Rainbow particle image velocimetry(PIV)can restore the three-dimensional velocity field of particles with a single camera;however,it requires a relatively long time to complete the reconstruction.This paper proposes a...Rainbow particle image velocimetry(PIV)can restore the three-dimensional velocity field of particles with a single camera;however,it requires a relatively long time to complete the reconstruction.This paper proposes a hybrid algorithm that combines the fast Fourier transform(FFT)based co-correlation algorithm and the Horn–Schunck(HS)optical flow pyramid iterative algorithm to increase the reconstruction speed.The Rankine vortex simulation experiment was performed,in which the particle velocity field was reconstructed using the proposed algorithm and the rainbow PIV method.The average endpoint error and average angular error of the proposed algorithm were roughly the same as those of the rainbow PIV algorithm;nevertheless,the reconstruction time was 20%shorter.Furthermore,the effect of velocity magnitude and particle density on the reconstruction results was analyzed.In the end,the performance of the proposed algorithm was verified using real experimental single-vortex and double-vortex datasets,from which a similar particle velocity field was obtained compared with the rainbow PIV algorithm.The results show that the reconstruction speed of the proposed hybrid algorithm is approximately 25%faster than that of the rainbow PIV algorithm.展开更多
The paper presents two methods for the formulation of free vibration analysis of collecting electrodes of precipitators.The first,called the hybrid finite element method, combines the finit element method used for cal...The paper presents two methods for the formulation of free vibration analysis of collecting electrodes of precipitators.The first,called the hybrid finite element method, combines the finit element method used for calculations of spring deformations with the rigid finite element method used to reflect mass and geometrical features,which is called the hybrid finite element method.As a result,a model with a diagonal mass matrix is obtained.Due to a specific geometry of the electrodes,which are long plates of complicated shapes,the second method proposed is the strip method which is a semi-analytical method.The strip method allows us to formulate the equations of motion with a considerably smaller number of generalized coordinates.Results of numerical calculations obtained by both methods are compared with those obtained using commercial software like ANSYS and ABAQUS.Good compatibility of results is achieved.展开更多
In order to analyze the electrostatic field concerned with electrostatic proximity fuze problem using the available finite analysis software package, the technology to model the problem with a scale reduction object a...In order to analyze the electrostatic field concerned with electrostatic proximity fuze problem using the available finite analysis software package, the technology to model the problem with a scale reduction object and boundary was presented. The boundary is determined by the maximum distance the sensor can detect. The object model is obtained by multiplying the terms in Poisson's equation with a scale reduction factor and the real value can be reconstructed with the same reverse process after software calculation. Using the finite element analysis program, the simulation value is close to the theoretical value with a little error. The boundary determination and scale reduction method is suitable to modeling the irregular electrostatic field around air targets, such as airplane, missile and so on, which is based on commonly used personal computer (PC). The technology reduces the calculation and storage cost greatly.展开更多
The model and analysis of the cantilever beam adhesion problem under the action of electrostatic force are given. Owing to the nonlinearity of electrostatic force, the analytical solution for this kind of problem is...The model and analysis of the cantilever beam adhesion problem under the action of electrostatic force are given. Owing to the nonlinearity of electrostatic force, the analytical solution for this kind of problem is not available. In this paper, a systematic method of generating polynomials which are the exact beam solutions of the loads with di?erent distributions is provided. The polynomials are used to approximate the beam displacement due to electrostatic force. The equilibrium equation o?ers an answer to how the beam deforms but no information about the unstuck length. The derivative of the functional with respect to the unstuck length o?ers such information. But to compute the functional it is necessary to know the beam deformation. So the problem is iteratively solved until the results are converged. Galerkin and Newton-Raphson methods are used to solve this nonlinear problem. The e?ects of dielectric layer thickness and electrostatic voltage on the cantilever beam stiction are studied. The method provided in this paper exhibits good convergence. For the adhesion problem of cantilever beam without electrostatic voltage, the analytical solution is available and is also exactly matched by the computational results given by the method presented in this paper.展开更多
