In this paper,we develop a multi-scalar auxiliary variables(MSAV)scheme for the Cahn-Hilliard Magnetohydrodynamics system by introducing two scalar auxiliary variables(SAV).This scheme is linear,fully decoupled and un...In this paper,we develop a multi-scalar auxiliary variables(MSAV)scheme for the Cahn-Hilliard Magnetohydrodynamics system by introducing two scalar auxiliary variables(SAV).This scheme is linear,fully decoupled and unconditionally stable in energy.Subsequently,we provide a detailed implementation procedure for full decoupling.Thus,at each time step,only a series of linear differential equations with constant coefficients need to be solved.To validate the effectiveness of our approach,we conduct an error analysis for this first-order scheme.Finally,some numerical experiments are provided to verify the energy dissipation of the system and the convergence of the proposed approach.展开更多
Six-axis numerical control spiral bevel gear grinder was taken as the object, multi-body system theory and Denavit-Hartenberg homogeneous transformed matrix （HTM） were utilized to establish the grinder synthesis err...Six-axis numerical control spiral bevel gear grinder was taken as the object, multi-body system theory and Denavit-Hartenberg homogeneous transformed matrix （HTM） were utilized to establish the grinder synthesis error model, and the validity of model was confirmed by the experiment. Additionally, in grinding wheel tool point coordinate system, the errors of six degrees of freedom were simulated when the grinding wheel revolving around C-axis, moving along X-axis and Y-axis. The influence of these six errors on teeth space, helix angle, pitch, teeth profile was discussed. The simulation results show that the angle error is in the range from -0.148 4 tad to -0.241 9 rad when grinding wheel moving along X, Y-axis; the translation error is in the range from 0.866 0 μm to 3.605 3μm when grinding wheel moving along X-axis. These angle and translation errors have a great influence on the helix angle, pitch, teeth thickness and tooth socket.展开更多
Accurate 3-D fracture network model for rock mass in dam foundation is of vital importance for stability,grouting and seepage analysis of dam foundation.With the aim of reducing deviation between fracture network mode...Accurate 3-D fracture network model for rock mass in dam foundation is of vital importance for stability,grouting and seepage analysis of dam foundation.With the aim of reducing deviation between fracture network model and measured data,a 3-D fracture network dynamic modeling method based on error analysis was proposed.Firstly,errors of four fracture volume density estimation methods(proposed by ODA,KULATILAKE,MAULDON,and SONG)and that of four fracture size estimation methods(proposed by EINSTEIN,SONG and TONON)were respectively compared,and the optimal methods were determined.Additionally,error index representing the deviation between fracture network model and measured data was established with integrated use of fractal dimension and relative absolute error(RAE).On this basis,the downhill simplex method was used to build the dynamic modeling method,which takes the minimum of error index as objective function and dynamically adjusts the fracture density and size parameters to correct the error index.Finally,the 3-D fracture network model could be obtained which meets the requirements.The proposed method was applied for 3-D fractures simulation in Miao Wei hydropower project in China for feasibility verification and the error index reduced from 2.618 to 0.337.展开更多
In order to improve the detection accuracy of Doppler asymmetric spatial heterodyne(DASH)interferometer in harsh temperatures,an opto-mechanical-thermal integration analysis is carried out.Firstly,the correlation betw...In order to improve the detection accuracy of Doppler asymmetric spatial heterodyne(DASH)interferometer in harsh temperatures,an opto-mechanical-thermal integration analysis is carried out.Firstly,the correlation between the interference phase and temperature is established according to the working principle and the phase algorithm of the interferometer.Secondly,the optical mechanical thermal analysis model and thermal deformation data acquisition model are designed.The deformation data of the interference module and the imaging optical system at different temperatures are given by temperature load simulation analysis,and the phase error caused by thermal deformation is obtained by fitting.Finally,based on the wind speed error caused by thermal deformation of each component,a reasonable temperature control scheme is proposed.The results show that the interference module occupies the main cause,the temperature must be controlled within(20±0.05)℃,and the temperature control should be carried out for the temperature sensitive parts,and the wind speed error caused by the part is 3.8 m/s.The thermal drift between the magnification of the imaging optical system and the thermal drift of the relative position between the imaging optical system and the detector should occupy the secondary cause,which should be controlled within(20±2)℃,and the wind speed error caused by the part is 3.05 m/s.In summary,the wind measurement error caused by interference module,imaging optical system,and the relative position between the imaging optical system and the detector can be controlled within 6.85 m/s.The analysis and temperature control schemes presented in this paper can provide theoretical basis for DASH interferometer engineering applications.展开更多
