A simplified analytical method for the computation of machine path in filament winding of axisymmetric structures: a case study on a bell-contoured rocket nozzle extension

摘要

This paper presents the simplified computational approach for the kinematic motions of a filament winding machine (FWM) manufacturing a bell-contoured rocket nozzle extension. Analytical equations were derived for the machine path to preclude expensive commercial software for the automated control of the FWM. The final solution is given through controllable degrees of freedom of a two or four-axis FWM. The mathematical approach adopted in the methodology for deriving executive expressions is based only on analytic geometry and consists of two stages. The equations for the machine path to lay fiber along a geodesic pathway on a conical surface were obtained in the first stage. In the second stage, several truncated cones were used to approximate the bell-shaped surface, whose contour is a polynomial curve. The solutions for every truncated cone were consolidated to obtain a continuous fiber pathway on the bell-shaped surface by matching the winding angles of the pathways from two adjacent conical surfaces. The feasibility of the proposed approach was successfully validated by manufacturing a small-scale bell-contoured nozzle extension.