Validation of a non-linear mathematical model for predicting the shape of brake hoses in automotive applications

Abstract

It is a challenge to depict the shape of flexible components in solid modeling software. This is because flexible components in an automobile are subject to large elastic deformations during the movement of the rigid components to which they are attached. The principles of computation of the orientation of entities in a simplified coordinate system, vector mathematics, the file I/O features and structured C++ programming were used to view the rubber hose in CAD after modeling the hose using simulation software. The deviations of the hose shape at 0°, 90°, and 180° twist position obtained from the non-linear mathematical model and the actual location of the real hose obtained by using ATOS II scanning equipment were reduced by modifying various parameters. At the end of the trials the mean deviation was below 1 mm at the 0° position and below 6 mm at the 90° and 180° twist positions. A regression analysis was performed for generalization of the force deformation values characterizing the non-linear behavior of off-axis elements. This analysis makes this modeling technique applicable for predicting the shape of hose lengths in the range of 227.8— 2474 mm between any two attachments in space. Subsequently, the regression model was used to predict the hose shape for a different length. The results show that non-linear model with off-axis elements predicts the hose shape much more accurately than the linear model with beams.