, according to one proposed embodiment. The mesh includes a plurality of points (vertices) arranged within an equilateral triangle array. Each point has respective X and Y coordinates within an X-Y-Z coordinate system. In this example, the Z coordinate (not shown in FIG. 10) is equal to zero for all points. [Figure 10A] A figure representing triangular mesh elements and vectors perpendicular to the triangular mesh elements. [Figure 11] A block diagram identifying components of a computer system suitable for performing the automated data processing functions disclosed herein. DETAILED DESCRIPTION OF THE INVENTION

[0019] Reference will now be made to the drawings, wherein like elements in different drawings are numbered alike.

[0020] Exemplary embodiments of methods for computer analysis of programmed surface quality of composite structures are described in some detail below. However, not all features of actual embodiments are described herein. Those skilled in the art will understand that in developing such embodiments, it is necessary to make decisions specific to numerous embodiments in order to achieve the developer's particular objectives, such as complying with different system-related constraints and business-related constraints depending on the embodiment. Furthermore, those skilled in the art will understand that the effort required for such development is complex and time-consuming, but is a predetermined matter to be addressed by those who benefit from this disclosure.

[0021] The innovative methodologies proposed herein may, without limitation, be used in connection with the design and manufacture of composite structures and components used in a variety of applications, including aircraft, spacecraft, ships, military aircraft, automobiles, trucks, buses, vessels, bridges, rotor blades for aircraft, rotor blades for power generation such as wind turbines, and other suitable structures and components. Accordingly, it will be recognized and understood by those skilled in the art that the methods of this disclosure can be used in any number of applications, including the design and manufacture of composite structures and components.

[0022] As mentioned above, when tape is cut in situ by a robotic material placement device, the resulting material has cut locations that are not fully specified by the engineering part specifications. Often, many of these cut locations are close together. In the manufactured part, there are so many places where these cut locations are too close together that the resulting laminate has a much steeper inclination angle than indicated in the engineering part specifications.

[0023] A typical method for defining ply boundaries in composite parts treats each orientation similarly. One characteristic of this type of specification is that the trimming of these plies is independent of the fiber orientation in the composite material used. Current manufacturing equipment operates under the constraint that the material is cut perpendicular to the fiber orientation. The exclusion of this manufacturing requirement results in fabricated parts that differ from engineering part specifications, particularly in ply drop-off areas. Current methods for separating plies within these drop-off areas aim to produce a smooth transition from thick to thin regions. Nominally, the steepest slope desired has a drop ratio of 20:1. This value is defined by the distance between two adjacent ply edges being 20 times the material thickness, which is equal to 2.87 degrees. However, when additional manufacturing cuts are made, the resulting transition will include areas steeper and less steep than the specified slope. For example, there may be areas in these transitions that are estimated to have a slope angle equal to approximately 5 degrees, or a drop ratio of 10:1, meaning they are almost twice as steep as designed. These steep areas can be problematic because areas of excessive steepness mask the data collected by the ultrasonic component inspection equipment, thereby preventing data processing from verifying that the laminate quality is sufficient. Therefore, additional time is required during the inspection process to assess the quality of the laminate in locally steep areas. While it usually takes several hours to scan without any steep areas, exemplary parts containing steep areas may require several more hours to scan in order to verify the quality of the laminate at all points.

[0024] Improving the inspectability of composite parts is desirable, but current methods do not provide the data necessary to do so. To improve the inspectability of modern parts, a first article must be manufactured and inspected. Only by evaluating the inspection data and relating any indications by spatial location to the engineering part specifications can areas requiring improvement be identified. Further complicating this process is the significant importance of the strength, rigidity, and durability of parts such as composite wing skins. In the current process, after the first article, the wing skin, is manufactured, it is assembled with the rest of the structural components and often undergoes several verification tests against part failure. One reason such tests are performed is to demonstrate that the fabricated part has properties very similar to the designed part, thereby confirming that the difference between the engineering part specifications and the fabricated part is minimal.

[0025] The innovative methodology proposed herein uses a computer system to analyze the programmed surface quality of a composite structure. A tow-positioning machine is programmed to fabricate the composite structure. In this case, overfill and underfill at the ply boundaries (within the ply drop-off area) are adjusted (modified) to minimize local angles resulting from the back-side surface that exceed an acceptable angle threshold. As proposed herein, the modification of the ply boundaries does not appear as a change to the engineering part specification, but rather modifies the fabricated part.

[0026] Proceeding with such modifications without verifying the new structural performance of the manufactured parts carries the risk of insufficient prediction of the parts' performance. Performing further structural tests to verify performance is expensive and time-consuming. Therefore, it is strongly desirable to avoid any changes to the engineering or manufacturing process that could invalidate previous tests.

[0027] A method for computer analysis of the programmed surface quality of composite laminates is proposed herein. The method includes simulating the back-side surface of the composite laminate and calculating the local angles at multiple points on the back-side surface. By improving the sloped areas and bringing the maximum angle significantly closer to the average angle, the process proposed herein aims to reduce the time required to inspect a given part. If these slopes are areas of interest in structural verification testing, they differ from the engineering part specifications, and therefore some further benefit to the structural performance of the part may exist. Potentially, there may be a benefit of improved strain or damage resistance as a result of smoother slopes. Analysis of sloped areas is a function that does not exist in the current design process. By generating this additional information and feeding it back into the part design process before any part manufacturing, the design of a part can be improved by adjusting the slopes, thereby relaxing the requirements for part manufacturing.