A finite element model was established for analyzing the geometric errors in turning operations and a two-step analyzing process was proposed. In the first analyzing step, the cutting force and the cutting heat for th...A finite element model was established for analyzing the geometric errors in turning operations and a two-step analyzing process was proposed. In the first analyzing step, the cutting force and the cutting heat for the cutting conditions were obtained using the AdvantEdge. Also, the deformation of a workpiece was estimated in the second step using the ANSYS. The deformation was analyzed for a 150 mm-long workpiece at three different measuring points, such as 10, 70 and 130 mm from a reference point, and the amounts of the deformation were compared through experiments. /n the results of the comparison and analysis, the values obtained from these comparison and analysis represent similar tendencies. Also, it is verified that their geometric errors increase with the increase in temperature. In addition, regarding the factors that affect the deformation of a workpiecc, it can be seen that the geometric error in the lathe is about 15%, the error caused by the cutting force is about 10%, and the deformation caused by the heat is about 75%.展开更多
Error analysis methods in frequency domain are developed in this paper for determining the characteristic root and transfer function errors when the linear multipass algorithms are used to solve linear differential eq...Error analysis methods in frequency domain are developed in this paper for determining the characteristic root and transfer function errors when the linear multipass algorithms are used to solve linear differential equations. The relation between the local truncation error in time domain and the error in frequency domain is established, which is the basis for developing the error estimation methods. The error estimation methods for the digital simulation model constructed by using the Runge-Kutta algorithms and the linear multistep predictor-corrector algorithms are also given.展开更多
This paper surveys a number of recent advances in the error analysis in the frequency domain for a digital simulation model. It is emphasized to discuss the errors in characteristic roots and transfer funcnon of the d...This paper surveys a number of recent advances in the error analysis in the frequency domain for a digital simulation model. It is emphasized to discuss the errors in characteristic roots and transfer funcnon of the digital simulation model, the frequency domain errors of the data transfers between thesimulation submodels, and some compensation methods for the errors. Some of the questions to be answered are also presented.展开更多
with the merits of the easy manufacture and the long service life and the processing the inside or outside form surface, round body form tool is extensive use in large scales production. Its main demerit is the big hy...with the merits of the easy manufacture and the long service life and the processing the inside or outside form surface, round body form tool is extensive use in large scales production. Its main demerit is the big hyperbolic error which is caused in the process of processing cone, but about the discussion of hyperbolic error, there are two drawbacks in the current books and documents: (1) The error measuring plane is established on the rake face of tool, which doesn’t coincide with the actual measuring plane (axial plane) of work piece; (2) When the influential elements of error are analyzed, single parameter is only discussed. In order to overcome these demerits, the mathematical model of hyperbolic error on the axial plane of work piece is built in this paper when round body form tool processes cone. The fundamental reason which causes hyperbolic error when round body form tool processes cone is that the line profile replaces the curve profile of theory in the radial cut plane of tool in the design and manufacture of tool. In order to evaluate the mathematical formula of its error, firstly, the equation of cone of work piece must be established, secondly, the equation of cutting lip in the rake face is established, then, the profile equation of the radial plane of tool is evaluated on the condition that coordinate is changed, at last, the hyperbolic error is derived according to the equation and the substitutional line equation, and the error is converted to the axial plane of work piece which is coincided with the measuring plane. The actual calculation and the theory analysis indicated that if the cone length and the coning of the cone of work piece are fixed, the main elements which affect the hyperbolic error in the axial plane of work piece are the outside diameter R of round body form tool, the rake angle and the rear angle in "base point". If these three parameters are combined rationally, the hyperbolic error is minimum when round body form tool process cone, and the machining precision of work piece can be improved, on the condition that neither the work capacity of the tool design nor the manufacture cost of tool increases.展开更多
