The infinite set of cycloids is created. Each cycloid of this set is defined as a movement trajectory of a point when this point circulates on the convex closed contour of arbitrary form when this contour moves rectil...The infinite set of cycloids is created. Each cycloid of this set is defined as a movement trajectory of a point when this point circulates on the convex closed contour of arbitrary form when this contour moves rectilinearly without rotation on the plane with a velocity equal to the tangential velocity of a point on circulation contour. The classical cycloid is elements of this set. The differential equation of a cycloid set is derived and its solution in quadratures is received. The inverse problem when for the given cycloid it is necessary to fine the form of a circulation contour is solved. The problem of differential equation of the second order with boundary conditions about a bend of big curvature of an elastic rod of infinite length is solved in quadratures. Geometry of the loop which is formed at such bend is investigated. It is discovered that at movement of an elastic loop on a rod when the form and the size of a loop don’t change, each point of a loop moves on a trajectory which named by us the cycloid and which represents a circumference arch.展开更多
A problem similar to the famous brachistochrone problem is examined in which, instead of a smooth curve, the path consists of two straight-line sections, one slant and one horizontal. The condition for minimum sliding...A problem similar to the famous brachistochrone problem is examined in which, instead of a smooth curve, the path consists of two straight-line sections, one slant and one horizontal. The condition for minimum sliding time is investigated, producing results that are both counterintuitive and interesting.展开更多
Based on the analysis of the pin-hole-output mechanism in the cycloid drive,a more accurate force analysis method is provided, in which the manufacture error is considered, bywhich the contact force between pin and pi...Based on the analysis of the pin-hole-output mechanism in the cycloid drive,a more accurate force analysis method is provided, in which the manufacture error is considered, bywhich the contact force between pin and pin-hole can be calculated more accurately in the wholedriving process.展开更多
Cycloid speed reducers are widely used in many industrial areas due to the advantages of compact size, high reduction ratio and high stiffness. However, currently, there are not many analytical models for the mesh sti...Cycloid speed reducers are widely used in many industrial areas due to the advantages of compact size, high reduction ratio and high stiffness. However, currently, there are not many analytical models for the mesh stiffness calculation, which is a crucial parameter for the high-fidelity gear dynamic model. This is partially due to the difficulty of backlash determination and the complexity of multi-tooth contact deformation during the meshing process. In this paper, a new method to calculate the mesh stiffness is proposed including the effects of tooth profile modification and eccentricity error. The time-varying mesh parameters and load distribution of cycloid-pin gear pair are determined based on the unloaded tooth contact analysis （TCA） and the nonlinear Hertzian contact theory, allowing accurate calculations of the contact stiffness of single tooth pair and the torsional stiffness of multi-tooth pairs. A detailed parametric study is presented to demonstrate the influences of tooth profile modification, applied torque and eccentricity error on the torsional mesh stiffness, loaded transmission error, Hertzian contact stiffness and load sharing factor. This model can be applied to further study the lost motion and dynamic characteristics of cycloid speed reducer and assist the optimization of its precision, vibration and noise levels.展开更多
The most conventional vehicle pretensioner system consists of an internal gear pair with involute teeth. However, it has been well known that the corresponding gear pairs are relatively weak under the situation of imp...The most conventional vehicle pretensioner system consists of an internal gear pair with involute teeth. However, it has been well known that the corresponding gear pairs are relatively weak under the situation of impact loadings. To improve this phenomenon, a new pretensioning gear system with cycloid teeth rather than the involute ones was proposed, and dual cycloidal gear mechanisms were designed for satisfying geometric constraints and dynamic loading conditions. The simulations of the prototypes were conducted by LS-DYNA program and the experiments for a prototype were performed for a dynamic model with impact loading devices. The results show that the better operation and the smoother motion are confirmed in the proposed cycloidal gear system rather than the conventional one without interferences between gear teeth under the impact of a crash.展开更多
