Based on the differential equation of the deflection curve for the beam,the equation of the deflection curve for the simple beamis obtained by integral. The equation of the deflection curve for the simple beamcarrying...Based on the differential equation of the deflection curve for the beam,the equation of the deflection curve for the simple beamis obtained by integral. The equation of the deflection curve for the simple beamcarrying the linear load is generalized,and then it is expanded into the corresponding Fourier series.With the obtained summation results of the infinite series,it is found that they are related to Bernoulli num-bers and π. The recurrent formula of Bernoulli numbers is presented. The relationships among the coefficients of the beam,Bernoulli numbers and Euler numbers are found,and the relative mathematical formulas are presented.展开更多
We develope a simple method to stabilize the beam during propagation. Combination of the self-developed control module and the large diameter mirrors reconstruct the beam stabilization system, and some important proce...We develope a simple method to stabilize the beam during propagation. Combination of the self-developed control module and the large diameter mirrors reconstruct the beam stabilization system, and some important procedures are presented, such as calibration arid average filter. The results show that the horizontal pointing and vertical pointing are stabilized to within 8.43 and 7.59 μrad, and the beam horizontal position and vertical position are stabilized to within 2.16 and 2.11 μm respectively. The regulating time is within 84 ms. Thus the method presented is effective for the current stabilization system applied in lithography tools.展开更多
基金Supported by the National Natural Science Foundation of China(51276017)
文摘Based on the differential equation of the deflection curve for the beam,the equation of the deflection curve for the simple beamis obtained by integral. The equation of the deflection curve for the simple beamcarrying the linear load is generalized,and then it is expanded into the corresponding Fourier series.With the obtained summation results of the infinite series,it is found that they are related to Bernoulli num-bers and π. The recurrent formula of Bernoulli numbers is presented. The relationships among the coefficients of the beam,Bernoulli numbers and Euler numbers are found,and the relative mathematical formulas are presented.
基金the National Science and Technology Major Project of China(No.2011ZX02402)the International Science & Technology Cooperation Program of China(No.2011DFR10010)
文摘We develope a simple method to stabilize the beam during propagation. Combination of the self-developed control module and the large diameter mirrors reconstruct the beam stabilization system, and some important procedures are presented, such as calibration arid average filter. The results show that the horizontal pointing and vertical pointing are stabilized to within 8.43 and 7.59 μrad, and the beam horizontal position and vertical position are stabilized to within 2.16 and 2.11 μm respectively. The regulating time is within 84 ms. Thus the method presented is effective for the current stabilization system applied in lithography tools.
