Über die kinetische stabilitaet der stösselstange in kurvengetrieben

Abstract

In many machines and especially in valve control mechanisms of internal combustion engines there are moving parts called followers that are subjected to buckling (Fig. 1-a). By reducing the spring and the masses of the rocker arm and valve to an equivalent spring and mass being located on the side of the follower, a model is obtained for such a mechanism as shown in Fig. 1-b. If the mass of the spring and the longitudinal vibrations of the rod are neglected, the rod shown in Fig. 1-c, loaded by a variable axial force, can be taken as a basis for the investigation of bending vibrations. The equation of bending vibrations of this rod is obtained using the classical bending theory and d'Alembert's principle. Then this partial differential equation with variable coefficients is reduced to a system of ordinary differential equations of second order with periodic coefficients using the Galerkin method. With the aid of this system the stability of the rod and consequently of the cam mechanism is investigated according to the parameters of speed and stroke. The boundaries of instability regions of various orders being only of the summed type are calculated up to the terms of first order according to the parameter ε that represents the stroke. Within the framework of this approach, any instability region of second type (r ≠s) and higher order (p > 1) could not be established. In the case of a simple harmonic active force, it is shown that the investigations in stability of the first type can be done by a single Strutt diagram.