This paper presents an alternate graphical procedure (Method 2), to that presented in earlier publications entitled, “A Procedure for Trisecting an Acute Angle” and “A Key to Solving the Angle Trisection Problem”....This paper presents an alternate graphical procedure (Method 2), to that presented in earlier publications entitled, “A Procedure for Trisecting an Acute Angle” and “A Key to Solving the Angle Trisection Problem”. The procedure, when applied to the 30˚ and 60˚ angles that have been “proven” to be nottrisectable and the 45˚ benchmark angle that is known to be trisectable, in each case produced a construction having an identical angular relationship with Archimedes’ Construction, as in Section 2 on THEORY of this paper, where the required trisection angle was found to be one-third of its respective angle (i.e. DE’MA = 1/3 DE’CG). For example, the trisection angle for the 30˚, 45˚ and 60˚ angles were 10.00000˚, 15.00000˚, and 20.00000˚, respectively, and Section 5 on PROOF in this paper. Therefore, based on this identical angular relationship and the numerical results (i.e. to five decimal places), which represent the highest degree of accuracy and precision attainable by The Geometer’s Sketch Pad software, one can only conclude that not only the geometric requirements for arriving at an exact trisection of the 30˚ and 60˚ angle (which have been “proven” to be not-trisectable) have been met, but also, the construction is valid for any arbitrary acute angle, despite theoretical proofs to the contrary by Wantzel, Dudley, and others.展开更多
This paper presents the evolution process of pressure angles from planar parallel mechanisms to spatial parallel mechanisms. Manipulability and condition number, which are frequently used in the optimum design of para...This paper presents the evolution process of pressure angles from planar parallel mechanisms to spatial parallel mechanisms. Manipulability and condition number, which are frequently used in the optimum design of parallel mechanisms, are introduced from serial robots at first. Then, both theoretical analysis and practical experiences demonstrate that these concepts seem imperfect when they are used in parallel mechanisms. For this reason, this paper introduces the pressure angles in planar 4-bar mechanisms to spatial parallel mechanisms, which include redundant parallel mechanisms. Two kinds of pressure angles extracted from the determinant of direct and indirect Jacobian matrices are investigated. Moreover, two comprehensive and visible global performance indices are defined, showing the advantages in evaluating the workspace, singularity and motion/force transmission capabilities. With a 2-DOF planar and a 3-DOF spatial parallel mechanism as examples, the application of the performance indices is investigated and compared with the condition number at last. The proposed concept can be extended to other spatial parallel mechanisms.展开更多
To study the effect of the contact angle and helix angle on slide-roll ratio at the ball contact points under the accelerated motion state of ball screw mechanisrm(B S M),the curve theory in differential geometry a d ...To study the effect of the contact angle and helix angle on slide-roll ratio at the ball contact points under the accelerated motion state of ball screw mechanisrm(B S M),the curve theory in differential geometry a d the homogeneous transformation matrix ae used to establish the acceleration kinematics model of BSM.The model can be used to describe the accelerated motion relationships among the screw,balls and nut,calculate the acceleration of relative motion at the contact points between the balls and raceways,and analyze five accelerated motion rules between the balls and raceways.It also conducts a simulation analysis of the slide-roll ratio relationship between the accelerations at the ball center and the contact point of ball under different contact angles and helix angles.As shownby the analysis,with the increase in the BSM’s contact angle,the slide-roll ratio at the contact points decreases,and the contact angle has a relatively significant effect on the slide-roll ratio.However,with the decrease in the BSM’helix angle,the slide-roll ratio at the contact points decreases,and the helix angle has a relatively insignificant effect on the slide-roll ratio.By measuring the accelerations of both the screw and nut under the accelerated motion state,it also verifies the existence of the slide-roll mixed motion at the ball contact point A between the ball and the screw racewayand pure rolling at the ball contact point B between the ball and the nut raceway during the accelerated motion.展开更多
Contact angle is an essential parameter to characterize substrate wettability.The measurement of contact angle in experiment and simulation is a complex and time-consuming task.In this paper,an improved method of meas...Contact angle is an essential parameter to characterize substrate wettability.The measurement of contact angle in experiment and simulation is a complex and time-consuming task.In this paper,an improved method of measuring contact angle in multiphase lattice Boltzmann simulations is proposed,which can accurately obtain the real-time contact angle at a low temperature and larger density ratio.The three-phase contact point is determined by an extrapolation,and its position is not affected by the local deformation of flow field in the three-phase contact region.A series of simulations confirms that the present method has high accuracy and gird-independence.The contact angle keeps an excellent linear relationship with the chemical potential of the surface,so that it is very convenient to specify the wettability of a surface.The real-time contact angle measurement enables us to obtain the dynamic contact angle hysteresis on chemically heterogeneous surface,while the mechanical analyses can be effectively implemented at the moving contact line.展开更多
