Measurement Model And Error Analysis Of Planar Two-dimensional Time-grating Displacement Sensor Based On Multi-frequency Magnetic Field Coupling

At present,high-end precision equipment represented by ultra-precision CNC machine tools and high-end lithography machines has become a major national strategic demand equipment.Ultra-precision displacement measurement technology and devices are one of the core technologies and key components of ultra-precision high-end equipment.It also puts forward higher requirements,that is,while ensuring high precision and high resolution,it also needs to meet multi-degree-of-freedom measurement.Ultra-precision processing equipment represented by lithography machines requires displacement measurement components to simultaneously realize large-scale ultra-precision displacement measurement in both X and Y directions of the system working platform within a limited installation space.At present,the relatively mature two-dimensional measurement technology includes two schemes,namely,the combined measurement scheme based on single-degree-of-freedom displacement measurement and the single-plane two-dimensional displacement sensor measurement scheme.The former achieves two-dimensional displacement measurement by installing two sets of single-degree-of-freedom displacement sensors orthogonally.The installation and positioning will introduce more error links,such as Abbe error,which limits the measurement accuracy,and has disadvantages such as high cost and complex structure.The latter eliminates the single-dimensional sensor combination link,and realizes twodimensional measurement through a single sensor.The most representative in the application and research level should be the planar two-dimensional grating technology.This technology has always been in the leading position in the industry,but the grating relies on ultra-my country is relatively weak in precision lithography technology,and the manufacturing accuracy of grating lines is limited by the optical diffraction limit,which hinders the further improvement of grating performance.To this end,the author’s research group proposed a planar two-dimensional time-grating displacement sensor based on the magnetic field type one-dimensional time-grating measurement technology.Focusing on how to realize twodimensional measurement based on one-dimensional time-grating measurement technology,the main research contents of this paper are as follows:(1)A planar two-dimensional time grating measurement method based on multifrequency magnetic field coupling and direct decoupling is proposed.Based on the law of electromagnetic induction,a planar coil magnetic field calculation model is established.According to the model,a uniform magnetic field array unit is designed and constructed.Based on this,two single-dimensional displacement sensors are designed to extend to a single dimension,and the two single-dimensional sensors are respectively developed.Experimental verification.Extending to the plane two-dimensionally,a two-dimensional uniform magnetic field array is constructed,a two-dimensional displacement measurement scheme of multi-frequency magnetic field coupling excitation and direct decoupling is proposed,a two-dimensional sensor structure model is designed,and how to avoid X and Y directions is discussed in detail.Crosstalk between signals and how to achieve direct decoupling and two-dimensional displacement calculation.(2)Based on the magnetic field-type planar two-dimensional time-grating measurement principle,the error analysis of the planar two-dimensional sensor is carried out.Firstly,starting from the uniform magnetic field array unit,a mathematical model of the excitation magnetic field is established,and the error components of unequal amplitude and nonorthogonal phase of the induced signal are respectively analyzed based on the harmonic analysis method.Secondly,the source and influence of the end effect of the sensor are analyzed,and the suppression scheme of the end effect is proposed,and further simulation and experimental verification are carried out for the proposed scheme.Finally,the sensor installation error is discussed,the common installation errors are analyzed respectively,and the corresponding error components are obtained.(3)The sensor simulation analysis research has been carried out.Firstly,a threedimensional simulation model of sensor direct decoupling and displacement calculation was established,and the direct decoupling simulation and single and two-dimensional marching simulation analysis were carried out respectively,and the correctness and feasibility of the direct decoupling scheme and two-dimensional measurement theory were verified.Secondly,the common installation errors of sensors and different installation air gaps are simulated and analyzed respectively,and the characteristics and laws of sensor errors are analyzed.Finally,the structure and parameters of the sensor are optimized based on the simulation results.(4)The sensor prototype was developed and a two-dimensional experimental platform was built to carry out experimental research on the sensor.The single-dimension inner traveling experiment,the two-dimensional inner traveling experiment under different air gaps,the differential structure performance test experiment and the sensor performance test experiment were respectively designed to verify the correctness of the theory and simulation.The experimental results show that: the sensor is in the Within the measurement range of150 mm×150 mm,the linearity of the X and Y measurement directions to the pole is 0.98%and 1.2%,respectively,and the measurement errors are ±33.08 μm and ±36.95 μm,respectively.