In order to evaluate the efficiency of the automated storage/retrieval system(AS/RS)accurately,and compare different layouts of the AS/RS using mean travel time,under randomized storage conditions,an exact,geometry-ba...In order to evaluate the efficiency of the automated storage/retrieval system(AS/RS)accurately,and compare different layouts of the AS/RS using mean travel time,under randomized storage conditions,an exact,geometry-based analytical model is presented.The model can be used to compute the expected single-command and dual-command travel time for a storage/retrieval(S/R)machine which can travel simultaneously horizontally and vertically as it moves along a storage aisle.The rack may be either square in time or non square in time.Additionally,the alternative layouts of the AS/RS and travel-time models are examined.Comparing with setting the I/O point at the left-lower corner of the rack,setting the I/O point at any point at the vertical edge can help enhance the efficiency of the AS/RS.展开更多
In this paper, we use a geometric identity in the n-dimensional Euclidean space En and give the further improveme nt of Klamkin inequality in the space En.
A crystal plasticity finite element(CPFE)model was established and 2D simulations were carried out to study the relationship between microvoids and the microplasticity deformation behavior of the dual-phase titanium a...A crystal plasticity finite element(CPFE)model was established and 2D simulations were carried out to study the relationship between microvoids and the microplasticity deformation behavior of the dual-phase titanium alloy under high cyclic loading.Results show that geometrically necessary dislocations(GND)tend to accumulate around the microvoids,leading to an increment of average GND density.The influence of curvature in the tip plastic zone(TPZ)on GND density is greater than that of the size of the microvoid.As the curvature in TPZ and the size of the microvoid increase,the cumulative shear strain(CSS)in the primaryα,secondaryα,andβphases increases.Shear deformation in the prismatic slip system is dominant in the primaryαphase.As the distance between the microvoids increases,the interactive influence of the microvoids on the cumulative shear strain decreases.展开更多
A mathematic model is established using infinitesimal geometry for the cutting edge design of special milling cutters which use equal lead helix as cutting edges; equations are given for front-end and proclitic surfac...A mathematic model is established using infinitesimal geometry for the cutting edge design of special milling cutters which use equal lead helix as cutting edges; equations are given for front-end and proclitic surface of revolution of ball pillar milling cutters, ball taper milling cutters and angularly conical milling cutters; and corresponding models are established for the continuity cutting edge curves of milling cutters. Typical examples are given to illustrate the applications of mathematic models, which prove the correctness and applicability of these geometric models.展开更多
This paper presents a new approach of designing the revolving cutter with constant pitch, and provides geometric models. The corresponding models in the non-numerically controlled manufacturing, such as designing the ...This paper presents a new approach of designing the revolving cutter with constant pitch, and provides geometric models. The corresponding models in the non-numerically controlled manufacturing, such as designing the helical groove, grinding wheel, relative feeding motion, and calculating the helical angle of the cutting edge, are introduced. The examples are given to testify that the design approach is simple and readily realized in machining the revolving cutter with constant pitch. The effective design and manufacture method provides general references for non-NC machining revolving cutter with constant pitch and reducing the equipments input.展开更多
The problem on the geometrc inequalities involving an n-dimensional simplex and its inscribed simplex is studied. An inequality is established, which reveals that the difference between the squared circumradius of the...The problem on the geometrc inequalities involving an n-dimensional simplex and its inscribed simplex is studied. An inequality is established, which reveals that the difference between the squared circumradius of the n-dimensional simplex and the squared distance between its circumcenter and barycenter times the squared circumradius of its inscribed simplex is not less than the 2(n-1)th power of n times its squared inradius, and is equal to when the simplex is regular and its inscribed siplex is a tangent point one. Deduction from this inequality reaches a generalization of n-dimensional Euler inequality indicating that the circumradius of the simplex is not less than the n-fold inradius. Another inequality is derived to present the relationship between the circumradius of the n-dimensional simplex and the circumradius and inradius of its pedal simplex.展开更多
