Study On Synchronization Theory In The Vibrating System Driven By Double-motor And Multi-motor

In a vibrating system with multiple unbalanced rotors (so called exciters) driven by induced motors separately, multiple exciters are usually demanded to operate synchronously. For this purpose, traditionally, mandatory synchronous mechanism, such as gear etc., is used to guarantee the effective operation of system, which results into the inconvenient maintenance and adding the structural complexity to system. Multiple exciters can still implement self-synchronization in the absence of mandatory synchronous mechanism, which leads to the simple and compact machine construction. Vibratory synchronization technology is one of the effective methods to solve such difficulty. Utilizing the principle of vibratory synchronization, an increasing number of self-synchronous vibrating machines have been widely used in a variety of industries at present, which has created the huge economics and social benefits.The intensive study on vibratory synchronization theory and broadening its fields of the corresponding applications to satisfy the requirements in engineering, has been being one of attentions of present researches. When the phase differences among exciters (PDAE) are stabilized in the vicinity of special values, a special motion type of system will be realized, and the total output power of exciters will also change. By utilizing this principle, the vibrating machines with certain amplitudes of vibration and motion trajectories satisfying all kinds of requirements, can be designed. The coupling dynamical characteristics of system (CDCS) must be understood perfectly in order to limit rationally PDAE. According to requirements abovementioned in engineering and with the help of the support of National Natural Science Foundations of China and National Basic Research Program of China (973 Program), and based on the previous literatures, in present work a research topic entitled "Study on synchronization theory in the vibrating system driven by double-motor and multi-motor" is proposed, in which the synchronization principle and regime of multiple exciters with the different distribution modes, different rotating directions, different vibrating conditions (i.e., far-super-resonant and near-resonant) and considering the friction of a roller, are studied, respectively. CDCS is discussed in detail, experiment prototypes are designed, the validity of theoretical results and the feasibility of method used are verified by experiments as well. The engineering application ways on vibratory synchronization theory are given, the related theory results on vibratory synchronization are applied to engineering successfully. A relatively complete systematic frame on vibratory synchronization theory of exciters is constructed. Some criterions of implementing synchronization of two and multiple exciters are proposed, as well as that of stability of the synchronous states. The main research contents are as follows:(1) The developing history and research methods on synchronization especially for vibratory synchronization are provided in chapter 1, as well as the preliminary knowledge related to the present work.(2) Based on the average method of small parameters, synchronization of two, three and more than three identical or non-identical exciters in a far-super-resonant vibrating system is studied. By introducing two groups dimensionless small parameters corresponding to the disturbance parameters of average angular velocity and that of PDAE, the frequency capture equations of system are constructed, the synchronization problem is reduced to an existence and stability problem of finding the zero solutions for the averaged differential equations of small parameters. The criterion of synchronization and that of stability of the synchronous states are derived, in which the latter satisfies the generalized Lagrange's equations and Routh-Hurwitz criterion. The coupling dynamical characteristics and general dynamical symmetry are analysed. The ability of the synchronization decided factors are the coefficients of synchronization ability, which is also called the coefficients of the general dynamical symmetry, the better the general dynamic symmetry is, the greater the ability of synchronization among exciters is, the easier the implementation of synchronization. The ability of stability decided factors are the coefficients of stability ability, the greater the absolute value of which, the stronger the ability of stability. Synchronization and stability of system result from the coupling dynamic characteristics with the selected motion (CDCSM), in which the former stems from the coupling dynamical characteristics, while the latter depends on the principle of motion selection of system.The dynamic characteristics of system that the vibrating system with two or more than two exciters can operate synchronously and stably by specific PDAE, is called as the general dynamic symmetry of system (GDSS), in which specific PDAE is called as the angle of general dynamic symmetry (AGDS), and there exists a AGDS between arbitrary two exciters. The AGDS corresponds to the minimum point of the average vibrating energy of system. It can be also said that synchronization of sytem stems from such GDSS existing in the load couping of system, and the coupling torques among exciters in the load coupling is called as the general dynamic symmetry torques (GDST), which limit the increase of angular velocity of exciter with leading phase and restrict the decrease of angular velocity of exciter with lag phase as well, and finally GDST forces the PDAE to near AGDS to reach synchronization.For the dynamic model of two symmetrical distributed exciters rotating in the opposite directions, PDAE is stabilized in the vicinity of zero, which keeps the symmetry with respect to the installing axis of symmetry of two exciters (SIASTE) to ensure the