[0028] Figure 1 shows the relationship between the designed ply drop-off schedule 30 and a cross-sectional view of a composite laminate 22 having an inclined surface 28 on the exterior and a ply drop-off region 24 within the interior, as illustrated by an exemplary simulation. The designed composite laminate 22 includes a stack of plies 26. The plies 26 within the ply drop-off region 24 have respective ply drops 32 that are positioned and spaced apart according to the designed ply drop-off schedule 30. This figure shows that each ply 26 of the designed composite laminate 22 has a ply boundary formed by its respective linear (without small toothed edges) 0-degree edge orientation. More specifically, ply drops with a fiber orientation of 0 degrees relative to the coordinate system are linear edges 2a indicated by alternating long and short dashed lines (―‐―), ply drops with a fiber orientation of 90 degrees relative to the coordinate system are linear edges 4a indicated by short dashed lines (‐‐‐‐), ply drops with a fiber orientation of 45 degrees relative to the coordinate system are linear edges 6a indicated by solid lines (――), and ply drops with a fiber orientation of -45 degrees relative to the coordinate system are linear edges 8a indicated by dashed lines of intermediate length (----). Again, it should be reiterated that all of these ply drops are simulated as linear edges with a 0-degree orientation and regular spacing.

[0029] The exemplary designed composite laminate 22 depicted in Figure 1 comprises a first constant-thickness area 34a having a first thickness, and a second constant-thickness area 34b having a second thickness greater than the first thickness. The intermediate portion of the designed composite laminate 22 connects the first constant-thickness area 34a to the second constant-thickness area 34b and includes a ply drop-off area 24. The intermediate portion includes a slope 28 on the exterior and a ply drop-off area 24 within the interior. In one embodiment depicted in Figure 1, the first constant-thickness area 34a contains 62 plies, the second constant-thickness area 34b contains 81 plies, and the ply drop-off area 24 contains 19 ply drops (81-19=62).

[0030] Figure 2 shows a designed ply drop-off schedule 30 that includes only straight ply edges, while Figure 3 shows a programmed ply drop-off schedule 40 that includes both straight ply edges and ply edges with small teeth. The ply edges with small teeth result from the material form and the type of manufacturing equipment. Figures 2 and 3 are shown side by side to illustrate the relationship between the designed ply drop-off schedule 30 and the programmed ply drop-off schedule 40. The fiber orientation of the plies with straight edges depicted in Figure 2 is shown by the same scheme as the dashed and solid lines used in Figure 1.

[0031] Figure 3 shows only the simulated portion of each ply within a small area of ​​the programmed composite laminate. Some of the ply boundaries have straight edges 2b and 4b, while others have finely toothed edges 6b and 8b. More specifically, drops of plies with a 0-degree fiber orientation have a straight edge 2b with a 0-degree orientation, drops of plies with a 90-degree fiber orientation have a straight edge 4b ​​with a 0-degree orientation, drops of plies with a 45-degree fiber orientation have a finely toothed edge 6b, and drops of plies with a -45-degree fiber orientation have a finely toothed edge 8b.

[0032] Therefore, each right angle represents the intersecting side and cut edge of each toe end section oriented at ±45 degrees, and right angles connected in series indicate adjacent toe cut end sections that are part of the same ply. In contrast, straight lines without right angles indicate either a straight edge 2b formed by one toe side oriented at 0 degrees, or a straight ply edge 4b ​​formed by multiple mutually parallel ply cut edges oriented at 90 degrees. The solid circle in Figure 3 schematically depicts the overfill area (OFA), where two straight edges 2b and two small toothed edges 8b intersect, and their stacking of toe edges creates a slope angle that can be excessively steep.

[0033] Figure 4 shows a ply drop-off schedule 30 designed for one embodiment of a slope in a composite laminate that transitions in the manner of a ply drop-off region from a first area of ​​constant thickness having N plies to a second area of ​​constant thickness having N-19 plies. That is, the ply drop-off region contains 19 ply drops. The fiber orientation of the plies with edges depicted in Figure 4 is shown by the same scheme as the dashed and solid lines used in Figure 1.

[0034] Figure 5 shows a top view of a single course 20 consisting of 20 tows 10 laid and cut in parallel by an automatic tow placement (tape laying) machine. The starting point 18 is the origin that defines the manufacturing part specifications. Any point within the ply boundary may be used as the starting point. From the starting point 18, a line is projected in both directions to the ply boundary in the direction of the material specifications. This line is the centerline 12 of the ply. Parallel lines are drawn for each adjacent tow to completely cover the material across the ply boundary.

[0035] In one embodiment depicted in Figure 5, the designed (virtual) ply boundary 16 has three straight edges, while the fabricated ply boundary includes two smaller toothed edges extending from the ends on either side of the straight edges. Each toe 10 has its own centerline 12 (only one centerline is shown in Figure 5 to avoid complexity). The cut for each toe 10 is made at the point 14 where the centerline 12 of the toe intersects with the designed ply boundary 16. The toe is cut perpendicular to the fiber orientation (cross-cut). In courses where the fiber orientation is ±45 degrees, the cross-cut results in a smaller toothed ply boundary, and the small triangles become excess or provide gaps (hereinafter referred to as "overfill" and "underfill," respectively). In one embodiment depicted in Figure 5, the result is as follows: In other words, the eight toes 10 within the central section of the course 20 have aligned cuts that form a straight edge, while each pair of toes 10 adjacent to and on either side of the central section has cuts that form their respective smaller teethed edges.