Orthogonal turn-milling is a high-efficiency and precision machining method.Its cutting layer directly affects chip formation,cutting forces,and chatter,and further affects tool life,machining quality,etc.We studied T...Orthogonal turn-milling is a high-efficiency and precision machining method.Its cutting layer directly affects chip formation,cutting forces,and chatter,and further affects tool life,machining quality,etc.We studied The cutting layer geometry(CLG)in orthogonal turn-milling with zero eccentricity(OTMZE)is studied to explore orthogonal turn-milling cutting layer formation process.OTMZE principles of motion and formation processes are analyzed statically without considering kinetic influences.Mathematical models of the entrance and exit angles,cutting thickness,and cutting depth are established.In addition,these models are validated experimentally and some influences of cutting parameters on the tool cutting layer are analyzed.The results show that OTMZE cutting layer formation can be divided into two stages,chip shapes are nearly consistent with the simulated CLGs,and the most influencial parameter in affecting the cutting layer is found to be the tool feed per revolation of workpiece fa,followed by the ratio of the tool and workpiece speedsλand the cutting depth ap.These models and results can provide theoretical guidance to clarify formation processes and quantitatively analyze changes in cutting layer geometry during OTMZE.In addition,they offer theoretical guidelines for cutting forces and chatter.展开更多
In this gape, we obtain thorem I on volum of a n-dirmensional simplex and theorem 2 on dihedral angies of a simplex. Besides. We obtain Vasic inequality in E^n and its extension. The resultsin this paper contain and i...In this gape, we obtain thorem I on volum of a n-dirmensional simplex and theorem 2 on dihedral angies of a simplex. Besides. We obtain Vasic inequality in E^n and its extension. The resultsin this paper contain and improve the results in paper [1], [2], [3], [4].展开更多
In this paper,the modern geometrical structure of analytical mechanics,the exterior differential forms and the geometrical meaning of dynamic equations are briefly discussed.
This paper presents methods for determining the basic geometry of end-gear with arc tooth external diameter, width of tooth, end module, number of teeth, pressure angle, tooth, tooth clearance parameters; at the same ...This paper presents methods for determining the basic geometry of end-gear with arc tooth external diameter, width of tooth, end module, number of teeth, pressure angle, tooth, tooth clearance parameters; at the same time gives the tooth bearing strength calculation method, and the formulas to calculate the tooth shear stress, surface stress and bolt fastening force of equivalent stress is established; finally write the software error simulation analysis.展开更多
A regime-switching geometric Brownian motion is used to model a geometric Brownian motion with its coefficients changing randomly according to a Markov chain.In this work, the author gives a complete characterization ...A regime-switching geometric Brownian motion is used to model a geometric Brownian motion with its coefficients changing randomly according to a Markov chain.In this work, the author gives a complete characterization of the recurrent property of this process. The long time behavior of this process such as its p-th moment is also studied. Moreover, the quantitative properties of the regime-switching geometric Brownian motion with two-state switching are investigated to show the difference between geometric Brownian motion with switching and without switching. At last, some estimates of its first passage probability are established.展开更多
Let （M, g） be an n-dimensional Riemannian manifold and T2M be its second- order tangent bundle equipped with a lift metric g. In this paper, first, the authors con- struct some Riemannian almost product structures ...Let （M, g） be an n-dimensional Riemannian manifold and T2M be its second- order tangent bundle equipped with a lift metric g. In this paper, first, the authors con- struct some Riemannian almost product structures on （T2M, g） and present some results concerning these structures. Then, they investigate the curvature properties of （T2M, g）. Finally, they study the properties of two metric connections with nonvanishing torsion on （T2M, g： The//-lift of the Levi-Civita connection of g to TaM, and the product conjugate connection defined by the Levi-Civita connection of g and an almost product structure.展开更多
