Nonlinear dynamic analysis was performed on a planetary gear transmission system with meshing beyond the pitch point.The parameters of the planetary gear system were optimized,and a two-dimensional nonlinear dynamic m...Nonlinear dynamic analysis was performed on a planetary gear transmission system with meshing beyond the pitch point.The parameters of the planetary gear system were optimized,and a two-dimensional nonlinear dynamic model was established using the lumped-mass method.Time-varying meshing stiffness was calculated by the energy method.The model consumes the backlash,bearing clearance,time-varying meshing stiffness,time-varying bearing stiffness,and time-varying friction coefficient.The time-varying bearing stiffness was calculated according to the Hertz contact theory.The load distribution among the gears was computed,and the time-varying friction coefficient was calculated according to elastohydrodynamic lubrication(EHL)theory.The dynamical equations were solved via numerical integration.The global bifurcation characteristics caused by the input speed,backlash,bearing clearance,and damping were analyzed.The system was in a chaotic state at natural frequencies or frequency multiplication.The system transitioned from a single-period state to a chaotic state with the increase of the backlash.The bearing clearance of the sun gear had little influence on the bifurcation characteristics.The amplitude was restrained in the chaotic state as the damping ratio increased.展开更多
The design of tubular steel scaffold-type shoring is usually performed by calculating the load capacity of the elements, taking into account their axial strength, mainly. Geometric stiffness effects and changes in the...The design of tubular steel scaffold-type shoring is usually performed by calculating the load capacity of the elements, taking into account their axial strength, mainly. Geometric stiffness effects and changes in the stiffness of connections are seldom considered. This paper assesses the stability of tubular steel shores using experimental and numerical approaches that take into account geometric nonlinearities as well as the features of the elements used to make the link between the steel tubes （pressed double coupler--right angle）. The increase in overall stiffness generated by diagonal bars used in the analyzed models was examined. The results obtained show the importance of using P-delta analyses in this kind of structure in order to evaluate structure＇s overall stability even when compressive stresses are within acceptable ranges of code limits.展开更多
The tangent stiffness matrix of Timoshenko beam element is applied in the buckling of multi-step beams under several concentrated axial forces with elastic supports. From the governing differential equation of lateral...The tangent stiffness matrix of Timoshenko beam element is applied in the buckling of multi-step beams under several concentrated axial forces with elastic supports. From the governing differential equation of lateral deflection including second-order effects,the relationship of force versus displacement is established. In the formulation of finite element method (FEM),the stiffness matrix developed has the same accuracy with the solution of exact differential equations. The proposed tangent stiffness matrix will degenerate into the Bernoulli-Euler beam without the effects of shear deformation. The critical buckling force can be determined from the determinant element assemblage by FEM. The equivalent stiffness matrix constructed by the topmost deflection and slope is established by static condensation method,and then a recurrence formula is proposed. The validity and efficiency of the proposed method are shown by solving various numerical examples found in the literature.展开更多
基金supported by the National Natural Science Foundation of China(No. 51975274)National Key Laboratory of Science and Technology on Helicopter Transmission(Nanjing University of Aeronautics and Astronautics)(No. HTL-A-19K03)
文摘Nonlinear dynamic analysis was performed on a planetary gear transmission system with meshing beyond the pitch point.The parameters of the planetary gear system were optimized,and a two-dimensional nonlinear dynamic model was established using the lumped-mass method.Time-varying meshing stiffness was calculated by the energy method.The model consumes the backlash,bearing clearance,time-varying meshing stiffness,time-varying bearing stiffness,and time-varying friction coefficient.The time-varying bearing stiffness was calculated according to the Hertz contact theory.The load distribution among the gears was computed,and the time-varying friction coefficient was calculated according to elastohydrodynamic lubrication(EHL)theory.The dynamical equations were solved via numerical integration.The global bifurcation characteristics caused by the input speed,backlash,bearing clearance,and damping were analyzed.The system was in a chaotic state at natural frequencies or frequency multiplication.The system transitioned from a single-period state to a chaotic state with the increase of the backlash.The bearing clearance of the sun gear had little influence on the bifurcation characteristics.The amplitude was restrained in the chaotic state as the damping ratio increased.
文摘The design of tubular steel scaffold-type shoring is usually performed by calculating the load capacity of the elements, taking into account their axial strength, mainly. Geometric stiffness effects and changes in the stiffness of connections are seldom considered. This paper assesses the stability of tubular steel shores using experimental and numerical approaches that take into account geometric nonlinearities as well as the features of the elements used to make the link between the steel tubes （pressed double coupler--right angle）. The increase in overall stiffness generated by diagonal bars used in the analyzed models was examined. The results obtained show the importance of using P-delta analyses in this kind of structure in order to evaluate structure＇s overall stability even when compressive stresses are within acceptable ranges of code limits.
基金Sponsored by the National Key Technology Research and Development Program (Grant No.2006BAJ12B03-2)
文摘The tangent stiffness matrix of Timoshenko beam element is applied in the buckling of multi-step beams under several concentrated axial forces with elastic supports. From the governing differential equation of lateral deflection including second-order effects,the relationship of force versus displacement is established. In the formulation of finite element method (FEM),the stiffness matrix developed has the same accuracy with the solution of exact differential equations. The proposed tangent stiffness matrix will degenerate into the Bernoulli-Euler beam without the effects of shear deformation. The critical buckling force can be determined from the determinant element assemblage by FEM. The equivalent stiffness matrix constructed by the topmost deflection and slope is established by static condensation method,and then a recurrence formula is proposed. The validity and efficiency of the proposed method are shown by solving various numerical examples found in the literature.