In order to analyze the lubricating characteristics at different meshing points in the cycloid pin wheel transmission process,the cycloid gear teeth were discretized,combined with the kinematic analysis of the cycloid...In order to analyze the lubricating characteristics at different meshing points in the cycloid pin wheel transmission process,the cycloid gear teeth were discretized,combined with the kinematic analysis of the cycloid pin gear transmission and the contact analysis of the gear teeth.The progressive mesh densification method(PMD)was used to numerically solve the film thickness.The influence of the design parameters and process parameters on the lubrication characteristics was analyzed.The elastohydrodynamic lubrication and mixed lubrication characteristics at different contact points were obtained.The optimal meshing area of the cycloid gear tooth was determined,and the film thickness ratio,contact load ratio,maximum contact pressure at different points,average film thickness and roughness after contact deformation were analyzed.The conclusion of this study provides effective guidance for the research on the modification of cycloid gear teeth.展开更多
Gas pore is a common defect in brazed joint. It lowers the brazing rate and affects the properties of joint. Experimental results show that the application of unequal-gap brazing seam effectively decreases the amount ...Gas pore is a common defect in brazed joint. It lowers the brazing rate and affects the properties of joint. Experimental results show that the application of unequal-gap brazing seam effectively decreases the amount and volume of gas pores, and increases brazing rate.This paper establishes a force model of unequal-gap brazing seam, and proposes the constitutive relationship between expulsion force and curvature. The force condition of gas bubble in geometrically different brazing seams were calculated, and the results were verified with experiments. The results show that the expulsion force of gas bubble is positively correlated to the curvature of the seam geometry. The gas bubble tends to move towards the direction with large curvature and wider gap. The directional bubble movement is obtained through varying the configuration of gas-liquid interface to meet geometric conditions. Gas bubble accelerates to expulse with arc, hyperbola and cycloid brazing seams, in which the best drainage effects of gas bubble occur for cycloid seams.展开更多
We consider a similarity kinematic of a deltoid by studying locally the scalar curvature for the corresponding two dimensional kinematic surfaces in the Euclidean space . We prove that there is no two dimensional kine...We consider a similarity kinematic of a deltoid by studying locally the scalar curvature for the corresponding two dimensional kinematic surfaces in the Euclidean space . We prove that there is no two dimensional kinematic surfaces with scalar curvature K is non-zero constant. We describe the equations that govern such the surfaces.展开更多
A cycloidal speed reducer employing gears with permanent magnets acting as teeth is described. The magnets, which have their axes radially oriented in both the orbiting gear and the fixed internal gear, are inserted i...A cycloidal speed reducer employing gears with permanent magnets acting as teeth is described. The magnets, which have their axes radially oriented in both the orbiting gear and the fixed internal gear, are inserted in holes drilled in nonmagnetic rims without protruding from the cylindrical exposed surfaces. Because the orbiting gear is not restrained radially, it contacts the fixed gear and rolls on its inner surface. A normal force is developed at the contact point between the gears to balance the magnetic attraction and the centrifugal force of the orbiting gear. The friction available due to this normal force increases the transmission’s torque capacity, which is further increased by elimination of the gap between the gears. Also, the radial load on the supporting orbiting gear bearing is eliminated. A prototype with a reduction ratio of 26 is being tested.展开更多
This paper introduces to fluid state physics （fluid mechanics） a new interpretation of physical phenomena taking place in a fluid in motion. It introduces the base of a new theory claiming that every flow has its ow...This paper introduces to fluid state physics （fluid mechanics） a new interpretation of physical phenomena taking place in a fluid in motion. It introduces the base of a new theory claiming that every flow has its own internal structure of motion, which is definite organization of motion, rather than a ＂molecular chaos＂, known from the fluid statics. The paper introduces the new notion of structures vector fields of power and momentum and shows every Newtonian fluid flows are dual in character. It shows that the flow of Newtonian fluid has a dual character. It demonstrates on models and further in mathematical interpretation of physical phenomena. It introduces, on the one hand, the cycloidal motion model into the fluid mechanics, ad on the other hand an addition to the known, the classical model of Poiseuille laminar motion. The theory of dualism （double nature of physical phenomena） allows the description of selected characteristics of the flow, either by using the theory ofcycloidal motion （semicycloidal）, or by using the supplemented theory of laminar motion. The dualism theory is useful to describe each type of flows both, laminar and turbulent. This paper is only an introduction to the theory. It has been assigned number 1. It has been granted a high priority, since it contains basic concepts that will be used in others, following papers of long cycle.展开更多