Let （Mn, g） and （N^n＋1, G） be Riemannian manifolds. Let TMn and TN^n＋1 be the associated tangent bundles. Let f ： （M^n, g） → （N^＋1, G） be an isometrical immersion with g = f^＊G, F = （f, df） ： （TM^n,g...Let （Mn, g） and （N^n＋1, G） be Riemannian manifolds. Let TMn and TN^n＋1 be the associated tangent bundles. Let f ： （M^n, g） → （N^＋1, G） be an isometrical immersion with g = f^＊G, F = （f, df） ： （TM^n,g） → （TN^n＋1, Gs） be the isometrical immersion with g= F＊Gs where （df）x ： TxM → Tf（x）N for any x∈ M is the differential map, and Gs be the Sasaki metric on TN induced from G. This paper deals with the geometry of TM^n as a submanifold of TN^n＋1 by the moving frame method. The authors firstly study the extrinsic geometry of TMn in TN^n＋1. Then the integrability of the induced almost complex structure of TM is discussed.展开更多
基金The National Key Technology R&D Program of China during the 11th Five-Year Plan Period(No.2006BAH02A06)
文摘In order to evaluate the efficiency of the automated storage/retrieval system(AS/RS)accurately,and compare different layouts of the AS/RS using mean travel time,under randomized storage conditions,an exact,geometry-based analytical model is presented.The model can be used to compute the expected single-command and dual-command travel time for a storage/retrieval(S/R)machine which can travel simultaneously horizontally and vertically as it moves along a storage aisle.The rack may be either square in time or non square in time.Additionally,the alternative layouts of the AS/RS and travel-time models are examined.Comparing with setting the I/O point at the left-lower corner of the rack,setting the I/O point at any point at the vertical edge can help enhance the efficiency of the AS/RS.
文摘In this paper, we use a geometric identity in the n-dimensional Euclidean space En and give the further improveme nt of Klamkin inequality in the space En.
基金the National Key Research and Development Program of China(No.2021YFB3702603).
文摘A crystal plasticity finite element(CPFE)model was established and 2D simulations were carried out to study the relationship between microvoids and the microplasticity deformation behavior of the dual-phase titanium alloy under high cyclic loading.Results show that geometrically necessary dislocations(GND)tend to accumulate around the microvoids,leading to an increment of average GND density.The influence of curvature in the tip plastic zone(TPZ)on GND density is greater than that of the size of the microvoid.As the curvature in TPZ and the size of the microvoid increase,the cumulative shear strain(CSS)in the primaryα,secondaryα,andβphases increases.Shear deformation in the prismatic slip system is dominant in the primaryαphase.As the distance between the microvoids increases,the interactive influence of the microvoids on the cumulative shear strain decreases.
文摘A mathematic model is established using infinitesimal geometry for the cutting edge design of special milling cutters which use equal lead helix as cutting edges; equations are given for front-end and proclitic surface of revolution of ball pillar milling cutters, ball taper milling cutters and angularly conical milling cutters; and corresponding models are established for the continuity cutting edge curves of milling cutters. Typical examples are given to illustrate the applications of mathematic models, which prove the correctness and applicability of these geometric models.
文摘This paper presents a new approach of designing the revolving cutter with constant pitch, and provides geometric models. The corresponding models in the non-numerically controlled manufacturing, such as designing the helical groove, grinding wheel, relative feeding motion, and calculating the helical angle of the cutting edge, are introduced. The examples are given to testify that the design approach is simple and readily realized in machining the revolving cutter with constant pitch. The effective design and manufacture method provides general references for non-NC machining revolving cutter with constant pitch and reducing the equipments input.
文摘The problem on the geometrc inequalities involving an n-dimensional simplex and its inscribed simplex is studied. An inequality is established, which reveals that the difference between the squared circumradius of the n-dimensional simplex and the squared distance between its circumcenter and barycenter times the squared circumradius of its inscribed simplex is not less than the 2(n-1)th power of n times its squared inradius, and is equal to when the simplex is regular and its inscribed siplex is a tangent point one. Deduction from this inequality reaches a generalization of n-dimensional Euler inequality indicating that the circumradius of the simplex is not less than the n-fold inradius. Another inequality is derived to present the relationship between the circumradius of the n-dimensional simplex and the circumradius and inradius of its pedal simplex.
