Because of the challenge of compounding lightweight,high-strength Ti/Al alloys due to their considerable disparity in properties,Al 6063 as intermediate layer was proposed to fabricate TC4/Al 6063/Al 7075 three-layer ...Because of the challenge of compounding lightweight,high-strength Ti/Al alloys due to their considerable disparity in properties,Al 6063 as intermediate layer was proposed to fabricate TC4/Al 6063/Al 7075 three-layer composite plate by explosive welding.The microscopic properties of each bonding interface were elucidated through field emission scanning electron microscope and electron backscattered diffraction(EBSD).A methodology combining finite element method-smoothed particle hydrodynamics(FEM-SPH)and molecular dynamics(MD)was proposed for the analysis of the forming and evolution characteristics of explosive welding interfaces at multi-scale.The results demonstrate that the bonding interface morphologies of TC4/Al 6063 and Al 6063/Al 7075 exhibit a flat and wavy configuration,without discernible defects or cracks.The phenomenon of grain refinement is observed in the vicinity of the two bonding interfaces.Furthermore,the degree of plastic deformation of TC4 and Al 7075 is more pronounced than that of Al 6063 in the intermediate layer.The interface morphology characteristics obtained by FEM-SPH simulation exhibit a high degree of similarity to the experimental results.MD simulations reveal that the diffusion of interfacial elements predominantly occurs during the unloading phase,and the simulated thickness of interfacial diffusion aligns well with experimental outcomes.The introduction of intermediate layer in the explosive welding process can effectively produce high-quality titanium/aluminum alloy composite plates.Furthermore,this approach offers a multi-scale simulation strategy for the study of explosive welding bonding interfaces.展开更多
Shale gas, as a clean, low-carbon, and abundant unconventional natural gas resource, plays a crucial role in achieving clean energy transformation and carbon neutrality. The Fuling shale gas reservoir in Sichuan Basin...Shale gas, as a clean, low-carbon, and abundant unconventional natural gas resource, plays a crucial role in achieving clean energy transformation and carbon neutrality. The Fuling shale gas reservoir in Sichuan Basin stands out as China's most promising area for shale gas exploration and recovery. However, the continuous recovery of shale gas in the southern Sichuan Basin has led to well interference events in hundreds of wells, with the furthest well distance reaching over 2000 m. This study introduces a multi-scale approach for transient analysis of a multi-well horizontal pad with well interference in shale gas reservoirs. The approach utilizes Laplace transform technology, boundary element theory, and the finite difference method to address the complexities of the system. Well interference is managed using the pressure superposition principle. To validate the proposed multi-scale method, a commercial numerical simulator is employed. The comprehensive pressure behavior of a multi-well horizontal pad in a shale gas reservoir is analyzed, encompassing wellbore storage effect, skin effect, bilinear flow, linear flow, pseudo-radial flow of primary fractures, well interference period, dual-porosity flow, pseudo-radial flow of the total system, and boundary-dominated flow. A case study is conducted on the typical well, the well with the longest production history in the Fuling shale gas reservoir. The rate transient analysis is conducted to integrate up to 229 days of shale gas production daily data and wellhead pressure data, enabling the generation of pressure behavior under unit flow rate. The results indicate that the linear flow, transitional flow, and boundary-dominated flow are more likely to be observed in the actual data. Secondary fractures are considered to be the primary pathways for fluid migration during well interference events. The evaluated formation permeability is 2.58 × 10^(-2) mD, the well spacing is 227.8 m, the diffusion coefficient is 1.49 × 10^(-4), and the skin factor is 0.09.展开更多
Parallel mechanisms with fewer degrees of freedom that incorporate two or more SPR limbs have been widely adopted in industrial applications in recent years.However,notable theoretical gaps persist,particularly in the...Parallel mechanisms with fewer degrees of freedom that incorporate two or more SPR limbs have been widely adopted in industrial applications in recent years.However,notable theoretical gaps persist,particularly in the field of analytical solutions for forward kinematics.To address this,this paper proposes an innovative forward kinematics analysis method based on Conformal Geometric Algebra(CGA)for complex hybrid mechanisms formed by serial concatenation of such parallel mechanisms.The method efficiently represents geometric elements and their operational relationships by defining appropriate unknown parameters.It constructs fundamental geometric objects such as spheres and planes,derives vertex expressions through intersection and dual operations,and establishes univariate high-order equations via inner product operations,ultimately obtaining complete analytical solutions for the forward kinematics of hybrid mechanisms.Using the(2-SPR+RPS)+(3-SPR)serial-parallel hybrid mechanism as a validation case,three configuration tests implemented in Mathematica demonstrate that:for each configuration,the upper 3-SPR mechanism yields 15 mathematical solutions,while the lower 2-SPR+RPS mechanism yields 4 mathematical solutions.After geometric constraint filtering,a unique physically valid solution is obtained for each mechanism.SolidWorks simulations further verify the correctness and reliability of the model.This research provides a reliable analytical method for forward kinematics of hybrid mechanisms,holding significant implications for advancing their applications in high-precision scenarios.展开更多
To improve design accuracy and reliability of structures,this study solves the uncertain natural frequencies with consideration for geometric nonlinearity and structural uncertainty.Frequencies of the laminated plate ...To improve design accuracy and reliability of structures,this study solves the uncertain natural frequencies with consideration for geometric nonlinearity and structural uncertainty.Frequencies of the laminated plate with all four edges clamped(CCCC)are derived based on Navier's method and Galerkin's method.The novelty of the current work is that the number of unknowns in the displacement field model of a CCCC plate with free midsurface(CCCC-2 plate)is only three compared with four or five in cases of other exposed methods.The present analytical method is proved to be accurate and reliable by comparing linear natural frequencies and nonlinear natural frequencies with other models available in the open literature.Furthermore,a novel method for analyzing effects of mean values and tolerance zones of uncertain structural parameters on random frequencies is proposed based on a self-developed Multiscale Feature Extraction and Fusion Network(MFEFN)system.Compared with a direct Monte Carlo Simulation(MCS),the MFEFNbased procedure significantly reduces the calculation burden with a guarantee of accuracy.Our research provides a method to calculate nonlinear natural frequencies under two boundary conditions and presentes a surrogate model to predict frequencies for accuracy analysis and optimization design.展开更多