[0036] Figure 5A shows the top view of a portion of a ply 26, which consists of tows 10 having cuts that define overfill and underfill areas relative to a designed ply boundary 16, indicated by a dashed rectangle. The ply boundary 16 defines the edge of the ply 26. The ply 26 includes a plurality of tows 10 oriented at Θ = 45 degrees with respect to the line of the ply boundary 16. The ply 26 further includes a plurality of tow interfaces positioned between adjacent tows 10. The tows 10 generally include a leading edge 46 and a trailing edge 48. In one embodiment depicted in Figure 5A, portions of the leading edge 46 and trailing edge 48 extend beyond the ply boundary 16.

[0037] As shown in Figure 5A, the tow 10 includes a center line 12. According to one embodiment, the tow 10 is positioned so that the center line 12, the ply boundary 16, and the front edge 46 or rear edge 48 converge or intersect. As a result, a portion or corner of the tow 10 extends to either side of the ply boundary 16, resulting in an overfill 52 and an underfill 54. In one particular embodiment in which the tow 10 is added to the ply boundary 16 at a 45-degree angle, the tow 10 includes a width 56(W) and the overfill 52 includes a height 58(h) which can be calculated using the following formula: h = W / 2√2

[0038] For example, given a width of 56 that is 3 inches (7.62 cm), the height 58 is approximately equal to 1.06 inches (2.69 cm). Similarly, the height 60 of the underfill 54 is essentially equal to the height 58.

[0039] Figure 6 shows a more enlarged area of ​​the programmed ply drop-off schedule 40 depicted in Figure 3. In this embodiment, there are 81 plies in the second constant-thickness area 34b, with the inclination containing 19 ply drops. The first constant-thickness area 34a contains 62 plies. In one embodiment depicted in Figure 6, the sum of the tow width and gap (between adjacent tows) is equal to 1.508 inches, while the offset between the adjacent small-toothed edges 6b of two plies with a 45-degree fiber orientation is 0.421 inches. The spacing between ply drops is 0.152 inches, as shown in Figure 4.

[0040] Using the methodology proposed herein, the configuration depicted in Figure 6 may be adjusted to eliminate excessively abrupt areas within the programmed composite laminate. Such excessively abrupt areas create areas within the fabricated part where ultrasound can be highly attenuated, making ultrasonic inspection more difficult and expensive. According to one proposed method, small toothed edges may be aligned so that they transition smoothly with reduced abruptness.

[0041] Figure 7 shows a programmed ply drop-off schedule 40. It is adjusted so that the small toothed edges 6b and 8b are intentionally separated from each other, avoiding areas where multiple ply edges intersect at a single location. For example, one simulation shows that the designed local slope of the ply drop-off area 24 depicted in Figure 7 was reduced (compared to the ply drop-off area 24 depicted in Figure 6), increasing the spacing between ply drops from 0.152 inches to 0.304 inches, while the misalignment between adjacent small toothed edges of two 45-degree prises was increased from 0.421 inches to 0.969 inches. As seen in Figure 7, the 45-degree and -45-degree small toothed edges are separated so that the overfill and underfill of the small toothed edges are aligned (hereinafter "aligned"). According to an alternative solution, the adjustment of the position of the peaks and valleys of the small toothed edges may be optimized without precise alignment. As a result of such adjustments, the tow placement machine may be programmed to fabricate a composite structure in which the overfill and underfill within the ply drop-off area are positioned to minimize the resulting tilt angle that exceeds an acceptable angle threshold.

[0042] Figures 8A and 8B are respective portions of a flowchart outlining the steps of a computer-based method 100 for analyzing ply drop-off areas of a simulated composite structure according to one proposed embodiment. Referring to Figure 8A, the designer acquires data representing defined tool surfaces and loads this data into a non-transient, tangible, computer-readable storage medium in a computer system (step 102). Furthermore, the designer acquires a designed geometric ply specification for the composite structure (hereinafter referred to as the "designed ply specification") from an engineering source (step 104). The designed ply specification may be defined using commercially available (COTS) composite design software. Such software may be obtained, for example, from Dassault Systèmes (CATIA - Computer Aided Three-Dimensional Interactive Application; Composite Workbench), Vistagy, Inc. of Waltham, Mass (FiberSim), Unigraphics Solutions, Inc. (PACKS), or other suitable sources.

[0043] Next, the computer system uses the designed ply specifications to generate tool path specifications and geometry specifications, including centerline data for each tow of each ply (step 106). More specifically, the geometric ply specifications may be input to a computer-aided manufacturing (CAM) software program to generate numerically encoded tool path specifications, including centerline data for each tow, along with the relevant drop or launch status for each tow at each centerline position. The numerically encoded tool path specifications include data for each tow required to cover the geometric ply geometry within the gap and overlap limits of the manufacturing specification used. The designed ply specifications may be converted to numerically encoded tool path specifications by known software developed by machine tool developers, such as Ingersoll, Cincinnati Lamb, ElectoImpact, and other sources. Next, the computer system uses the tool path specifications and geometry specifications to generate a number of initial programmed ply specifications for each ply (step 108).

[0044] Referring further to Figure 8A, the computer system is further configured to generate a first dataset representing the initial programmed top surface of the composite structure to be fabricated (step 110). The computer system then generates a second dataset representing the coordinates of multiple points in order to form a first mesh on the first (e.g., initial) programmed top surface (step 112), and generates a third dataset representing the coordinates of multiple points in order to form a second mesh on the defined tool surface (step 114). The first and second meshes are required to be aligned with each other for subsequent analysis.

