CHARACTERIZATION OF TORSIONAL INSTABILITIES IN A HOOKES JOINT DRIVEN SYSTEM VIA MAXIMAL LYAPUNOV EXPONENTS

Dynamic instabilities in a torsional system which incorporates a Hooke 's joint are investigated by means of Lyapunov exponents. Linearized a nalytical models for the torsional system are established for the purp ose of stability analysis. The resulting two-degree-of-freedom system is parametrically excited due to an inherent non-linear velocity ratio across the Hooke's joint. Instabilities which correspond to sub-harmo nic as well as combination resonances have been identified by studying the sign of the top Lyapunov exponent. An efficient forward differenc e scheme is employed to simulate directly the Lyapunov exponents. Inst ability conditions have been presented graphically in the excitation f requency-excitation amplitude-top Lyapunov exponent space. Predicted i nstability conditions are adequate for the design of two-degree-of-fre edom Hooke's joint driven systems. (C) 1996 Academic Press Limited