This paper presents a simplified graphical procedure for constructing, using an unmarked straightedge and a compass only, a 10˚ to 20˚ angle, which is in other words, trisecting a 30˚ or 60˚ angle. The procedure, when...This paper presents a simplified graphical procedure for constructing, using an unmarked straightedge and a compass only, a 10˚ to 20˚ angle, which is in other words, trisecting a 30˚ or 60˚ angle. The procedure, when applied to the 30˚ and 60˚ angles that have been “proven” to be not trisectable, produced a construction having the identical angular relationship with Archimedes’ Construction, in which the required trisection angles were found to be 10.00000˚ and 20.00000˚ respectively (i.e. exactly one-third of the given angle or ∠E’MA = 1/3∠E’CG). Based on this identical angular relationship as well as the numerical results obtained, one can only conclude that the geometric requirements for arriving at an exact trisection of the 30˚ or 60˚ angle, and therefore the construction of a 10˚ or 20˚ angle, have been met, notwithstanding the theoretical proofs of Wantzel, Dudley, and others. Thus, the solution to the age-old trisection problem, with respect to these two angles, has been accomplished.展开更多
Analyzed the support instable mode of sliding,tripping,and so on,and believed the key point of the support stability control of fully mechanized coal caving face with steep coal seams was to maintain that the seam tru...Analyzed the support instable mode of sliding,tripping,and so on,and believed the key point of the support stability control of fully mechanized coal caving face with steep coal seams was to maintain that the seam true angle was less than the hydraulic support instability critical angle.Through the layout of oblique face,the improvement of support setting load,the control of mining height and nonskid platform,the group support system of end face,the advance optimization of conveyor and support,and the other control tech- nical measures,the true angle of the seam is reduced and the instable critical angle of the support is increased,the hydraulic support stability of fully mechanized coal caving face with steep coal seams is effectively controlled.展开更多
This paper describes the methodology (or approach) that was key to the solution of the angle trisection problem published earlier in article entitled, “A Procedure For Trisecting An Acute Angle.” It was an approach ...This paper describes the methodology (or approach) that was key to the solution of the angle trisection problem published earlier in article entitled, “A Procedure For Trisecting An Acute Angle.” It was an approach that required first, designing a working model of a trisector mechanism, second, studying the motion of key elements of the mechanism and third, applying the fundamental principles of kinematics to arrive at the desired results. In presenting these results, since there was no requirement to provide a detailed analysis of the final construction, this information was not included. However, now that the publication is out, it is considered appropriate as well as instructive to explain more fully the mechanism analysis of the trisector in graphical detail, as covered in Section 3 of this paper, that formed the basis of the long sought solution to the age-old Angle Trisection Problem.展开更多
This study aims to investigate mechanical properties and failure mechanisms of layered rock with rough joint surfaces under direct shear loading.Cubic layered samples with dimensions of 100 mm×100 mm×100 mm ...This study aims to investigate mechanical properties and failure mechanisms of layered rock with rough joint surfaces under direct shear loading.Cubic layered samples with dimensions of 100 mm×100 mm×100 mm were casted using rock-like materials,with anisotropic angle(α)and joint roughness coefficient(JRC)ranging from 15°to 75°and 2-20,respectively.The direct shear tests were conducted under the application of initial normal stress(σ_(n))ranging from 1-4 MPa.The test results indicate significant differences in mechanical properties,acoustic emission(AE)responses,maximum principal strain fields,and ultimate failure modes of layered samples under different test conditions.The peak stress increases with the increasingαand achieves a maximum value atα=60°or 75°.Asσ_(n)increases,the peak stress shows an increasing trend,with correlation coefficients R²ranging from 0.918 to 0.995 for the linear least squares fitting.As JRC increases from 2-4 to 18-20,the cohesion increases by 86.32%whenα=15°,while the cohesion decreases by 27.93%whenα=75°.The differences in roughness characteristics of shear failure surface induced byαresult in anisotropic post-peak AE responses,which is characterized by active AE signals whenαis small and quiet AE signals for a largeα.For a given JRC=6-8 andσ_(n)=1 MPa,asαincreases,the accumulative AE counts increase by 224.31%(αincreased from 15°to 60°),and then decrease by 14.68%(αincreased from 60°to 75°).The shear failure surface is formed along the weak interlayer whenα=15°and penetrates the layered matrix whenα=60°.Whenα=15°,asσ_(n)increases,the adjacent weak interlayer induces a change in the direction of tensile cracks propagation,resulting in a stepped pattern of cracks distribution.The increase in JRC intensifies roughness characteristics of shear failure surface for a smallα,however,it is not pronounced for a largeα.The findings will contribute to a better understanding of the mechanical responses and failure mechanisms of the layered rocks subjected to shear loads.展开更多