An active design method of tooth profiles for cycloid gears based on their meshing efficiency is proposed.This method takes the meshing efficiency as one of the design variables to determine the tooth profiles.The cal...An active design method of tooth profiles for cycloid gears based on their meshing efficiency is proposed.This method takes the meshing efficiency as one of the design variables to determine the tooth profiles.The calculation method for the meshing efficiency of planetary transmission is analyzed and the equation of the meshing efficiency is deduced.Relationships between the meshing efficiency,the radius of the pin wheel and the eccentric distance are revealed.The design constraint quations and the strength constraint quations are deduced.On the basis of this,a design procedure is laid out.Some examples using different input parameters are conducted to demonstrate the feasibility of the approach.A dynamic simulation of the rigid flexible coupling of cycloid gears is also presented.The results show that the proposed design method is more flexible to control the tooth profiles by changing the input values of the transmission efficiency.展开更多
The paper considers the modification or the manufacture error of cycloidal gear, then analyzes the relationship of pin circle meshed with the modified cycloidal gear, discuases the amount of error that leads to destro...The paper considers the modification or the manufacture error of cycloidal gear, then analyzes the relationship of pin circle meshed with the modified cycloidal gear, discuases the amount of error that leads to destroying conjugate action and results in the changes of tbe instantaneous velocity ratio and so as to affect the smooth operation of cycloidal pin gearing. The idea of the relationship between amount of modification aud manufacture error and the smooth operation can be gotten from the curve diagrams of the instantaneous velocity ratio. Therefore, the directions for improving the reature of the cycloidal pin gear transmission are clear.展开更多
The ferroelectric polarization and phase diagram in Tm-doped Gd MnO3 are studied by means of Monte Carlo simulation based on the Mochizuki–Furukawa model. Our work well reproduces the low temperature polarization at ...The ferroelectric polarization and phase diagram in Tm-doped Gd MnO3 are studied by means of Monte Carlo simulation based on the Mochizuki–Furukawa model. Our work well reproduces the low temperature polarization at various substitution levels observed experimentally. It is demonstrated that the Tm-doping can control the multiferroic behaviors through modulating the spin structures, resulting in the flop of the electric polarization. In addition, the polarization in the ab-plane cycloidal spin phase arises from comparable contributions of the symmetric exchange striction and antisymmetric exchange striction, leading to much bigger polarization than that in the bc-plane cycloidal spin phase where only the contribution of the latter striction is available. The phase diagram obtained in our simulation is helpful for clarifying the multiferroic properties in doped manganite systems and other related multiferroics.展开更多
Based on the requirements of the two-phase rapier loom’s beat-up system characteristics, the dynamic responses of its beat-up system to three different types of cam input motion are studied in this paper. Also, their...Based on the requirements of the two-phase rapier loom’s beat-up system characteristics, the dynamic responses of its beat-up system to three different types of cam input motion are studied in this paper. Also, their corresponding analytical comparisons are made. At the end of the paper, the authors put forward a proposal of new type cam beat-up motion for future practice.展开更多
文摘The infinite set of cycloids is created. Each cycloid of this set is defined as a movement trajectory of a point when this point circulates on the convex closed contour of arbitrary form when this contour moves rectilinearly without rotation on the plane with a velocity equal to the tangential velocity of a point on circulation contour. The classical cycloid is elements of this set. The differential equation of a cycloid set is derived and its solution in quadratures is received. The inverse problem when for the given cycloid it is necessary to fine the form of a circulation contour is solved. The problem of differential equation of the second order with boundary conditions about a bend of big curvature of an elastic rod of infinite length is solved in quadratures. Geometry of the loop which is formed at such bend is investigated. It is discovered that at movement of an elastic loop on a rod when the form and the size of a loop don’t change, each point of a loop moves on a trajectory which named by us the cycloid and which represents a circumference arch.
文摘A problem similar to the famous brachistochrone problem is examined in which, instead of a smooth curve, the path consists of two straight-line sections, one slant and one horizontal. The condition for minimum sliding time is investigated, producing results that are both counterintuitive and interesting.
基金National Natural Science Foundation of China(No.59075230).
文摘Based on the analysis of the pin-hole-output mechanism in the cycloid drive,a more accurate force analysis method is provided, in which the manufacture error is considered, bywhich the contact force between pin and pin-hole can be calculated more accurately in the wholedriving process.
