A mathematical model to estimate the shape of a brake hose has been developed. A few papers applying Finite Element Methods (FEM) to this problem have been reported. However, the solutions require a large amounts of computational time even if a super computer is used.
A brake hose is made of a flexible material such as rubber, and exhibits large scale deformation when it is mounted on a chassis. Element node displacements are chosen as the independent variables for FEM, so the method becomes a successive iteration of hose shape modifications based on displacements of the nodes.
The developed model is approached from the standpoint of mechanical dynamics. A brake hose is divided into small beam elements and particles. The particles are driven by element forces and move around in three-dimensional space. Choosing the coordinates and orientations of the particles as the independent variables, the shape of the brake hose can be determined directly by solving the equations of static equilibrium resulting from the element forces exerted on the particles.
Element forces can be derived by simple beam theory if the elements are divided small enough to be approximated as linear elastic beams. This is because element deformation is small relative to particle displacement. The orientation of the particles can be represented by Euler Parameter notation. This notation makes the model simple and reliable, and contributes to a rapid computation. The Newton-Raphson method is incorporated for solution of the governing equations. Numerical results closely agree with the experimental data.