Published studies in regard to coupler systems have been mainly focused on the manufacturing process or coupler strength issues. With the ever increasing of tonnage and length of heavy haul trains, lateral in-train fo...Published studies in regard to coupler systems have been mainly focused on the manufacturing process or coupler strength issues. With the ever increasing of tonnage and length of heavy haul trains, lateral in-train forces generated by longitudinal in-train forces and coupler rotations have become a more and more significant safety issue for heavy haul train operations. Derailments caused by excessive lateral in-train forces are frequently reported. This article studies two typical coupler systems used on heavy haul locomotives. Their structures and stabilizing mechanism are analyzed before the corresponding models are developed. Coupler systems models are featured by two distinct stabilizing mechanism models and draft gear models with hysteresis considered. A model set which consists of four locomotives and three coupler systems is developed to study the rotational behavior of different coupler systems and their implications for locomotive dynamics. Simulated results indicate that when the locomotives are equipped with the type B coupler system, locomotives can meet the dynamics standard on tangent tracks; while the dynamics performance on curved tracks is very poor. The maximum longitudinal in-train force for locomotives equipped with the type B coupler system is 2000 kN. Simulations revealed a distinct trend for the type A coupler system. Locomotive dynamics are poorer for the type A case when locomotives are running on tangent tracks, while the dynamics are better for the type A case when locomotives are running on curved tracks. Theoretical studies and simulations carried out in this article suggest that a combination of the two types of stabilizing mechanism can result in a good design which can significantly decrease the relevant derailments.展开更多
We first design and analyze the contour surface of the globoidal indexing cam with the aid of computer, and then do optimum design according to the requirements of dynamics. Finally, we discuss the problem of the pres...We first design and analyze the contour surface of the globoidal indexing cam with the aid of computer, and then do optimum design according to the requirements of dynamics. Finally, we discuss the problem of the pressure angle of the globoidal indexing cam mechanism in detail and put forward a new concept of equivalent pressure angle.展开更多
There have been various theoretical attempts by researchers worldwide to link up different scales of plasticity studies from the nano-, micro- and macro-scale of observation, based on molecular dynamics, crystal plast...There have been various theoretical attempts by researchers worldwide to link up different scales of plasticity studies from the nano-, micro- and macro-scale of observation, based on molecular dynamics, crystal plasticity and continuum mechanics. Very few attempts, however, have been reported in ultra-precision machining studies. A mesoplasticity approach advocated by Lee and Yang is adopted by the authors and is successfully applied to studies of the micro-cutting mechanisms in ultra-precision machining. Traditionally, the shear angle in metal cutting, as well as the cutting force variation, can only be determined from cutting tests. In the pioneering work of the authors, the use of mesoplasticity theory enables prediction of the fluctuation of the shear angle and micro-cutting force, shear band formation, chip morphology in diamond turning and size effect in nano-indentation. These findings are verified by experiments. The mesoplasticity formulation opens up a new direction of studies to enable how the plastic behaviour of materials and their constitutive representations in deformation processing, such as machining can be predicted, assessed and deduced from the basic properties of the materials measurable at the microscale.展开更多
Small angle neutron scattering(SANS) technique has been used to investigate the Ni_(50)Mo_(50) system prepared by mechanical alloying(MA). Significant changes of the scattering intensity have been observed among the s...Small angle neutron scattering(SANS) technique has been used to investigate the Ni_(50)Mo_(50) system prepared by mechanical alloying(MA). Significant changes of the scattering intensity have been observed among the samples with different milling time.Interesting fractal-like behavior of the sample system have been found and attempts have been made to determine the fractal dimensions. It is expected that the fractal dimension can be related to the different stages of MA to some extent.展开更多