基金Project(51575062)supported by the National Natural Science Foundation of ChinaProject(51605049)supported by the National Natural Science Foundation for Young Scholar of ChinaProject(BA2015177)supported by the Science and Technology Achievements Transformation Program of Jiangsu Province of China
文摘Cycloid speed reducers are widely used in many industrial areas due to the advantages of compact size, high reduction ratio and high stiffness. However, currently, there are not many analytical models for the mesh stiffness calculation, which is a crucial parameter for the high-fidelity gear dynamic model. This is partially due to the difficulty of backlash determination and the complexity of multi-tooth contact deformation during the meshing process. In this paper, a new method to calculate the mesh stiffness is proposed including the effects of tooth profile modification and eccentricity error. The time-varying mesh parameters and load distribution of cycloid-pin gear pair are determined based on the unloaded tooth contact analysis （TCA） and the nonlinear Hertzian contact theory, allowing accurate calculations of the contact stiffness of single tooth pair and the torsional stiffness of multi-tooth pairs. A detailed parametric study is presented to demonstrate the influences of tooth profile modification, applied torque and eccentricity error on the torsional mesh stiffness, loaded transmission error, Hertzian contact stiffness and load sharing factor. This model can be applied to further study the lost motion and dynamic characteristics of cycloid speed reducer and assist the optimization of its precision, vibration and noise levels.
基金supported by the Changwon National University in 2011-2012,Korea
文摘The most conventional vehicle pretensioner system consists of an internal gear pair with involute teeth. However, it has been well known that the corresponding gear pairs are relatively weak under the situation of impact loadings. To improve this phenomenon, a new pretensioning gear system with cycloid teeth rather than the involute ones was proposed, and dual cycloidal gear mechanisms were designed for satisfying geometric constraints and dynamic loading conditions. The simulations of the prototypes were conducted by LS-DYNA program and the experiments for a prototype were performed for a dynamic model with impact loading devices. The results show that the better operation and the smoother motion are confirmed in the proposed cycloidal gear system rather than the conventional one without interferences between gear teeth under the impact of a crash.
基金Project(E2019209153)supported by the Natural Science Foundation of Hebei Province,China。
文摘In order to analyze the lubricating characteristics at different meshing points in the cycloid pin wheel transmission process,the cycloid gear teeth were discretized,combined with the kinematic analysis of the cycloid pin gear transmission and the contact analysis of the gear teeth.The progressive mesh densification method(PMD)was used to numerically solve the film thickness.The influence of the design parameters and process parameters on the lubrication characteristics was analyzed.The elastohydrodynamic lubrication and mixed lubrication characteristics at different contact points were obtained.The optimal meshing area of the cycloid gear tooth was determined,and the film thickness ratio,contact load ratio,maximum contact pressure at different points,average film thickness and roughness after contact deformation were analyzed.The conclusion of this study provides effective guidance for the research on the modification of cycloid gear teeth.
基金supported by the 2020 Ningbo"3315 Talent Introduction Plan"Innovative Team (C-Class)Henan Province's Major Key Technology Demand Unveiling and Tackling Key Projects (Grant No. 191110111000)。
文摘Gas pore is a common defect in brazed joint. It lowers the brazing rate and affects the properties of joint. Experimental results show that the application of unequal-gap brazing seam effectively decreases the amount and volume of gas pores, and increases brazing rate.This paper establishes a force model of unequal-gap brazing seam, and proposes the constitutive relationship between expulsion force and curvature. The force condition of gas bubble in geometrically different brazing seams were calculated, and the results were verified with experiments. The results show that the expulsion force of gas bubble is positively correlated to the curvature of the seam geometry. The gas bubble tends to move towards the direction with large curvature and wider gap. The directional bubble movement is obtained through varying the configuration of gas-liquid interface to meet geometric conditions. Gas bubble accelerates to expulse with arc, hyperbola and cycloid brazing seams, in which the best drainage effects of gas bubble occur for cycloid seams.
文摘We consider a similarity kinematic of a deltoid by studying locally the scalar curvature for the corresponding two dimensional kinematic surfaces in the Euclidean space . We prove that there is no two dimensional kinematic surfaces with scalar curvature K is non-zero constant. We describe the equations that govern such the surfaces.