[0045] Figure 10 is a diagram representing a mesh 50 according to one proposed embodiment. The mesh 50 includes a plurality of points 42 (vertices) arranged in an equilateral triangle array. Each point 42 has its own X and Y coordinates in the X-Y-Z coordinate system. In this embodiment, the Z coordinate (not shown in Figure 10) is equal to zero for all points 42. In this embodiment, the mesh 50 includes a plurality of points 42 arranged to form triangular mesh elements 44. The triangles may be equilateral triangles. More specifically, the vertices of each triangular mesh element 44 are formed by a pair of three adjacent points 42. The size of the mesh elements is very important; mesh elements that are too large will not show sufficient detail, and mesh elements that are too small will not represent the covered material as well. The calculation software includes a process called adaptive meshing, which is configured to optimize the size of the elements where finer detail is desired.

[0046] After the first and second meshes are generated and aligned, the computer system calculates the respective angles of each mesh element of the first mesh relative to the corresponding mesh elements of the second mesh (step 116). Optionally, the computer system also converts these angles into slope ratios. The computer system is further configured to compare each angle to an acceptable angle threshold (step 118). The computer system includes a graphics processor for controlling the display screen of a display device. The graphics processor is configured to display symbols (for viewing by the designer) indicating any angle that exceeds the acceptable angle threshold (step 120).

[0047] Next, referring to Figure 8B, Method 100 proceeds to the determination block 122. The designer determines whether the number of excessively steep angles is acceptable (step 122). On the other hand, if step 122 determines that the number of excessively steep angles is acceptable, Method 100 proceeds to program the tow-positioning machine to fabricate the composite structure according to multiple programmed ply specifications (step 136). The data is typically sent to a numerically encoded custom controller to drive the tow-positioning machine.

[0048] On the other hand, if step 122 determines that the number of excessively steep angles is unacceptable, the designer inputs commands and data into the computer system to generate multiple revised programmed ply specifications depending on one or more excessive angles (step 124). Referring further to Figure 8B, the computer system is further configured to generate a new (e.g., fourth) dataset representing the next programmed top surface of the composite structure to be fabricated (step 126). The data representing the next programmed top surface differs from the data representing the initial programmed top surface. The difference corresponds to the adjustment data input by the designer, which represents modifications adapted to reduce the number of excessively steep angles in the inclined portion of the programmed composite laminate. The computer system then generates a new (e.g., fifth) dataset representing the coordinates of multiple points to form a third mesh on the next programmed top surface (step 128). The third mesh is aligned with the second mesh to enable further analysis.

[0049] After the third mesh is generated and aligned with the second mesh, the computer system calculates the angle of each mesh element of the third mesh relative to the corresponding mesh element of the second mesh (step 130). The computer system is further configured to compare each calculated angle with an acceptable angle threshold (step 132). As previously mentioned, the computer system is configured to display a symbol indicating any angle that exceeds the acceptable angle threshold (step 134).

[0050] Referring further to Figure 8B, Method 100 proceeds to step 122. On the one hand, if step 122 determines that the number of excessively steep angles is acceptable, Method 100 proceeds to step 136. On the other hand, if step 122 determines that the number of excessively steep angles is not acceptable, the designer inputs commands and data into the computer system to generate further revised programmed ply specifications (step 124), etc. Steps 124 to 134 are performed sequentially for each iteration. The sequential iterations are performed until step 122 determines that the number of excessively steep angles is acceptable.

[0051] Figure 9 is a flowchart outlining the steps of algorithm 150 performed by the computer to calculate the respective angles of each mesh element of the first mesh with respect to the corresponding mesh elements of the second mesh. The first mesh includes multiple points on a programmed top surface, and the second mesh includes multiple points on a defined tool surface. Figure 10A is a diagram representing a triangular mesh element 44 having three vertices formed by points 42a to 42c. First, the computer system calculates first vectors V1 and second vectors V2 (see Figure 10A) corresponding to the first and second sides of the triangular mesh element 44 of the first mesh (step 152). Next, the computer system calculates a third vector V3 (see Figure 10A), which is perpendicular to the first and second vectors V1 and V2 (step 154). More specifically, each vector is calculated based on the (X, Y, Z) coordinates of the associated pair of mesh points. Perpendicular vectors are calculated by calculating the cross product of the two vectors.

[0052] In a similar manner, the computer system calculates a fourth vector perpendicular to the corresponding mesh element of the second mesh. The fourth vector includes multiple points on the defined tool surface. First, the computer system calculates the fifth and sixth vectors corresponding to the first and second sides of the triangular mesh element 44 of the second mesh (step 156). Next, the computer system calculates the fourth vector perpendicular to the fifth and sixth vectors (step 158). Then, the computer system calculates the angle between the two normal (third and fourth) vectors (step 160). More specifically, the angle is calculated by calculating the dot product of the two normal vectors.

[0053] Optionally, the computer system then converts the calculated angle to a slope at the corresponding X-Y position within the coordinate system of the defined tool surface (step 162). The coordinates of the center point of each triangle may also be calculated. If the defined tool surface is flat, the fourth (normal) vector is always straight in the same direction, e.g., the Z direction. In that case, no mesh calculation is necessary to derive the fifth and sixth vectors.