Compared to the rank reduction estimator （RARE） based on second-order statistics （called SOS-RARE）, the RARE employing fourth-order cumulants （referred to as FOC-RARE） is capable of dealing with more sources and...Compared to the rank reduction estimator （RARE） based on second-order statistics （called SOS-RARE）, the RARE employing fourth-order cumulants （referred to as FOC-RARE） is capable of dealing with more sources and mitigating the negative influences of the Gaussian colored noise. However, in the presence of unexpected modeling errors, the resolution behavior of the FOC-RARE also deteriorate significantly as SOS-RARE, even for a known array covariance matrix. For this reason, the angle resolution capability of the FOC-RARE was theoretically analyzed. Firstly, the explicit formula for the mathematical expectation of the FOC-RARE spatial spectrum was derived through the second-order perturbation analysis method. Then, with the assumption that the unexpected modeling errors were drawn from complex circular Gaussian distribution, the theoretical formulas for the angle resolution probability of the FOC-RARE were presented. Numerical experiments validate our analytical results and demonstrate that the FOC-RARE has higher robustness to the unexpected modeling en＇ors than that of the SOS-RARE from the resolution point of view.展开更多
A complex geometric modeling method of a helical face gear pair with arc-tooth generated by an arc-profile cutting(APC)disc is proposed,and its tooth contact characteristics are analyzed.Firstly,the spatial coordinate...A complex geometric modeling method of a helical face gear pair with arc-tooth generated by an arc-profile cutting(APC)disc is proposed,and its tooth contact characteristics are analyzed.Firstly,the spatial coordinate system of an APC face gear pair is established based on meshing theory.Combining the coordinate transformation matrix and the tooth profile of the cutter,the equations of the curve envelope of the APC face gear pair are obtained.Then the surface equations are solved to extract the point clouds data by programming in MATLAB,which contains the work surface and the fillet surface of the APC face gear pair.And the complex geometric model of the APC face gear pair is built by fitting its point clouds.At last,through the analysis of the tooth surface contact,the sensitivity of the APC face gear to the different types of mounting errors is obtained.The results show that the APC face gear pair is the most sensitive to mounting errors in the tooth thickness direction,and it should be strictly controlled in the actual application.展开更多
基金Research Project Supported by Shanxi Scholarship Council of China(2021-029)International Cooperation Base and Platform Project of Shanxi Province(202104041101019)Basic Research Plan of Shanxi Province(202203021211129)。
文摘In this paper,we develop a multi-scalar auxiliary variables(MSAV)scheme for the Cahn-Hilliard Magnetohydrodynamics system by introducing two scalar auxiliary variables(SAV).This scheme is linear,fully decoupled and unconditionally stable in energy.Subsequently,we provide a detailed implementation procedure for full decoupling.Thus,at each time step,only a series of linear differential equations with constant coefficients need to be solved.To validate the effectiveness of our approach,we conduct an error analysis for this first-order scheme.Finally,some numerical experiments are provided to verify the energy dissipation of the system and the convergence of the proposed approach.
基金Project(2005CB724104) supported by the Major State Basic Research Development Program of ChinaProject(1343-77202) supported by the Graduate Students Innovate of Central South University
文摘Six-axis numerical control spiral bevel gear grinder was taken as the object, multi-body system theory and Denavit-Hartenberg homogeneous transformed matrix （HTM） were utilized to establish the grinder synthesis error model, and the validity of model was confirmed by the experiment. Additionally, in grinding wheel tool point coordinate system, the errors of six degrees of freedom were simulated when the grinding wheel revolving around C-axis, moving along X-axis and Y-axis. The influence of these six errors on teeth space, helix angle, pitch, teeth profile was discussed. The simulation results show that the angle error is in the range from -0.148 4 tad to -0.241 9 rad when grinding wheel moving along X, Y-axis; the translation error is in the range from 0.866 0 μm to 3.605 3μm when grinding wheel moving along X-axis. These angle and translation errors have a great influence on the helix angle, pitch, teeth thickness and tooth socket.