approximate linear motion of machine.For the dynamic model of two homodromy and symmetrical distributed exciters, if the distance between axes of two exciters and the mass centre of rigid frame (DBATEMCRF) is smaller than (?)2 times of the equivalent rotating radius of system (ERRS), and the parameters of system is complete symmetry, then PDAE is stabilized in the vicinity of ?, which keeps the symmetry with respect to the mass centre of rigid frame (SMCRF) to implement the swing of machine; if DBATEMCRF is greater than (?)2 times of ERRS, then the stable PDAE nears to zero, which keeps the SIASTE to implement the approximate circular motion.In light of the dynamic model of three homodromy exciters with straight line distribution if the virbaing system is complete symmetry, then the phase difference between two separated exciters is stabilized in the vicinity of zero and the others are close to ±? when the distance between two separated exciters is long enough, the characteristics of symmetry are similar with the above principle.When three homodromy exciters are distributed uniformly and symmetrically in a circumference and their axes near to the mass centre of system as possible, the stable PDAEs near to ±2?/3 which keeps the SMCRF, the rigid frame is at rest in this case; the double-equilibrium state is occurred, i.e, PDAEs are close to 0 and ±2n/3 when their axes are far enough from the mass centre of rigid frame, the former (PDAE with zero) keeps the SIASTE to implement circular motion and the latter keeps the SMCRF to result into no vibration, which kind of equilibrium state to appear is determined by initial conditions and external disturbances. The number of the above exciters in a circumference can be extended to n(n>3), the principle is similar with the above one, such as the adjacent PDAE nears ±2?/n which keeps the SMCRF to ensure no vibration when their axes are near enough from the mass centre, etc.For the dynamic model of three or multiple exciters with arbitrary distribution types, if exciters are installed asymmetrically or the parameters of system is not complete symmetry, then the stable PDAEs depend on the nonlinear average balance equations of exciters and stability criterion, such stable PDAEs are special values depending on the dynamical parameters of system and the mounting positions of exciters, which determines the motion types of system resulting from the vector superposition of vibrations corresponding to the minimum point of the average vibrating energy of system, excited by multiple exciters.The numeric simulation and experiment results verify the correctness of the above theories and the feasibility of the method used. The related theoretical results in the above far-super-resonant vibrating system have been applied to engineering successfully, for example, utilizing the principle of vibratory synchronization transmission can achieve the goal of energy-saving; based on the synchronization theory of two non-identical homodromy exciters, the technological effect of the world's largest vibrating screen (56m2) is improved.(3) Using the average method and asymptotic method, synchronization of two exciters in a near-resonant vibrating system with rigid nonlinear characteristics, characterized by piecewise linear, is investigated. Taking double-rigid-frame with two opposite exciters as a dynamic model, and based on the average method, the criterion of implementing synchronization is derived. According to the principle that the stable solution of the synchronous states corresponds to a minimum point of Hamilton's average action amplitude of total system, the criterion of stability of the synchronous states is achieved analytically. The CDCSM is analyzed. The frequency-amplitude characteristics on the relative motion with the inverse phases for two rigid frames in the horizontal direction is analysed, as well as the ability of synchronization and that of stability, and phase relationships. It is shown that the best working point of system should be selected to be in a sub-resonant or sub-near-resonant state, corresponding to the natural frequency of the relative motion with the inverse phases in the horizontal direction for two rigid frames. The experimental results verify the validity of theory. Applying such theory to engineering successfully, leads to overcoming of two key technical difficult problems in terms of enterprises, in other words, vibratory synchronization theory in the near-resonant vibrating system, has been serving as the theoretical guidance of optimization of structural parameters matching in designing two types vibrating centrifuges for a certain company.(4) On the basis of the above theoretical investigated results on synchronization of two exciters or multiple exciters in a far-super-resonant vibrating system, especially for the synchronization theory of two and three homodromy exciters distributed symmetrically, vibratory synchronization transmission of a circular roller with dry friction in a vibrating system excited by two exciters, is studied. Using the average method, the criterion of implementing synchronization for two exciters and that of implementing vibratory synchronization transmission for a roller, are achieved. The criterion of stability of the synchronous states satisfies the Routh-Hurwitz principle. The influences of the structural parameters of system to synchronization and stability, are discussed, which can be as the theoretical foundation for engineering designs. An experiment is set up, the results thereof verify the validity of theory. Utilizing the vibratory synchronization transmission theory of a roller, a new type vibrating crushing & grinding equipment, such as vibrating crusher and vibrating grinder, etc., can be designed, which opens up a new engineering application way for vibratory synchronization transmission theory.Lastly, conclusions are provided, which are followed by giving the future work.