In this paper, the effect of van der Waals (vdW) force on the pull-in behavior of electrostatically actuated nano/micromirrors is investigated. First, the minimum po- tential energy principle is utilized to find the...In this paper, the effect of van der Waals (vdW) force on the pull-in behavior of electrostatically actuated nano/micromirrors is investigated. First, the minimum po- tential energy principle is utilized to find the equation gov- erning the static behavior of nano/micromirror under electro- static and vdW forces. Then, the stability of static equilib- rium points is analyzed using the energy method. It is found that when there exist two equilibrium points, the smaller one is stable and the larger one is unstable. The effects of dif- ferent design parameters on the mirror's pull-in angle and pull-in voltage are studied and it is found that vdW force can considerably reduce the stability limit of the mirror. At the end, the nonlinear equilibrium equation is solved numer- ically and analytically using homotopy perturbation method (HPM). It is observed that a sixth order perturbation approx- imation can precisely model the mirror's behavior. The re- suits of this paper can be used for stable operation design and safe fabrication of torsional nano/micro actuators.展开更多
The plane medium and point charge are regarded as an integral system. The static field's distribution situation of the point charge is studied in the medium structure of plane division layers by using mirror image me...The plane medium and point charge are regarded as an integral system. The static field's distribution situation of the point charge is studied in the medium structure of plane division layers by using mirror image method, drawing the point charge's calculation expression of the electric potential in every medium space. The mathematics model of passive electrostatic detecting people through the medium (regular distance between the goal point charge and the medium) is established, using MATLAB software to carry out emulation of the model and analysing the result, establishing the theoretical foundation for studying the technology of the passive static detecting people through the wall.展开更多
This paper uses the Lie algebraic method to analyse the charged particle trajectories in the spherical electrostatic analyser, and obtains the nonlinear solutions. The results show that the focusing abilities both in ...This paper uses the Lie algebraic method to analyse the charged particle trajectories in the spherical electrostatic analyser, and obtains the nonlinear solutions. The results show that the focusing abilities both in the x and y directions of the analyser are almost the same. Moreover, there exist dispersion effects in the x direction, and no dispersion effects in the y direction.展开更多
Asymmetric electrostatic forces are a very interesting and new phenomenon. The magnitude of an electrostatic force that acts on a point charge does not change when the direction of the electric field is reversed. On t...Asymmetric electrostatic forces are a very interesting and new phenomenon. The magnitude of an electrostatic force that acts on a point charge does not change when the direction of the electric field is reversed. On the contrary, the magnitude of the electrostatic force that acts on a charged asymmetric shaped conductor does change when the direction of the electric field is reversed. 5 years ago, this phenomenon was reported by a simple experiment and a simulation and named as an Asymmetric electrostatic force unofficially by the author. After that, several simulations confirmed this phenomenon. However, several experiments did not yet confirm it clearly. The difference between the simulations and the experiments depends upon differences of their conditions. The simulations had been done under ideal (perfect) conditions;the experiments, on the contrary, had been done under actual (not perfect) conditions. In the new experiment, its conditions were improved to near ideal (perfect) conditions. As a result the existence of the Asymmetric electrostatic force was more clearly confirmed.展开更多
The effect of a high frequency (HF) electric field on the propagation of electrostatic wave in a 2D non-uniform relativistic plasma waveguide is investigated. A variable separation method is applied to the two-fluid...The effect of a high frequency (HF) electric field on the propagation of electrostatic wave in a 2D non-uniform relativistic plasma waveguide is investigated. A variable separation method is applied to the two-fluid plasma model. An analytical study of the reflection of electrostatic wave propagation along a magnetized non-uniform relativistic plasma slab subjected to an intense HF electric field is presented and compared with the case of a non relativistic plasma. It is found that, when the frequency of the incident wave is close to the relativistic electron plasma frequency, the plasma is less reflective due to the presence of both an HF field and the effect of relativistic electrons. On the other hand, for a low-frequency incident wave the reflection coefficient is directly proportional to the amplitude of the HF field. Also, it is shown that the relativistic electron plasma leads to a decrease in the value of reflection coefficient in comparison with the case of the non relativistic plasma.展开更多