[0054] According to one proposed embodiment, slope angles less than 2.87 degrees are acceptable. On the other hand, angles greater than 5.75 degrees are not acceptable. Depending on the engineering specifications for a particular composite laminate product, simulations may be performed to identify an appropriate value T for the acceptable angle threshold. Here, 2.87 degrees < T < 5.75 degrees. The display results may be returned and plotted on top of the top mesh and / or numerically tabulated.

[0055] FIG. 11 is a block diagram identifying components of a computer system 200 suitable for performing the automated data processing functions disclosed herein. According to one embodiment, computer system 200 includes a memory device 202 (e.g., within a non-transitory tangible computer-readable storage medium) and a processor 204 connected to the memory device 202 for use in executing instruction commands. More specifically, computer system 200 can be configured to perform one or more operations described herein by programming the memory device 202 and / or the processor 204. For example, processor 204 can be programmed by encoding the operations as one or more executable instruction commands and providing the executable instruction commands to the memory device 202.

[0056] The processor 204 may include one or more processing units (for example, in a multi-core configuration). As used herein, the term “processor” is not limited to integrated circuits referred to as computers in the art, but rather broadly refers to controllers, microcontrollers, microcomputers, programmable logic controllers, application-specific integrated circuits, field-programmable gate arrays, and other programmable circuits.

[0057] In exemplary embodiments, the memory device 202 includes one or more devices (not shown) that enable the selective storage and retrieval of information such as executable instructions and / or other data. In exemplary embodiments, such data may include, but is not limited to, material properties of metals and composite materials, ultrasonic properties, modeling data, imaging data, calibration curves, operating data, and / or control algorithms. In one exemplary embodiment, the computer system 200 is configured to simulate a top surface, form a mesh on the simulated top surface, and then perform an analysis to generate a tilt angle as a function of position. Alternatively, the computer system 200 may use any algorithm and / or method that enables the method and system to function as described herein. The memory device 202 may also include, non-limited, one or more non-transient, tangible, computer-readable storage media, such as dynamic random-access memory, static random-access memory, semiconductor disks, and / or hard disks.

[0058] In an exemplary embodiment, the computer system 200 further comprises a display interface 206 connected to a processor 204 for use in presenting information to a user. For example, the display interface 206 may include, for example, a display adapter (not shown) that can be coupled to a display device 208 such as a cathode ray tube, liquid crystal display, light-emitting diode (LED) display, organic LED display, "electronic ink" display, and / or printer.

[0059] In exemplary embodiments, the computer system 200 further comprises an input interface 212 for receiving user input. For example, in exemplary embodiments, the input interface 212 receives information from an input device 210 suitable for use with the methods described herein. The input interface 212 is connected to a processor 204 and the input device 210. The input device 210 may include, for example, a joystick, a keyboard, a pointing device, a mouse, a stylus, a touch-sensitive panel (e.g., a touchpad or touchscreen), and / or a position detector.

[0060] In an exemplary embodiment, the computer system 200 further comprises a communication interface 214 connected to a processor 204. In an exemplary embodiment, the communication interface 214 communicates with at least one remote device, for example, a transceiver 216. For example, the communication interface 214 may, but is not limited to, a wired network adapter, a wireless network adapter, and / or a mobile telecommunications adapter. The network (not shown) used to connect the computer system 200 to the remote device may, but is not limited to, 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 means of communication.

[0061] In an exemplary embodiment, the computer system 200 further comprises simulation software that enables at least a portion of the method and system to function as described herein. In one proposed embodiment, the simulation software includes a top surface generation module 218, a mesh generation module 220, and an analysis module 222. These modules may take the form of code executed by the processor 204. In an exemplary embodiment, the top surface generation module 218 is configured to generate a 3D model of a programmed top surface of a composite component or other ultrasonic scattering structure having an inclination; the mesh generation module 220 is configured to form and process a mesh as described herein; and the analysis module 222 is configured to perform inclination angle calculations and analysis of inclination angle data to determine whether each angle exceeds an acceptable angle threshold. The processor 204 is configured to control the display screen of the display device 208 to display symbols indicating any angle that exceeds an acceptable angle threshold.

[0062] Further exemplary and non-exclusive embodiments of this disclosure are described in the following paragraphs.

[0063] In one embodiment of the present disclosure, a method (100) for computer analysis of the quality of a programmed surface of a composite structure includes (a) generating a first dataset representing a first programmed top surface of a composite structure based on a plurality of initial programmed ply specifications and a tool surface specification representing a defined tool surface (110); (b) generating a second dataset representing the coordinates of a plurality of points (42) on the first programmed top surface, which are arranged to form a first mesh (50) comprising a plurality of mesh elements (44) (112); (c) generating a third dataset representing the coordinates of a plurality of points on a defined tool surface, which are arranged to form a second mesh comprising a plurality of mesh elements (114); (d) calculating the respective angles of each mesh element of the first mesh with respect to the corresponding mesh elements of the second mesh (116); and (e) comparing each angle calculated in step (d) with an acceptable angle threshold (118).

[0064] Optionally, the methods of the preceding paragraph further include controlling the display screen to display a symbol indicating an angle that exceeds an acceptable angle threshold (120).

[0065] Optionally, one of the methods described in the preceding paragraphs further includes programming a tow-positioning machine to fabricate a composite structure according to a plurality of initial programmed ply specifications in response to the fact that in step (e) an acceptable number of angles have exceeded an acceptable angle threshold (136).

[0066] Optionally, in one of the methods described in the preceding paragraphs, each mesh element of the first mesh is a triangular mesh element having three sides, each of which is shared by its adjacent triangular elements, except where it lies along the boundary of the first mesh.

