Chatter vibrations in robotic milling considering structural nonlinearity




Mohammadi, Yaser

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The application of robotic manipulators in machining systems has gained a great interest in manufacturing because of their lower prices, higher kinematic flexibility and larger workspace compared to conventional CNC machine tools. However, their performance is limited due to the much lower structural rigidity which makes them more susceptible to excessive and unstable vibrations, known as chatter, during the machining process. Highly effective chatter modeling and avoidance methods that have been developed for CNC machining in the past decades are now being used by the industry to design high-performance chatter-free machining operations. The available methods, however, face major difficulties when applied to robotic machining, mainly due to the high flexibility and pose-dependency of the vibration response in robots. High flexibility leads to high-amplitude vibrations which affect the process dynamics and excite structural nonlinearities. The existing approaches to modeling machining vibrations assume linearity of the structural dynamics of the robotic manipulator. This assumption, considering the inherent nonlinearities in the robot’s revolute joints, may cause considerable inaccuracies in predicting the stability of vibrations during the process. This thesis studies the high flexibility and nonlinearity of the robot’s structural dynamics and their effects on chatter vibrations. The research starts with investigating the effects of high flexibility of robot's structure in the process dyamics by considering the modulation of cutting forces by axial vibrations, which is normally ignored in CNC milling due to high rigidity of the machine in this direction. The results of chatter prediction considering this effect are shown and discussed. The rest of the thesis focuses on the structural nonlinearity. Firstly, an experimental study is presented to investigate the extent of nonlinearity in structural dynamics of the robot. The results confirm that structural nonlinearities in robotic machining systems can be effectively excited in the presence of high-amplitude vibrations due to milling forces, such that they cause remarkable differences in chatter prediction. The following step is modeling the structural nonlinearities. For this purpose, the variation of restoring forces with the dynamic response (displacement and velocity) are observed when the robot is subjected to harmonic excitation. Based on the experimental observations, the nonlinear effects are modeled by cubic stiffness and damping characteristics. Parameters of the nonlinear model are then identified using Higher-order Frequency Response Functions (HFRF) extracted from measurements. The identified model can predict the vibration behavior of the robotic machining system when subjected to periodic loads such as milling forces. The developed model of nonlinear structural dynamics is then coupled with the chatter model. Consequently, the system is described by nonlinear Delay Differential Equations (DDE) with periodic coefficients. Bifurcation diagrams for the forced vibrations in the described system are developed using the numerical continuation method. The effects of cutting parameters such as feedrate as well as the nonlinear parameters are studied. The thesis is concluded by proposing the use of in-process FRF in the linear model of chatter stability for quick prediction of stability limits. In this approach, the exact characteristics of the nonlinear mechanisms are not studied; instead, the measured FRF during the milling process are used, which are assumed to represent the nonlinear structural dynamics that are linearized about the applied operational conditions. Two methods of measuring in-process FRF are proposed and employed in the robotic milling system. The measured FRF are then used in the linear chatter model to develop the Stability Lobes Diagram (SLD) which shows the combination of cutting parameters that lead to stable or unstable vibrations. Experimental chatter tests show that better agreement with predictions can be achieved by using in-process FRF instead of FRF measured at the idle state of the system. The results of this thesis contribute to better characterization of vibrations in robotic machining with high-amplitude forces and selecting suitable strategies to enhance productivity of the operation.



Vibration, Dynamics, Machining, Robot, Nonlinearity, Nonlinear dynamics, Chatter, Robotic Milling, Frequency Response Function (FRF)