A novel method of realizing the optimal transmission of the crank-and-rockermechanism is presented. The optimal combination design is made by finding the related optimaltransmission parameters. The diagram of the opti...A novel method of realizing the optimal transmission of the crank-and-rockermechanism is presented. The optimal combination design is made by finding the related optimaltransmission parameters. The diagram of the optimal transmission is drawn. In the diagram, therelation among mini-mum transmission angle, the coefficient of travel speed variation, theoscillating angle of the rocker and the length of the bars is shown, concisely, conveniently anddirectly. The method possesses the main characteristic. That it is to achieve the optimaltransmission parameters under the transmission angle by directly choosing in the diagram, accordingto the given requirements. The characteristics of the mechanical transmission can be improved togain the optimal transmission effect by the method. Especially, the method is simple and convenientin practical use.展开更多
As one of the typical less-mobility parallel mechanisms, the spherical parallel mechanism Up.s with two degrees of freedom (2-DOF) possess high order overconstraints, and the calculation of its stiffness is partly d...As one of the typical less-mobility parallel mechanisms, the spherical parallel mechanism Up.s with two degrees of freedom (2-DOF) possess high order overconstraints, and the calculation of its stiffness is partly different with general parallel mechanisms owing to the bars in each branch are assumed to be arc-shaped. By means of small deformation superposition principle, the relationship between the angle displacement and line displacement of moving platform and the forces acted on the branches were derived out. Based on the results of static analysis, the relationship between the applied force, the line displacement and the angle displacement of the mechanism was set up. And then the stiffness matrix was obtained. The six principal stiffness of the mechanism and the corresponding directions were achieved by the orthogonal transformation. The numerical calculation was performed and the results showed that the principal stiffness and directions are varied with the pose-position of the mechanism, and the principal stiffness is gradually enlarged when it is far away from the anigin. In addition, the torsion stiffness is much greater and the line deformation stiffness is smaller, the difference between the two parts is huge. The research content of this paper supplies the theoretical foundation for the further engineering design and application of the spherical parallel mechanism.展开更多
Slopes consisting of interbedded strata of soft and hard rock mass, such as purplish red mudstone and grey brown arkosic sandstone of Jurassic age, are very common in Sichuan basin of China. The mudstone is soft whil...Slopes consisting of interbedded strata of soft and hard rock mass, such as purplish red mudstone and grey brown arkosic sandstone of Jurassic age, are very common in Sichuan basin of China. The mudstone is soft while the sandstone is hard and contains many opening or closing joints with a high dip angle. Some are nearly parallel and the others are nearly decussated with the trend of the slopes. Many natural slopes are in deformation or sliding because of those reasons. The stability of cutting slopes and supporting method to be taken for their stability in civil engineering are important. In this paper, the stability and deformation of the slopes are studied. The methods of analysis and support design principle are analyzed also. Finally, the method put forward is applied to study Fengdian high cutting slope in Sichuan section of the express way from Chengdu to Shanghai. The results indicate that the method is effective.展开更多
Objective :To investigate the role the lens dimensions played on the pathogenesis of primary angle-closure glaucoma. Methods:38 eyes of 20 patients with primary angle-closure glaucoma (PACG) and 35 eyes of 22 norm...Objective :To investigate the role the lens dimensions played on the pathogenesis of primary angle-closure glaucoma. Methods:38 eyes of 20 patients with primary angle-closure glaucoma (PACG) and 35 eyes of 22 normal individuals without ocular abnormalities were examined. The anatomical parameters of the lens and other structures of the anterior segment were calculated using B ultrasound, computer image processing and ultrasound biomicroscopy (UBM). The parameters were compared between the patients and normal subjects. Correlation analysis was used to determine the relationship between the radii of curvature of the anterior lens surface (RCALS) and the other parameters of the anterior segment. Results:Compared with the normal eyes, the eyes of PACG had thicker lens, steeper curvature of anterior lens surface, decreased depth of the anterior chamber, narrower chamber angle, and more anterior position of the ciliary bodies and lens. All these differences were significant(P 〈 0.05 or P 〈 0.01). In the PACG group, the RCALS had significantly negative correlation with the central and peripheral lens thickness (P 〈 0.01 and P 〈 0.05 respectively), and had positive correlation with relative lens position, anterior chamber depth(ACD), angle-open distance at 500 um(AOD500), trabecular iris angle (TIA) and trabecular ciliary processes distance(TCPD, P 〈 0.05 or P 〈 0.01 ). Conclusion:The occurrence of PACG is relevant to the abnormal anatomical structures of the anterior segment. Among all factors, the lens parameters play an important role in the pathogenesis. Increased lens thickness, relative more anterior position of lens, especially steepened curvature of anterior lens surface are predisposing factors of the pathologic phenomenon in PACG including pupillary blockage, shallow anterior chamber, secondary closure of chamber angle and elevation of intraocular pressure.展开更多
