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
Load sharing behavior is very important for power-split gearing system, star gearing reducer as a new type and special transmission system can be used in many industry fields. However, there is few literature regardin...Load sharing behavior is very important for power-split gearing system, star gearing reducer as a new type and special transmission system can be used in many industry fields. However, there is few literature regarding the key multiple-split load sharing issue in main gearbox used in new type geared turbofan engine. Further mechanism anal- ysis are made on load sharing behavior among star gears of star gearing reducer for geared turbofan engine. Compre- hensive meshing error analysis are conducted on eccentricity error, gear thickness error, base pitch error, assembly error, and bearing error of star gearing reducer respectively. Floating meshing error resulting from meshing clearance variation caused by the simultaneous floating of sun gear and annular gear are taken into account. A refined mathematical model for load sharing coefficient calculation is established in consideration of different meshing stiffness and support- ing stiffness for components. The regular curves of load sharing coefficient under the influence of interactions, single action and single variation of various component errors are obtained. The accurate sensitivity of load sharing coefficienttoward different errors is mastered. The load sharing coef- ficient of star gearing reducer is 1.033 and the maximum meshing force in gear tooth is about 3010 N. This paper provides scientific theory evidences for optimal parameter design and proper tolerance distribution in advanced devel- opment and manufacturing process, so as to achieve optimal effects in economy and technology.展开更多
A series-parallel system was proposed with common bus performance sharing in which the performance and failure rate of the element depended on the load it was carrying. In such a system,the surplus performance of a su...A series-parallel system was proposed with common bus performance sharing in which the performance and failure rate of the element depended on the load it was carrying. In such a system,the surplus performance of a sub-system can be transmitted to other deficient sub-systems. The transmission capacity of the common bus performance sharing mechanism is a random variable. Effects of load on element performance and failure rate were considered in this paper. A reliability evaluation algorithm based on the universal generating function technique was suggested. Numerical experiments were conducted to illustrate the algorithm.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
On the basis of capacity flow model, a new model is developed for a load-sharing k-out-of-n： G system consisting of different components, to describe the increase of the same component＇s failure rates under differen...On the basis of capacity flow model, a new model is developed for a load-sharing k-out-of-n： G system consisting of different components, to describe the increase of the same component＇s failure rates under different loads. All components have exponential life distributions and are nonrepairable in the system. Reliability of load- sharing 2-out- of-3： G system is calculated and some special cases for the system are discussed. The calculation and discussions show that the model is right and practical.展开更多
The failure of the key parts, such as gears, in cutter head driving system of tunneling boring machine has not been properly solved under the interaction of driving motors asynchronously and wave tunneling torque load...The failure of the key parts, such as gears, in cutter head driving system of tunneling boring machine has not been properly solved under the interaction of driving motors asynchronously and wave tunneling torque load. A dynamic model of multi-gear driving system is established considering the inertia effects of driving mechanism and cutter head as well as the bending-torsional coupling. By taking into account the nonlinear coupling factors between ring gear and multiple pinions, the influence for meshing angle by bending-torsional coupling and the dynamic load-sharing characteristic of multiple pinions driving are analyzed. Load-sharing coefficients at different rotating cutter head speeds and input torques are presented. Numerical results indicate that the load-sharing coefficients can reach up to 1.2-1.3. A simulated experimental platform of the multiple pinions driving is carried out and the torque distributions under the step load in driving shaft of pinions are measured. The imbalance of torque distribution of pinions is verified and the load-sharing coefficients in each pinion can reach 1.262. The results of simulation and test are similar, which shows the correctness of theoretical model. A loop coupling control method is put forward based on current torque master slave control method. The imbalance of the multiple pinions driving in cutter head driving system of tunneling boring machine can be greatly decreased and the load-sharing coefficients can be reduced to 1.051 by using the loop coupling control method. The proposed research provides an effective solution to the imbalance of torque distribution and synchronous control method for multiple pinions driving of TBM.展开更多
