Dynamic Modeling And Analysis Of Robot Arm With Consideration Of Clearance In Gear Reducer

Gear reducer is widely used in manipulator system, in which the gear pairs have certainbacklash because of manufacture error and other reasons. However nonlinear factors in gearreducer, such as backlash and time-varying meshing stiffness, can lead the manipulator armsystem to have strong nonlinear dynamic characteristics. Because the nonlinear factors ofreducer can make considerable contribution to dynamic response of the manipulator system,the dynamic modeling of manipulator system with consideration of these factors wasdiscussed and the influence of different factors on the dynamic response was analyzed, whichcan provide a theoretical basis for the vibration control of manipulator system.The flexible manipulator system with a planetary gear reducer was studied. The dynamicmodel of planetary gear reducer with consideration of clearance and time-varying meshingstiffness was built by adopting lumped mass method. Based on assumption of Euler-Bernoullibeam and the assumed mode method, the elastic deformation of the flexible robot arm waspresented. Based on the dynamic model, an energy criterion which is based on theconvergence degree of vibration energy was introduced to act as a new method of modaltruncation and the influence of different factors and working conditions on the number oftruncation modal when dynamic response of manipulator system is convergent, and the changeof convergent modal with the variation of factors was made clear which provides a foundationfor the system model order reduction and subsequent dynamics analysis. Nonlinear dynamicsanalysis methods was used to analyze the influence o f backlash on the manipulator system,and the results indicate that the dynamic responses of the manipulator system changeobviously when clearance in gear reducer is considered and the clearance become thedominant factor to influence the positioning precision of the robot arm with the increment ofclearance. In addition, the variation of the excitation frequency and the coupled effect ofclearance in the reducer and the flexibility of manipulator arm can also have influence ondynamic response of the manipulator system.The concept of modal energy was introduced to research modal energy distributions indifferent working conditions and to analyze the modal energy transfer between differentmodals. The residual vibration of flexible manipulator arm and the influence of factors on themodal energy distribution and transfer of the manipulator arm system were analyzed. Theresults can contribute to find out the mechanism of manipulator vibration and provide atheoretical reference to the vibration control of the manipulator system.