The Theories Of Self-synchronization For Vibrating System With Multi-mass-frame And Multi-motor Drives

There are a lot of vibration engineering problems need people to research, analysis and processing, in particular the positive power of modern mechanical structure, high speed and precise light technology, and miniaturization and other directions, thus increasing vibration prominent, so it is very important to master the law of vibration, only master the rules and characteristics of vibration can the vibration be effectively used its useful aspects and limitation of its harmful aspects.Self-synchronization of rotors is one of the most remarkable phenomena, and has open up fresh opportunities in the vibration technology. Since the discovery of self-synchronization phenomenon, the theory of mechanic-electric coupling in self-synchronization vibrating system has been developed for nearly half century, many valuable theoretical results have been obtained. At present, a variety of vibrating machinery has been widely used in industry.There are also some deficiencies in such theories so far. Firstly, the current theories are based on the phase dynamic approach and ignore the feature of frequency capture. They are only suitable to analyze the synchronization of the system with two asynchronous motor of the close dynamic parameters and lack of the study on the self-synchronization. Well, there are many outstanding strongpoint of non-resonating system in practicality and the parameters of the more induction motors(such as four induction motors) can not be escaped. Secondly, the dynamic characteristics of asynchronous motor are less considered.Actually, self-synchronization of vibration systems is the effect of mechanic electric coupling and the state of motion of considered systems is closely relative to the dynamic parameters of asynchronous motor in the system. Therefore, it is necessary to develop the theory of mechanic-electric coupling in synchronization for non-resonating system to supervise the system designing and the manufacture. It has the value not only in study but also in reality.The theories of self-synchronization for vibrating system with multi-mass-frame and multi-motor drives are studied in this paper. The works in this paper are described as follows:(1) Theoretical analysis of self-synchronization for vibrating system with three-mass-frame and four-motor drives,including Circular motion and linear motion.1) The force analysis for the eccentric lumps in the vibrating system of circular motion has been carried out 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.2) An analytical approach is developed to study the coupling dynamic characteristics of the four unbalanced rotors by using mechanical-electric coupling theory. which converts the problem of synchronization of the four unbalanced rotors into the existence and the stability of zero solutions for the non-dimensional differential equations of the angular velocity disturbance parameters (NDDEDP). The stability of zero solutions of the NNDDEDP is decomposed into that of its generalized system and a system of the three first order differential equations for the disturbance parameters of the phase differences. The coupling dynamic characteristic of the four unbalanced rotors includes the inertia coupling, the stiffness coupling of angular velocity and the load torque coupling. The non-dimensional inertia coupling matrix is symmetric, the non-dimensional matrix of the stiffness coupling of angular velocity is antisymmetric and its diagonal elements are all negative.3) Hence, the general system of the NNDDEDP automatically satisfies the generalized Lyapunov equations when the non-dimensional inertia coupling matrix is positive definite and its elements are all positive. Using Routh-Hurwitz criterion the condition of stability of differential equations for the disturbance parameters of the phase differences is obtained. The load torque coupling makes the vibrating system have the dynamic characteristic of selecting motions and self-synchronization of the four unbalanced rotors arises from the dynamic characteristic of selecting motion of the vibrating system. When the two coefficients of coupling cosine effect of phase angles are all greater than0and the three indexes of synchronization are all far greater than1, the vibrating system can implement an elliptical motion of the main rigid frame required in engineering.4) Numeric results show that the structural parameters of the proposed mechanism can guarantee the non-dimensional inertia matrix to be always positive definite. Computer simulation is carried out to verify the results of the theoretical investigation.(2) Theoretical analysis of self-synchronization for vibrating system with three-mass-frame and four-motor drives on an Isolation Frame.1) Taking two self-synchronous vibrating machines on an isolation rigid frame for example, this paper establishes dnamic model of a vibration isolation system and extends our previous works on the synchronization of two vibrating machines into the self-synchronization for multiple unbalanced rotors in a vibrating system.2) Using the modified average method of small parameters, we deduce the non-dimensional coupling differential equation of the disturbance parameters for the angular velocities of the four unbalanced rotors, which converts the problem of synchronization for the four unbalanced rotors into the stability problem of a generalized system and a system of three first order differential equations for the three phase differences.3) We deduce The condition of implementing synchronization, which is that the torque of frequency capture between each pair of the unbalanced rotors on a vibrating machine is greater than the absolute values of the output electromagnetic torque difference between each pair of motors and that the torque of frequency capture between the two vibrating machines is greater than the absolute value of the output electromagnetic torque difference between the two pairs of motors on the two vibrating machines. The stability condition of synchronization of the two vibrating machines is that the inertia coupling matrix of the generalized system is definite positive.4) Numeric simulation is carried out to verify the above theoretical results.