Special Motion Characteristics of a Vibrating System with a Main Working Rigid Frame Driven by the Pendulum Bob

Purpose For the vibrating machine with linear motion, the traditional driving method is utilizing the self-synchronization of double vibrators, or using a single motor to drive a pair of forced synchronization vibrators by the gear meshing. In this paper, we propose and study a special linear motion vibrating system (VS) driven by only the single vibrator, where the vibrator is mounted on a pendulum (so called pendulum bob) and no synchronization strategy is involved. Methods The Lagrange’s equation is used to obtain the motion differential equations of the system. Based on the vibration mechanics principle, the theory condition to guarantee the linear motion of the main working rigid frame (MWRF) is deduced, and the double frequency vibrating transmission (VT) between the pendulum and the MWRF is investigated. Simultaneously, some qualitative analyses are given to further reveal the special motion characteristics of the system by numeric. The the Runge-Kutta routine is applied directly to the motion differential equations of the system and the experiment is carried out to further verify the validity of the theoretical results. Results The results show that the special linear motion of the MWRF can be realized for the proposed dynamic model when satisfying the corresponding theory condition in the absence of self-synchronous or forced synchronization strategy, and in this case the system stability is relatively strong. Conclusion To guarantee the linear motion of the MWRF, the stiffness and damping, generating from the connection coupling between the pendulum and the MWRF, should be minimized. The present work can offer a reference to design a new kind of vibrating machine with linear motion. In engineering, the desired linear motion vibration amplitude of MWRF can be reached by adjusting the parameters of vibrator and considering the theory condition of implementing linear motion.