Study On Nonlinear Dynamic Characteristics Of Single-and Multi-Motor Systems Based On Rigid And Elastic Models

The beam structure is a typical continuous structural unit,which is widely used in modern industrial production.As the support structures,the beam structures will vibrate because of the excitation functions of various power equipment.The vibration of the beam structures affects the motion state of the power equipment.On the contrary,the changes of the motion state of power equipment can affect the vibration of the beam structure as well.A system fully considering the interaction between vibration system and power equipment is called a non-ideal vibration system,where the power equipment providing the limite power is called the non-ideal source.However,the interaction between the vibration system and power equipment was neglected in many researches on the non-ideal vibration systems,which could have a large influence on their results.Hence,on considering the limte power provided by power equipment,it is very necessary to study the interaction between elastic support structure and power equipment.In respect of such issues above,choosing the induction motors with eccentric rotors and the elastic beams as objects,the coupling mechanism of single-and multi-motor driven vibration system based on elastic models(single-and multi-motor system for short)is studied to provide the theoretical reference for the vibration attenuation of the power equipment on the elastic support structures.The concrete content of the thesis is as follows:(1)The coupling mechanism of a single-degree-of-freedom vibration system supported induction motor system is studied,which provides a foundation for the study of the coupling mechanism of the simple beam supported single/multi-motor systems.Combining the dynamic models of the induction motor and a single-degree-of-freedom vibration system,the dynamic model of a non-ideal vibration system is developed.Based on the average perturbation method,the steady solutions and their stability of the non-ideal vibration system are obtained and analyzed,respectively.The simulations are carried out based on Matlab/Simulink to validate the correctness of the theoretical results.Finally,the influences of eccentric mass and motor power on the non-ideal vibration system are analyzed.Through research,it is found that the coupling function has a large influence on the dynamic response of the non-ideal vibration system.(2)The coupling mechanism of a simple cantilever beam structure supported induction motor system is studied.On the basis of fully considering the interaction between the beam structure and the induction motor and the non-ideal characteristics,based on the Hamilton principle,a continuous model of the cantilever beam sturcture supported induction motor system is established.The continuous model is discretized by using the assumued mode method.Then,the discrete electromechanical coupling model of the cantilever beam supported induction motor system is obtained.The steady solutions and their stability of the whole coupling system are calculated and analyzed by using the average perturbation method,respectively.Finally,some numerical simulations are operated to verify the theoritical results.The results show that there appears a speed jump phenomenon in the beam-motor coupling system,namely the Sommerfeld effect.Additionally,the influences of the unbalanced mass and power of the induction motor on the Sommerfeld effect are analyzed.(3)The coupling mechanism of a simply supported beam supported dual induction motor system is studied.On the basis of fully considering the non-ideal characteristics of the induction motor,the interaction between the beam structure and the induction motor,and that between two motors,the discrete electromagnetic coupling model of a dual motor system on the simply supported beam is obtained by using the Hamilton principle and the assumed mode method.By using the average perturbation method,the synchronization and stability conditions of the dual motor system on the simply supported beam are obtained.The correctness of the theoritical results is verified by using the theoretical analyses and numerical simulations.Finally,the influences of the structue and motor parameters on the coupling effect of the system are analyzed.The results show there appear not only the Sommerfled effect,but also the synchronization phenomenon of two motors.Moreover,two nonlinear phenomena are coupling and both determining the motion states of the system.(4)The coupling mechanism of three induction motors on a simply supported beam system is studied.On the basis of fully considering the non-ideal and nonlinear characteristics of the motor,the interactions between the simply supported beam structure,and those among three motors,the electromechanical coupling model of the motor is introduced into the simply supported beam structure,and the continuous model of the whole system is established based on the Hamilton principle.The continuous model is discretized to establish the electromechanical coupling dynamic model of the whole system by using the assumed mode method.The average speed and phase differences of three motors under arbitrary power frequency conditions are obtained by using the average perturbation method.Moreover,their stability is analyzed.The synchronization and stability conditions of the system are established.Finally,the feasibility of the proposed theoretical method is verified by using the numerical simulations.The results show that the Sommerfeld effect occurs near the beam resonant frequency.Moreover,the synchronous states among three motors change before and after the resonant frequency of the beam.(5)The coupling mechanism of single/multi-motor systems on the simply supported beam sturcture is studied by using experiments.The experiment bench of the single,dual and three motors on the beam structure is constructed.By using the experiment bench,the change rules of the speed and synchronous states of the motors with different supply power frequencies are obtained by adjusting the supply power frequencies of the motors.The results show that there appear the speed jump phenomenon in the single motor system,namely Sommerfeld effect;there appear the speed jump phenomenon and the synchronous states among motors change before and after the resonant frequency of the beam.The feasibility of the proposed average perturbation method and the correctness of the theorical results are verified again through epxerimental studies.