[0067] Optionally, in one of the methods described in the preceding paragraph, step (d) includes calculating first and second vectors corresponding to the first and second edges of the triangular mesh elements of the first mesh (152), calculating a third vector perpendicular to the first and second vectors (154), calculating a fourth vector perpendicular to the defined tool surface (158), and calculating the angle between the third and fourth vectors (160).

[0068] Optionally, one of the methods in the preceding paragraph further includes converting the angle between the third and fourth vectors into a slope ratio (162).

[0069] Optionally, in one of the methods described in the preceding paragraph, each mesh element of the second mesh is a triangular mesh element having three sides, each of which is shared by its adjacent triangular element except where it lies along the boundary of the first mesh, and step (d) further comprises calculating fifth and sixth vectors corresponding to the first and second sides of the triangular mesh elements of the second mesh (156), the fourth vector being perpendicular to the fifth and sixth vectors.

[0070] Optionally, one of the methods described in the preceding paragraph further includes (f) generating a number of revised programmed ply specifications in accordance with angles exceeding an acceptable angle threshold (124), (g) generating a fourth dataset representing a second programmed top surface of a composite structure based on the number of revised programmed ply specifications and tool surface specifications (126), (h) generating a fifth dataset representing the coordinates of a number of points on the second programmed top surface that are arranged to form a third mesh containing a number of mesh elements (128), (i) calculating the respective angles of each mesh element of the third mesh with respect to the defined tool surface (130), and (j) comparing each angle calculated in step (i) with an acceptable angle threshold (132).

[0071] Optionally, one of the methods described in the preceding paragraphs further includes programming a tow-positioning machine to fabricate a composite structure in accordance with a number of revised programmed ply specifications in response to a number of acceptable angles exceeding an acceptable angle threshold in step (j) (136).

[0072] Optionally, in one of the methods described in the preceding paragraphs, the tow positioning machine is programmed to produce a composite structure in which the overfill and underfill within the ply drop-off region (24) are positioned such that the resulting angle exceeding a threshold is minimized.

[0073] In another embodiment of the present disclosure, a computer system (200) comprises a processor (204) and a non-transient, tangible, computer-readable storage medium (202) storing executable code. The executable code is configured to enable the processor to perform data processing operations, including the following operations: That is, (a) generating a first dataset representing a first programmed top surface of a composite structure based on a plurality of initial programmed ply specifications and a tool surface specification representing a defined tool surface (110); (b) generating a second dataset representing the coordinates of a plurality of points (42) on the first programmed top surface, which are arranged to form a first mesh (50) including a plurality of mesh elements (44) (112); (c) generating a third dataset representing the coordinates of a plurality of points on the defined tool surface, which are arranged to form a second mesh including a plurality of mesh elements (114); (d) calculating the respective angles of each mesh element of the first mesh with respect to the corresponding mesh elements of the second mesh (116); and (e) comparing each angle calculated in step (d) with an acceptable angle threshold (118).

[0074] Optionally, the computer system of the preceding paragraph further comprises a display screen (208). In this case, the executable code is further configured to allow the processor to control the display screen (120) to display a symbol indicating an angle exceeding an acceptable angle threshold.

[0075] Optionally, in one of the computer systems described in the preceding paragraph, each mesh element of the first mesh is a triangular mesh element having three sides, each of which is shared by its adjacent triangular elements, except where it lies along the boundary of the first mesh.

[0076] Optionally, in one of the computer systems described in the preceding paragraph, operation (d) includes calculating first and second vectors corresponding to the first and second edges of the triangular mesh elements of the first mesh (152), calculating a third vector perpendicular to the first and second vectors (154), calculating a fourth vector perpendicular to the defined tool surface (158), and calculating the angle between the third and fourth vectors (160).

[0077] Optionally, in one of the computer systems mentioned in the preceding paragraph, the executable code is further configured to allow the processor to convert the angle between the third and fourth vectors into a slope ratio (162).

[0078] Optionally, in one of the computer systems in the preceding paragraph, each mesh element of the second mesh is a triangular mesh element having three sides, each of the three sides being shared by its adjacent triangular elements except where it lies along the boundary of the first mesh, and operation (d) further comprises (156) calculating fifth and sixth vectors corresponding to the first and second sides of the triangular mesh elements of the second mesh, the fourth vector being perpendicular to the fifth and sixth vectors.

[0079] Optionally, in one of the computer systems described in the preceding paragraph, the executable code is further configured to enable the processor to perform data processing operations including: (f) generating a number of revised programmed ply specifications in accordance with angles exceeding an acceptable angle threshold (124); (g) generating a fourth dataset representing a second programmed top surface of a composite structure based on the number of revised programmed ply specifications and tool surface specifications (126); (h) generating a fifth dataset representing the coordinates of a number of points on the second programmed top surface that are arranged to form a third mesh containing a number of mesh elements (128); (i) calculating the respective angles of each mesh element of the third mesh with respect to the defined tool surface (130); and (j) comparing each angle calculated in step (i) with an acceptable angle threshold (132).

