Abstract
The increased interest for improved gear design has led to extensive research into the field of non-linear dynamics of such systems. The paper reveals a complex dynamic model to study the coupled lateral, torsional and axial vibrations in a helical geared system. In many applications including turbo machinery, machine tools and car gears non-linearitys are present due tooth stiffness and they induced micro-vibrations of parametric type. Using the Languages equations, the paper highlights this type of vibrations coupled with the above mentioned vibrations. Also the paper presents a new modern mathematical algorithm to solve the differential system of equations witch represent the non-linear dynamic behavior of a geared system due to self-induced parametric excitations caused by the tooth stiffness. It was computed the frontiers of stability in the space (s,v), s , where s is the amplitude of non-linear parametric vibrations and ν is the frequency for the stiffness of the geared system. In the mean time in the region of principal parametric resonance v = 2v o,vo being the fundamental frequency of the geared system, the instability region increases but there are instability areas even for the sub-harmonic resonances.
By this way the paper reveals a powerful mathematical tool that predicts the regions of instability produced by the self-induced vibrations of the geared systems. Therefore the algorithm is very useful to predict the non-linear dynamic behavior of car gear transmission and to compute their conditions when failure could occur.