Shield machine is the major technical equipment badly in need in national infrastructure construction. The service conditions of shield machine are extremely complex. The driving interface load fluctuation caused by g...Shield machine is the major technical equipment badly in need in national infrastructure construction. The service conditions of shield machine are extremely complex. The driving interface load fluctuation caused by geological environment changes and multi field coupling of stress field may lead into imbalance of redundant drive motors output torque in main driving system. Therefore, the shield machine driving synchronous control is one of the key technologies of shield machine. This paper is in view of the shield machine main driving synchronous control, achieving the system＇s adaptive load sharing. From the point of view of cutterhead load changes, nonlinear factors of mechanical transmission mechanism and the control system synchronization performance, the authors analyze the load sharing performance of shield machine main drive system in the event of load mutation. The paper proposes a data-driven synchronized control method applicable to the main drive system. The effectiveness of the method is verified through simulation and experimental methods. The new method can make the system synchronization error greatly reduced, thus it can effectively adapt to load mutation, and reduce shaft broken accident.展开更多
Accurately and efficiently predicting the load sharing of multi^bolt thick laminate joints is necessary to quicken the optimization of the large-scale structures over various design variables, and a two-dimensional ...Accurately and efficiently predicting the load sharing of multi^bolt thick laminate joints is necessary to quicken the optimization of the large-scale structures over various design variables, and a two-dimensional （2D） finite element method （FEM） is introduced to meet such a demand. The deformation contributions of the joint zone are analyzed and calculated separately, including the shearing deformation of the fasteners shank, the bending deformation of the fasteners shank, and the bearing deformation of the fasteners and joint plates. These deformations are all transferred and incorporated into the components of the fastener＇s flexibility. In the 2D finite element model, the flexibilities of the beam elements and bush elements are used to simulate different components of the fastener＇s flexibility. The parameters of the beam elements which include the bending moment of inertia and intersection area, and the parameters of the bush elements which include the stiffness in different directions, are all obtained through equalizing the fasteners flexibilities. In addition, the secondary bending effect introduced by the single-lap joints is also taken into account to verify the flexibilities of the fasteners in practical application. The proposed FEM is testified to be more accurate than the traditional 2D FEMs and more efficient than the three-dimensional （3D） FEM in solving load sharing problem of multi-bolt single-lap thick laminate joints. With the increase of joint plates＇ thickness, the advantages of the proposed method tend to be more obvious. The proposed 2D FEM is an effective tool for designing bolted joints in large-scale composite structures.展开更多
Based on solid modeling, the geometry and the FE model of the hourglass worm gearing are established. By the hybrid method of FEM and penalty function, the load sharing among tooth paris and the stress of contact teet...Based on solid modeling, the geometry and the FE model of the hourglass worm gearing are established. By the hybrid method of FEM and penalty function, the load sharing among tooth paris and the stress of contact teeth are calculated, the contact zones and the distribution of the contact pressure are investigated. The variation of the contact states with the load is investigated by comparision of its contact patterns under different loads.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Supported by National Key Technology R&D Program(No.2014BAF08B01)Natural Science Foundation of Tianjin(Grant No.17JCQNJC04300)
文摘Load sharing behavior is very important for power-split gearing system, star gearing reducer as a new type and special transmission system can be used in many industry fields. However, there is few literature regarding the key multiple-split load sharing issue in main gearbox used in new type geared turbofan engine. Further mechanism anal- ysis are made on load sharing behavior among star gears of star gearing reducer for geared turbofan engine. Compre- hensive meshing error analysis are conducted on eccentricity error, gear thickness error, base pitch error, assembly error, and bearing error of star gearing reducer respectively. Floating meshing error resulting from meshing clearance variation caused by the simultaneous floating of sun gear and annular gear are taken into account. A refined mathematical model for load sharing coefficient calculation is established in consideration of different meshing stiffness and support- ing stiffness for components. The regular curves of load sharing coefficient under the influence of interactions, single action and single variation of various component errors are obtained. The accurate sensitivity of load sharing coefficienttoward different errors is mastered. The load sharing coef- ficient of star gearing reducer is 1.033 and the maximum meshing force in gear tooth is about 3010 N. This paper provides scientific theory evidences for optimal parameter design and proper tolerance distribution in advanced devel- opment and manufacturing process, so as to achieve optimal effects in economy and technology.
基金National Natural Science Foundations of China(Nos.71231001,11001005,71301009)China Postdoctoral Science Foundation(No.2013M530531)+1 种基金the Fundamental Research Funds for the Central Universities of China(Nos.FRF-M P-13-009A,FRF-TP-13-026A)the MOE PhD Supervisor Fund of China(No.20120006110025)
文摘A series-parallel system was proposed with common bus performance sharing in which the performance and failure rate of the element depended on the load it was carrying. In such a system,the surplus performance of a sub-system can be transmitted to other deficient sub-systems. The transmission capacity of the common bus performance sharing mechanism is a random variable. Effects of load on element performance and failure rate were considered in this paper. A reliability evaluation algorithm based on the universal generating function technique was suggested. Numerical experiments were conducted to illustrate the algorithm.