The development of metallic mineral resources generates a significant amount of solid waste,such as tailings and waste rock.Cemented tailings and waste-rock backfill(CTWB)is an effective method for managing and dispos...The development of metallic mineral resources generates a significant amount of solid waste,such as tailings and waste rock.Cemented tailings and waste-rock backfill(CTWB)is an effective method for managing and disposing of this mining waste.This study employs a macro-meso-micro testing method to investigate the effects of the waste rock grading index(WGI)and loading rate(LR)on the uniaxial compressive strength(UCS),pore structure,and micromorphology of CTWB materials.Pore structures were analyzed using scanning electron microscopy(SEM)and mercury intrusion porosimetry(MIP).The particles(pores)and cracks analysis system(PCAS)software was used to quantitatively characterize the multi-scale micropores in the SEM images.The key findings indicate that the macroscopic results(UCS)of CTWB materials correspond to the microscopic results(pore structure and micromorphology).Changes in porosity largely depend on the conditions of waste rock grading index and loading rate.The inclusion of waste rock initially increases and then decreases the UCS,while porosity first decreases and then increases,with a critical waste rock grading index of 0.6.As the loading rate increases,UCS initially rises and then falls,while porosity gradually increases.Based on MIP and SEM results,at waste rock grading index 0.6,the most probable pore diameters,total pore area(TPA),pore number(PN),maximum pore area(MPA),and area probability distribution index(APDI)are minimized,while average pore form factor(APF)and fractal dimension of pore porosity distribution(FDPD)are maximized,indicating the most compact pore structure.At a loading rate of 12.0 mm/min,the most probable pore diameters,TPA,PN,MPA,APF,and APDI reach their maximum values,while FDPD reaches its minimum value.Finally,the mechanism of CTWB materials during compression is analyzed,based on the quantitative results of UCS and porosity.The research findings play a crucial role in ensuring the successful application of CTWB materials in deep metal mines.展开更多
In this paper,a framework is established for nonlinear flutter and gust response analyses based on an efficient Reduced Order Model(ROM).The proposed method can be used to solve the aeroelastic response problems of wi...In this paper,a framework is established for nonlinear flutter and gust response analyses based on an efficient Reduced Order Model(ROM).The proposed method can be used to solve the aeroelastic response problems of wings containing geometric nonlinearities.A structural modeling approach presented herein describes the stiffness nonlinearities with a modal formulation.Two orthogonal spanwise modes describe the foreshortening effects of the wing.Dynamic linearization of the ROM under nonlinear equilibrium states is applied to a nonlinear flutter analysis,and the fully nonlinear ROM coupled with the non-planar Unsteady Vortex Lattice Method(UVLM)is applied to gust response analysis.Furthermore,extended Precise Integration Method(PIM)ensures accuracy of the dynamic equation solutions.To demonstrate applicability and accuracy of the method presented,a wind tunnel test is conducted and good agreements between theoretical and test results of nonlinear flutter speed and gust response deflection are reached.The method described in this paper is suitable for predicting the nonlinear flutter speed and calculating the gust responses of a large-aspect-ratio wing in time domain.Meanwhile,the results derived highlight the effects of geometric nonlinearities obviously.展开更多
The genus Eysarcoris can be easily distinguished from other genera through the two spots in the basal angle of the scutellum. Nevertheless, Eysarcoris species show complex variances. Geometric morphometric methods hav...The genus Eysarcoris can be easily distinguished from other genera through the two spots in the basal angle of the scutellum. Nevertheless, Eysarcoris species show complex variances. Geometric morphometric methods have been increasingly applied to distinguish species and to define the boundary of genera among insects. In the present study, geometric morphometric approach was firstly employed to evaluate the shape variation of three characters （fore wing, hind wing and pygophore） of E. guttiger, E. annamita and E. ventralis using E. aeneus as outgroup to ascertain whether this approach is a reliable method for the taxonomy of Eysarcoris. Analysis was conducted on the landmarks of the three characters of these species. Multivariate regression of procrustes coordinates against centroid size was conducted to test the presence of allometry. Principal component analysis （PCA）, canonical variate analysis （CVA） and cluster analysis were utilized to describe variations in shapes among the studied species. For all of the three characters, though PCA analysis showed some overlap among species, p-values for procrustes distance and mahalanobis distance were all less than 0.0001. The distribution of the three studied species corresponds with their species status. This study demonstrates that the geometric morphometrics of both the fore wing and the hind wing might represent a possible tool for the identification of species within this genus.展开更多
This research is focused on the singularity analysis for single-gimbal control moment gyros systems （SCMGs） which include two types, with constant speed （CSCMG） or variable speed （VSCMG） rotors. Through angular ...This research is focused on the singularity analysis for single-gimbal control moment gyros systems （SCMGs） which include two types, with constant speed （CSCMG） or variable speed （VSCMG） rotors. Through angular momentum hypersurfaces of singular states, the passable and impassable singular points are discriminated easily, meanwhile the information about how much the angular momentum workspace as well as the steering capability available is provided directly. It is obvious that the null motions of steering laws are more effective for the five pyramid configuration（FPC） than for the pyramid configuration（PC） from the singular plots. The possible degenerate hyperbolic singular points of the preceding configurations are calculated and the distinctness of them is denoted by the Gaussian curvature. Furthermore, failure problems to steer integrated power and attitude control system （IPACS） are also analyzed. A sufficient condition of choosing configurations of VSCMGs to guarantee the IPACS steering is given. The angular momentum envelops of VSCMGs, in a given energy and a limited range of rotor speeds, are plotted. The connection and distinctness between CSCMGs and VSCMGs are obtained from the point of view of envelops.展开更多
Prediction of melt index （MI）, the most important parameter in determining the product＇s grade and quality control of polypropylene produced in practical industrial processes, is studied. A novel soft-sensor model ...Prediction of melt index （MI）, the most important parameter in determining the product＇s grade and quality control of polypropylene produced in practical industrial processes, is studied. A novel soft-sensor model with principal component analysis （PCA）, radial basis function （RBF） networks, and multi-scale analysis （MSA） is proposed to infer the MI of manufactured products from real process variables, where PCA is carried out to select the most relevant process features and to eliminate the correlations of the input variables, MSA is introduced to a^quire much more information and to reduce the uncertainty of the system, and RBF networks are used to characterize the nonlinearity of the process. The research results show that the proposed method provides promising prediction reliability and accuracy, and supposed to have extensive application prospects in propylene polymerization processes.展开更多
Efficient and accurate strength analysis of bolted connections is essential in analyzing the integral thermal protection system（ITPS） of hypersonic vehicles, since the system bears severe loads and structural failur...Efficient and accurate strength analysis of bolted connections is essential in analyzing the integral thermal protection system（ITPS） of hypersonic vehicles, since the system bears severe loads and structural failures usually occur at the connections. Investigations of composite mechanical properties used in ITPS are still in progress as the architecture of the composites is complex. A new method is proposed in this paper for strength analysis of bolted connections by investigating the elastic behavior and failure strength of three-dimensional C/C orthogonal composites used in ITPS. In this method a multi-scale finite element method incorporating the global–local method is established to ensure high efficiency in macro-scale and precision in meso-scale in analysis.Simulation results reveal that predictions of material properties show reasonable accuracy compared with test results. And the multi-scale method can analyze the strength of connections efficiently and accurately.展开更多