[0080] In another embodiment of the present disclosure, a method (100) for computer analysis of the programmed surface quality of a composite structure comprises: (a) obtaining data representing a defined tool surface (102); (b) obtaining a designed geometric ply specification for a composite structure from an engineering source (104), wherein each ply specification includes fiber orientation data and ply edge data; (c) using the designed geometric ply specification to generate a tool path specification and a shape specification including centerline data for each tow of each ply (106); and (d) using the tool path specification and the shape specification to generate an initial number of programmed specifications for each ply. The process includes (108) generating ply specifications, (e) generating a first dataset representing a first programmed top surface of a composite structure based on a plurality of initial programmed ply specifications and tool surface specifications, (110) generating a second dataset representing the coordinates of a plurality of points (42) on the first programmed top surface, which are arranged to form a first mesh (50) comprising a plurality of mesh elements (44), (g) calculating the respective angles of each mesh element of the first mesh with respect to the defined tool surface, (116) and (h) comparing each angle calculated in step (g) with an acceptable angle threshold, (118).

[0081] Optionally, the method of the preceding paragraph includes (i) generating a number of revised programmed ply specifications in accordance with angles exceeding an acceptable angle threshold (124), (j) generating a third dataset representing a second programmed top surface of a composite structure based on the number of revised programmed ply specifications and tool surface specifications (126), (k) generating a fourth dataset representing the coordinates of a number of points on the second programmed top surface that are arranged to form a second mesh containing a number of mesh elements (128), (l) calculating the respective angles of each mesh element of the second mesh with respect to the defined tool surface (130), and (m) comparing each angle calculated in step (l) with an acceptable angle threshold (132).

[0082] Optionally, one of the methods described in the preceding paragraphs further includes programming a tow-positioning machine to fabricate a composite structure in accordance with a number of revised programmed ply specifications in response to a number of acceptable angles exceeding an acceptable angle threshold in step (m) (136).

[0083] Optionally, in one of the methods described in the preceding paragraphs, the tow positioning machine is programmed to produce a composite structure in which the overfill and underfill within the ply drop-off region (24) are positioned such that the resulting angle exceeding a threshold is minimized.

[0084] In another embodiment of the present disclosure, a computer system (200) comprises a processor (204) and a non-transient, tangible, computer-readable storage medium (202) storing executable code. The executable code is configured to enable the processor to perform data processing operations, including: (a) obtaining data representing a defined tool surface (102); (b) obtaining a designed geometric ply specification for a composite structure from an engineering source (104), wherein each ply specification includes fiber orientation data and ply edge data; (c) using the designed geometric ply specification to generate a tool path specification and shape specification including centerline data for each tow of each ply (106); (d) using the tool path specification and shape specification to generate a plurality of initial programmed ply specifications for each ply (108); (e) initial multiple (110) generating a first dataset representing a first programmed top surface of a composite structure based on a number of programmed ply specifications and tool surface specifications; (f) generating a second dataset representing the coordinates of a plurality of points (42) on the first programmed top surface, which are arranged to form a first mesh (50) comprising a plurality of mesh elements (44); (g) calculating the respective angles of each mesh element of the first mesh with respect to the defined tool surface (116); and (h) comparing each angle calculated in operation (g) with an acceptable angle threshold (118).

[0085] The flowcharts and block diagrams in the various embodiments shown illustrate the structure, function, and operation of several possible embodiments of the apparatus and method in an exemplary embodiment. In this case, each block in the flowchart or block diagram may represent a module, segment, function, and / or part of a process or step. For example, one or more of the blocks are executable in hardware as program code, or as a combination of program code and hardware. When implemented in hardware, the hardware may take the form of an integrated circuit manufactured or configured to perform, for example, one or more operations in the flowchart or block diagram.

[0086] The methods described herein may be encoded as executable instructions embodied in a non-transient, tangible, computer-readable storage medium, including storage devices and / or memory devices. When such instructions are executed in a processing system or computer system, they cause system devices to perform at least a portion of the methods described herein.

[0087] Methods for computer analysis of programmed surface quality of composite material structures have been described with reference to various embodiments, and it will be understood by those skilled in the art that various modifications are possible and elements can be substituted with equivalents without departing from the scope of the teachings herein. In addition, numerous modifications can be made to adapt the teachings herein to specific circumstances without departing from the scope. Accordingly, the claims are not intended to be limited to the specific embodiments disclosed herein.

[0088] In the claims of the methods appended to this specification, the alphabetical order of the steps is intended solely to allow subsequent abbreviated references to preceding steps, and is not intended to limit the scope of the claims to require that the steps of the method be performed in alphabetical order.

[0089] When used in patent claims, the term “acceptable number” may be a positive integer or equal to zero. In the latter case, it indicates that the calculation result shows no angles exceeding the threshold of acceptable angles.

Claims

1. A method (100) for computer analysis of the quality of a programmed surface of a composite structure, comprising: (a) generating a first dataset representing a first programmed upper surface of the composite structure based on a plurality of initial programmed ply specifications and a tool surface specification representing a defined tool surface (110); (b) generating a second dataset representing the coordinates of a plurality of points (42) on the first programmed upper surface, the plurality of points being arranged to form a first mesh (50) including a plurality of mesh elements (44) (112); (c) generating a third dataset representing the coordinates of a plurality of points on the defined tool surface, the plurality of points being arranged to form a second mesh including a plurality of mesh elements (114); (d) calculating, for each mesh element of the first mesh, the respective angle with respect to the corresponding mesh element of the second mesh (116); and (e) comparing each angle calculated in step (d) with a threshold of acceptable angles (118).

2. The method of claim 1, further comprising controlling a display screen to display a symbol indicating an angle exceeding the threshold of acceptable angles (120).

