The point and the line contacts of a toroidal continuously variable transmission (CVT) are studied. The contact shapes between the roller and input and output disks are formulated by using the classical Hertz contact ...The point and the line contacts of a toroidal continuously variable transmission (CVT) are studied. The contact shapes between the roller and input and output disks are formulated by using the classical Hertz contact theory. Based on the formulated equations, different system factors affecting the maximum Hertz stress in the elliptical and strip contacts of the full toroidal CVT are explored, which include the properties of the contacting material (Young’s modulus), operating condition (pushing load) and geometrical parameters (aspect cavity ratio, aspect roller ratio). The comparative results reveal the relations between the maximum Hertz stress and the speed ratio in the form of graphs. These graphs give useful information for designer to know the maximum Hertz stress during operation in such systems.展开更多
In this study, the interaction between cylindrical specimen made ofhomogeneous, isotropic, and linearlyelastic material and loading jaws of any curvature is considered in the Brazilian test. It is assumed thatthe spec...In this study, the interaction between cylindrical specimen made ofhomogeneous, isotropic, and linearlyelastic material and loading jaws of any curvature is considered in the Brazilian test. It is assumed thatthe specimen is diametrically compressed by elliptic normal contact stresses. The frictional contactstresses between the specimen and platens are neglected. The analytical solution starts from the contactproblem of the loading jaws of any curvature and cylindrical specimen. The contact width, correspondingloading angle （2 ^0）, and elliptical stresses obtained through solution of the contact problems are used asboundary conditions for a cylindrical specimen. The problem of the theory of elasticity for a cylinder issolved using Muskhelishvili＇s method. In this method, the displacements and stresses are represented interms of two analytical functions of a complex variable. In the main approaches, the nonlinear interactionbetween the loading bearing blocks and the specimen as well as the curvature of their surfacesand the elastic parameters of their materials are taken into account. Numerical examples are solved usingMATLAB to demonstrate the influence of deformability, curvature of the specimen and platens on thedistribution of the normal contact stresses as well as on the tensile and compressive stresses actingacross the loaded diameter. Derived equations also allow calculating the modulus of elasticity, totaldeformation modulus and creep parameters of the specimen material based on the experimental data ofradial contraction of the specimen.展开更多
The most general contact in mechanical transmission is the elliptical one. In particular, a toroidal continuously variable transmission (CVT) has an elliptical shape in the contact area under the elastohydrodynamic lu...The most general contact in mechanical transmission is the elliptical one. In particular, a toroidal continuously variable transmission (CVT) has an elliptical shape in the contact area under the elastohydrodynamic lubrication regime, where the shearing of the fluid subjects to high contact stress and transmits the power. Many parameters affect the contact service performance of the half toroidal CVT, which include the properties of the contacting material (Young抯 modulus), operating parameters (input torque and maximum traction coefficient) and geometrical parameters (aspect cavity ratio, curvature ratio and half cone angle of the power roller). In this paper, the contacts between the input disk, the power roller and the output disk are formulated using the classical Hertzian contact theory. Based on the formulated equations, different system parameters, which affect the maximum Hertzian stresses, are compared. The comparative results will provide some observations of the relations between the maximum Hertzian stresses and transmission ratios in the form of graphs. These graphs give useful information for designer to know the maximum Hertzian stress during operation in such systems.展开更多
The automotive industry is seeking new concepts for a continuously variabletransmission (CVT) in the driveline. One possible solution for a CVT design is half toroidaltraction drive, providing a high torque capacity w...The automotive industry is seeking new concepts for a continuously variabletransmission (CVT) in the driveline. One possible solution for a CVT design is half toroidaltraction drive, providing a high torque capacity with quick ratio change. An analytical study on thecontact points of the half toroidal CVT has been detailed. The shapes of the contact areas amongthe input disk, power roller and output disk are considered ellipses. Mathematical equations forestimating the torque capacity, power loss due to spin action, and contact efficiency of theelliptical contacts of the half toroidal CVT are formulated and expressed in the form of integralswhich can be readily evaluated by numerical scheme. The contact efficiency calculations of the halftoroidal CVT have been developed for the proper spin point locations under the effect of systemparameters. Numerical results are presented hi graphical forms for considered parameters, which canhelp the designer to select the proper system parameters to minimize the undesirable spin effects.展开更多
Thin film and elastohydrodynamic lubrication regimes are rather young domains of tribology and they are still facing unresolved issues.As they rely upon a full separation of the moving surfaces by a thin (or very thin...Thin film and elastohydrodynamic lubrication regimes are rather young domains of tribology and they are still facing unresolved issues.As they rely upon a full separation of the moving surfaces by a thin (or very thin) fluid film,the knowledge of its thickness is of paramount importance,as for instance to developing lubricated mechanisms with long lasting and efficient designs.As a consequence,a large collection of formulae for point contacts have been proposed in the last 40 years.However,their accuracy and validity have rarely been investigated.The purpose of this paper is to offer an evaluation of the most widespread analytical formulae and to define whether they can be used as qualitative or quantitative predictions.The methodology is based on comparisons with a numerical model for two configurations,circular and elliptical,considering both central and minimum film thicknesses.展开更多
基金Funded by the Ford-NSFC Foundation of China (No.50122151).
