Investigation Of Key Technologies On Spring Constant Calibration Of AFM Cantilevers

Atomic force microscope(AFM)is widely used as a tool for micro/nano surface morphology measurement,nanomanipulation and nanofabrication.It has become an indispensable and important measuring instrument in the field of micro/nanometer investigation.In recent years,the application of micro-newton force measurement has gradually become one of topic researches.However,the spring constant of AFM cantilever plays a vital role in micro/nanometer scale mechanical testing.The accuracy of spring constant directly affects the reliability of measurement result.Therefore,to calibrate spring constant accurately has great theoretical value and practical significance.Based on the characteristics of cantilevers and the practical problems in AFM mechanical measurement,this dissertation is mainly focusing on the spring constant calibration technology,establishing an electromagnetic driving system and a balance measurement system.Furthermore,the experiments of spring constant calibration have been implemented according to the null position measurement method,realizing to calibrate the spring constant of various types of cantilevers.The main contents are shown as follows:In order to improve the accuracy of spring constant calibration,a novel calibration method for actively loading electromagnetic force and displacement is proposed.An electromagnetic force actuator is designed,and the effects of structural parameters,current and permanent magnet on the electromagnetic force performance are investigated.A theoretical model of electromagnetic force is established.The conversion rate between current and electromagnetic force is studied by experiments,which also verifies the correctness of the theoretical model.Furthermore,the micro/nano positioning stage is used to drive the cantilever,combining with the null position measurement method,which solves the cumbersome problems during the calibration process.This research can provide effective theoretical guidance for spring constant calibration.In order to calibrate the spring constant of various types of cantilevers.Based on the null position measurement method,three types of flexible beam balancing devices with different stiffnesses are designed,through which the output displacement of the micro/nano positioning stage is transferred to the cantilever.Furthermore,the compliance matrix of flexible beam,Castigliano's theorem and theory of elasticity are used to analyze the stiffness of the single-arm flexible beam,the rotational symmetric flexible beam and the spiral flexible beam.The effects of the key parameters on the stiffness have been investigated,which are verified by simulation analysis and experimental test.This research improves the high precision spring constant calibration system and provides a hardware support for the research of spring constant calibration.To solve the problem of low calibration accuracy of cantilevers with low spring constant.Based on the elliptic integral method and pseudo-rigid-body method,the theoretical model of zero-stiffness mechanism has been established.The output displacement of the piezoelectric actuator is amplified by the Scott-Russell amplification mechanism and the lever mechanism.The dynamic characteristics of the stage are studied by simulation method and experiments.A PID controller is designed for closed-loop control of piezoelectric actuator,which reduces the hysteresis influence of the piezoelectric actuator,improving the motion accuracy of the zero-stiffness mechanism.This research provides a hardware foundation for the spring constant calibration.Based on the designed three types of flexible beams and zero-stiffness mechanism,the spring constant calibration systems are established,respectively.Then,several kinds of cantilevers are calibrated successfully.The effects of installation angle of cantilevers on the spring constant calibration results are studied,and a correction method for the spring constant calibration is proposed.Furthermore,the uncertainties of each calibration system are analyzed and summarized,respectively.The experimental results show that the developed spring constant calibration systems have good stability and reliability,which can effectively realize to calibrate the spring constant of AFM cantilevers accurately.