Synchronization characteristics in a vibrator-pendulum coupling system with spatial motion

Due to complex dynamic coupling relationships in the system, the research that couples pendulum and vibrators in the same system is rarely found. Especially in the vibrating system with spatial motion, the theoretical derivation may be too complex to be easy to implement. In this paper, we present a vibrator-pendulum coupling system with spatial motion characteristics; here, the pendulum is driven by the two vibrators mounted on it. The synchronization of the vibrators and the motion characteristics of the system are studied via theory, numeric, and experiment. In theory, the synchronization and stability criteria of the two vibrators are deduced. According to the theoretical results, some numerical qualitative analyses are given to further reveal the synchronous stable states and spatial motion characteristics of the system. The validity of the theoretical methods and the correctness of the numerical qualitative results are examined by simulation and experiment. Taking the pendulum as the working rigid frame, the proposed dynamic model and research results can be applied to design a new kind of vibrating jaw crusher with spatial motion characteristics.