A geometrical analysis based algorithm is proposed to achieve the stereo matching of a single-lens prism based stereovision system. By setting the multi- face prism in frontal position of the static CCD （CM-140MCL） ...A geometrical analysis based algorithm is proposed to achieve the stereo matching of a single-lens prism based stereovision system. By setting the multi- face prism in frontal position of the static CCD （CM-140MCL） camera, equivalent stereo images with different orientations are captured synchronously by virtual cameras which are defined by two boundary lines： the optical axis and CCD camera field of view boundary. Subsequently, the geometrical relationship between the 2D stereo images and corresponding 3D scene is established by employing two fundamentals： ray sketching in which all the pertinent points, lines, and planes are expressed in the 3D camera coordinates and the rule of refraction. Landing on this relationship, the epipolar geometry is thus obtained by fitting a set of corresponding candidate points and thereafter, stereo matching of the prism based stereovision system is obtained. Moreover, the unique geometrical properties of the imaging system allow the proposed method free from the complicated camera calibration procedures and to be easily generalized from binocular and tri-oeular to multi-ocular stereovision systems. The performance of the algorithm is presented through the experiments on the binocular imaging system and the comparison with a conventional projection method demonstrates the efficient assessment of our novel contributions.展开更多
The nonlinear biased ship rolling motion and capsizing in randoro waves are studied by utilizing a global geometric method. Thompson＇ s α-parameterized family of restoring functions is adopted in the vessel equation...The nonlinear biased ship rolling motion and capsizing in randoro waves are studied by utilizing a global geometric method. Thompson＇ s α-parameterized family of restoring functions is adopted in the vessel equation of motion for the representation of bias. To take into account the presence of randomness in the excitation and the response, a stochastic Melnikov method is developed and a mean-square criterion is obtained to provide an upper bound on the domain of the potential chaotic rolling motion. This criterion can be used to predict the qualitative nature of the invariant manifolds which represent the boundary botween safe and unsafe initial conditions, and how these depend on system parameters of the specific ship model. Phase space transport theory and lobe dynamics are used to demonstrate how motions starting from initial conditions inside the regions bounded by the intersected manifolds will evolve and how unexpected capsizing can occur.展开更多
Inevitable geometric variations significantly affect the performance of turbines or even that of entire engines;thus,it is necessary to determine their actual characteristics and accurately estimate their impact on pe...Inevitable geometric variations significantly affect the performance of turbines or even that of entire engines;thus,it is necessary to determine their actual characteristics and accurately estimate their impact on performance.In this study,based on 1781 measured profiles of a typical turbine blade,the statistical characteristics of the geometric variations and the uncertainty impact are analyzed,and some commonly used uncertainty modelling methods based on Principal-Component Analysis(PCA)are verified.The geometric variations are found to be evident,asymmetric,and non-uniform,and the non-normality of the random distributions is non-negligible.The performance is notably affected,which is manifested as an overall offset,a notable scattering,and significant deterioration in several extreme cases.Additionally,it is demonstrated that the PCA reconstruction model is effective in characterizing major uncertainty characteristics of the geometric variations and their impact on the performance with almost the first 10 PCA modes.Based on a reasonable profile error and mean geometric deviation,the Gaussian assumption and stochasticprocess-based model are also found to be effective in predicting the mean values and standard deviations of the performance variations.However,they fail to predict the probability of some extreme cases with high loss.Finally,a Chi-square-based correction model is proposed to compensate for this deficiency.The present work can provide a useful reference for uncertainty analysis of the impact of geometric variations,and the corresponding uncertainty design of turbine blades.展开更多
This paper deals with geometric error modeling and sensitivity analysis of an overconstrained parallel tracking mechanism. The main contribution is the consideration of overconstrained features that are usually ignore...This paper deals with geometric error modeling and sensitivity analysis of an overconstrained parallel tracking mechanism. The main contribution is the consideration of overconstrained features that are usually ignored in previous research. The reciprocal property between a motion and a force is applied to tackle this problem in the framework of the screw theory. First of all, a nominal kinematic model of the parallel tracking mechanism is formulated. On this basis, the actual twist of the moving platform is computed through the superposition of the joint twist and geometric errors. The actuation and constrained wrenches of each limb are applied to exclude the joint displacement. After eliminating repeated errors brought by the multiplication of wrenches, a geometric error model of the parallel tracking mechanism is built. Furthermore,two sensitivity indices are defined to select essential geometric errors for future kinematic calibration. Finally, the geometric error model with minimum geometric errors is verified by simulation with SolidWorks software. Two typical poses of the parallel tracking mechanism are selected, and the differences between simulation and calculation results are very small. The results confirm the correctness and accuracy of the geometric error modeling method for over-constrained parallel mechanisms.展开更多
The magneto-plastic instability of a ferromagnetic beam-type plate with simple supports and small initial imperfection is analytically investigated in this paper for that the plastic deformation of the plate with a ...The magneto-plastic instability of a ferromagnetic beam-type plate with simple supports and small initial imperfection is analytically investigated in this paper for that the plastic deformation of the plate with a linear-strain hardening relation is considered when the plate is located in a strong uniformly distributed magnetic ?eld. After the distribution of magnetic ?elds related to the de?ected con?guration of plate is imaginably divided into two parts, i.e., one is related to the ?at plate and the other dependent on the perturbation of magnetic ?elds for which the plate con?guration changes from the ?at into the deformed state, the perturbation technique is employed to analyze the distribution of the perturbation magnetic ?elds in and out-of the magnetic medium of the ferromagnetic structure in a transverse magnetic ?eld, which leads to some analytical formulae/solutions for the magnetic ?elds and the resulting magnetic force exerted on the plate. Based on them, the magneto-plastic buckling and snapping of the plate in a transverse magnetic ?eld is discussed, and the critical magnetic ?eld is analytically formulated in terms of the parameters of geometry and material of the plate employed by solving the governing equation of the magneto-plastic plate in the applied magnetic ?eld. Further, the sensitivity of the initial imperfection on the magneto-plastic instability, expressed by an ampli?cation function, is obtained by solving the dynamic equation of de?ection of the plate after the inertial force in the transverse direction is taken into account. The results obtained show that the critical magnetic ?eld is sensitive to the plastic characteristic, e.g., hardening coe?cient, and the instability mode and de?ection of the plate are dependent on the geometrical imperfection as well.展开更多
Worm grinding has been applied to manufacture gears to pursue high accuracy and fine surface finish.When the worm used to grind face gears is manufactured with multi-axis computer numerical control(CNC)machining,the m...Worm grinding has been applied to manufacture gears to pursue high accuracy and fine surface finish.When the worm used to grind face gears is manufactured with multi-axis computer numerical control(CNC)machining,the machining accuracy is usually improved by increasing the number of tool paths with more time cost.Differently,this work proposes a generated method to improve the efficiency by dressing the worm surface with only one path,and a closed-loop manufacturing process is applied to ensure the machining accuracy.According to an advanced geometric analysis,the worm surface is practically approximated as a swept surface generated by a planar curve.Meanwhile,this curve is applied as the profile of a dressing wheel,which is used to dress the worm surface.The practical machining is carried out in a CNC machine tool,which was originally used to grind helical gears.Finally,a closed-loop manufacturing process including machining,measurement,and modification is proposed to compensate the machining errors.The proposed method is validated with simulations and practical experiments.展开更多