Stochastic resonance (SR) is studied in a gain-noise model of a single-mode laser driven by a coloured pump noise and a quantum noise with cross-correlation between real and imaginary parts under a direct signal mod...Stochastic resonance (SR) is studied in a gain-noise model of a single-mode laser driven by a coloured pump noise and a quantum noise with cross-correlation between real and imaginary parts under a direct signal modulation. By using a linear approximation method, we find that the SR appears during the variation of signal-to-noise ratio (SNR) separately with the pump noise self-correlation time τ, the noise correlation coefficient between the real part and the imaginary part of the quantum noise λq, the attenuation coefficient γ' and the deterministic steady-state intensity I0. In addition, it is found that the SR can be characterized not only by the dependence of SNR on the noise variables of and λq, but also by the dependence of SNR on the laser system variables of γ and I0. Thus our investigation extends the characteristic quantity of SR proposed before.展开更多
A trial solution for bending deflection of a multilayered micro-bridge subject to a voltage induced load is presented. The relation between the applied voltage and the displacements of the micro-bridge in the pull-in ...A trial solution for bending deflection of a multilayered micro-bridge subject to a voltage induced load is presented. The relation between the applied voltage and the displacements of the micro-bridge in the pull-in state is analyzed by energy method. Furthermore, two analytical expressions about normalized displacement and pull-in voltage are carried out. It’s proved that the value of normalized displacement is not influenced by residual stress if axial and shear deformation is ignored. Finally, the theoretical results are compared with that of FEM, and they show good agreement.展开更多
The precision and reliability of first-arrival picking are crucial for determining the accuracy of geological structure inversion using active source ocean bottom seismometer(OBS)refraction data.Traditional methods fo...The precision and reliability of first-arrival picking are crucial for determining the accuracy of geological structure inversion using active source ocean bottom seismometer(OBS)refraction data.Traditional methods for first-arrival picking based on sample points are characterized by theoretical errors,especially in low-sampling-frequency OBS data because the travel time of seismic waves is not an integer multiple of the sampling interval.In this paper,a first-arrival picking method that utilizes the spatial waveform variation characteristics of active source OBS data is presented.First,the distribution law of theoretical error is examined;adjacent traces exhibit variation characteristics in their waveforms.Second,a label cross-correlation superposition method for extracting highfrequency signals is presented to enhance the first-arrival picking precision.Results from synthetic and field data verify that the proposed approach is robust,successfully overcomes the limitations of low sampling frequency,and achieves precise outcomes that are comparable with those of high-sampling-frequency data.展开更多
Copper azide(CA), as a primary explosive with high energy density, has not been practically used so far because of its high electrostatic sensitivity. The Cu2O@HKUST-1 core-shell structure hybrid material was synthesi...Copper azide(CA), as a primary explosive with high energy density, has not been practically used so far because of its high electrostatic sensitivity. The Cu2O@HKUST-1 core-shell structure hybrid material was synthesized by the “bottle around ship” methodology in this research by regulating the dissolution rate of Cu2O and the generation rate of metal-organic framework(MOF) materials. Cu2O@HKUST-1 was carbonized to form a Cu O@porous carbon(CuO@PC) composite material. CuO@PC was synthesized into a copper azide(CA) @PC composite energetic material through a gas-solid phase in-situ azidation reaction.CA is encapsulated in PC framework, which acts as a nanoscale Faraday cage, and its excellent electrical conductivity prevents electrostatic charges from accumulating on the energetic material’s surface. The CA@PC composite energetic material has a CA content of 89.6%, and its electrostatic safety is nearly 30times that of pure CA(1.47 mJ compared to 0.05 mJ). CA@PC delivers an outstanding balance of safety and energy density compared to similar materials.展开更多
目的研究清瘟护肺颗粒的化学成分。方法查阅中国知网、PubMed、Web of Science等数据库,检索该制剂组方药材化学成分的相关文献,结合文献报道和ChemicalBook数据库信息,建立化学成分数据库。采用超高效液相色谱-四极杆/静电场轨道阱高...目的研究清瘟护肺颗粒的化学成分。方法查阅中国知网、PubMed、Web of Science等数据库,检索该制剂组方药材化学成分的相关文献,结合文献报道和ChemicalBook数据库信息,建立化学成分数据库。采用超高效液相色谱-四极杆/静电场轨道阱高分辨质谱(UHPLC-Q Exactive Focus MS/MS)法分析制剂的图谱数据,并以Xcalibur 4.0软件拟合分子式,与自建数据库信息进行匹配,初步推测分子式信息,与ChemicalBook或ChemSpider数据库比对,推测化学成分结构。结果共鉴定出158个化学成分,包括苷类36个,黄酮类29个,苯丙素类28个,有机酸类18个,萜类17个,色原酮类8个,其他类22个。结论所建立的方法可系统、准确、快速地定性分析清瘟护肺颗粒中的化学成分。展开更多
