Study On Piezoelectric Actuators Based Active Control For Suppressing Chatter In Milling

Because the milling is capable of manufacturing products with high precision,special structures and new materials,which are widely used in the areas of aerospace,defense industry and precision instrument,and the micro-milling is able to manufacture products with 3D features,miniature sizes and various materials,which are highly demanded in the areas of biomedical,precision optics and electronics manufacturing,they have been attracting the attention from the industry and academia.However,one of the obstacles in both the milling and micro-milling is the regenerative chatter which is known as the self-excited vibration between cutter and workpiece.It can lead to catastrophic results,such as tool wear and even tool breakage.And unstable regenerative chatter will leave vibration waves on workpiece surface,producing poor surface finish(mainly refers to the surface roughness)and reducing the manufacturing reliability.Therefore,it is critical to suppress the regenerative chatter for satisfying the increasing demands of higher surface finish and higher manufacturing reliability.In this dissertation,the regenerative chatter in the micro-milling with the process damping effect and that in the milling with the nonlinear cutting forces are investigated.Based on the active control strategy with the piezoelectric actuators(PZTAs)as control elements,three controllers will be developed to suppress the regenerative chatter in the micro-milling and milling,provide a new perspective on chatter control and promote the practical application of active control system.The main contents and features of this dissertation are summarized as follows:1.The whole system for suppressing the regenerative chatter in the micro-milling is established by combining the models of PZTA and the regenerative chatter.Considering the parameter uncertainties and the time-delayed effect of regenerative chatter,an active control approach is developed to suppress the regenerative chatter by employing the backstepping design method,adaptive control scheme,Lyapunov-Krasovskii functionals,and neural networks(NNs).The main features of the developed control strategy are: 1)The Lyapunov-Krasovskii functionals are used to deal with the time-delayed effect of the regenerative mechanism of chatter.2)The NNs are applied to estimate the unknown terms,including the uncertain parts of the regenerative chatter model and the unknown bounding functions related to the time-delayed tool vibrations.3)The adaptive control scheme is adopted to achieve the robustness of the developed controller.The stability and convergence of the whole system with the developed controller are proved.Simulations are showed to present the validity of the investigated control approach.2.An adaptive control approach for suppressing the regenerative chatter in the micromilling is developed by using the fuzzy neural networks(FNNs),dynamic surface control method,Lyapunov-Krasovskii functionals,prescribed performance functions and backstepping design scheme,where the parameter uncertainties and time-delayed effect of the regenerative chatter,and the hysteresis nonlinearity of PZTAs are considered.The main features of the developed control approach are: 1)FNNs are employed to approximate the unknown functions related to the unknown parts of the regenerative chatter model,time-delayed tool vibrations and intermediate virtual control signals;2)To reduce the calculation burden of computing the adaptation law for each individual weight of the FNNs,the squared 2-norms of the weight vectors are applied;3)The utilization of two prescribed performance functions guarantee the boundedness of the tracking errors with the prescribed performance;4)The Prandtl-Ishlinskii(PI)model is adopted to demonstrate the hysteresis nonlinearity of PZTAs and its inverse construction is employed to eliminate the hysteresis influence;5)The control approach with the application of dynamic surface control method,Lyapunov-Krasovskii functionals,adaptive backstepping design scheme based on FNNs and prescribed performance functions is investigated to suppress the regenerative chatter in the micro-milling.The stability of the whole system with the developed controller is proved.Simulation results are provided to validate the effectiveness of the developed control approach.3.Considering the regenerative chatter model for the milling with the nonlinear cutting forces which are nonlinear functions of variations of tool vibrations,the feedback control strategy is employed to suppress the regenerative chatter.The main features of this work are: 1)The feedback control algorithm and the regenerative chatter model are combined for suppressing the regenerative chatter.2)Two PZTAs are adopted to suppress the regenerative chatter in the milling with the nonlinear cutting forces.The stability of the whole system is proved.And several simulations are carried out to verify the effectiveness of the developed controller.4.Based on the previous research work,the active control strategy developed by the research work 2,which can address the parameter uncertainties and time-delayed effect of the regenerative chatter,and the hysteresis influence of the PZTAs,will be further explored for suppressing the regenerative chatter in the milling with the nonlinear cutting forces.The differences between this work and the research work 2 are: 1)The employed regenerative chatter models are different.The nonlinear cutting forces which are nonlinear functions of variations of tool vibrations are included and the process damping effect is neglected in the regenerative chatter model used in this research work;The regenerative chatter model for the micro-milling considered by the research work 2 involves with the process damping effect;2)The processes of proving the closed loop stability are not the same.In this work,the mathematical expressions related to the nonlinear functions of variations of tool vibrations are separated,scaled and approximated to accomplish the stability proof.The stability of the closed loop system is included.The validity of the developed control strategy is revealed by simulations.This part of the dissertation illustrates that the active controller developed by the research work 2 can be adopted to suppress the regenerative chatter in the milling.