Analysis And Control Of The Parametrically-excited Instability Of Axially Moving Materials

Axially moving materials is applied in many engineering devices,such as power transmission belts,elevator cables,magnetic tapes and papers in processing.The transverse vibrations associated with these devices have limited their application.One major problem is parametric vibrations due to axial speed fluctuations,which often occur when the drive motor run at high speed. So studying the dynamic instability and control strategy will be valuable both in theory and engineering.The first part of this thesis is the theories.The govern equation of parametric vibrations of axially moving string is established.The Galerkin approach is employed to transform the governing partial differential equations to ordinary differential equations. Using the method of multiple scales,the dynamic instability of principal parametric resonance excitation is obtained and analyzed.The response curves are derived by MATLAB.The theoretical analysis indicates that the principal parametric resonances may occur during the speed fluctuation frequency approaches twice natural frequency of the system.In the second part,the experimental platform is established to analyze the parametric vibrations of axially moving materials.A brushless DC motor control system based on the embedded microcontroller LPC1768is presented.The hardware of the system is designed,including the control module,the power inverting module,the position detection module and the rotational speed measurement module.The system control algorithm is achieved by the software programs.The rotation speed of the motor is adjusted by the BLDC control system to drive the metal conveyor belt moving to meet the requirement of the parametric vibrations.The experimental datas are analyzed by virtual vibration test system.The results show the transverse vibrations phenomenon is closely connected with the speed fluctuation frequency.Finally,the vibrations control of axially moving materials is investigated.The method of fuzzy sliding-mode control is employed to control the vibrations. Matlab/Simulink was used to build the simulation model.The simulation results indicate the effectiveness of control strategy.