N-level complex helical structure modeling method

Abstract

This paper primarily explores the modeling method of n-level complex helical structures with coal mining machine cables as the research object. The paper first elaborately introduces the modeling method of n-level helix curves based on parametric equations and coordinate transformations, and compensates for the n-level helix curves with corrected pitch, which can obtain more accurate n-level helix curves and improve the accuracy of n-level helix curves modeling. Subsequently, based on this high-precision n-level helix curves modeling method, the paper elaborates on the method of solving pitch and twisting radius of multi-layer helical structure. Calculation scripts were written based on the above methods, which can be used to batch calculate the twisting radius and pitch of each layer structure in multi-layer structures when satisfying the conditions of in-layer tangency, inter-layer tangency, and extrusion deformation, and retain the actual results through logical judgment. Then, based on the above two methods, the paper developed a modeling method for braided structures based on piecewise functions containing fifth-order polynomials, which can effectively avoid the problem of insufficiently dense arrangement of braided lines and easy interference in traditional methods. Finally, a set of modeling tools was developed using C# and Python in Grasshopper to implement the modeling algorithm. Taking the MCPT-1.9/3.3 3120 + 170 + 4 * 10 coal mining machine cable as an example. The cable was modeled using both the method proposed in this paper and the traditional method. Comparative data shows that the method proposed in this paper can reduce errors by 3.31E6 times in the second-level and above helical structures. In addition this paper compares the standard line length, measured line length, and the line length established by the proposed model, showing that the relative errors are both less than 0.1941%. This paper provides a new, systematic, high-precision, and full-process cable modeling method, in which all parameters except the process parameters are accurately solved by equations. It lays a theoretical foundation for the high-precision simulation and intelligent sensing cables, which is of great significance for improving the safety, stability, and efficient development of the coal mining industry. The research results of the paper can not only be applied to the modeling of coal mining machine cables but also can be extended to the modeling of other complex multi-layer helical structures.