In order to satisfy the increasing demand on high performance planetary transmissions, an important line of research is focused on the understanding of some of the underlying phenomena involved in this mechanical syst...In order to satisfy the increasing demand on high performance planetary transmissions, an important line of research is focused on the understanding of some of the underlying phenomena involved in this mechanical system. Through the development of models capable of reproduce the system behavior, research in this area contributes to improve gear transmission insight, helping developing better maintenance practices and more efficient design processes. A planetary gear model used for the design of profile modifications ratio based on the levelling of the load sharing ratio is presented. The gear profile geometry definition, following a vectorial approach that mimics the real cutting process of gears, is thoroughly described. Teeth undercutting and hypotrochoid definition are implicitly considered, and a procedure for the incorporation of a rounding arc at the tooth tip in order to deal with corner contacts is described. A procedure for the modeling of profile deviations is presented, which can be used for the introduction of both manufacturing errors and designed profile modifications. An easy and flexible implementation of the profile deviation within the planetary model is accomplished based on the geometric overlapping. The contact force calculation and dynamic implementation used in the model are also introduced, and parameters from a real transmission for agricultural applications are presented for the application example. A set of reliefs is designed based on the levelling of the load sharing ratio for the example transmission, and finally some other important dynamic factors of the transmission are analyzed to assess the changes in the dynamic behavior with respect to the non-modified case. Thus, the main innovative aspect of the proposed planetary transmission model is the capacity of providing a simulated load sharing ratio which serves as design variable for the calculation of the tooth profile modifications.展开更多
A new non-linear bending-torsional coupled model for double-row planetary gear set was proposed, and planet's eccentricity error, static transmission error, and time-varying meshing stiffness were taken into consi...A new non-linear bending-torsional coupled model for double-row planetary gear set was proposed, and planet's eccentricity error, static transmission error, and time-varying meshing stiffness were taken into consideration. The solution of differential governing equation of motion is determined by applying the Fourier series method. The behaviors of dynamic load sharing characteristics affected by the system parameters including gear eccentricities error, ring gear's supporting stiffness, planet's bearing stiffness, torsional stiffness of first stage carrier and input rotation rate were investigated qualitatively and systematically, and sun gear radial orbits at first and second stage were explored as well. Some theoretical results are summarized as guidelines for further research and design of double-row planetary gear train at last.展开更多
A new nonlinear transverse-torsional coupled model with backlash and bearing clearance was proposed for planetary gear set. Meanwhile, sun gear and planet's eccentricity errors, static transmission error, and time...A new nonlinear transverse-torsional coupled model with backlash and bearing clearance was proposed for planetary gear set. Meanwhile, sun gear and planet's eccentricity errors, static transmission error, and time-varying meshing stiffness were taken into consideration. The differential governing equations of motion were solved by employing variable step-size Rung-Kutta numerical integration method. The behavior of dynamic load sharing characteristics affected by the system parameters including input rate, sun gear's supporting stiffness and eccentricity error, planet's eccentricity error, sun gear's bearing clearance, backlashes of sun-planet and planet-ring meshes were investigated qualitatively and systematically. Some theoretical results are summarized at last which extend the current understanding of the dynamic load sharing behavior of planet gear train, enrich the related literature and provide references for the design of planetary gear train.展开更多
基金Supported by the Project DPI2013-44860 funded by the Spanish Ministry of Science and Technology
文摘In order to satisfy the increasing demand on high performance planetary transmissions, an important line of research is focused on the understanding of some of the underlying phenomena involved in this mechanical system. Through the development of models capable of reproduce the system behavior, research in this area contributes to improve gear transmission insight, helping developing better maintenance practices and more efficient design processes. A planetary gear model used for the design of profile modifications ratio based on the levelling of the load sharing ratio is presented. The gear profile geometry definition, following a vectorial approach that mimics the real cutting process of gears, is thoroughly described. Teeth undercutting and hypotrochoid definition are implicitly considered, and a procedure for the incorporation of a rounding arc at the tooth tip in order to deal with corner contacts is described. A procedure for the modeling of profile deviations is presented, which can be used for the introduction of both manufacturing errors and designed profile modifications. An easy and flexible implementation of the profile deviation within the planetary model is accomplished based on the geometric overlapping. The contact force calculation and dynamic implementation used in the model are also introduced, and parameters from a real transmission for agricultural applications are presented for the application example. A set of reliefs is designed based on the levelling of the load sharing ratio for the example transmission, and finally some other important dynamic factors of the transmission are analyzed to assess the changes in the dynamic behavior with respect to the non-modified case. Thus, the main innovative aspect of the proposed planetary transmission model is the capacity of providing a simulated load sharing ratio which serves as design variable for the calculation of the tooth profile modifications.
基金Projects(NZ2013303,NZ2014201)supported by the National Natural Science Foundation of ChinaProjects(51375226,51305196,51475226)supported by the Fundamental Research Funds for the Central Universities,China
文摘A new non-linear bending-torsional coupled model for double-row planetary gear set was proposed, and planet's eccentricity error, static transmission error, and time-varying meshing stiffness were taken into consideration. The solution of differential governing equation of motion is determined by applying the Fourier series method. The behaviors of dynamic load sharing characteristics affected by the system parameters including gear eccentricities error, ring gear's supporting stiffness, planet's bearing stiffness, torsional stiffness of first stage carrier and input rotation rate were investigated qualitatively and systematically, and sun gear radial orbits at first and second stage were explored as well. Some theoretical results are summarized as guidelines for further research and design of double-row planetary gear train at last.
基金Project(51105194)supported by the National Natural Science Foundation of ChinaProject(20113218110017)supported by the Doctoral Program Foundation of Institutions of Higher Education of China+2 种基金Project supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions,ChinaProject(CXZZ11_0199)supported by the Funding of Jiangsu Innovation Program for Graduate Education,ChinaProjects(NZ2013303,NZ2014201)supported by the Fundamental Research Funds for the Central Universities,China
文摘A new nonlinear transverse-torsional coupled model with backlash and bearing clearance was proposed for planetary gear set. Meanwhile, sun gear and planet's eccentricity errors, static transmission error, and time-varying meshing stiffness were taken into consideration. The differential governing equations of motion were solved by employing variable step-size Rung-Kutta numerical integration method. The behavior of dynamic load sharing characteristics affected by the system parameters including input rate, sun gear's supporting stiffness and eccentricity error, planet's eccentricity error, sun gear's bearing clearance, backlashes of sun-planet and planet-ring meshes were investigated qualitatively and systematically. Some theoretical results are summarized at last which extend the current understanding of the dynamic load sharing behavior of planet gear train, enrich the related literature and provide references for the design of planetary gear train.