By using LS-DYNA simulation software,the influences of some structure parameters,such as top cone angle,wall thickness,liner height and height ratio of top cone,of double-angle liner on the jet formation were studied ...By using LS-DYNA simulation software,the influences of some structure parameters,such as top cone angle,wall thickness,liner height and height ratio of top cone,of double-angle liner on the jet formation were studied respectively.Their influences on jet tip velocity,tail velocity and penetration depth were revealed.The simulation results show that the formation is better if the top cone angle is selected as 28°,the wall is 2.6mm,the liner height is 140mm,and the height ratio of top cone is 60%.In large stand-off distance,the jet has a higher tip velocity,and the tip does not break.With the stand-off distance of 8 times of the charge diameter,the experiment penetrating steel target was carried out.The experiment and simulation results are in good agreement.展开更多
文摘This paper presents an alternate graphical procedure (Method 2), to that presented in earlier publications entitled, “A Procedure for Trisecting an Acute Angle” and “A Key to Solving the Angle Trisection Problem”. The procedure, when applied to the 30˚ and 60˚ angles that have been “proven” to be nottrisectable and the 45˚ benchmark angle that is known to be trisectable, in each case produced a construction having an identical angular relationship with Archimedes’ Construction, as in Section 2 on THEORY of this paper, where the required trisection angle was found to be one-third of its respective angle (i.e. DE’MA = 1/3 DE’CG). For example, the trisection angle for the 30˚, 45˚ and 60˚ angles were 10.00000˚, 15.00000˚, and 20.00000˚, respectively, and Section 5 on PROOF in this paper. Therefore, based on this identical angular relationship and the numerical results (i.e. to five decimal places), which represent the highest degree of accuracy and precision attainable by The Geometer’s Sketch Pad software, one can only conclude that not only the geometric requirements for arriving at an exact trisection of the 30˚ and 60˚ angle (which have been “proven” to be not-trisectable) have been met, but also, the construction is valid for any arbitrary acute angle, despite theoretical proofs to the contrary by Wantzel, Dudley, and others.
基金Supported by the National Natural Science Foundation of China(No.51305293)Tianjin Technical Innovation Funds for the Minor Sci-tech Enterprise(No.14C26211200362)
文摘This paper presents the evolution process of pressure angles from planar parallel mechanisms to spatial parallel mechanisms. Manipulability and condition number, which are frequently used in the optimum design of parallel mechanisms, are introduced from serial robots at first. Then, both theoretical analysis and practical experiences demonstrate that these concepts seem imperfect when they are used in parallel mechanisms. For this reason, this paper introduces the pressure angles in planar 4-bar mechanisms to spatial parallel mechanisms, which include redundant parallel mechanisms. Two kinds of pressure angles extracted from the determinant of direct and indirect Jacobian matrices are investigated. Moreover, two comprehensive and visible global performance indices are defined, showing the advantages in evaluating the workspace, singularity and motion/force transmission capabilities. With a 2-DOF planar and a 3-DOF spatial parallel mechanism as examples, the application of the performance indices is investigated and compared with the condition number at last. The proposed concept can be extended to other spatial parallel mechanisms.
基金The National Natural Science Foundation of China(No.51575014,51505012)the Natural Science Foundation of Beijing(No.KZ201410005010)+1 种基金China Postdoctoral Science Foundation(No.2016M591033)Beijing Postdoctoral Research Foundation(No.2015ZZ-13)
文摘To study the effect of the contact angle and helix angle on slide-roll ratio at the ball contact points under the accelerated motion state of ball screw mechanisrm(B S M),the curve theory in differential geometry a d the homogeneous transformation matrix ae used to establish the acceleration kinematics model of BSM.The model can be used to describe the accelerated motion relationships among the screw,balls and nut,calculate the acceleration of relative motion at the contact points between the balls and raceways,and analyze five accelerated motion rules between the balls and raceways.It also conducts a simulation analysis of the slide-roll ratio relationship between the accelerations at the ball center and the contact point of ball under different contact angles and helix angles.As shownby the analysis,with the increase in the BSM’s contact angle,the slide-roll ratio at the contact points decreases,and the contact angle has a relatively significant effect on the slide-roll ratio.However,with the decrease in the BSM’helix angle,the slide-roll ratio at the contact points decreases,and the helix angle has a relatively insignificant effect on the slide-roll ratio.By measuring the accelerations of both the screw and nut under the accelerated motion state,it also verifies the existence of the slide-roll mixed motion at the ball contact point A between the ball and the screw racewayand pure rolling at the ball contact point B between the ball and the nut raceway during the accelerated motion.