Electrostatic chucks are one of the core components of semiconductor devices. As a key index of electrostatic chucks, the clamping force must be controlled within a reasonable range. Therefore, it is essential to accu...Electrostatic chucks are one of the core components of semiconductor devices. As a key index of electrostatic chucks, the clamping force must be controlled within a reasonable range. Therefore, it is essential to accurately measure the clamping force. To reduce the negative factors influencing measurement precision and repeatability, this article presents a novel method to measure the clamping force and we elaborate both the principle and the key procedure. A micro-force probe component is introduced to monitor, adjust, and eliminate the gap between the wafer and the electrostatic chuck. The contact force between the ruby probe and the wafer is selected as an important parameter to characterize de-chucking, and we have found that the moment of de-chucking can be exactly judged. Moreover, this article derives the formula calibrating equivalent action area of backside gas pressure under real working conditions, which can effectively connect the backside gas pressure at the moment of de-chucking and the clamping force. The experiments were then performed on a self-designed measuring platform.The de-chucking mechanism is discussed in light of our analysis of the experimental data. Determination criteria for de-chucking point are summed up. It is found that the relationship between de-chucking pressure and applied voltage conforms well to quadratic equation. Meanwhile, the result reveals that actual de-chucking behavior is much more complicated than the description given in the classical empirical formula.展开更多
基金the National Natural Science Foundation of China(Grant Nos.51874264 and 52076200)。
文摘Rainbow particle image velocimetry(PIV)can restore the three-dimensional velocity field of particles with a single camera;however,it requires a relatively long time to complete the reconstruction.This paper proposes a hybrid algorithm that combines the fast Fourier transform(FFT)based co-correlation algorithm and the Horn–Schunck(HS)optical flow pyramid iterative algorithm to increase the reconstruction speed.The Rankine vortex simulation experiment was performed,in which the particle velocity field was reconstructed using the proposed algorithm and the rainbow PIV method.The average endpoint error and average angular error of the proposed algorithm were roughly the same as those of the rainbow PIV algorithm;nevertheless,the reconstruction time was 20%shorter.Furthermore,the effect of velocity magnitude and particle density on the reconstruction results was analyzed.In the end,the performance of the proposed algorithm was verified using real experimental single-vortex and double-vortex datasets,from which a similar particle velocity field was obtained compared with the rainbow PIV algorithm.The results show that the reconstruction speed of the proposed hybrid algorithm is approximately 25%faster than that of the rainbow PIV algorithm.
基金Research is financed from the project NR03-0036-04/2008
文摘The paper presents two methods for the formulation of free vibration analysis of collecting electrodes of precipitators.The first,called the hybrid finite element method, combines the finit element method used for calculations of spring deformations with the rigid finite element method used to reflect mass and geometrical features,which is called the hybrid finite element method.As a result,a model with a diagonal mass matrix is obtained.Due to a specific geometry of the electrodes,which are long plates of complicated shapes,the second method proposed is the strip method which is a semi-analytical method.The strip method allows us to formulate the equations of motion with a considerably smaller number of generalized coordinates.Results of numerical calculations obtained by both methods are compared with those obtained using commercial software like ANSYS and ABAQUS.Good compatibility of results is achieved.
文摘In order to analyze the electrostatic field concerned with electrostatic proximity fuze problem using the available finite analysis software package, the technology to model the problem with a scale reduction object and boundary was presented. The boundary is determined by the maximum distance the sensor can detect. The object model is obtained by multiplying the terms in Poisson's equation with a scale reduction factor and the real value can be reconstructed with the same reverse process after software calculation. Using the finite element analysis program, the simulation value is close to the theoretical value with a little error. The boundary determination and scale reduction method is suitable to modeling the irregular electrostatic field around air targets, such as airplane, missile and so on, which is based on commonly used personal computer (PC). The technology reduces the calculation and storage cost greatly.
