| Valve springs play a very important role in the performance of the automobile engine. For example, in high speed fatigue tests of automobile engines, valve springs often fail first. In the past, the dynamics of valve spring was modeled by a second order partial differential equation, the wave equation. In formulating this dynamic equation, only two terms of strain and kinetic energy were included. The springs were assumed to have circular cross section wire, constant pitch angle and radius.;This research is based on the more general assumption that the valve spring has varying pitch angle and radius. This type of spring is named the general helix spring. A total of six energy terms are included in deriving the dynamic equations. Static compression tests have shown that the force computed from this new model is more accurate than from other formulae. This investigation revealed that widely used Kelvin curvature and torsion formulae, and spring force formulae are in error when applied to the general helix spring. A set of new formulae for calculating curvature, torsion and spring force are derived, which contain the old formulae as a subset.;It is found that during high speed compression, the numerical solution of a simple wave equation is not physically feasible, because of coil clash. It is necessary to adopt a moving boundary condition. The general valve spring dynamic equation is solved by the finite difference method with tracking of the moving boundary. The moving boundary solution allows the model to accurately predict coil clash and spring force. The numerical results are in very good agreement with the experimental data taken from a 1983 Pontiac, family-II, 1.8 liter, four cylinder OHC engine.;This mathematical model of a valve spring is useful in optimal spring design, and could be used in larger cam-follower-valve models to study the dynamics of automobile cam systems. The static and dynamic behavior of a newly designed spring can be predicted accurately by this model before any prototype is actually made. This model of the general helix spring can be applied to any helical springs. |
