Geodesic and Non-Geodesic Winding Patterns for Elliptical Elbow Pipes
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Solution Overview
Problem
Current filament winding technologies are limited to pattern design for circular section elbow pipes and lack effective methods for elliptical section elbow pipes, hindering the manufacturing efficiency and forming quality of composite elbow pipes.
Innovation Solution
A method involving geodesic and non-geodesic mathematical models is employed to determine the number of yarns and trajectory information for elliptical section elbow pipes, using continued fraction theory to design a uniformly covered and stable filament winding pattern.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If conventional pattern design methods are used for circular section elbow pipes, then the winding process is stable and uniform coverage is achieved, but the method cannot be applied to elliptical section elbow pipes
Solution Approach 1:
The patent transforms the elliptical section elbow pipe pattern design problem into a circular section equivalent problem by changing geometric parameters. It calculates equivalent radius and central angle based on elliptical geometry parameters (long axis a, short axis b, bending radius R, bending angle θ), then applies circular section winding formulas to obtain the pattern, achieving adaptability while maintaining precision
Solution Approach 2:
The patent introduces an intermediary coordinate transformation system that maps elliptical section coordinates to circular equivalent coordinates. By establishing transformation relationships between elliptical parameters and circular parameters, it enables the use of established circular section patterns for elliptical sections
2Adaptability or versatility
If commercially available software is used for pattern design, then elliptical section elbow pipes can be designed, but the specific method is confidential and not publicly reported
Solution Approach 1:
The patent copies the successful circular section pattern design methodology and adapts it for elliptical sections through parameter transformation. Instead of developing a completely new method, it replicates the proven circular approach with modified parameters, making the design process transparent and reproducible
Solution Approach 2:
The patent segments the complex elliptical pattern design into distinct calculation steps: (1) calculate equivalent radius Re = (a²+b²)/(2a), (2) calculate central angle θ' = 2arcsin(a/R), (3) apply circular section formulas with transformed parameters. This segmentation makes the confidential-adjacent process transparent and understandable
3Strength
If filament winding technology is applied to elliptical section elbow pipes, then high strength and corrosion resistance can be achieved, but uniform coverage and winding stability are difficult to ensure
Solution Approach 1:
The patent changes the geometric parameters used in pattern calculation from direct elliptical parameters to equivalent circular parameters. By using equivalent radius Re and transformed central angle θ', it ensures that the winding pattern maintains uniform fiber distribution and stable winding process, thereby ensuring manufacturing precision while achieving the mechanical properties
Data Source
AI summary
A method, device, medium, and product for pattern design in filament winding is provided. The method includes: acquiring parameter data of a target elbow pipe mandrel; constructing a mandrel geometric model according to the geometric dimension parameters; the mandrel geometric model includes a geodesic mathematical model of a ring segment and a non-geodesic mathematical model of a cylindrical segment; the ring segment is an elliptical section annular elbow pipe; the cylindrical segment is an elliptical section pipe; determining number of yarns of the ring segment according to the geodesic mathematical model and set parameter data, and determining geodesic trajectory information of the ring segment; determining non-geodesic trajectory information of the cylindrical segment according to the non-geodesic mathematical model and a set slip coefficient; determining a filament winding pattern according to the geodesic trajectory information of the ring segment and the non-geodesic trajectory information of the cylindrical segment.