基金supported by the National Natural Science Foundation of China (No. 51475233)the Natural Science Foundation of Jiangsu Province(No. BK20171170)+2 种基金the Six Talent Peaks Project of Jiangsu Province(No. JXQC-049)the Major Program of the Natural Science Foundation for Colleges and Universities of Jiangsu Province(No. 19KJA560007)the Project of Jiangsu Key Laboratory of Large Engineering Equipment Detection and Control(No. JSKLEDC201512)
文摘Orthogonal turn-milling is a high-efficiency and precision machining method.Its cutting layer directly affects chip formation,cutting forces,and chatter,and further affects tool life,machining quality,etc.We studied The cutting layer geometry(CLG)in orthogonal turn-milling with zero eccentricity(OTMZE)is studied to explore orthogonal turn-milling cutting layer formation process.OTMZE principles of motion and formation processes are analyzed statically without considering kinetic influences.Mathematical models of the entrance and exit angles,cutting thickness,and cutting depth are established.In addition,these models are validated experimentally and some influences of cutting parameters on the tool cutting layer are analyzed.The results show that OTMZE cutting layer formation can be divided into two stages,chip shapes are nearly consistent with the simulated CLGs,and the most influencial parameter in affecting the cutting layer is found to be the tool feed per revolation of workpiece fa,followed by the ratio of the tool and workpiece speedsλand the cutting depth ap.These models and results can provide theoretical guidance to clarify formation processes and quantitatively analyze changes in cutting layer geometry during OTMZE.In addition,they offer theoretical guidelines for cutting forces and chatter.
文摘In this gape, we obtain thorem I on volum of a n-dirmensional simplex and theorem 2 on dihedral angies of a simplex. Besides. We obtain Vasic inequality in E^n and its extension. The resultsin this paper contain and improve the results in paper [1], [2], [3], [4].
基金Work supported by NSF of Henan Education Commission
文摘In this paper,the modern geometrical structure of analytical mechanics,the exterior differential forms and the geometrical meaning of dynamic equations are briefly discussed.
文摘This paper presents methods for determining the basic geometry of end-gear with arc tooth external diameter, width of tooth, end module, number of teeth, pressure angle, tooth, tooth clearance parameters; at the same time gives the tooth bearing strength calculation method, and the formulas to calculate the tooth shear stress, surface stress and bolt fastening force of equivalent stress is established; finally write the software error simulation analysis.
基金supported by the National Natural Science Foundation of China(Nos.11301030,11431014)
文摘A regime-switching geometric Brownian motion is used to model a geometric Brownian motion with its coefficients changing randomly according to a Markov chain.In this work, the author gives a complete characterization of the recurrent property of this process. The long time behavior of this process such as its p-th moment is also studied. Moreover, the quantitative properties of the regime-switching geometric Brownian motion with two-state switching are investigated to show the difference between geometric Brownian motion with switching and without switching. At last, some estimates of its first passage probability are established.
文摘Let （M, g） be an n-dimensional Riemannian manifold and T2M be its second- order tangent bundle equipped with a lift metric g. In this paper, first, the authors con- struct some Riemannian almost product structures on （T2M, g） and present some results concerning these structures. Then, they investigate the curvature properties of （T2M, g）. Finally, they study the properties of two metric connections with nonvanishing torsion on （T2M, g： The//-lift of the Levi-Civita connection of g to TaM, and the product conjugate connection defined by the Levi-Civita connection of g and an almost product structure.
基金supported by the National Natural Science Foundation of China(No.61473059)the Fundamental Research Funds for the Central University(No.DUT11LK47)
文摘Let （Mn, g） and （N^n＋1, G） be Riemannian manifolds. Let TMn and TN^n＋1 be the associated tangent bundles. Let f ： （M^n, g） → （N^＋1, G） be an isometrical immersion with g = f^＊G, F = （f, df） ： （TM^n,g） → （TN^n＋1, Gs） be the isometrical immersion with g= F＊Gs where （df）x ： TxM → Tf（x）N for any x∈ M is the differential map, and Gs be the Sasaki metric on TN induced from G. This paper deals with the geometry of TM^n as a submanifold of TN^n＋1 by the moving frame method. The authors firstly study the extrinsic geometry of TMn in TN^n＋1. Then the integrability of the induced almost complex structure of TM is discussed.
