Study On Measurement Model And Error Mechanism Of Long-range Nanometer Time-grating Displacement Sensors

The technologies and devices of long-range displacement measurement with nanometer accuracy and resolution are the key points of ultra-precision high-end equipments including CNC machine tools,grand scale integration circuit equipments,and national defense industry equipments.They are important indicators for evaluating the development level of the national precision manufacturing industry.However,it is technically challenging to achieve nanometer resolution and accuracy for displacement measuring over a long range in the world,which means they cannot be achieved simultaneously.Among the sensors which are presently available for meeting this challenge,optical encoders are in the dominant position in industrial application fields due to the advantages of high precision,long range,and high reliability.Because of the fundamental diffraction limit of the optical scanning method and grating fabrication,it is difficult to improve the performance of the optical encoders.In addition,the relevant original ideas and core technologies have been mastered by a few developed countries,and strictly blocked for other countries.The study of optical encoders in our country is mainly focused on the tracking study,which result in the technological laggard and dependent on imports of high-end optical encoders.Based on the time-grating technology with independent intellectual property,author's research group proposes a third generation time-grating sensor named nanometer time-grating,which is based on the capacitor array structure,and adopting the alternating electric field to construct a reference frame with stable motion.The time-grating measurement technology is adopted to break through the restriction of the resolution improvement;the plate capacitor structure serves as the sensing unit to reduce the required manufacturing precision;micro-nanofabrication technology is employed to realize the high efficient production.The above advantages offer great promise for breaking through the bottleneck of long-range nanometer measurement,achieving low cost production,and breaking up the foreign monopoly on this technique.Therefore,the deep research work of the nanometer time-grating sensor is launched in this paper,and the main research contents and innovations are listed as follows.(1)A feasible solution on the realization of the nanometer time-grating sensor with combining the time-grating measurement technology and electric field sensing mode is proposed.Based on this solution,three mathematical models including geometric model,circuit model,and electric field model,are established for the nanometer time-grating measurement principle.Doppler effect caused by the velocity of measured objects,the influence of the complex impedance in sinusoidal steady-state RC circuit,and the corresponding relationship between the spatial potential distribution,the capacitance variation and the sensing parameters are theoretically explained in detail,which lay the theoretical foundation for the sensor parameter design and error analysis.(2)From the aspect of the generation mechanism of traveling wave signals,the error theory based on the nanometer time-grating measurement principle is established,which explain the causes of the periodic errors and the long-range errors and the relationship between them.The error fitting model based on complex arithmetic is established for the first time,and the internal relations between the abnormal variables of amplitude,phase and frequency of each harmonic component of the periodic signals are revealed;thus,the measurement errors can be accurately quantified.This model can also be applied to the optical encoders or encoder-type capacitive sensors with using the tangent method.(3)The design of the sensing structures and sensing parameters and the error correction method are studied.A lead wire structure based on multilayer thin film is presented,which can suppress the influence of the cross interference.A single-row type sensing structure and a common mode rejection method based on differential induction electrodes are presented,which can further improve the signal stability,installation adaptability and anti-jamming ability of the sensor.Three features of the capacitive sensors including the filtering effect of the area integral method,the smoothing effect of the electric field,and the averaging effect of multiple induction electrodes are first revealed,which can greatly reduce the required manufacturing precision.Two kinds of spatial harmonic suppression methods including the interval to width ratio modulation method and the offset phase shift method are proposed.Finally,a set of design criteria for the nanometer time-grating sensor is formed,which lays the foundation for the development of the high-precision nanometer time-grating sensor.(4)An ultra-precision experimental platform is established,and a variety of prototype sensors with different materials and structures are developed.The performances including measurement accuracy,linearity,and periodic repeatability etc.are tested,which verify the correctness of the theoretical analysis.Finally,a prototype sensor with a stable measurement accuracy of ±200 nm over a 200 mm measurement range is developed,which has excellent anti-interference ability,stability,installation adaptability and lower manufacturing cost.In conclusion,through the combination of theory and practice,a complete theoretical system and design method of the nanometer time-grating are established in this paper,which have important significance in theoretical guidance.In addition,the error correction methods,the structure and the parameter optimization methods and the function expansion methods proposed in the paper also have important practical significance in engineering.The achievements in this paper make it possible to realize the substitution of optical encoders.