Synchronization of two coupled exciters in a vibrating system of spatial motion
The paper proposes an analytical approach to investigate the synchronization of the two coupled exciters in a vibrating system of spatial motion. Introducing the disturbance parameters for average angular velocity of two exciters, we deduce the non-dimensional coupling equations of angular velocities of two exciters, in which the inertia coupling matrix is symmetric and the stiffness coupling matrix is antisymmetric in a non-resonant vibrating system. The analysis of the coupling dynamic characteristic shows that the coupled cosine effect of the phase angles will cause the torque acting on two motors to limit the increase of phase difference between two exciters as well as sustain its symmetry of two exciters during the running process. It physically explains the peculiarity of self-synchronization of two exciters. The cosine effect of phase angles of the vibrations excited by each exciter will decrease its moment of inertia. The residual moment of inertia of each exciter represents its relative moment of inertia. The stability condition of synchronization of two exciters is that the relative non-dimensional moments of inertia of two exciters are all greater than zero and four times their product is greater than the square of their coefficient of coupled cosine effect of phase angles, which is equivalent to that the inertia coupling matrix is positive definite and all its elements are positive. The numeric results show that the structure of the vibrating system can ensure the stability condition of synchronous operation.