3. The method of claim 1 or 2, further comprising programming a tow placement machine to fabricate the composite structure according to the plurality of initial programmed ply specifications in response to an acceptable number of angles exceeding the threshold of acceptable angles in step (e) (136).

4. The method of claim 1, wherein each mesh element of the first mesh is a triangular mesh element having three sides, and each of the three sides is shared by respective adjacent triangular elements, except when along the boundary of the first mesh.

5. Step (d) comprises: calculating a first vector and a second vector corresponding to a first side and a second side of the triangular mesh element of the first mesh (152); calculating a third vector perpendicular to the first vector and the second vector (154); calculating a fourth vector perpendicular to the defined tool surface (158); and 5. The method of claim 4, further comprising calculating (160) an angle between the third vector and the fourth vector.

6. 6. The method of claim 5, further comprising converting (162) the angle between the third vector and the fourth vector to a tilt rate.

7. 6. The method of claim 5, wherein each mesh element of the second mesh is a triangular mesh element having three sides, each of the three sides being shared by a respective adjacent triangular element except along a boundary of the first mesh, and step (d) further comprises calculating (156) a fifth vector and a sixth vector corresponding to a first side and a second side of the triangular mesh element of the second mesh, the fourth vector being perpendicular to the fifth vector and the sixth vector.

8. (f) generating a plurality of revised programmed ply prescriptions in response to angles exceeding the acceptable angle threshold (124); (g) generating a fourth data set representing a second programmed top surface of the composite structure based on the revised plurality of programmed ply definitions and the tool surface definition (126); (h) generating (128) a fifth data set representing coordinates of a plurality of points on the second programmed top surface, the plurality of points being arranged to form a third mesh including a plurality of mesh elements; (i) calculating (130) a respective angle of each mesh element of the third mesh relative to the defined tool surface; and 2. The method of claim 1, further comprising: (j) comparing (132) each angle calculated in step (i) to the acceptable angle threshold.

9. 10. The method of claim 8, further comprising: in response to an acceptable number of angles exceeding the acceptable angle threshold in step (j), programming (136) a tow placement machine to fabricate the composite structure in accordance with the revised plurality of programmed ply prescriptions.

10. 10. The method of claim 9, wherein the tow placement machine is programmed to fabricate the composite structure in which overfill and underfill in ply drop-off areas (24) are placed to minimize the resulting angle above the threshold.

11. A method (100) for computer analysis of the quality of a programmed surface of a composite structure, comprising: (a) obtaining data representing a defined tool surface (102); (b) obtaining designed geometric ply specifications for the composite structure from an engineering source (104), each ply specification including fiber orientation data and ply edge data; (c) using the designed geometric ply specifications to generate tool path specifications and shape specifications including centerline data for each tow of each ply (106); (d) using the tool path specifications and the shape specifications to generate an initial plurality of programmed ply specifications for each ply (108); (e) generating a first data set representing a first programmed upper surface of the composite structure based on the initial plurality of programmed ply specifications and a tool surface specification (110); (f) generating a second data set representing coordinates of a plurality of points (42) on the first programmed upper surface, the plurality of points being arranged to form a first mesh (50) including a plurality of mesh elements (44) (112); (g) calculating, for each mesh element of the first mesh, its respective angle with respect to the defined tool surface (116); and (h) comparing each angle calculated in step (g) with a threshold of an acceptable angle (118). **Claim 12** (i) generating a revised plurality of programmed ply specifications in response to angles exceeding the threshold of the acceptable angle (124); (j) generating a third data set representing a second programmed upper surface of the composite structure based on the revised plurality of programmed ply specifications and the tool surface specification (126); (k) generating a fourth data set representing coordinates of a plurality of points on the second programmed upper surface, the plurality of points being arranged to form a second mesh including a plurality of mesh elements (128); (l) calculating, for each mesh element of the second mesh, its respective angle with respect to the defined tool surface (130); and (m) further comprising comparing each angle calculated in step (l) with the threshold of the acceptable angle (132). The method according to claim 11.

13. 13. The method of claim 12, further comprising: in response to an acceptable number of angles exceeding the acceptable angle threshold in step (m), programming (136) a tow placement machine to fabricate the composite structure in accordance with the revised plurality of programmed ply prescriptions.

14. 14. The method of claim 13, wherein the tow placement machine is programmed to fabricate the composite structure in which overfill and underfill in ply drop-off areas (24) are placed to minimize the resulting angle above the threshold.

15. 1. A computer system (200) comprising a processor (204) and a non-transitory, tangible, computer-readable storage medium (202) having executable code stored thereon, the executable code configured to enable the processor to perform data processing operations including the operations of: (a) acquiring data representative of a defined tool surface (102); (b) obtaining (104) designed geometric ply prescriptions for a composite structure from an engineering source, each ply prescription including fiber orientation data and ply edge data; (c) generating tool path and shape prescriptions, including centerline data for each tow of each ply, using the designed geometric ply prescriptions (106); (d) generating an initial plurality of programmed ply prescriptions for each ply using the tool path prescription and the shape prescription (108); (e) generating a first data set representing a first programmed top surface of the composite structure based on the initial plurality of programmed ply definitions and a tool surface definition (110); (f) generating (112) a second data set representing coordinates of a plurality of points (42) on the first programmed top surface, the plurality of points being arranged to form a first mesh (50) including a plurality of mesh elements (44); (g) calculating (116) a respective angle of each mesh element of the first mesh relative to the defined tool surface; and (h) comparing (118) each angle calculated in act (g) to a threshold of acceptable angles.

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