Research On Fractional Order Nonlinear Dynamic Characteristics And Chaos Control Of Rotating Module

The rotating module,which consists of a driving motor and a reduction gear mechanism,is widely used in automobiles,aerospace,robotics,and defense industries due to its high transmission ratio,high precision,and high efficiency.At present,although there are many studies on the dynamics of motor and the gear mechanism respectively,it is rare to combine the two system into a whole system to be studied.In addition,the dynamic model used in the existing research is usually an integer order differential equation,which does not fully reflect some of the special properties of the system.Therefore,it is necessary to analyze and study the driving motor and the reduction gear mechanism as a whole,and take the special dynamic properties existing in the rotating module into consideration for getting the more real insight of motion for a rotating module.In this paper,the rotating module composed of permanent magnet synchronous motor and involute spur gear transmission mechanism is regard as the subject of the study.The fractional order dynamic model of rotating module system is established by dynamic circuit method and concentrated parameter method.The influences of internal and external parameters of the system on the dynamics performent of the rotating module system are analyzed.Aiming at the controlling the chaos of the rotating module under certain parameters,a controller is designed to realize the control of chaos.The main research work and conclusions of this paper are as follows:1.Considering the fractional nature of the inductance component and the uneven distribution of the mass distribution of the rotor and the gear,the fractional-order dynamic model for the the rotating module,composeing of permanent magnet synchronous motor and the involute spur gear mechanism,is established by dynamic circuit method and parameter concentration method for the motor and for the gear mechanism respectively.Further more,the dynamic model of the entire rotary module system is obtained.2.Since the dynamic model of the entire rotating module system is of multi-variable,multi-input,strong coupling and nonlinearity,the definition of G-L and the fractional differential numerical method are employed to analyze the dynamic characteristics of the rotating module system under some internal and external parameters such as input voltage,load torque,gear meshing stiffness harmonic component amplitude and transmission error amplitude.The results show that the dynamic characteristics of the rotating module system are mainly affected by the input voltage and load torque,and with the change of input voltage and load torque,more complex state of motion will appear.The variations of gear meshing stiffness harmonic component amplitude and transmission error amplitude within a certain value range mainly affect the torsional displacement and torsional speed of the gear transmission mechanism.Results also show that the output angular velocity of the motor is critical in determining the motion state of the rotating module,only when the output angular velocity of the motor is a constant,can the rotating module be in stable priodic motion.3.In order to control the chaotic motion of the rotating module,the controller is designed according to the stability theorem of the fractional differential equations.And by means of controlling output angular velocity of the motor,the chaotic motion is suppressed.The research work in this paper not only has practical application significance for rotating module,but also provides a reference for the theoretical study of the nonlinear dynamic characteristics of electromechanical coupling systems.