Jia Lei, Tian Yang, Liu Ziliang, Zhang Xin
School of Mechanical Engineering, Shenyang Ligong University, Shenyang, 110159, China.
School of Mechanical Engineering, Liaoning Engineering Vocational College, Tieling, 112008, China.
Sci Rep. 2024 Feb 29;14(1):5026. doi: 10.1038/s41598-024-55680-8.
In this article, an engineering problem of three co-rotating exciters with the circular distribution in a vibrating system is investigated. The dynamical model constructed by the motion differential equations is established. By introducing the small parameter averaged method in the dynamic equation, the synchronization and stability conditions of the electromechanical coupling dynamical model is derived. To illustrate the necessity of the controlling method, the self-synchronization of the vibrating system is firstly analyzed with the theory, numerical simulations and experiments. With the self-synchronization results, it is indicated that the ellipse trajectory which is needed in the industry can't be realizefd by the self-synchronization motion of the vibrating system. And then, a fuzzy PID controlling method based on the master-slave controlling strategy is introduced in the vibrating system to realize the controlled synchronization. The Lyapunov stability criterion is given to certify the stability of the controlling system. Through some simulations and experiments, the effectiveness of controlled synchronization is illustrated in the discussion. Finally, the present work illuminates the feasibility and practicality for designing some new types of vibrating screens in the industry.
本文研究了振动系统中三个呈圆形分布的同向旋转激振器的工程问题。建立了由运动微分方程构成的动力学模型。通过在动力学方程中引入小参数平均法，推导了机电耦合动力学模型的同步和稳定性条件。为了说明控制方法的必要性，首先运用理论、数值模拟和实验对振动系统的自同步进行了分析。根据自同步结果表明，振动系统的自同步运动无法实现工业所需的椭圆轨迹。然后，在振动系统中引入基于主从控制策略的模糊PID控制方法来实现受控同步。给出了李雅普诺夫稳定性判据以证明控制系统的稳定性。通过一些模拟和实验，在讨论中说明了受控同步的有效性。最后，本研究阐明了在工业中设计新型振动筛的可行性和实用性。