文摘The point and the line contacts of a toroidal continuously variable transmission (CVT) are studied. The contact shapes between the roller and input and output disks are formulated by using the classical Hertz contact theory. Based on the formulated equations, different system factors affecting the maximum Hertz stress in the elliptical and strip contacts of the full toroidal CVT are explored, which include the properties of the contacting material (Young’s modulus), operating condition (pushing load) and geometrical parameters (aspect cavity ratio, aspect roller ratio). The comparative results reveal the relations between the maximum Hertz stress and the speed ratio in the form of graphs. These graphs give useful information for designer to know the maximum Hertz stress during operation in such systems.
文摘In this study, the interaction between cylindrical specimen made ofhomogeneous, isotropic, and linearlyelastic material and loading jaws of any curvature is considered in the Brazilian test. It is assumed thatthe specimen is diametrically compressed by elliptic normal contact stresses. The frictional contactstresses between the specimen and platens are neglected. The analytical solution starts from the contactproblem of the loading jaws of any curvature and cylindrical specimen. The contact width, correspondingloading angle （2 ^0）, and elliptical stresses obtained through solution of the contact problems are used asboundary conditions for a cylindrical specimen. The problem of the theory of elasticity for a cylinder issolved using Muskhelishvili＇s method. In this method, the displacements and stresses are represented interms of two analytical functions of a complex variable. In the main approaches, the nonlinear interactionbetween the loading bearing blocks and the specimen as well as the curvature of their surfacesand the elastic parameters of their materials are taken into account. Numerical examples are solved usingMATLAB to demonstrate the influence of deformability, curvature of the specimen and platens on thedistribution of the normal contact stresses as well as on the tensile and compressive stresses actingacross the loaded diameter. Derived equations also allow calculating the modulus of elasticity, totaldeformation modulus and creep parameters of the specimen material based on the experimental data ofradial contraction of the specimen.
基金the Ford-NSFC Foundation of China (No. 50122151).
文摘The most general contact in mechanical transmission is the elliptical one. In particular, a toroidal continuously variable transmission (CVT) has an elliptical shape in the contact area under the elastohydrodynamic lubrication regime, where the shearing of the fluid subjects to high contact stress and transmits the power. Many parameters affect the contact service performance of the half toroidal CVT, which include the properties of the contacting material (Young抯 modulus), operating parameters (input torque and maximum traction coefficient) and geometrical parameters (aspect cavity ratio, curvature ratio and half cone angle of the power roller). In this paper, the contacts between the input disk, the power roller and the output disk are formulated using the classical Hertzian contact theory. Based on the formulated equations, different system parameters, which affect the maximum Hertzian stresses, are compared. The comparative results will provide some observations of the relations between the maximum Hertzian stresses and transmission ratios in the form of graphs. These graphs give useful information for designer to know the maximum Hertzian stress during operation in such systems.
基金This project is supported by Ford National Natural Science Foundation of China (No.50122151).
文摘The automotive industry is seeking new concepts for a continuously variabletransmission (CVT) in the driveline. One possible solution for a CVT design is half toroidaltraction drive, providing a high torque capacity with quick ratio change. An analytical study on thecontact points of the half toroidal CVT has been detailed. The shapes of the contact areas amongthe input disk, power roller and output disk are considered ellipses. Mathematical equations forestimating the torque capacity, power loss due to spin action, and contact efficiency of theelliptical contacts of the half toroidal CVT are formulated and expressed in the form of integralswhich can be readily evaluated by numerical scheme. The contact efficiency calculations of the halftoroidal CVT have been developed for the proper spin point locations under the effect of systemparameters. Numerical results are presented hi graphical forms for considered parameters, which canhelp the designer to select the proper system parameters to minimize the undesirable spin effects.
文摘Thin film and elastohydrodynamic lubrication regimes are rather young domains of tribology and they are still facing unresolved issues.As they rely upon a full separation of the moving surfaces by a thin (or very thin) fluid film,the knowledge of its thickness is of paramount importance,as for instance to developing lubricated mechanisms with long lasting and efficient designs.As a consequence,a large collection of formulae for point contacts have been proposed in the last 40 years.However,their accuracy and validity have rarely been investigated.The purpose of this paper is to offer an evaluation of the most widespread analytical formulae and to define whether they can be used as qualitative or quantitative predictions.The methodology is based on comparisons with a numerical model for two configurations,circular and elliptical,considering both central and minimum film thicknesses.