Uniaxial tension tests were conducted on single-edge-notched tensile specimens of pure molybdenum with a mesh grid pattern in front of the notch. A series of images of crack initialization and propagation with a disto...Uniaxial tension tests were conducted on single-edge-notched tensile specimens of pure molybdenum with a mesh grid pattern in front of the notch. A series of images of crack initialization and propagation with a distorted mesh grid pattern were obtained by means of in situ scanning electron microscopy. Strain fields around the crack tip were mapped successively using geometric phase analysis and digital image correlation techniques, and then compared with the predictions obtained through linear elastic fracture mechanics （LEFM）. The comparison shows that the measured strain distribution ahead of the crack tip is consistent with the LEFM predictions of up to 25 μm from the crack tip.展开更多
In the diagnosis of rotor crack based on wavelet analysis, it is a painful task to find out an adaptive mother wavelet as many of them can be chosen and the analytic results of different mother wavelets are yet not th...In the diagnosis of rotor crack based on wavelet analysis, it is a painful task to find out an adaptive mother wavelet as many of them can be chosen and the analytic results of different mother wavelets are yet not the same. For this limitation of wavelet analysis, a novel diagnostic approach of rotor crack based on multi-scale singular-spectrum analysis （MS-SSA） is proposed. Firstly, a Jeffcott model of a cracked rotor is developed and the forth-order Runge-Kutta method is used to solve the motion equations of this rotor to obtain its time response （signals）. Secondly, a comparatively simple approach of MS-SSA is presented and the empirical orthogonal functions of different orders in various scales are regarded as analyzing functions. At last, the signals of the cracked rotor and an uncracked rotor are analyzed using the proposed approach of MS-SSA, and the simulative results are compared. The results show that, the data-adaptive analyzing functions can capture many features of signals and the rotor crack can be identified and diagnosed effectively by comparing the analytic results of signals of the cracked rotor with those of the uncracked rotor using the analyzing functions of different orders.展开更多
The trade-offs and synergies of forest ecosystem service are important research topics for several disciplines.The multi-scale analysis of service trade-offs and synergies assists in the implementation of more effecti...The trade-offs and synergies of forest ecosystem service are important research topics for several disciplines.The multi-scale analysis of service trade-offs and synergies assists in the implementation of more effective forest resource management.Based on multi-source data including forest distribution,topography,NDVI,meteorology and soil conditions,key forest ecosystem services,including total forest volume,carbon storage,water yield,soil retention and habitat quality were mapped and evaluated for the Funiu Mountain Region through integrated deployment of the CASA model,the InVEST3.2 model and the ArcGIS10.2 software.The characteristics of trade-offs and synergies among different ecosystem services were then mapped and considered across multiple spatial scales(i.e.,by region,north and south slopes,vertical belt)using the spatial overlay analysis method.The main results are as follows:(1)Mean forest volume is 49.26 m^(3)/ha,carbon density is 156.94 t/ha,water yield depth is 494.46 mm,the unit amount of soil retention is 955.4 t/ha,and the habitat quality index is 0.79.(2)The area of forests with good synergy is 28.79%,and the area of forests with poor synergy is 10.15%,while about 61.06%of forests show severe trade-offs and weak trade-offs.The overall benefits of forest ecosystem services in the study area are still low.In the future,bad synergy and severe trade-off areas should be the focus of forest resource management and efficiency regulation.(3)Synergy between ecosystem services is better for forest on south slope than that on north slope.Deciduous broad-leaved forest belt at moderate elevations on south slope in the mountains(SIII)has the highest synergies,while that at low elevations on north slope(NI)exhibits the lowest synergy levels.展开更多
Part variation characterization is essential to analyze the variation propagation in flexible assemblies. Aiming at two governing types of surface variation,warping and waviness,a comprehensive approach of geometric c...Part variation characterization is essential to analyze the variation propagation in flexible assemblies. Aiming at two governing types of surface variation,warping and waviness,a comprehensive approach of geometric covariance modeling based on hybrid polynomial approximation and spectrum analysis is proposed,which can formulate the level and the correlation of surface variations accurately. Firstly,the form error data of compliant part is acquired by CMM. Thereafter,a Fourier-Legendre polynomial decomposition is conducted and the error data are approximated by a Legendre polynomial series. The weighting coefficient of each component is decided by least square method for extracting the warping from the surface variation. Consequently,a geometrical covariance expression for warping deformation is established. Secondly,a Fourier-sinusoidal decomposition is utilized to approximate the waviness from the residual error data. The spectrum is analyzed is to identify the frequency and the amplitude of error data. Thus,a geometrical covariance expression for the waviness is deduced. Thirdly,a comprehensive geometric covariance model for surface variation is developed by the combination the Legendre polynomials with the sinusoidal polynomials. Finally,a group of L-shape sheet metals is measured along a specific contour,and the covariance of the profile errors is modeled by the proposed method. Thereafter,the result is compared with the covariance from two other methods and the real data. The result shows that the proposed covariance model can match the real surface error effectively and represents a tighter approximation error compared with the referred methods.展开更多
基金Opening Foundation of Key Laboratory of Explosive Energy Utilization and Control,Anhui Province(BP20240104)Graduate Innovation Program of China University of Mining and Technology(2024WLJCRCZL049)Postgraduate Research&Practice Innovation Program of Jiangsu Province(KYCX24_2701)。
文摘Because of the challenge of compounding lightweight,high-strength Ti/Al alloys due to their considerable disparity in properties,Al 6063 as intermediate layer was proposed to fabricate TC4/Al 6063/Al 7075 three-layer composite plate by explosive welding.The microscopic properties of each bonding interface were elucidated through field emission scanning electron microscope and electron backscattered diffraction(EBSD).A methodology combining finite element method-smoothed particle hydrodynamics(FEM-SPH)and molecular dynamics(MD)was proposed for the analysis of the forming and evolution characteristics of explosive welding interfaces at multi-scale.The results demonstrate that the bonding interface morphologies of TC4/Al 6063 and Al 6063/Al 7075 exhibit a flat and wavy configuration,without discernible defects or cracks.The phenomenon of grain refinement is observed in the vicinity of the two bonding interfaces.Furthermore,the degree of plastic deformation of TC4 and Al 7075 is more pronounced than that of Al 6063 in the intermediate layer.The interface morphology characteristics obtained by FEM-SPH simulation exhibit a high degree of similarity to the experimental results.MD simulations reveal that the diffusion of interfacial elements predominantly occurs during the unloading phase,and the simulated thickness of interfacial diffusion aligns well with experimental outcomes.The introduction of intermediate layer in the explosive welding process can effectively produce high-quality titanium/aluminum alloy composite plates.Furthermore,this approach offers a multi-scale simulation strategy for the study of explosive welding bonding interfaces.