基金the Guangxi Bagui Scholar Teams for Innovation and Research Projectthe National Natural Science Foundation of China(Grant Nos.12272100,81860635,and 12062005)。
文摘Contact angle is an essential parameter to characterize substrate wettability.The measurement of contact angle in experiment and simulation is a complex and time-consuming task.In this paper,an improved method of measuring contact angle in multiphase lattice Boltzmann simulations is proposed,which can accurately obtain the real-time contact angle at a low temperature and larger density ratio.The three-phase contact point is determined by an extrapolation,and its position is not affected by the local deformation of flow field in the three-phase contact region.A series of simulations confirms that the present method has high accuracy and gird-independence.The contact angle keeps an excellent linear relationship with the chemical potential of the surface,so that it is very convenient to specify the wettability of a surface.The real-time contact angle measurement enables us to obtain the dynamic contact angle hysteresis on chemically heterogeneous surface,while the mechanical analyses can be effectively implemented at the moving contact line.
文摘This paper presents a simplified graphical procedure for constructing, using an unmarked straightedge and a compass only, a 10˚ to 20˚ angle, which is in other words, trisecting a 30˚ or 60˚ angle. The procedure, when applied to the 30˚ and 60˚ angles that have been “proven” to be not trisectable, produced a construction having the identical angular relationship with Archimedes’ Construction, in which the required trisection angles were found to be 10.00000˚ and 20.00000˚ respectively (i.e. exactly one-third of the given angle or ∠E’MA = 1/3∠E’CG). Based on this identical angular relationship as well as the numerical results obtained, one can only conclude that the geometric requirements for arriving at an exact trisection of the 30˚ or 60˚ angle, and therefore the construction of a 10˚ or 20˚ angle, have been met, notwithstanding the theoretical proofs of Wantzel, Dudley, and others. Thus, the solution to the age-old trisection problem, with respect to these two angles, has been accomplished.
基金the National Natrual Science Foundation of China(50504014)
文摘Analyzed the support instable mode of sliding,tripping,and so on,and believed the key point of the support stability control of fully mechanized coal caving face with steep coal seams was to maintain that the seam true angle was less than the hydraulic support instability critical angle.Through the layout of oblique face,the improvement of support setting load,the control of mining height and nonskid platform,the group support system of end face,the advance optimization of conveyor and support,and the other control tech- nical measures,the true angle of the seam is reduced and the instable critical angle of the support is increased,the hydraulic support stability of fully mechanized coal caving face with steep coal seams is effectively controlled.
文摘This paper describes the methodology (or approach) that was key to the solution of the angle trisection problem published earlier in article entitled, “A Procedure For Trisecting An Acute Angle.” It was an approach that required first, designing a working model of a trisector mechanism, second, studying the motion of key elements of the mechanism and third, applying the fundamental principles of kinematics to arrive at the desired results. In presenting these results, since there was no requirement to provide a detailed analysis of the final construction, this information was not included. However, now that the publication is out, it is considered appropriate as well as instructive to explain more fully the mechanism analysis of the trisector in graphical detail, as covered in Section 3 of this paper, that formed the basis of the long sought solution to the age-old Angle Trisection Problem.
基金financial support from the National Natural Science Foundation of China(Nos.52174092,51904290,52004272,52104125,42372328,and U23B2091)Natural Science Foundation of Jiangsu Province,China(Nos.BK20220157 and BK20240209)+3 种基金the Fundamental Research Funds for the Central Universities,China(No.2022YCPY0202)Xuzhou Science and Technology Project,China(Nos.KC21033 and KC22005)Yunlong Lake Laboratory of Deep Underground Science and Engineering Project,China(No.104023002)the Graduate Innovation Program of China University of Mining and Technology(No.2023WLTCRCZL052)。
文摘This study aims to investigate mechanical properties and failure mechanisms of layered rock with rough joint surfaces under direct shear loading.Cubic layered samples with dimensions of 100 mm×100 mm×100 mm were casted using rock-like materials,with anisotropic angle(α)and joint roughness coefficient(JRC)ranging from 15°to 75°and 2-20,respectively.The direct shear tests were conducted under the application of initial normal stress(σ_(n))ranging from 1-4 MPa.The test results indicate significant differences in mechanical properties,acoustic emission(AE)responses,maximum principal strain fields,and ultimate failure modes of layered samples under different test conditions.The peak stress increases with the increasingαand achieves a maximum value atα=60°or 75°.Asσ_(n)increases,the peak stress shows an increasing trend,with correlation coefficients R²ranging from 0.918 to 0.995 for the linear least squares fitting.As JRC increases from 2-4 to 18-20,the cohesion increases by 86.32%whenα=15°,while the cohesion decreases by 27.93%whenα=75°.The differences in roughness characteristics of shear failure surface induced byαresult in anisotropic post-peak AE responses,which is characterized by active AE signals whenαis small and quiet AE signals for a largeα.For a given JRC=6-8 andσ_(n)=1 MPa,asαincreases,the accumulative AE counts increase by 224.31%(αincreased from 15°to 60°),and then decrease by 14.68%(αincreased from 60°to 75°).The shear failure surface is formed along the weak interlayer whenα=15°and penetrates the layered matrix whenα=60°.Whenα=15°,asσ_(n)increases,the adjacent weak interlayer induces a change in the direction of tensile cracks propagation,resulting in a stepped pattern of cracks distribution.The increase in JRC intensifies roughness characteristics of shear failure surface for a smallα,however,it is not pronounced for a largeα.The findings will contribute to a better understanding of the mechanical responses and failure mechanisms of the layered rocks subjected to shear loads.
