Analytical Models for Low Cost Manufacturing of Composite Components by Filament Winding, Part II: Inverse Kinematics

Abstract

There are no available techniques for the prediction of fiber angle distribution for various mandrel shapes under different conditions of mandrel's rotations and delivery point motions. In the present paper a novel approach based on the geometric and trigonometric relations is developed for predicting the fiber laydown path for a given equation of motion for the delivery point. This is important during the start-up and reversal periods of the filament winding operation. During the start-up period, the delivery point accelerates from a velocity of zero to a final value in some interval of time, whereas during the reversal period the delivery point decelerates to zero velocity and then accelerates to a final velocity. Equations of motion for the delivery point are presented to have smooth start-up and reversal periods. Closed form solution are developed to compute the fiber winding angle distribution on various types of cylindrical mandrels with axisymmetric and non-axisymmetric cross-sections, whereas numerical solutions are presented for non-cylindrical mandrels. Fiber slackening phenomena during a reversal period is discussed. Based on the current approach, an interactive computer program INVERSEKIN is developed to determine fiber winding angle distributions for a given equation of motion, mandrel shape geometry and experimental set-up conditions. Effects of winding parameters on fiber position and fiber winding angle distributions are discussed. Experimental verification of the model is done on a McClean Anderson filament winding machine for a conical mandrel for various equations of delivery point motion.