基金support from the National Natural Science Foundation of China(12202042)the Fundamental Research Funds for the Central Universities(QNXM20220011,FRF-TP-22-119A1,FRF-IDRY-22-001)+2 种基金the Open Fund Project of Sinopec State Key Laboratory of Shale Oil and Gas Enrichment Mechanisms and Effective Development(33550000-22-ZC0613-0269)China Postdoctoral Science Foundations(2021M700391)High-end Foreign Expert Introduction Program(G2023105006L).
文摘Shale gas, as a clean, low-carbon, and abundant unconventional natural gas resource, plays a crucial role in achieving clean energy transformation and carbon neutrality. The Fuling shale gas reservoir in Sichuan Basin stands out as China's most promising area for shale gas exploration and recovery. However, the continuous recovery of shale gas in the southern Sichuan Basin has led to well interference events in hundreds of wells, with the furthest well distance reaching over 2000 m. This study introduces a multi-scale approach for transient analysis of a multi-well horizontal pad with well interference in shale gas reservoirs. The approach utilizes Laplace transform technology, boundary element theory, and the finite difference method to address the complexities of the system. Well interference is managed using the pressure superposition principle. To validate the proposed multi-scale method, a commercial numerical simulator is employed. The comprehensive pressure behavior of a multi-well horizontal pad in a shale gas reservoir is analyzed, encompassing wellbore storage effect, skin effect, bilinear flow, linear flow, pseudo-radial flow of primary fractures, well interference period, dual-porosity flow, pseudo-radial flow of the total system, and boundary-dominated flow. A case study is conducted on the typical well, the well with the longest production history in the Fuling shale gas reservoir. The rate transient analysis is conducted to integrate up to 229 days of shale gas production daily data and wellhead pressure data, enabling the generation of pressure behavior under unit flow rate. The results indicate that the linear flow, transitional flow, and boundary-dominated flow are more likely to be observed in the actual data. Secondary fractures are considered to be the primary pathways for fluid migration during well interference events. The evaluated formation permeability is 2.58 × 10^(-2) mD, the well spacing is 227.8 m, the diffusion coefficient is 1.49 × 10^(-4), and the skin factor is 0.09.
基金Supported by Hebei Provincial Natural Science Foundation(Grant No.F2024202052)National Natural Science Foundation of China(Grant No.52175019)+3 种基金Beijing Municipal Natural Science Foundation(Grant No.L222038)Beijing Nova Programme Interdisciplinary Cooperation Project(Grant No.20240484699)Joint Funds of Industry-University-Research of Shanghai Academy of Spaceflight Technology(Grant No.SAST2022-017)Beijing Municipal Key Laboratory of Space-ground Interconnection and Convergence of China and Key Laboratory of IoT Monitoring and Early Warning,Ministry of Emergency Management。
文摘Parallel mechanisms with fewer degrees of freedom that incorporate two or more SPR limbs have been widely adopted in industrial applications in recent years.However,notable theoretical gaps persist,particularly in the field of analytical solutions for forward kinematics.To address this,this paper proposes an innovative forward kinematics analysis method based on Conformal Geometric Algebra(CGA)for complex hybrid mechanisms formed by serial concatenation of such parallel mechanisms.The method efficiently represents geometric elements and their operational relationships by defining appropriate unknown parameters.It constructs fundamental geometric objects such as spheres and planes,derives vertex expressions through intersection and dual operations,and establishes univariate high-order equations via inner product operations,ultimately obtaining complete analytical solutions for the forward kinematics of hybrid mechanisms.Using the(2-SPR+RPS)+(3-SPR)serial-parallel hybrid mechanism as a validation case,three configuration tests implemented in Mathematica demonstrate that:for each configuration,the upper 3-SPR mechanism yields 15 mathematical solutions,while the lower 2-SPR+RPS mechanism yields 4 mathematical solutions.After geometric constraint filtering,a unique physically valid solution is obtained for each mechanism.SolidWorks simulations further verify the correctness and reliability of the model.This research provides a reliable analytical method for forward kinematics of hybrid mechanisms,holding significant implications for advancing their applications in high-precision scenarios.
基金the research project funded by the Fundamental Research Funds for the Central Universities(No.HIT.OCEP.2024038)the National Natural Science Foundation of China(No.52372351)the State Key Laboratory of Micro-Spacecraft Rapid Design and Intelligent Cluster,China(No.MS02240107)。
文摘To improve design accuracy and reliability of structures,this study solves the uncertain natural frequencies with consideration for geometric nonlinearity and structural uncertainty.Frequencies of the laminated plate with all four edges clamped(CCCC)are derived based on Navier's method and Galerkin's method.The novelty of the current work is that the number of unknowns in the displacement field model of a CCCC plate with free midsurface(CCCC-2 plate)is only three compared with four or five in cases of other exposed methods.The present analytical method is proved to be accurate and reliable by comparing linear natural frequencies and nonlinear natural frequencies with other models available in the open literature.Furthermore,a novel method for analyzing effects of mean values and tolerance zones of uncertain structural parameters on random frequencies is proposed based on a self-developed Multiscale Feature Extraction and Fusion Network(MFEFN)system.Compared with a direct Monte Carlo Simulation(MCS),the MFEFNbased procedure significantly reduces the calculation burden with a guarantee of accuracy.Our research provides a method to calculate nonlinear natural frequencies under two boundary conditions and presentes a surrogate model to predict frequencies for accuracy analysis and optimization design.
