Speaker
Description
Hoses for applications in the automotive industry are mainly made of fiber-reinforced rubber, with reinforcements ranging from nylon to steel. The properties of this reinforcement layer largely determine the deformation behaviour under internal pressure loading. For optimal space utilization and to meet certain design requirements, hoses are rarely straight but are often curved. These curved sections can be regarded as parts of a torus. This work investigates the role of fiber orientation in the analysis and simulation of helically reinforced, pressurized tori. Therefore, the concept of the neutral wrapping angle of a straight hose is analytically extended to a torus. This specific angle establishes an iso-sinusoidal load condition by balancing axial and circumferential stresses. It varies for a torus along the cross-section due to fluctuating circumferential stresses. Additionally, because of the curvature of the torus, the geometrical wrapping angle is not constant. Bending a reinforced straight hose or winding fibers onto a toroidal part inherently creates varying geometrical wrapping angles, which follow a similar pattern to the neutral wrapping angles but differ quantitatively. Using the finite element method and suitable modeling approaches, we analyze this difference as well as the interplay between fiber orientation and curvature effects on toroidal deformations. Specifically, we examine how deviations from the neutral wrapping angle superpose with the Bourdon effect. These interactions underscore the need for precise modeling of varying wrapping angles, especially in highly curved toroidal geometries. Finally, the potential of toroidal geodesics for optimal reinforcement paths is explored, as they wind around the torus in a spiral manner.
