Theoretical And Experimental Research On Displacement Measurement Of Two-dimensional Nanometer Time-grating

With the continuous development of high-end manufacturing industry,nano displacement measurement technology not only ensures high precision and high resolution,but also has an increasingly urgent demand for large range,multi-dimensional and multi parameter measurement.Especially,the ultra precision machining equipment represented by nano CNC machine tool and high-end lithography machine is required to realize a large number of nanometer displacement measurement in X and Y directions.At present,there are mainly two methods to realize the two-dimensional displacement measurement: one is to realize the two-dimensional displacement measurement by using two sets of single degree of freedom sensors in the form of orthogonal installation,and the combined measurement method;the other is to realize the two-dimensional displacement measurement directly through a single sensor.In the first method,Abbe error is usually introduced into the installation and positioning,which reduces the measurement accuracy of the system,and has the disadvantages of complex structure and high cost.In the second method,the planar two-dimensional grating has always been in the leading position in this technical field,but it is difficult to achieve large-scale and high-precision manufacturing,which makes it difficult to further improve its performance.In addition,the research on planar two-dimensional grating in China lags behind the developed countries,and is still in the state of tracking research,lacking original core technology.Because of the long-term dependence on foreign high-precision displacement sensors,China has implemented a long-term blockade.Therefore,it is very important to study the two-dimensional displacement measurement technology with independent intellectual property rights.Therefore,based on the original one-dimensional nanometer time grating measurement technology,the author proposes a planar two-dimensional nano time grating displacement sensor based on the planar discrete capacitor array structure.The displacement reference is traced to the time by constructing a double uniform velocity coordinate system by alternating electric field,which solves the problem that the resolution is restricted by the grid distance.The requirement of manufacturing accuracy can be effectively reduced by using the flat capacitance as the sensor unit.Based on the nano time grating displacement measurement technology,this paper studies how to achieve the goal of large range and high precision displacement measurement in two-dimensional plane.The main research contents and innovations are as follows:(1)The principle of nanometer time grating measurement is described,and a planar two-dimensional nano time grating measurement method based on discrete grating array sensor is proposed.Firstly,an excitation electrode coding method based on planar orthogonal discrete grid space arrangement set is proposed.Firstly,the two one-dimensional excitation electrode arrays are discretized into square electrodes with equal spacing,and then staggered in the same plane in the form of black-and-white squares on the chess board.The two-dimensional encoding of excitation electrodes is ingeniously realized.Secondly,a planar two-dimensional nano time grating measurement model is established,and the output signal coupling mechanism of the sensor is explained.Finally,a signal decoupling method based on multi-channel signal combination operation is proposed.By constructing a kind of induction electrode array with special spatial arrangement law,a simple combination operation is used to filter out the spatial displacement information of non measurement direction,and the two-dimensional displacement measurement signal decoupling is realized.(2)The error theory based on the measurement principle of planar two-dimensional nanometer time grating is established,and the spatial harmonic characteristics caused by the electric field distribution of the sensor and the error coupling mechanism are revealed.A two-dimensional electric field model is constructed to reveal the spatial harmonic characteristics caused by the electric field distribution of the sensor.Based on the coupling mechanism of the output signal of the sensor,the error mathematical model is established,and the internal relationship between the spatial harmonics of different frequencies in the output signal and the measurement error is analyzed.The error coupling characteristics of the planar two-dimensional nano time grating sensor are studied under the conditions of different installation gap,unequal excitation amplitude,non orthogonal phase and high-frequency spatial harmonics.The coupling mechanism of non measurement direction spatial harmonics to measurement direction error before and after decoupling is analyzed,and the characteristics of large range error are revealed.(3)The simulation analysis of sensor measurement method and error coupling characteristics is carried out,and the spatial harmonic suppression method based on the shape structure of induction electrode is proposed.Firstly,the three-dimensional simulation model of planar two-dimensional nanometer time grating displacement sensor is established by finite element simulation software,and the output signal and coupling error characteristics of each link in the decoupling process are simulated and analyzed.Secondly,a spatial harmonic component suppression method based on the shape structure of the induction electrode is proposed.According to the characteristics of the variable area integral function curve of the induction electrode,the shape structure of the induction electrode is optimized with the sine function curve as the reference.The simulation results show that the spatial harmonic component is suppressed.(4)The experimental platform was built,and a 160mm×160mm planar two-dimensional nanometer time grating sensor prototype was developed.Many performances of the sensor including period error,coupling error,linearity,stability,repeatability,etc.were tested to verify the correctness of the theoretical analysis and simulation results.The experimental results show that the sensor prototype manufactured by PCB process has a measurement accuracy of ±5.88?m and a linearity of 0.059% in a period of 20 mm.The repeatability of error within the period is 0.0026%,which is better than 510 nm.In the two-dimensional plane160mm×160mm measuring range,the original measurement accuracy of X and Y directions are better than ±18.78?m and ±23.48?m,respectively.To sum up,according to the proposed method,theoretical analysis,electric field simulation and experimental verification,a relatively complete theoretical system and practical method of planar two-dimensional nanometer time grating are established.In addition,the coding and decoupling method,error coupling characteristics and error suppression method proposed in this paper have reference significance for the research of other capacitive displacement sensors.