文摘The model and analysis of the cantilever beam adhesion problem under the action of electrostatic force are given. Owing to the nonlinearity of electrostatic force, the analytical solution for this kind of problem is not available. In this paper, a systematic method of generating polynomials which are the exact beam solutions of the loads with di?erent distributions is provided. The polynomials are used to approximate the beam displacement due to electrostatic force. The equilibrium equation o?ers an answer to how the beam deforms but no information about the unstuck length. The derivative of the functional with respect to the unstuck length o?ers such information. But to compute the functional it is necessary to know the beam deformation. So the problem is iteratively solved until the results are converged. Galerkin and Newton-Raphson methods are used to solve this nonlinear problem. The e?ects of dielectric layer thickness and electrostatic voltage on the cantilever beam stiction are studied. The method provided in this paper exhibits good convergence. For the adhesion problem of cantilever beam without electrostatic voltage, the analytical solution is available and is also exactly matched by the computational results given by the method presented in this paper.
文摘In this paper, the effect of van der Waals (vdW) force on the pull-in behavior of electrostatically actuated nano/micromirrors is investigated. First, the minimum po- tential energy principle is utilized to find the equation gov- erning the static behavior of nano/micromirror under electro- static and vdW forces. Then, the stability of static equilib- rium points is analyzed using the energy method. It is found that when there exist two equilibrium points, the smaller one is stable and the larger one is unstable. The effects of dif- ferent design parameters on the mirror's pull-in angle and pull-in voltage are studied and it is found that vdW force can considerably reduce the stability limit of the mirror. At the end, the nonlinear equilibrium equation is solved numer- ically and analytically using homotopy perturbation method (HPM). It is observed that a sixth order perturbation approx- imation can precisely model the mirror's behavior. The re- suits of this paper can be used for stable operation design and safe fabrication of torsional nano/micro actuators.
文摘The plane medium and point charge are regarded as an integral system. The static field's distribution situation of the point charge is studied in the medium structure of plane division layers by using mirror image method, drawing the point charge's calculation expression of the electric potential in every medium space. The mathematics model of passive electrostatic detecting people through the medium (regular distance between the goal point charge and the medium) is established, using MATLAB software to carry out emulation of the model and analysing the result, establishing the theoretical foundation for studying the technology of the passive static detecting people through the wall.
基金Project supported by the National Natural Science Foundation of China (Grant No 1057009).
文摘This paper uses the Lie algebraic method to analyse the charged particle trajectories in the spherical electrostatic analyser, and obtains the nonlinear solutions. The results show that the focusing abilities both in the x and y directions of the analyser are almost the same. Moreover, there exist dispersion effects in the x direction, and no dispersion effects in the y direction.
文摘Asymmetric electrostatic forces are a very interesting and new phenomenon. The magnitude of an electrostatic force that acts on a point charge does not change when the direction of the electric field is reversed. On the contrary, the magnitude of the electrostatic force that acts on a charged asymmetric shaped conductor does change when the direction of the electric field is reversed. 5 years ago, this phenomenon was reported by a simple experiment and a simulation and named as an Asymmetric electrostatic force unofficially by the author. After that, several simulations confirmed this phenomenon. However, several experiments did not yet confirm it clearly. The difference between the simulations and the experiments depends upon differences of their conditions. The simulations had been done under ideal (perfect) conditions;the experiments, on the contrary, had been done under actual (not perfect) conditions. In the new experiment, its conditions were improved to near ideal (perfect) conditions. As a result the existence of the Asymmetric electrostatic force was more clearly confirmed.
文摘The effect of a high frequency (HF) electric field on the propagation of electrostatic wave in a 2D non-uniform relativistic plasma waveguide is investigated. A variable separation method is applied to the two-fluid plasma model. An analytical study of the reflection of electrostatic wave propagation along a magnetized non-uniform relativistic plasma slab subjected to an intense HF electric field is presented and compared with the case of a non relativistic plasma. It is found that, when the frequency of the incident wave is close to the relativistic electron plasma frequency, the plasma is less reflective due to the presence of both an HF field and the effect of relativistic electrons. On the other hand, for a low-frequency incident wave the reflection coefficient is directly proportional to the amplitude of the HF field. Also, it is shown that the relativistic electron plasma leads to a decrease in the value of reflection coefficient in comparison with the case of the non relativistic plasma.
基金Project supported by the National Natural Science Foundation of China (Grant No 10275025).