基金Project(51321065)supported by the Innovative Research Groups of the National Natural Science Foundation of ChinaProject(2013CB035904)supported by the National Basic Research Program of China(973 Program)Project(51439005)supported by the National Natural Science Foundation of China
文摘Accurate 3-D fracture network model for rock mass in dam foundation is of vital importance for stability,grouting and seepage analysis of dam foundation.With the aim of reducing deviation between fracture network model and measured data,a 3-D fracture network dynamic modeling method based on error analysis was proposed.Firstly,errors of four fracture volume density estimation methods(proposed by ODA,KULATILAKE,MAULDON,and SONG)and that of four fracture size estimation methods(proposed by EINSTEIN,SONG and TONON)were respectively compared,and the optimal methods were determined.Additionally,error index representing the deviation between fracture network model and measured data was established with integrated use of fractal dimension and relative absolute error(RAE).On this basis,the downhill simplex method was used to build the dynamic modeling method,which takes the minimum of error index as objective function and dynamically adjusts the fracture density and size parameters to correct the error index.Finally,the 3-D fracture network model could be obtained which meets the requirements.The proposed method was applied for 3-D fractures simulation in Miao Wei hydropower project in China for feasibility verification and the error index reduced from 2.618 to 0.337.
文摘In order to improve the detection accuracy of Doppler asymmetric spatial heterodyne(DASH)interferometer in harsh temperatures,an opto-mechanical-thermal integration analysis is carried out.Firstly,the correlation between the interference phase and temperature is established according to the working principle and the phase algorithm of the interferometer.Secondly,the optical mechanical thermal analysis model and thermal deformation data acquisition model are designed.The deformation data of the interference module and the imaging optical system at different temperatures are given by temperature load simulation analysis,and the phase error caused by thermal deformation is obtained by fitting.Finally,based on the wind speed error caused by thermal deformation of each component,a reasonable temperature control scheme is proposed.The results show that the interference module occupies the main cause,the temperature must be controlled within(20±0.05)℃,and the temperature control should be carried out for the temperature sensitive parts,and the wind speed error caused by the part is 3.8 m/s.The thermal drift between the magnification of the imaging optical system and the thermal drift of the relative position between the imaging optical system and the detector should occupy the secondary cause,which should be controlled within(20±2)℃,and the wind speed error caused by the part is 3.05 m/s.In summary,the wind measurement error caused by interference module,imaging optical system,and the relative position between the imaging optical system and the detector can be controlled within 6.85 m/s.The analysis and temperature control schemes presented in this paper can provide theoretical basis for DASH interferometer engineering applications.
基金Project(RTI04-01-03) supported by the Regional Technology Innovation Program of the Ministry of Knowledge Economy (MKE),Korea
文摘A finite element model was established for analyzing the geometric errors in turning operations and a two-step analyzing process was proposed. In the first analyzing step, the cutting force and the cutting heat for the cutting conditions were obtained using the AdvantEdge. Also, the deformation of a workpiece was estimated in the second step using the ANSYS. The deformation was analyzed for a 150 mm-long workpiece at three different measuring points, such as 10, 70 and 130 mm from a reference point, and the amounts of the deformation were compared through experiments. /n the results of the comparison and analysis, the values obtained from these comparison and analysis represent similar tendencies. Also, it is verified that their geometric errors increase with the increase in temperature. In addition, regarding the factors that affect the deformation of a workpiecc, it can be seen that the geometric error in the lathe is about 15%, the error caused by the cutting force is about 10%, and the deformation caused by the heat is about 75%.
基金This project was supported by the National Natural Science Foundation of China (No. 19871080).
文摘Error analysis methods in frequency domain are developed in this paper for determining the characteristic root and transfer function errors when the linear multipass algorithms are used to solve linear differential equations. The relation between the local truncation error in time domain and the error in frequency domain is established, which is the basis for developing the error estimation methods. The error estimation methods for the digital simulation model constructed by using the Runge-Kutta algorithms and the linear multistep predictor-corrector algorithms are also given.
文摘This paper surveys a number of recent advances in the error analysis in the frequency domain for a digital simulation model. It is emphasized to discuss the errors in characteristic roots and transfer funcnon of the digital simulation model, the frequency domain errors of the data transfers between thesimulation submodels, and some compensation methods for the errors. Some of the questions to be answered are also presented.