基金Project(2022YFC2904103)supported by the National Key Research and Development Program of ChinaProjects(52374112,52274108)supported by the National Natural Science Foundation of China+1 种基金Projects(BX20220036,BX20230041)supported by the Postdoctoral Innovation Talents Support Program,ChinaProject(2232080)supported by the Beijing Natural Science Foundation,China。
文摘The development of metallic mineral resources generates a significant amount of solid waste,such as tailings and waste rock.Cemented tailings and waste-rock backfill(CTWB)is an effective method for managing and disposing of this mining waste.This study employs a macro-meso-micro testing method to investigate the effects of the waste rock grading index(WGI)and loading rate(LR)on the uniaxial compressive strength(UCS),pore structure,and micromorphology of CTWB materials.Pore structures were analyzed using scanning electron microscopy(SEM)and mercury intrusion porosimetry(MIP).The particles(pores)and cracks analysis system(PCAS)software was used to quantitatively characterize the multi-scale micropores in the SEM images.The key findings indicate that the macroscopic results(UCS)of CTWB materials correspond to the microscopic results(pore structure and micromorphology).Changes in porosity largely depend on the conditions of waste rock grading index and loading rate.The inclusion of waste rock initially increases and then decreases the UCS,while porosity first decreases and then increases,with a critical waste rock grading index of 0.6.As the loading rate increases,UCS initially rises and then falls,while porosity gradually increases.Based on MIP and SEM results,at waste rock grading index 0.6,the most probable pore diameters,total pore area(TPA),pore number(PN),maximum pore area(MPA),and area probability distribution index(APDI)are minimized,while average pore form factor(APF)and fractal dimension of pore porosity distribution(FDPD)are maximized,indicating the most compact pore structure.At a loading rate of 12.0 mm/min,the most probable pore diameters,TPA,PN,MPA,APF,and APDI reach their maximum values,while FDPD reaches its minimum value.Finally,the mechanism of CTWB materials during compression is analyzed,based on the quantitative results of UCS and porosity.The research findings play a crucial role in ensuring the successful application of CTWB materials in deep metal mines.
基金supported by the National Key Research and Development Program of China(No.2016YFB 0200703).
文摘In this paper,a framework is established for nonlinear flutter and gust response analyses based on an efficient Reduced Order Model(ROM).The proposed method can be used to solve the aeroelastic response problems of wings containing geometric nonlinearities.A structural modeling approach presented herein describes the stiffness nonlinearities with a modal formulation.Two orthogonal spanwise modes describe the foreshortening effects of the wing.Dynamic linearization of the ROM under nonlinear equilibrium states is applied to a nonlinear flutter analysis,and the fully nonlinear ROM coupled with the non-planar Unsteady Vortex Lattice Method(UVLM)is applied to gust response analysis.Furthermore,extended Precise Integration Method(PIM)ensures accuracy of the dynamic equation solutions.To demonstrate applicability and accuracy of the method presented,a wind tunnel test is conducted and good agreements between theoretical and test results of nonlinear flutter speed and gust response deflection are reached.The method described in this paper is suitable for predicting the nonlinear flutter speed and calculating the gust responses of a large-aspect-ratio wing in time domain.Meanwhile,the results derived highlight the effects of geometric nonlinearities obviously.
基金supported by the National Natural Sciences Foundation of China(31440078,31501876,31501840)Shanxi Province Programs for Science and Technology Development(20150311010-7)+1 种基金the Research Equipment Development Project of Chinese Academy of Sciences(YZ201509)the Graduate Innovation Project in Shanxi Province,China(2016BY067)
文摘The genus Eysarcoris can be easily distinguished from other genera through the two spots in the basal angle of the scutellum. Nevertheless, Eysarcoris species show complex variances. Geometric morphometric methods have been increasingly applied to distinguish species and to define the boundary of genera among insects. In the present study, geometric morphometric approach was firstly employed to evaluate the shape variation of three characters （fore wing, hind wing and pygophore） of E. guttiger, E. annamita and E. ventralis using E. aeneus as outgroup to ascertain whether this approach is a reliable method for the taxonomy of Eysarcoris. Analysis was conducted on the landmarks of the three characters of these species. Multivariate regression of procrustes coordinates against centroid size was conducted to test the presence of allometry. Principal component analysis （PCA）, canonical variate analysis （CVA） and cluster analysis were utilized to describe variations in shapes among the studied species. For all of the three characters, though PCA analysis showed some overlap among species, p-values for procrustes distance and mahalanobis distance were all less than 0.0001. The distribution of the three studied species corresponds with their species status. This study demonstrates that the geometric morphometrics of both the fore wing and the hind wing might represent a possible tool for the identification of species within this genus.
文摘This research is focused on the singularity analysis for single-gimbal control moment gyros systems （SCMGs） which include two types, with constant speed （CSCMG） or variable speed （VSCMG） rotors. Through angular momentum hypersurfaces of singular states, the passable and impassable singular points are discriminated easily, meanwhile the information about how much the angular momentum workspace as well as the steering capability available is provided directly. It is obvious that the null motions of steering laws are more effective for the five pyramid configuration（FPC） than for the pyramid configuration（PC） from the singular plots. The possible degenerate hyperbolic singular points of the preceding configurations are calculated and the distinctness of them is denoted by the Gaussian curvature. Furthermore, failure problems to steer integrated power and attitude control system （IPACS） are also analyzed. A sufficient condition of choosing configurations of VSCMGs to guarantee the IPACS steering is given. The angular momentum envelops of VSCMGs, in a given energy and a limited range of rotor speeds, are plotted. The connection and distinctness between CSCMGs and VSCMGs are obtained from the point of view of envelops.
基金Supported by the National Natural Science Foundation of China (No. 20106008)National HI-TECH Industrialization Program of China (No. Fagai-Gaoji-2004-2080)Science Fund for Distinguished Young Scholars of Zhejiang University (No. 111000-581645).
文摘Prediction of melt index （MI）, the most important parameter in determining the product＇s grade and quality control of polypropylene produced in practical industrial processes, is studied. A novel soft-sensor model with principal component analysis （PCA）, radial basis function （RBF） networks, and multi-scale analysis （MSA） is proposed to infer the MI of manufactured products from real process variables, where PCA is carried out to select the most relevant process features and to eliminate the correlations of the input variables, MSA is introduced to a^quire much more information and to reduce the uncertainty of the system, and RBF networks are used to characterize the nonlinearity of the process. The research results show that the proposed method provides promising prediction reliability and accuracy, and supposed to have extensive application prospects in propylene polymerization processes.
