The discontinuity of linear tool path(or G01 blocks) brings about unnecessary feedrate deceleration and fluctuation during machining. To improve the continuity, the linear tool path is usually smoothed by the local tr...The discontinuity of linear tool path(or G01 blocks) brings about unnecessary feedrate deceleration and fluctuation during machining. To improve the continuity, the linear tool path is usually smoothed by the local transition method or the global fitting method. For micro-line tool path, the transition method will significantly decrease the machining efficiency and introduce feedrate fluctuation. The global fitting method cannot be directly used in the NC interpolation because the indispensable chord error checking and iterative fitting processes are computation-intensive. This paper presents a general, fast and robust B-spline fitting scheme under chord error constraint for high speed interpolation of micro-line tool path. The proposed fitting method guarantees the chord error by utilizing the strong convex hull property of B-spline curves. The knot vector and control points are initially generated by a progressive iterative approximation method and locally refined to conform to the chord error constraint by using an analytical method. The analytical approximation and refining methods avoid solving a linear system of equations that is necessary in the standard B-spline fitting method. The feasibility and efficiency of the proposed scheme has been verified via simulations and experiments. Compared with the traditional fitting method, the proposed scheme can strictly constrain the chord error and can significantly decrease the computational load. Compared with the transition scheme, the proposed scheme can significantly increase the machining efficiency for the same micro-line tool path under the same chord error tolerance.展开更多
Adopted the distribution feedback type (DFB) laser to measure the coal mine gas methane,according to the methane located 1.6 tJm nearby 2v3 with a R9 direct ab- sorption spectrum,attraction wire intensity of each line...Adopted the distribution feedback type (DFB) laser to measure the coal mine gas methane,according to the methane located 1.6 tJm nearby 2v3 with a R9 direct ab- sorption spectrum,attraction wire intensity of each line was calculated through the multi-line Voigt fitting.The experimental result indicates that in the obtained four attraction recover of wire,the maximum deviation is 2.7%,and the minimum deviation is 0.02%, other results are all in experimental error scope.This research method may apply in the spectrum survey methane gas density,it has characteristics including high precision, strong selectivity,fast response and so on.展开更多
For absorption linewidth inversion with wavelength modulation spectroscopy（WMS）, an optimized WMS spectral line fitting method was demonstrated to infer absorption linewidth effectively, and the analytical expressio...For absorption linewidth inversion with wavelength modulation spectroscopy（WMS）, an optimized WMS spectral line fitting method was demonstrated to infer absorption linewidth effectively, and the analytical expressions for relationships between Lorentzian linewidth and the separations of first harmonic peak-to-valley and second harmonic zero-crossing were deduced. The transition of CO_2 centered at 4991.25 cm^（-1） was used to verify the optimized spectral fitting method and the analytical expressions. Results showed that the optimized spectra fitting method was able to infer absorption accurately and compute more than 10 times faster than the commonly used numerical fitting procedure. The second harmonic zero-crossing separation method calculated an even 6 orders faster than the spectra fitting without losing any accuracy for Lorentzian dominated cases. Additionally, linewidth calculated through second harmonic zero-crossing was preferred for much smaller error than the first harmonic peak-to-valley separation method. The presented analytical expressions can also be used in on-line optical sensing applications, electron paramagnetic resonance, and further theoretical characterization of absorption lineshape.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.51475302,U1537209)the Shanghai Municipal Scienceand Technology Commission(Grant No.17XD1422500)
文摘The discontinuity of linear tool path(or G01 blocks) brings about unnecessary feedrate deceleration and fluctuation during machining. To improve the continuity, the linear tool path is usually smoothed by the local transition method or the global fitting method. For micro-line tool path, the transition method will significantly decrease the machining efficiency and introduce feedrate fluctuation. The global fitting method cannot be directly used in the NC interpolation because the indispensable chord error checking and iterative fitting processes are computation-intensive. This paper presents a general, fast and robust B-spline fitting scheme under chord error constraint for high speed interpolation of micro-line tool path. The proposed fitting method guarantees the chord error by utilizing the strong convex hull property of B-spline curves. The knot vector and control points are initially generated by a progressive iterative approximation method and locally refined to conform to the chord error constraint by using an analytical method. The analytical approximation and refining methods avoid solving a linear system of equations that is necessary in the standard B-spline fitting method. The feasibility and efficiency of the proposed scheme has been verified via simulations and experiments. Compared with the traditional fitting method, the proposed scheme can strictly constrain the chord error and can significantly decrease the computational load. Compared with the transition scheme, the proposed scheme can significantly increase the machining efficiency for the same micro-line tool path under the same chord error tolerance.
基金the National Natural Science Foundation of China(50574005)Natural Science Foundation of Education Department of Anhui,China(2005KJ081)
文摘Adopted the distribution feedback type (DFB) laser to measure the coal mine gas methane,according to the methane located 1.6 tJm nearby 2v3 with a R9 direct ab- sorption spectrum,attraction wire intensity of each line was calculated through the multi-line Voigt fitting.The experimental result indicates that in the obtained four attraction recover of wire,the maximum deviation is 2.7%,and the minimum deviation is 0.02%, other results are all in experimental error scope.This research method may apply in the spectrum survey methane gas density,it has characteristics including high precision, strong selectivity,fast response and so on.
基金Project supported by the National Natural Science Foundation of China(Grant No.61505142)the Tianjin Natural Science Foundation(Grant No.16JCQNJC02100)
文摘For absorption linewidth inversion with wavelength modulation spectroscopy（WMS）, an optimized WMS spectral line fitting method was demonstrated to infer absorption linewidth effectively, and the analytical expressions for relationships between Lorentzian linewidth and the separations of first harmonic peak-to-valley and second harmonic zero-crossing were deduced. The transition of CO_2 centered at 4991.25 cm^（-1） was used to verify the optimized spectral fitting method and the analytical expressions. Results showed that the optimized spectra fitting method was able to infer absorption accurately and compute more than 10 times faster than the commonly used numerical fitting procedure. The second harmonic zero-crossing separation method calculated an even 6 orders faster than the spectra fitting without losing any accuracy for Lorentzian dominated cases. Additionally, linewidth calculated through second harmonic zero-crossing was preferred for much smaller error than the first harmonic peak-to-valley separation method. The presented analytical expressions can also be used in on-line optical sensing applications, electron paramagnetic resonance, and further theoretical characterization of absorption lineshape.