文摘Stochastic resonance (SR) is studied in a gain-noise model of a single-mode laser driven by a coloured pump noise and a quantum noise with cross-correlation between real and imaginary parts under a direct signal modulation. By using a linear approximation method, we find that the SR appears during the variation of signal-to-noise ratio (SNR) separately with the pump noise self-correlation time τ, the noise correlation coefficient between the real part and the imaginary part of the quantum noise λq, the attenuation coefficient γ' and the deterministic steady-state intensity I0. In addition, it is found that the SR can be characterized not only by the dependence of SNR on the noise variables of and λq, but also by the dependence of SNR on the laser system variables of γ and I0. Thus our investigation extends the characteristic quantity of SR proposed before.
文摘A trial solution for bending deflection of a multilayered micro-bridge subject to a voltage induced load is presented. The relation between the applied voltage and the displacements of the micro-bridge in the pull-in state is analyzed by energy method. Furthermore, two analytical expressions about normalized displacement and pull-in voltage are carried out. It’s proved that the value of normalized displacement is not influenced by residual stress if axial and shear deformation is ignored. Finally, the theoretical results are compared with that of FEM, and they show good agreement.
基金supported by the Major Research Plan on West-Pacific Earth System Multispheric Interactions (Nos.91858215,91958206)the National Natural Science Foundation of China (NSFC)Shiptime Sharing Project (No.41949581)the Key Research and Development Program of Shandong Province (No.2019GHY112019)。
文摘The precision and reliability of first-arrival picking are crucial for determining the accuracy of geological structure inversion using active source ocean bottom seismometer(OBS)refraction data.Traditional methods for first-arrival picking based on sample points are characterized by theoretical errors,especially in low-sampling-frequency OBS data because the travel time of seismic waves is not an integer multiple of the sampling interval.In this paper,a first-arrival picking method that utilizes the spatial waveform variation characteristics of active source OBS data is presented.First,the distribution law of theoretical error is examined;adjacent traces exhibit variation characteristics in their waveforms.Second,a label cross-correlation superposition method for extracting highfrequency signals is presented to enhance the first-arrival picking precision.Results from synthetic and field data verify that the proposed approach is robust,successfully overcomes the limitations of low sampling frequency,and achieves precise outcomes that are comparable with those of high-sampling-frequency data.
基金the financial support by Postgraduate Research & Practice Innovation Program from Jiangsu Science and Technology Department under Grant number KYCX19_0320。
文摘Copper azide(CA), as a primary explosive with high energy density, has not been practically used so far because of its high electrostatic sensitivity. The Cu2O@HKUST-1 core-shell structure hybrid material was synthesized by the “bottle around ship” methodology in this research by regulating the dissolution rate of Cu2O and the generation rate of metal-organic framework(MOF) materials. Cu2O@HKUST-1 was carbonized to form a Cu O@porous carbon(CuO@PC) composite material. CuO@PC was synthesized into a copper azide(CA) @PC composite energetic material through a gas-solid phase in-situ azidation reaction.CA is encapsulated in PC framework, which acts as a nanoscale Faraday cage, and its excellent electrical conductivity prevents electrostatic charges from accumulating on the energetic material’s surface. The CA@PC composite energetic material has a CA content of 89.6%, and its electrostatic safety is nearly 30times that of pure CA(1.47 mJ compared to 0.05 mJ). CA@PC delivers an outstanding balance of safety and energy density compared to similar materials.
基金Project supported by No.02 National Science and Technology Major Project of China(No.2011ZX02403-004)
文摘Electrostatic chucks are one of the core components of semiconductor devices. As a key index of electrostatic chucks, the clamping force must be controlled within a reasonable range. Therefore, it is essential to accurately measure the clamping force. To reduce the negative factors influencing measurement precision and repeatability, this article presents a novel method to measure the clamping force and we elaborate both the principle and the key procedure. A micro-force probe component is introduced to monitor, adjust, and eliminate the gap between the wafer and the electrostatic chuck. The contact force between the ruby probe and the wafer is selected as an important parameter to characterize de-chucking, and we have found that the moment of de-chucking can be exactly judged. Moreover, this article derives the formula calibrating equivalent action area of backside gas pressure under real working conditions, which can effectively connect the backside gas pressure at the moment of de-chucking and the clamping force. The experiments were then performed on a self-designed measuring platform.The de-chucking mechanism is discussed in light of our analysis of the experimental data. Determination criteria for de-chucking point are summed up. It is found that the relationship between de-chucking pressure and applied voltage conforms well to quadratic equation. Meanwhile, the result reveals that actual de-chucking behavior is much more complicated than the description given in the classical empirical formula.