基金co-supported by the Priority Academic Program Development of Jiangsu Higher Education Institutionsthe National Natural Science Foundation of China (No. 11302105)
文摘Efficient and accurate strength analysis of bolted connections is essential in analyzing the integral thermal protection system（ITPS） of hypersonic vehicles, since the system bears severe loads and structural failures usually occur at the connections. Investigations of composite mechanical properties used in ITPS are still in progress as the architecture of the composites is complex. A new method is proposed in this paper for strength analysis of bolted connections by investigating the elastic behavior and failure strength of three-dimensional C/C orthogonal composites used in ITPS. In this method a multi-scale finite element method incorporating the global–local method is established to ensure high efficiency in macro-scale and precision in meso-scale in analysis.Simulation results reveal that predictions of material properties show reasonable accuracy compared with test results. And the multi-scale method can analyze the strength of connections efficiently and accurately.
基金supported by the Ministry of Education of Singapore under Grant No.R265-000-277-112
文摘A geometrical analysis based algorithm is proposed to achieve the stereo matching of a single-lens prism based stereovision system. By setting the multi- face prism in frontal position of the static CCD （CM-140MCL） camera, equivalent stereo images with different orientations are captured synchronously by virtual cameras which are defined by two boundary lines： the optical axis and CCD camera field of view boundary. Subsequently, the geometrical relationship between the 2D stereo images and corresponding 3D scene is established by employing two fundamentals： ray sketching in which all the pertinent points, lines, and planes are expressed in the 3D camera coordinates and the rule of refraction. Landing on this relationship, the epipolar geometry is thus obtained by fitting a set of corresponding candidate points and thereafter, stereo matching of the prism based stereovision system is obtained. Moreover, the unique geometrical properties of the imaging system allow the proposed method free from the complicated camera calibration procedures and to be easily generalized from binocular and tri-oeular to multi-ocular stereovision systems. The performance of the algorithm is presented through the experiments on the binocular imaging system and the comparison with a conventional projection method demonstrates the efficient assessment of our novel contributions.
文摘The nonlinear biased ship rolling motion and capsizing in randoro waves are studied by utilizing a global geometric method. Thompson＇ s α-parameterized family of restoring functions is adopted in the vessel equation of motion for the representation of bias. To take into account the presence of randomness in the excitation and the response, a stochastic Melnikov method is developed and a mean-square criterion is obtained to provide an upper bound on the domain of the potential chaotic rolling motion. This criterion can be used to predict the qualitative nature of the invariant manifolds which represent the boundary botween safe and unsafe initial conditions, and how these depend on system parameters of the specific ship model. Phase space transport theory and lobe dynamics are used to demonstrate how motions starting from initial conditions inside the regions bounded by the intersected manifolds will evolve and how unexpected capsizing can occur.
基金supported by the National Science and Technology Major Project, China (No. J2019-II-0012-0032)
文摘Inevitable geometric variations significantly affect the performance of turbines or even that of entire engines;thus,it is necessary to determine their actual characteristics and accurately estimate their impact on performance.In this study,based on 1781 measured profiles of a typical turbine blade,the statistical characteristics of the geometric variations and the uncertainty impact are analyzed,and some commonly used uncertainty modelling methods based on Principal-Component Analysis(PCA)are verified.The geometric variations are found to be evident,asymmetric,and non-uniform,and the non-normality of the random distributions is non-negligible.The performance is notably affected,which is manifested as an overall offset,a notable scattering,and significant deterioration in several extreme cases.Additionally,it is demonstrated that the PCA reconstruction model is effective in characterizing major uncertainty characteristics of the geometric variations and their impact on the performance with almost the first 10 PCA modes.Based on a reasonable profile error and mean geometric deviation,the Gaussian assumption and stochasticprocess-based model are also found to be effective in predicting the mean values and standard deviations of the performance variations.However,they fail to predict the probability of some extreme cases with high loss.Finally,a Chi-square-based correction model is proposed to compensate for this deficiency.The present work can provide a useful reference for uncertainty analysis of the impact of geometric variations,and the corresponding uncertainty design of turbine blades.
基金supported by the National Natural Science Foundation of China [No. 51475321]Tianjin Research Program of Application Foundation and Advanced Technology [No. 15JCZDJC38900 and 16JCYBJC19300]the International Postdoctoral Exchange Fellowship Program [No. 32 Document of OCPC, 2017]
文摘This paper deals with geometric error modeling and sensitivity analysis of an overconstrained parallel tracking mechanism. The main contribution is the consideration of overconstrained features that are usually ignored in previous research. The reciprocal property between a motion and a force is applied to tackle this problem in the framework of the screw theory. First of all, a nominal kinematic model of the parallel tracking mechanism is formulated. On this basis, the actual twist of the moving platform is computed through the superposition of the joint twist and geometric errors. The actuation and constrained wrenches of each limb are applied to exclude the joint displacement. After eliminating repeated errors brought by the multiplication of wrenches, a geometric error model of the parallel tracking mechanism is built. Furthermore,two sensitivity indices are defined to select essential geometric errors for future kinematic calibration. Finally, the geometric error model with minimum geometric errors is verified by simulation with SolidWorks software. Two typical poses of the parallel tracking mechanism are selected, and the differences between simulation and calculation results are very small. The results confirm the correctness and accuracy of the geometric error modeling method for over-constrained parallel mechanisms.
基金Project supported by the National Key Basic Pre-Research Fund of the Ministry of Science and Technology of Chinathe Fund for Outstanding Young Researchers of the National Natural Sciences Foundation of China (No.10025208)+2 种基金 the KeyFund of the National Natural Science Foundation of China the Youth Fund of the National Natural Science Foundationof China (No.10302009) and the Youth Fund of Lanzhou University (Lzu200305).
