Size Optimization Of2-DOF Parallel Micro-positional Stage Driven By Piezo-actuator

In order to improve the static and dynamic characteristics of the2-DOF prototype micro-positional stage in our laboratory, the structural improvement and multi-target size optimization onthe prototype stage were proposed. And the simulation results of the analysis on static and dynamiccharacteristics based on finite element analysis (FEA) were presented. And the static and dynamiccharacteristic experiments on the new improved stage were implemented to verify the effectivenessof the structural optimization. The main contents of this study are as follows:Firstly, the structure improvement and size optimization on the original prototype stage werestudied. The redesign of the structure was made to overcome the shortage of the original prototypestage at the displacement uncoupling part. This new structural design can eliminate thedisplacement uncoupling of the stage. For the purpose to maintain the maximum stiffness under thecondition of given maximum displacement of the stage, the mathematical model for multi-targetsize optimization of the micro-positional stage was developed based on the deformation theory ofuniform section cantilever beam and the linear weighting method. Sequential quadraticprogramming (SQP) method based on the solution of the K-T equations was adopted to solve theoptimization problems. So the optimal size of circular arc flexible plate (32.9mm in radius,0.5mm in thickness,10.1mm in height) which meet the requirement be obtained.Secondly, the FEA on the static and dynamic characteristics of the stage after structuralimprovement and size optimization were presented. The static characteristics such as outputdisplacement and stress, and the dynamic characteristics such as vibration modal, frequencyresponse and step response of the stage were obtained by the finite element software ANSYS andWorkbench. And the simulation results of the analysis on static and dynamic characteristics werepresented. The maximum displacement of the stage is31.7μm under the maximum driving forceof500N, the simulation result meets the design requirement for the maximum output displacementat least30μm. The maximum deformation of the stage at the z direction is1.46μm under thevertical load of100N, the result is slightly beyond the design requirement for the maximum outputdeformation of1.0μm. The maximum stress of the stage is far less than the allowable stress underthe maximum driving force of500N and the vertical load of100N. The dynamic characteristicanalysis results show that: the natural frequencies of the stage after size optimization are increasedabout230Hz in the x or y direction at least, and about500Hz around the z axis at most. The response time of stage after size optimization is0.8ms at the step input displacement of5μm. Andthe biggest displacement oscillation amplitude is0.26μm. The oscillation time is12ms. The staticand dynamic characteristic analysis results show that the performance of the stage after structuralimprovement and size optimization is better than the original prototype. According to the results ofFEA after the structure improvement and size optimization, a new stage device was fabricated.Finally, the static and dynamic characteristic experiments on the new improved stage wereimplemented. From the experiments of the static and dynamic characteristics of the stage such asoutput displacement, displacement coupling, frequency response, and step response were obtained.The results of static characteristic experiments show that: under driving voltage up to150V on thepiezoelectric actuator, the displacements of the stage in x and y directions are13.7μm and12.6μmrespectively. These slightly difference in two directions is caused by the manufacture errors. Thecoupling displacements of the stage after structure improvement in x and y directions are0.47μmand0.50μm respectively. They are far less than3.18μm and4.19μm before structureimprovement. The reason is that the preload force direction of the screws for preloading to thepiezoelectric actuators is different from the driving direction, which causes the deflection of themovable part on the stage. The dynamic characteristic measurement results indicate: after structuraloptimization, the natural frequencies of x, y and z directions in the stage are1.725kHz,1.725kHzand1.781kHz respectively. The natural frequencies of x, y directions are superior to1.35kHz, thatof the original stage. And the response times in x and y directions are10ms and20ms respectively,greatly shorter than180ms and270ms of the original stage.