基金Supported by National Basic Research Program of China (973 Program,Grant No.2001CB711104)National Natural Science Foundation of China (Grant No.51005190)Fok Ying Tung Education Foundation of China (Grant No.122014)
文摘Published studies in regard to coupler systems have been mainly focused on the manufacturing process or coupler strength issues. With the ever increasing of tonnage and length of heavy haul trains, lateral in-train forces generated by longitudinal in-train forces and coupler rotations have become a more and more significant safety issue for heavy haul train operations. Derailments caused by excessive lateral in-train forces are frequently reported. This article studies two typical coupler systems used on heavy haul locomotives. Their structures and stabilizing mechanism are analyzed before the corresponding models are developed. Coupler systems models are featured by two distinct stabilizing mechanism models and draft gear models with hysteresis considered. A model set which consists of four locomotives and three coupler systems is developed to study the rotational behavior of different coupler systems and their implications for locomotive dynamics. Simulated results indicate that when the locomotives are equipped with the type B coupler system, locomotives can meet the dynamics standard on tangent tracks; while the dynamics performance on curved tracks is very poor. The maximum longitudinal in-train force for locomotives equipped with the type B coupler system is 2000 kN. Simulations revealed a distinct trend for the type A coupler system. Locomotive dynamics are poorer for the type A case when locomotives are running on tangent tracks, while the dynamics are better for the type A case when locomotives are running on curved tracks. Theoretical studies and simulations carried out in this article suggest that a combination of the two types of stabilizing mechanism can result in a good design which can significantly decrease the relevant derailments.
文摘We first design and analyze the contour surface of the globoidal indexing cam with the aid of computer, and then do optimum design according to the requirements of dynamics. Finally, we discuss the problem of the pressure angle of the globoidal indexing cam mechanism in detail and put forward a new concept of equivalent pressure angle.
基金the Research Committee of The Hong Kong Polytechnic University and the Innovation Technology Commission of The Hong Kong SAR Government for their financial support of the Hong Kong Partner State Key Laboratory of Ultra-Precision Machining Technology
文摘There have been various theoretical attempts by researchers worldwide to link up different scales of plasticity studies from the nano-, micro- and macro-scale of observation, based on molecular dynamics, crystal plasticity and continuum mechanics. Very few attempts, however, have been reported in ultra-precision machining studies. A mesoplasticity approach advocated by Lee and Yang is adopted by the authors and is successfully applied to studies of the micro-cutting mechanisms in ultra-precision machining. Traditionally, the shear angle in metal cutting, as well as the cutting force variation, can only be determined from cutting tests. In the pioneering work of the authors, the use of mesoplasticity theory enables prediction of the fluctuation of the shear angle and micro-cutting force, shear band formation, chip morphology in diamond turning and size effect in nano-indentation. These findings are verified by experiments. The mesoplasticity formulation opens up a new direction of studies to enable how the plastic behaviour of materials and their constitutive representations in deformation processing, such as machining can be predicted, assessed and deduced from the basic properties of the materials measurable at the microscale.
文摘Small angle neutron scattering(SANS) technique has been used to investigate the Ni_(50)Mo_(50) system prepared by mechanical alloying(MA). Significant changes of the scattering intensity have been observed among the samples with different milling time.Interesting fractal-like behavior of the sample system have been found and attempts have been made to determine the fractal dimensions. It is expected that the fractal dimension can be related to the different stages of MA to some extent.
文摘A novel method of realizing the optimal transmission of the crank-and-rockermechanism is presented. The optimal combination design is made by finding the related optimaltransmission parameters. The diagram of the optimal transmission is drawn. In the diagram, therelation among mini-mum transmission angle, the coefficient of travel speed variation, theoscillating angle of the rocker and the length of the bars is shown, concisely, conveniently anddirectly. The method possesses the main characteristic. That it is to achieve the optimaltransmission parameters under the transmission angle by directly choosing in the diagram, accordingto the given requirements. The characteristics of the mechanical transmission can be improved togain the optimal transmission effect by the method. Especially, the method is simple and convenientin practical use.