文摘The magneto-plastic instability of a ferromagnetic beam-type plate with simple supports and small initial imperfection is analytically investigated in this paper for that the plastic deformation of the plate with a linear-strain hardening relation is considered when the plate is located in a strong uniformly distributed magnetic ?eld. After the distribution of magnetic ?elds related to the de?ected con?guration of plate is imaginably divided into two parts, i.e., one is related to the ?at plate and the other dependent on the perturbation of magnetic ?elds for which the plate con?guration changes from the ?at into the deformed state, the perturbation technique is employed to analyze the distribution of the perturbation magnetic ?elds in and out-of the magnetic medium of the ferromagnetic structure in a transverse magnetic ?eld, which leads to some analytical formulae/solutions for the magnetic ?elds and the resulting magnetic force exerted on the plate. Based on them, the magneto-plastic buckling and snapping of the plate in a transverse magnetic ?eld is discussed, and the critical magnetic ?eld is analytically formulated in terms of the parameters of geometry and material of the plate employed by solving the governing equation of the magneto-plastic plate in the applied magnetic ?eld. Further, the sensitivity of the initial imperfection on the magneto-plastic instability, expressed by an ampli?cation function, is obtained by solving the dynamic equation of de?ection of the plate after the inertial force in the transverse direction is taken into account. The results obtained show that the critical magnetic ?eld is sensitive to the plastic characteristic, e.g., hardening coe?cient, and the instability mode and de?ection of the plate are dependent on the geometrical imperfection as well.
基金Project(2019 YFB 2004700)supported by the National Key R&D Project of ChinaProject(HTL-O-19 K 02)supported by National Key Laboratory of Science and Technology on Helicopter Transmission,Nanjing University of Aeronautics and Astronautics,China。
文摘Worm grinding has been applied to manufacture gears to pursue high accuracy and fine surface finish.When the worm used to grind face gears is manufactured with multi-axis computer numerical control(CNC)machining,the machining accuracy is usually improved by increasing the number of tool paths with more time cost.Differently,this work proposes a generated method to improve the efficiency by dressing the worm surface with only one path,and a closed-loop manufacturing process is applied to ensure the machining accuracy.According to an advanced geometric analysis,the worm surface is practically approximated as a swept surface generated by a planar curve.Meanwhile,this curve is applied as the profile of a dressing wheel,which is used to dress the worm surface.The practical machining is carried out in a CNC machine tool,which was originally used to grind helical gears.Finally,a closed-loop manufacturing process including machining,measurement,and modification is proposed to compensate the machining errors.The proposed method is validated with simulations and practical experiments.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11562016 and 11672175)
文摘Uniaxial tension tests were conducted on single-edge-notched tensile specimens of pure molybdenum with a mesh grid pattern in front of the notch. A series of images of crack initialization and propagation with a distorted mesh grid pattern were obtained by means of in situ scanning electron microscopy. Strain fields around the crack tip were mapped successively using geometric phase analysis and digital image correlation techniques, and then compared with the predictions obtained through linear elastic fracture mechanics （LEFM）. The comparison shows that the measured strain distribution ahead of the crack tip is consistent with the LEFM predictions of up to 25 μm from the crack tip.
基金This project is supported by National Fundamental Research and Development Project Foundation of China(No.G1998020321).
文摘In the diagnosis of rotor crack based on wavelet analysis, it is a painful task to find out an adaptive mother wavelet as many of them can be chosen and the analytic results of different mother wavelets are yet not the same. For this limitation of wavelet analysis, a novel diagnostic approach of rotor crack based on multi-scale singular-spectrum analysis （MS-SSA） is proposed. Firstly, a Jeffcott model of a cracked rotor is developed and the forth-order Runge-Kutta method is used to solve the motion equations of this rotor to obtain its time response （signals）. Secondly, a comparatively simple approach of MS-SSA is presented and the empirical orthogonal functions of different orders in various scales are regarded as analyzing functions. At last, the signals of the cracked rotor and an uncracked rotor are analyzed using the proposed approach of MS-SSA, and the simulative results are compared. The results show that, the data-adaptive analyzing functions can capture many features of signals and the rotor crack can be identified and diagnosed effectively by comparing the analytic results of signals of the cracked rotor with those of the uncracked rotor using the analyzing functions of different orders.
基金National Natural Science Foundation of China,No.41671090National Basic Research Program(973 Program),No.2015CB452702。
文摘The trade-offs and synergies of forest ecosystem service are important research topics for several disciplines.The multi-scale analysis of service trade-offs and synergies assists in the implementation of more effective forest resource management.Based on multi-source data including forest distribution,topography,NDVI,meteorology and soil conditions,key forest ecosystem services,including total forest volume,carbon storage,water yield,soil retention and habitat quality were mapped and evaluated for the Funiu Mountain Region through integrated deployment of the CASA model,the InVEST3.2 model and the ArcGIS10.2 software.The characteristics of trade-offs and synergies among different ecosystem services were then mapped and considered across multiple spatial scales(i.e.,by region,north and south slopes,vertical belt)using the spatial overlay analysis method.The main results are as follows:(1)Mean forest volume is 49.26 m^(3)/ha,carbon density is 156.94 t/ha,water yield depth is 494.46 mm,the unit amount of soil retention is 955.4 t/ha,and the habitat quality index is 0.79.(2)The area of forests with good synergy is 28.79%,and the area of forests with poor synergy is 10.15%,while about 61.06%of forests show severe trade-offs and weak trade-offs.The overall benefits of forest ecosystem services in the study area are still low.In the future,bad synergy and severe trade-off areas should be the focus of forest resource management and efficiency regulation.(3)Synergy between ecosystem services is better for forest on south slope than that on north slope.Deciduous broad-leaved forest belt at moderate elevations on south slope in the mountains(SIII)has the highest synergies,while that at low elevations on north slope(NI)exhibits the lowest synergy levels.
基金Supported by the National Natural Science Foundation of China(50905084,51275236)the Aeronautical Science Foundation of China(2010ZE52054)
文摘Part variation characterization is essential to analyze the variation propagation in flexible assemblies. Aiming at two governing types of surface variation,warping and waviness,a comprehensive approach of geometric covariance modeling based on hybrid polynomial approximation and spectrum analysis is proposed,which can formulate the level and the correlation of surface variations accurately. Firstly,the form error data of compliant part is acquired by CMM. Thereafter,a Fourier-Legendre polynomial decomposition is conducted and the error data are approximated by a Legendre polynomial series. The weighting coefficient of each component is decided by least square method for extracting the warping from the surface variation. Consequently,a geometrical covariance expression for warping deformation is established. Secondly,a Fourier-sinusoidal decomposition is utilized to approximate the waviness from the residual error data. The spectrum is analyzed is to identify the frequency and the amplitude of error data. Thus,a geometrical covariance expression for the waviness is deduced. Thirdly,a comprehensive geometric covariance model for surface variation is developed by the combination the Legendre polynomials with the sinusoidal polynomials. Finally,a group of L-shape sheet metals is measured along a specific contour,and the covariance of the profile errors is modeled by the proposed method. Thereafter,the result is compared with the covariance from two other methods and the real data. The result shows that the proposed covariance model can match the real surface error effectively and represents a tighter approximation error compared with the referred methods.