文摘with the merits of the easy manufacture and the long service life and the processing the inside or outside form surface, round body form tool is extensive use in large scales production. Its main demerit is the big hyperbolic error which is caused in the process of processing cone, but about the discussion of hyperbolic error, there are two drawbacks in the current books and documents: (1) The error measuring plane is established on the rake face of tool, which doesn’t coincide with the actual measuring plane (axial plane) of work piece; (2) When the influential elements of error are analyzed, single parameter is only discussed. In order to overcome these demerits, the mathematical model of hyperbolic error on the axial plane of work piece is built in this paper when round body form tool processes cone. The fundamental reason which causes hyperbolic error when round body form tool processes cone is that the line profile replaces the curve profile of theory in the radial cut plane of tool in the design and manufacture of tool. In order to evaluate the mathematical formula of its error, firstly, the equation of cone of work piece must be established, secondly, the equation of cutting lip in the rake face is established, then, the profile equation of the radial plane of tool is evaluated on the condition that coordinate is changed, at last, the hyperbolic error is derived according to the equation and the substitutional line equation, and the error is converted to the axial plane of work piece which is coincided with the measuring plane. The actual calculation and the theory analysis indicated that if the cone length and the coning of the cone of work piece are fixed, the main elements which affect the hyperbolic error in the axial plane of work piece are the outside diameter R of round body form tool, the rake angle and the rear angle in "base point". If these three parameters are combined rationally, the hyperbolic error is minimum when round body form tool process cone, and the machining precision of work piece can be improved, on the condition that neither the work capacity of the tool design nor the manufacture cost of tool increases.
基金Project(61201381)supported by the National Nature Science Foundation of ChinaProject(YP12JJ202057)supported by the Future Development Foundation of Zhengzhou Information Science and Technology College,China
文摘Compared to the rank reduction estimator （RARE） based on second-order statistics （called SOS-RARE）, the RARE employing fourth-order cumulants （referred to as FOC-RARE） is capable of dealing with more sources and mitigating the negative influences of the Gaussian colored noise. However, in the presence of unexpected modeling errors, the resolution behavior of the FOC-RARE also deteriorate significantly as SOS-RARE, even for a known array covariance matrix. For this reason, the angle resolution capability of the FOC-RARE was theoretically analyzed. Firstly, the explicit formula for the mathematical expectation of the FOC-RARE spatial spectrum was derived through the second-order perturbation analysis method. Then, with the assumption that the unexpected modeling errors were drawn from complex circular Gaussian distribution, the theoretical formulas for the angle resolution probability of the FOC-RARE were presented. Numerical experiments validate our analytical results and demonstrate that the FOC-RARE has higher robustness to the unexpected modeling en＇ors than that of the SOS-RARE from the resolution point of view.
基金Project(51805368)supported by the National Natural Science Foundation of ChinaProject(2018QNRC001)supported by the Young Elite Scientists Sponsorship Program,China+1 种基金Project(DMETKF2021017)supported by the Fund of State Key Laboratory of Digital Manufacturing Equipment and Technology,Huazhong University of Science and Technology,ChinaProject(HTL-0-21G07)supported by the National key Laboratory of Science and Technology on Heicopter Transmission,China。
文摘A complex geometric modeling method of a helical face gear pair with arc-tooth generated by an arc-profile cutting(APC)disc is proposed,and its tooth contact characteristics are analyzed.Firstly,the spatial coordinate system of an APC face gear pair is established based on meshing theory.Combining the coordinate transformation matrix and the tooth profile of the cutter,the equations of the curve envelope of the APC face gear pair are obtained.Then the surface equations are solved to extract the point clouds data by programming in MATLAB,which contains the work surface and the fillet surface of the APC face gear pair.And the complex geometric model of the APC face gear pair is built by fitting its point clouds.At last,through the analysis of the tooth surface contact,the sensitivity of the APC face gear to the different types of mounting errors is obtained.The results show that the APC face gear pair is the most sensitive to mounting errors in the tooth thickness direction,and it should be strictly controlled in the actual application.