基金Sponsored by the National Natural Science Foundation of China(Grant No.51275443 and 51005195)Key Project of Chinese Ministry of Education(Grant No.212012)+1 种基金Research Fund for the Doctoral Program of Higher Education of China(Grant No.20111333120004)Natural Science Foundationof Hebei Province(Grant No.E2012203034)
文摘As one of the typical less-mobility parallel mechanisms, the spherical parallel mechanism Up.s with two degrees of freedom (2-DOF) possess high order overconstraints, and the calculation of its stiffness is partly different with general parallel mechanisms owing to the bars in each branch are assumed to be arc-shaped. By means of small deformation superposition principle, the relationship between the angle displacement and line displacement of moving platform and the forces acted on the branches were derived out. Based on the results of static analysis, the relationship between the applied force, the line displacement and the angle displacement of the mechanism was set up. And then the stiffness matrix was obtained. The six principal stiffness of the mechanism and the corresponding directions were achieved by the orthogonal transformation. The numerical calculation was performed and the results showed that the principal stiffness and directions are varied with the pose-position of the mechanism, and the principal stiffness is gradually enlarged when it is far away from the anigin. In addition, the torsion stiffness is much greater and the line deformation stiffness is smaller, the difference between the two parts is huge. The research content of this paper supplies the theoretical foundation for the further engineering design and application of the spherical parallel mechanism.
文摘Slopes consisting of interbedded strata of soft and hard rock mass, such as purplish red mudstone and grey brown arkosic sandstone of Jurassic age, are very common in Sichuan basin of China. The mudstone is soft while the sandstone is hard and contains many opening or closing joints with a high dip angle. Some are nearly parallel and the others are nearly decussated with the trend of the slopes. Many natural slopes are in deformation or sliding because of those reasons. The stability of cutting slopes and supporting method to be taken for their stability in civil engineering are important. In this paper, the stability and deformation of the slopes are studied. The methods of analysis and support design principle are analyzed also. Finally, the method put forward is applied to study Fengdian high cutting slope in Sichuan section of the express way from Chengdu to Shanghai. The results indicate that the method is effective.
基金This work was supported by Science and Technology Foundation ofShanxi Province [No: 2005K12- G(3)]
文摘Objective :To investigate the role the lens dimensions played on the pathogenesis of primary angle-closure glaucoma. Methods:38 eyes of 20 patients with primary angle-closure glaucoma (PACG) and 35 eyes of 22 normal individuals without ocular abnormalities were examined. The anatomical parameters of the lens and other structures of the anterior segment were calculated using B ultrasound, computer image processing and ultrasound biomicroscopy (UBM). The parameters were compared between the patients and normal subjects. Correlation analysis was used to determine the relationship between the radii of curvature of the anterior lens surface (RCALS) and the other parameters of the anterior segment. Results:Compared with the normal eyes, the eyes of PACG had thicker lens, steeper curvature of anterior lens surface, decreased depth of the anterior chamber, narrower chamber angle, and more anterior position of the ciliary bodies and lens. All these differences were significant(P 〈 0.05 or P 〈 0.01). In the PACG group, the RCALS had significantly negative correlation with the central and peripheral lens thickness (P 〈 0.01 and P 〈 0.05 respectively), and had positive correlation with relative lens position, anterior chamber depth(ACD), angle-open distance at 500 um(AOD500), trabecular iris angle (TIA) and trabecular ciliary processes distance(TCPD, P 〈 0.05 or P 〈 0.01 ). Conclusion:The occurrence of PACG is relevant to the abnormal anatomical structures of the anterior segment. Among all factors, the lens parameters play an important role in the pathogenesis. Increased lens thickness, relative more anterior position of lens, especially steepened curvature of anterior lens surface are predisposing factors of the pathologic phenomenon in PACG including pupillary blockage, shallow anterior chamber, secondary closure of chamber angle and elevation of intraocular pressure.
文摘By using LS-DYNA simulation software,the influences of some structure parameters,such as top cone angle,wall thickness,liner height and height ratio of top cone,of double-angle liner on the jet formation were studied respectively.Their influences on jet tip velocity,tail velocity and penetration depth were revealed.The simulation results show that the formation is better if the top cone angle is selected as 28°,the wall is 2.6mm,the liner height is 140mm,and the height ratio of top cone is 60%.In large stand-off distance,the jet has a higher tip velocity,and the tip does not break.With the stand-off distance of 8 times of the charge diameter,the experiment penetrating steel target was carried out.The experiment and simulation results are in good agreement.