Nonlinear Deflection Analysis,Optimization Design,and Applications Of Corner-Fillet Leaf-Spring

With the rapid development of consumer electronics,the micro-electronics manufacturing industry has become a new economic growth point.But the micro-electronics manufacturing technologies of China are far behind that of the developed countries.High-speed precise positioning systems are the key component of many types of manufacturing equipment used for microelectronics manufacturing processing,such as wafer manufacturing,chip processing,and packaging.Micro-macro compound systems are commonly used to balance the conflict between work-stroke and positioning accuracy,but the laminated design presents some disadvantages such as micro driver saturation,serious coupling of the switching process,low positioning efficiency,and high cost.Two sets of drive control systems of these systems also lead to an accumulation of manufacturing error and positioning error.In order to handle the drawbacks of these systems,we proposed a single drive rigid-flexible coupling motion stage by combining the large stroke of linear motors and the elastic deflection of nano stage based on flexure hinge in our previous works.This motion stage improves the positioning accuracy by compensating the friction of the rigid guide with the elastic deflection of the flexure hinge.Corner-fillet leaf-spring(CFLS)is proposed as an alternative to straight beams to improve the stress concentration effect caused by the sudden shape change.The nonlinear deflection of CFLSs is investigated for the large stroke applications and the mechanical design using this nonlinear theory is also carried out in the rest sections of this work.Firstly,the nonlinear deflection of CFLS under the fixed-free and fixed-guided constraints are investigated and the accuracy of the closed-form formulas are verified by finite element analysis(FEA)results and experimental results.An optimization design case is provided to illustrate the usage of the proposed nonlinear model and the maximum stress of the CFLS design is decreased by 33%when compared with the optimal results of beam-based design under the same optimization model.The buckling deflection of CFLS is also researched and the formula of critical buckling load for CFLS is provided.The design of a multi-beam compliant parallelogram mechanism is accomplished by utilizing the energy formulas of CFLSs whose efficiency is verified by FEA results.Secondly,a guiding mechanism using orthogonally oriented corner-fillet leaf-spring(CFLS)and hybrid leaf spring(HLS)is proposed to improve the stiffness along the degrees-of-constraint(DOC)and reduce stress concentration.A kinetostatic model is developed by taking the nonlinear deflection of CFLS and HLS into account,based on which the mechanism is optimized by simultaneously considering the topology and size.As compared to the performance of traditional design obtained with the same optimization objective and constraints,the optimal design effectively improves the stiffness along the DOC,which is also validated by the FEA results and experimental results.Then,a stiffness-adjustable micro-motion is proposed to offset the gaps between the design values and actual performance caused by the modeling errors accumulation and machining error by utilizing the nonlinearity of corner-fillet leaf spring(CFLS).Simplified stiffness formulas of right circular flexure hinge(RCFH)and fixed-guided CFLS are provided for easy design.The accurate model is built for the calculation of the displacement amplification ratio and stiffness by taking the deflection of the link lever and adjustment mechanism into account.The adjustment performance of the proposed mechanism is modeled by utilizing the nonlinear deflection of CFLS.The design models are verified using FEA results which presents a good agreement.Experimental investigations are carried out to illustrate the adjustment performance of the proposed micro-motion stage.Finally,the optimization model of the micro-motion stage is modified for the large stroke,fast dynamic response,and better capabilities to resist disturbances and the optimization algorithm is introduced.A self-adaptive penalty function is adopted to handle the nonlinear constraints for its advantage of avoiding the definition of penalty parameters,and the differential evolution algorithm is utilized to obtain the globally optimal solution for its high computational efficiency.A new scheme for the layout of flexure hinges is proposed to enhance the torsional stiffness.The micro-motion stage is designed using the modified optimization model and the results show that the modified optimization model provides a more compact structure and larger resonant frequency.