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.
基金the Natural Science Foundation of the Education Department of Sichuan Province([2006]A067)the Talent Introduction Foundation of Sichuan Normal University.
文摘On the basis of capacity flow model, a new model is developed for a load-sharing k-out-of-n： G system consisting of different components, to describe the increase of the same component＇s failure rates under different loads. All components have exponential life distributions and are nonrepairable in the system. Reliability of load- sharing 2-out- of-3： G system is calculated and some special cases for the system are discussed. The calculation and discussions show that the model is right and practical.
基金supported by National Basic Research Program of China(973 Program, Grant No. 2013CB035402)
文摘The failure of the key parts, such as gears, in cutter head driving system of tunneling boring machine has not been properly solved under the interaction of driving motors asynchronously and wave tunneling torque load. A dynamic model of multi-gear driving system is established considering the inertia effects of driving mechanism and cutter head as well as the bending-torsional coupling. By taking into account the nonlinear coupling factors between ring gear and multiple pinions, the influence for meshing angle by bending-torsional coupling and the dynamic load-sharing characteristic of multiple pinions driving are analyzed. Load-sharing coefficients at different rotating cutter head speeds and input torques are presented. Numerical results indicate that the load-sharing coefficients can reach up to 1.2-1.3. A simulated experimental platform of the multiple pinions driving is carried out and the torque distributions under the step load in driving shaft of pinions are measured. The imbalance of torque distribution of pinions is verified and the load-sharing coefficients in each pinion can reach 1.262. The results of simulation and test are similar, which shows the correctness of theoretical model. A loop coupling control method is put forward based on current torque master slave control method. The imbalance of the multiple pinions driving in cutter head driving system of tunneling boring machine can be greatly decreased and the load-sharing coefficients can be reduced to 1.051 by using the loop coupling control method. The proposed research provides an effective solution to the imbalance of torque distribution and synchronous control method for multiple pinions driving of TBM.
文摘Shield machine is the major technical equipment badly in need in national infrastructure construction. The service conditions of shield machine are extremely complex. The driving interface load fluctuation caused by geological environment changes and multi field coupling of stress field may lead into imbalance of redundant drive motors output torque in main driving system. Therefore, the shield machine driving synchronous control is one of the key technologies of shield machine. This paper is in view of the shield machine main driving synchronous control, achieving the system＇s adaptive load sharing. From the point of view of cutterhead load changes, nonlinear factors of mechanical transmission mechanism and the control system synchronization performance, the authors analyze the load sharing performance of shield machine main drive system in the event of load mutation. The paper proposes a data-driven synchronized control method applicable to the main drive system. The effectiveness of the method is verified through simulation and experimental methods. The new method can make the system synchronization error greatly reduced, thus it can effectively adapt to load mutation, and reduce shaft broken accident.
文摘Accurately and efficiently predicting the load sharing of multi^bolt thick laminate joints is necessary to quicken the optimization of the large-scale structures over various design variables, and a two-dimensional （2D） finite element method （FEM） is introduced to meet such a demand. The deformation contributions of the joint zone are analyzed and calculated separately, including the shearing deformation of the fasteners shank, the bending deformation of the fasteners shank, and the bearing deformation of the fasteners and joint plates. These deformations are all transferred and incorporated into the components of the fastener＇s flexibility. In the 2D finite element model, the flexibilities of the beam elements and bush elements are used to simulate different components of the fastener＇s flexibility. The parameters of the beam elements which include the bending moment of inertia and intersection area, and the parameters of the bush elements which include the stiffness in different directions, are all obtained through equalizing the fasteners flexibilities. In addition, the secondary bending effect introduced by the single-lap joints is also taken into account to verify the flexibilities of the fasteners in practical application. The proposed FEM is testified to be more accurate than the traditional 2D FEMs and more efficient than the three-dimensional （3D） FEM in solving load sharing problem of multi-bolt single-lap thick laminate joints. With the increase of joint plates＇ thickness, the advantages of the proposed method tend to be more obvious. The proposed 2D FEM is an effective tool for designing bolted joints in large-scale composite structures.
文摘Based on solid modeling, the geometry and the FE model of the hourglass worm gearing are established. By the hybrid method of FEM and penalty function, the load sharing among tooth paris and the stress of contact teeth are calculated, the contact zones and the distribution of the contact pressure are investigated. The variation of the contact states with the load is investigated by comparision of its contact patterns under different loads.
