Study on the Theory of Vibration Isolation for Multi-Vibrating Machines Based on Self-synchronization
|Course||Mechanical and Electronic Engineering|
|Keywords||Secondary isolation Frequency capture Self-synchronous vibration Stability Generalized euation|
Synchronous vibrating machinery is used widely in industrial departments. In order to ensure the machinery in an efficient, reliable and stable operation, the reseach on the technolgy of vibration isolation for this type of machines is pretty significant. In 1960s, Soviet Union’s resecher, Blekhamn, first studied the theories of self-synchronization for vibratiing system with two exciters. Since then, the self-synchronization theory has been widely applied for its simple structure, easy maintenance, reliability and many other advantages. However, it is inevitable to pass dynamic load of the vibrating machines to the supporting foundation (usually ground) and cause noises and swing of the rigid frame of factory when they work. It is common to use a simple spring-damper system to isolate the equipment from the ground. In this way, the dynamic load is always reduced, can not be completely eliminated.Based on the theory of self-synchronization, this paper proposes the technique of vibration isolation by symmetrically installing four vibrating machines on an isolating frame to counteract the dynamic load that each machine passes to the isolation frame, which causes itself zero-vibration when seady synchronization operates. The tasks in this paper are described as follows:(1) The kinetic energy, the potential egergy, and the viscous dissipation function of a vibrating system, which cosists of four vibrating machines with dual-motor drives rotating in opposite directions, are deduced by using multiple reference frames. Applying kinetic energy, the potential egergy, and the viscous dissipation function to Lagrange’s equations, the equations of motion of the vibrating system are set up. The equations of frequency capture of the vibrating system are derived by using the principle of electro-mechanic coupling, which converts the problem of self-synchronization of multiple unbalanced rotors in a vibrating system into that of existence and stability of zero solutions for the equations of frequency capture. The conditions of frequency capture are derived by using the existence of zero solution. Then, the problem of the stability of synchronization of eight unbalanced rotors is converted into that of the generized equations of the disturbance parameters for angular velocities of the eight unbalanced rotors and seven phase differences. In the generalize equations, the matrix of inertia coupling of the eight unbalanced rotors is symmetric and the matix of stiffness coupling of the motors is reversely symmetric, which simplify greatly the analysis of the stability of synchronization. The condition of synchronous stability is obtained using Routh-Hurwitz criterion.(2) By using the results of the above theoretical analysis, the conditions of frequency capture and stability of synchronization for a vibrating system with two vibrating machine are derived. The expression of torque of frequency capture for synchronization of the two vibrating machines is given. The results of the theoretical anaylsis show that the two vibrating machines can operate synchronously when the torque of frequency capture is greater that the difference of the output electromagnetic torque between the two pairs of the motors on the two vibrating machines. When the distance between the mass center of the isolation frame and the installation position of vibrating machines is less, the two vibrating machines can synchronize at the phase difference in the vicinity of 180°; when it is greater, the two vibrating machines can synchronize at the phase difference in the vicinity of 0°.(3) Using the multiple reference frames, the kinetic energy, the potential egergy, and the viscous dissipation function of a vibrating system, which cosists of four vibrating machines with dual-motor drives rotating in the same direction, are deduced. Applying the kinetic energy, the potential egergy, and the viscous dissipation function to Lagrange’s equations, the equations of motion of the vibrating system are set up. The conditions of frequency capture and stability of the synchronization are obtained.(4) The programes of computer simulations for the above systems are developed by using C++language. Through differently initializing parameters of the system, the multi-group synchronous steady solutions of the system are derived; the analytical solution can be validated that installation distance changes affects the synchronous steady solution; the observation of isolation rigid verify the theory of vibration isolation based on synchronization.