N-level complex helical structure modeling method

Area of Science:

• Engineering
• Computational Modeling
• Materials Science

Background:

• Complex helical structures, such as those found in coal mining machine cables, present significant modeling challenges.
• Existing methods often suffer from inaccuracies in representing multi-layer helices and braided configurations.

Purpose of the Study:

• To develop a systematic, high-precision, and full-process modeling method for n-level complex helical structures.
• To improve the accuracy of modeling coal mining machine cables and other multi-layer helical systems.
• To provide a theoretical foundation for high-precision simulation and intelligent sensing of cables.

Main Methods:

• Modeling n-level helix curves using parametric equations and coordinate transformations with corrected pitch compensation.
• Solving pitch and twisting radius for multi-layer helical structures considering tangency and deformation conditions.
• Developing a braided structure modeling method using piecewise functions with fifth-order polynomials.
• Implementing the modeling algorithm using C# and Python in Grasshopper.

Main Results:

• The proposed method reduced errors by 3.31E6 times in second-level and above helical structures compared to traditional methods.
• Relative errors in line length established by the model were less than 0.1941% compared to standard and measured lengths.
• The developed method effectively models complex braided structures, avoiding issues of sparse arrangement and interference.

Conclusions:

• A new, systematic, and highly accurate modeling method for complex multi-layer helical structures, particularly coal mining machine cables, has been established.
• The method accurately solves parameters through equations, laying groundwork for advanced simulation and intelligent sensing.
• The research has significant implications for improving the safety, stability, and efficiency of the coal mining industry and is applicable to other complex helical structures.