Study On Electromechanical Coupling Dynamic And Vibration Characteristics Of The Cartesian Flexible Robotic Manipulator

As an important part in industrial robots, Cartesian robots have aceived significant applications in various processes, such as machining, precision assembly, loading and unloading, and spraying. Robotic manipulators are the key components for executing operating tasks, and their structural performances and dynamic properties have significant impacts on the executing accuracy of the Cartesian robots. In the manner of maximizing the stiffness, accordingly traditional rigid robotic manipulators are relatively heavy, increasing the volume, quality and energy consumption of the system.Thanks to the advantages of light weight, flexibility and low energy consumption, flexible manipulators can be used in robotics which effectively decrease the volume and quality of the system, approaching the development request for robots from rigid to flexible and are consistent with the trend of lightweight, high speed and integrated. However, due to the structural stiffness and damping are generally lower, the flexible manipulator surfers an issue about elastic deformations and residual vibrations during especially high speed executions, which are inevitable and seriously affect the executing accuracy and service life of the end-effector and even casue operation failure and economic lose. Thus, the research on the dynamic and vibration characteristics is the foundation of achieving the vibration control of the flexible manipulator as well as is significant for effectively addressing the urgent scientific issue about the development of robot from rigidity to flexibility. It should be noted that, as a complex electromechanical system, the flexible robot contains drive, sensing and mechanical components, and there are multi-field coupling in these subsystems which will arouase excitations through the transimission system, which is relatively obvious for the high speed light structure. For the mode of flexible manipulators are genegerally lower, these system excitations are considerable for flexible manipulators. Moreover, the mechanical joints and flexible factors in the flexible manipulator will further enhance the influence of the system excitations. Therefore, to accurately grasp the dynamic and vibration characteristics of the flexible manipulator, the coupling effects in the system should be fully considered. Funded by the National Natural Science Foundation of China, the Ministry of Education Doctoral Ffund Project, the Scientific and Technological Project of Jiangsu Province and the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions, with combining the structure and process feature of the Cartesian robot, this paper conducted the electromechanical coupling dynamics and vibrations of the flexible manipulator based on theoretical modeling, numerical simulation, virtual prototype and experimental tests. The main contents of this paper are as follows:(1) Establishing the dynamic model of the Cartesian flexible robot and constructing the experimental system. Combined with the motion features of the Cartesian robots, the dynamic model of the Cartesian flexible robot was established, and based on the Hamilton variational principle, the dynamic equations under translating movements, deploying movements and oblique movements were derived. According to these dynamic equations, the vibration characteristics of the flexible manipulator were analyzed. The initial conditions of the flexible manipulator during uniform movements were discussed and determined; then the vibration responses of flexible manipulator during uniform movements process were studied and compared with the result of virtual prototype for verification. Considering the structural properties of the flexible manipulator, the mechanical joints and the electromechanical coupling factors of the system, the Cartesian flexible robot experiment system was constructed based on the Cartesian robot structure, epoxy resin material flexible manipulator and bolted joints. The structure composition and feasibility of modeling the coupling system were detailed. With the experimental system, the vibration response tests of the flexible manipulator under different movements were conducted.(2) Establishing the elastic restraint model of the bolted joints in the flexible manipulator and exploring the mechanism of elastic restraints. Firstly, the elastic model of the bolted joints was established considering the linear restraint and torsional restraint, and according to the principle of virtual work, the boundary conditions of the flexible manipulator with elastic restraint were determined as well as the frequency equation and mode shape function were derivated. Based on this, the modal frequency and shape characteristics of the flexible manipulator under different restraint stiffness were analyzed, which clearly indicates the influence of the elastic restraint. Secondly, the influences of the linear stiffness and torsional stiffness on the frequency were analyzed using sensitivity method, as well as the elastic restraint region was determined, which was used for the curve fitting to characterize the relationship between the restraint stiffness and the frequencies. Based on this, the effect of the elastic restraint on the vibration characteristic was shown. Finally, the effectivity of the established elastic restraint model was verified through modal experiment, which provides the theoretical model for the electromechanical coupling dynamic characterisitics of the flexible manipulator with elastic restraint joints.(3) Conducting the electromechanical coupling dynamic modeling and virtual co-simulation experiments of the flexible manipulator. Considering the coupling effect in the system, a global coupling relationship and physical model was established, which contains electromagnetic system and mechanical system and integrates the drive system, transmission system and load actuators as a whole. Based on the electromechanical dynamics analysis method, the electromechanical coupling dynamic equation was derived, and according to this dynamic equation, the simulation model of flexible manipulator was establish using Matlab/Simulink software, which was used for revealing the motion fluctuations mechanism under electromechanical coupling. Based on the Matlab/Simulink and Adams/controls virtual prototype, the co-simulation prototype model was constructed, and then the co-simulation virtual experiment for the vibration responses of the flexible manipulator under electromechanical coupling was conducted.(4) Studying the parametrical vibration and stability of the flexible manipulator under electromechanical coupling effects. Firstly, based on the motion characteristic equation of the moving base, the parametrical vibration displacement equation of the flexible manipulator was derived. According to the parametrical vibration responses and spectrum, the influence of the motion fluctuations under electromechanical coupling was demonstrated. Secondly, the steady-state power flow was introduced which clearly reflected the vibration energy distribution in the flexible manipulator and the influence of the elastic restraint of the bolted joints. Finally, the multiple scales method was introduced to derive and determined the stability boundary of the parametrical vibration for the flexible manipulator, and the impact of the elastic restraint stiffness and the end-effector on the instability region was discussed. The theoretical model and analysis results were verified through experimental tests of the parametrical vibration.The results obtained in this paper are significant for conducting the dynamic and vibration characteristics of the flexible manipulator under multi-coupling state, which are the theoretical foundation of the electromechanical coupling vibration control of the flexible manipulator and contributes to the integrated design of robots.