Refined Modeling And Dynamic Simulation For Vibrating System With Multi-motor Drives

At present, a variety of vibrating machinery has been widely used in industry, such as self-synchronous vibrating feeders, self-synchronous vibrating conveyors, etc. Researchers around the world have deeply studied on this kind of vibrating system and got a large number of research achievements which have solved the problem of vibrating system with two-motor drives design. However, in order to simplify the analysis process, the influence of the coupling terms between the exciters and the airframe are always ignored. It causes the simulation results of dynamics characteristic are not very accurate. Therefore this problem hinders the development of self-synchronization theory. For example, researchers around the world can’t establish the design theories for vibrating system with multi-motor drives for the past years. This paper is presented for the problem mentioned above. The influence of the ignored coupling terms between the exciters and the airframe are studied in this paper. And this paper has completed the dynamic simulation for vibrating system with multi-motor drives. The works in this paper are described as follows:(1) Deformation of the spring and the coordinate of the eccentric lumps and vibrating system centre are carried out under the theory of multi-body dynamics coordinate transformation. And the mathematical equations have been developed by means of calculating the kinetic energy, the potential energy and the viscous dissipation of the vibrating system. The complete differential equations of motion for vibrating system have been developed by using Lagrange equation. By this way, this paper has achieved refined modeling for vibrating system with multi-motor drives.(2) A dynamic simulation software for vibrating system with multi-motor drives is developed by using MATLAB and Runge-Kutta method. This paper studies on the time-varying characteristics of the motor rotational speed, phase difference and response in all directions for vibrating system with two-motor drives rotating in opposite directions, vibrating system with two-motor drives rotating in same directions, vibrating system with three-motor drives rotating in opposite directions and vibrating system with three-motor drives rotating in same directions by dynamic simulation. The results show:1) When the vibrating system is driven by two different motors, the simulation result of the simplified dynamic model is different from the simulation result of completed dynamic model. A 2-6° deviation appears between the two simulation result in phase difference.2) Omitting the coupling terms between the eccentric lumps rotational speed and speed in all direction causes the deviation between the two simulation results in phase difference.3) When the vibrating system is driven by three same motors, the simulation result of the simplified dynamic model is similar to the simulation result of completed dynamic model.(3) Using the modified average method of small parameters, this paper develops the condition of implementing synchronization and the stability condition of synchronization for the refined modeling of vibrating system with multi-motor drives. By comparing the numerical results, this paper studies the influence of model simplifying for the condition of implementing synchronization, the stability condition of synchronization and the vibrating system response for vibrating system with two-motor drives rotating in opposite directions, vibrating system with two-motor drives rotating in same directions, vibrating system with three-motor drives rotating in opposite directions and vibrating system with three-motor drives rotating in same directions. The results show:1) The smaller difference between the two motor parameters is, the smaller deviation in phase difference by omitting the coupling terms will be found. When the two motors are the same, the deviation no longer exists.2) Comparing with the simplified dynamic model and the refined dynamic model, the conditions of implementing synchronization are different. But when the vibrating system in the simplified dynamic model can be synchronous, the the vibrating system in the refined dynamic model is synchronous.3) Comparing with the simplified dynamic model and the refined dynamic model, the three indexes for stability condition of synchronization judgment are all different, so under the simplified dynamic model the stability condition of synchronization judgment may not be accurate.