文摘A cycloidal speed reducer employing gears with permanent magnets acting as teeth is described. The magnets, which have their axes radially oriented in both the orbiting gear and the fixed internal gear, are inserted in holes drilled in nonmagnetic rims without protruding from the cylindrical exposed surfaces. Because the orbiting gear is not restrained radially, it contacts the fixed gear and rolls on its inner surface. A normal force is developed at the contact point between the gears to balance the magnetic attraction and the centrifugal force of the orbiting gear. The friction available due to this normal force increases the transmission’s torque capacity, which is further increased by elimination of the gap between the gears. Also, the radial load on the supporting orbiting gear bearing is eliminated. A prototype with a reduction ratio of 26 is being tested.
文摘This paper introduces to fluid state physics （fluid mechanics） a new interpretation of physical phenomena taking place in a fluid in motion. It introduces the base of a new theory claiming that every flow has its own internal structure of motion, which is definite organization of motion, rather than a ＂molecular chaos＂, known from the fluid statics. The paper introduces the new notion of structures vector fields of power and momentum and shows every Newtonian fluid flows are dual in character. It shows that the flow of Newtonian fluid has a dual character. It demonstrates on models and further in mathematical interpretation of physical phenomena. It introduces, on the one hand, the cycloidal motion model into the fluid mechanics, ad on the other hand an addition to the known, the classical model of Poiseuille laminar motion. The theory of dualism （double nature of physical phenomena） allows the description of selected characteristics of the flow, either by using the theory ofcycloidal motion （semicycloidal）, or by using the supplemented theory of laminar motion. The dualism theory is useful to describe each type of flows both, laminar and turbulent. This paper is only an introduction to the theory. It has been assigned number 1. It has been granted a high priority, since it contains basic concepts that will be used in others, following papers of long cycle.
基金supported by the National Natural Science Foundation of China (Nos.51205335, 51375411)the Scientific Research for the High Level Talent of Nanjing Institute of Technology (No.YKJ201702)
文摘An active design method of tooth profiles for cycloid gears based on their meshing efficiency is proposed.This method takes the meshing efficiency as one of the design variables to determine the tooth profiles.The calculation method for the meshing efficiency of planetary transmission is analyzed and the equation of the meshing efficiency is deduced.Relationships between the meshing efficiency,the radius of the pin wheel and the eccentric distance are revealed.The design constraint quations and the strength constraint quations are deduced.On the basis of this,a design procedure is laid out.Some examples using different input parameters are conducted to demonstrate the feasibility of the approach.A dynamic simulation of the rigid flexible coupling of cycloid gears is also presented.The results show that the proposed design method is more flexible to control the tooth profiles by changing the input values of the transmission efficiency.
文摘The paper considers the modification or the manufacture error of cycloidal gear, then analyzes the relationship of pin circle meshed with the modified cycloidal gear, discuases the amount of error that leads to destroying conjugate action and results in the changes of tbe instantaneous velocity ratio and so as to affect the smooth operation of cycloidal pin gearing. The idea of the relationship between amount of modification aud manufacture error and the smooth operation can be gotten from the curve diagrams of the instantaneous velocity ratio. Therefore, the directions for improving the reature of the cycloidal pin gear transmission are clear.
基金supported by the National Natural Science Foundation of China(Grant Nos.11204091,11274094,and 51332007)the National Basic Research Program of China(Grant Nos.2015CB921202 and 2011CB922101)
文摘The ferroelectric polarization and phase diagram in Tm-doped Gd MnO3 are studied by means of Monte Carlo simulation based on the Mochizuki–Furukawa model. Our work well reproduces the low temperature polarization at various substitution levels observed experimentally. It is demonstrated that the Tm-doping can control the multiferroic behaviors through modulating the spin structures, resulting in the flop of the electric polarization. In addition, the polarization in the ab-plane cycloidal spin phase arises from comparable contributions of the symmetric exchange striction and antisymmetric exchange striction, leading to much bigger polarization than that in the bc-plane cycloidal spin phase where only the contribution of the latter striction is available. The phase diagram obtained in our simulation is helpful for clarifying the multiferroic properties in doped manganite systems and other related multiferroics.
文摘Based on the requirements of the two-phase rapier loom’s beat-up system characteristics, the dynamic responses of its beat-up system to three different types of cam input motion are studied in this paper. Also, their corresponding analytical comparisons are made. At the end of the paper, the authors put forward a proposal of new type cam beat-up motion for future practice.
