A design algorithm to model fibre paths for manufacturing of structurally optimised composite laminates

TL;DR: This work develops a design for manufacturing (DFM) tool for the introduction in design of the manufacturing requirements and limitations derived from the fibre placement technology, which enables the automatic generation of continuous fibre paths for manufacturing.

About: This article is published in Composite Structures.The article was published on 2018-11-15 and is currently open access. It has received 14 citations till now. The article focuses on the topics: Design for manufacturability & Composite laminates.

Summary

1 Introduction

• Fibre-reinforced composites are traditionally designed by stacking plies built with a discrete set of constant fibre orientation angles: 0°, ±45° and 90° [1].
• Recently, a new manufacturing technology called continuous tow shearing (CTS) has been developed, avoiding gaps and overlaps at the expense of thickness variation [16,17].
• In addition, to overcome this issue, many authors have employed a functional parametrisation to represent the fibre paths.
• This method reduces the number of design variables an ease the consideration of manufacturing constraints while modelling continuous paths.
• Hence, generic capabilities for the design of fibre-steered laminates and analysis of manufacturing features are required [89].

2 Tool to design variable stiffness laminates for

• A software tool for manufacturing analysis and optimisation of fibre steering named FIPAM (Fibre Paths for Manufacturing) has been developed.
• It provides 6 a post-processing of the design configurations from structural optimisation prior to manufacturing.
• This tool enables the automatic generation of fibre paths (i.e., machine trajectories), imposing manufacturing requirements.
• Structural approximations of the Finite Element (FE) response are used to reduce the required number of FE analyses [92].
• The loading condition was shear force (1N) at the top and bottom edges.

2.1 Modelling of continuous fibre paths

• The objective of this step is to generate continuous paths following the optimal discrete fibre orientations.
• This process is repeated iteratively until the segments reach the boundary of the part or ply.
• Assuming the orientation of a segment to be always equal to the interpolated orientation at the starting point of this section introduces some inaccuracy to the generated curve.
• Measure minimum radius of curvature (section 3.2) and smooth the curve in case it does not comply with the minimum turning radius, also known as 8. Curve smoothing.
• The selection of the starting points is done iteratively, by choosing first a point contained in a parallel curve to the previous reference with an offset equal to the course width.

2.2 Modelling of manufacture compliant fibre paths

• In a second step, new fibre paths for manufacturing are modelled approaching the previously defined paths.
• Choosing one curve as starting path, the method consists of defining a feasible region where the next path should be placed to comply with the specifications on course width, maximum gap and maximum overlap.
• The feasible region where the fibre path must be contained to comply with the manufacturing constraints is defined by: a parallel curve to the current fibre path with a distance equal to the course width minus 12 the maximum overlap allowance, and a parallel offset of the course width plus the allowable gap .
• Any coverage different from 100% will result in the appearance of triangular gaps in the ply.
• When the contours of two adjacent courses intersect, tows will be dropped.

3 Analysis of manufacturing features of variable stiffness

• For the implementation of manufacturing constraints in the algorithms discussed in section 2, tools to analyse these manufacturing features are required.
• Specifically, methods to compute the gaps and overlaps of a particular fibre path design and to calculate the minimum curvature radius are presented.

3.1 Analysis of gaps and overlaps

• Gaps and overlaps are automatically modelled in CATIA, which enables an evaluation of this design constraint and a visual representation in the model.
• Select two adjacent paths to start 3. Compute edges of the fibre paths o Create parallel path: Distance = CourseWidth/2 17 o Extend and split parallel with curvature continuity to cover the surface 4. Compute intersection points of adjacent fibre path 5. Sort intersection points.
• Identify whether area limited by intersection points and path boundaries represents a gap or an overlap (if there is no intersection, the whole area between the boundaries will be either a gap or an overlap) 7. Perform measures of the gap/overlap regions: area and maximum size.
• For curves on surfaces, further measures of curvature can be defined: the geodesic curvature (]b), the normal curvature (]!), and the geodesic torsion (τr).
• This induces a deflection of the fibres in the out-of-plane direction, which does not represent an issue.

4.1 Design of flat square plate with a hole

• The variable stiffness design of a plate with a circular cut-out loaded in tension and optimised for strength has been undertaken.
• Initially, tow-dropping is not allowed and a constraint to limit the maximum allowable angle deviation from optimal has not been imposed.
• The resulting maximum angle deviation is lower than 22° for all plies and the average angle deviation is inferior to 8°.
• For comparison, it includes the results for the reference paths (that correspond to a 0° maximum deviation constraint) and the optimal paths when the constraint is not imposed.
• The gaps and overlaps of each design are modelled in Figure 10.

4.2 Design of a windshield front fairing

• This structure has a double curved shape with reinforcement areas.
• It is an aircraft component designed with conventional straight orientations (0°, ±45° and 90°).
• The objective is to provide a fibre path design complying with all the manufacturing constraints.
• For the 90° ply, the reference paths do not yield large overlaps and they can be completely eliminated with angle deviations below 3°.
• The gap area increases as a result of the objective to minimise overlaps, although in a much inferior proportion than the overlap area reduction, and, in every case, respecting the maximum allowable gap size constraint.

5 Conclusions

• The potential of fibre steering is limited by current manufacturing constraints of fibre placement technologies and design specifications.
• A novel approach to automatically model fibre paths based on structurally optimised fibre angle distributions and considering manufacturing requirements is proposed.
• This approach enables to design variable stiffness laminates with curvilinear paths as well as conventional complex structures that require fibre steering.
• The algorithms are designed to minimise gaps, overlaps and angle deviation.
• As the manufacturing variables are captured in the design process, variance between designed and manufactured parts can be reduced.

Figures

Figure 9. Flat square plate with a hole: reference paths optimised for structures and paths optimised for manufacturing with gap and overlap analysis for each ply (green: gap and blue: overlap)

Figure 2. Curve smoothing approach to comply with minimum turning radius constraint

Table 2. Analysis of results of ply 4 of flat square plate with a hole showing angle deviations, gaps and overlaps, and tow-drops that would be needed to remove the overlaps

Table 3. Analysis of results for the design of reference (Ref) and manufacturing (Mfg) fibre paths of windshield front fairing Case study Windshield front fairing Ply orientation (deg) 0 45 90 Description Ref.

Figure 1. Approach for fibre path modelling for manufacturing, including for each step (boxes): input and output variables (left and right side of boxes), conditions and constraints applicable (in bold at top side of boxes), and enablers and algorithms used (in italic at bottom side of boxes).

Figure 3. (a) Case study used and representation of modelled curves; (b) graph of the effect of refinement of interpolation on computation time; (c) graph of the effect of refinement on average angle deviation

Figure 11. Tow modelling of different design solutions with tow-dropping (coverage = 10% overlap; MCL= 80 mm) for ply 4 of flat square plate with a hole

Figure 4. Generation of two reference curves on a plate with a hole with course width = 25.4mm and different input values for gap/overlap proportion (coverage)

Figure 5. Process rationale to create fibre paths for manufacturing approaching reference curves

Figure 13. Definition of case study for windshield front fairing: dimensions, design and manufacturing constraints

Figure 8. Definition of case study for flat square plate with a hole: dimensions, design and manufacturing constraints

Figure 7. Geometrical interpretation of curvature of a curve at point P