以液压缸的运动特性为研究对象,首先通过揭示其非线性弹簧刚度呈现出软硬弹簧现象的产生机理,以及时变摩擦力处于负阻尼状态时引起"自激振荡"现象的原因,深入研究了二者耦合作用下液压缸的非线性时变动力学方程;而后,基于Tay...以液压缸的运动特性为研究对象,首先通过揭示其非线性弹簧刚度呈现出软硬弹簧现象的产生机理,以及时变摩擦力处于负阻尼状态时引起"自激振荡"现象的原因,深入研究了二者耦合作用下液压缸的非线性时变动力学方程;而后,基于Taylor展开法将非线性动力学方程简化为可解的线性微分方程形式,并根据离散时域步长的原理反复迭代解决非线性弹簧刚度和时变摩擦力对液压缸运动特性的耦合作用问题;最后,采用Matlab软件编制数值仿真程序,模拟液压缸低速运动时的爬行现象。仿真结果显示,爬行现象模拟效果良好,且与以往解决非线性耦合问题的Van Der Pol-Duffing方程和Lienard方程相比,本文所提的数值仿真方法具有求解方便、适用性广,精度较高等优点。展开更多
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
A nonlinear model of anti-backlash gear with time-varying friction and mesh stiffness was proposed for the further study on dynamic characteristics of anti-backlash gear. In order to improve the model precision, appli...A nonlinear model of anti-backlash gear with time-varying friction and mesh stiffness was proposed for the further study on dynamic characteristics of anti-backlash gear. In order to improve the model precision, applied force analysis was completed in detail, and single or double tooth meshing states of two gear pairs at any timing were determined according to the meshing characteristic of anti-backlash gear. The influences of friction and variations of damping ratio on dynamic transmission error were analyzed finally by numerical calculation and the results show that anti-backlash gear can increase the composite mesh stiffness comparing with the mesh stiffness of the normal gear pair. At the pitch points where the frictions change their signs, additional impulsive effects are observed. The width of impulsive in the same value of center frequency is wider than that without friction, and the amplitude is lower. When gear pairs mesh in and out, damping can reduce the vibration and impact.展开更多
Creep ageing forming(CAF)has been widely used in the aerospace engineering,but how to optimize the processing conditions,especially under complex stress state of the CAF process for large-size components produced by f...Creep ageing forming(CAF)has been widely used in the aerospace engineering,but how to optimize the processing conditions,especially under complex stress state of the CAF process for large-size components produced by friction-stir welding is still a great challenge to now.In this work,the creep ageing behaviors and underlying microstructure evolution of a thick friction-stir welded Al-Cu alloy plate after CAF process under different stress levels are systematically investigated.The creep strain and the strength of the joint are both significantly increased when the stress is close to the average yield strength of the initial weld joint.The grain size reduces while the local strain and dislocation density increase from top to bottom of the NZ;hence,the bottom layer of the weld joint exhibits higher creep strain and steady-stage creep strain rate during the CAF process.The results reveal that the gradient microstructures sensitive to the stress level effectively govern the creep-ageing performance from the upper to the bottom layer in a thick friction stir welded Al-Cu alloy plate.Rationally increasing the initial dislocation density of the weld joint can both enhance the tensile properties and promote the creep deformation of the weld joint for CAF process.展开更多
文摘以液压缸的运动特性为研究对象,首先通过揭示其非线性弹簧刚度呈现出软硬弹簧现象的产生机理,以及时变摩擦力处于负阻尼状态时引起"自激振荡"现象的原因,深入研究了二者耦合作用下液压缸的非线性时变动力学方程;而后,基于Taylor展开法将非线性动力学方程简化为可解的线性微分方程形式,并根据离散时域步长的原理反复迭代解决非线性弹簧刚度和时变摩擦力对液压缸运动特性的耦合作用问题;最后,采用Matlab软件编制数值仿真程序,模拟液压缸低速运动时的爬行现象。仿真结果显示,爬行现象模拟效果良好,且与以往解决非线性耦合问题的Van Der Pol-Duffing方程和Lienard方程相比,本文所提的数值仿真方法具有求解方便、适用性广,精度较高等优点。
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.
基金Project(51175505)supported by the National Natural Science Foundation of China
文摘A nonlinear model of anti-backlash gear with time-varying friction and mesh stiffness was proposed for the further study on dynamic characteristics of anti-backlash gear. In order to improve the model precision, applied force analysis was completed in detail, and single or double tooth meshing states of two gear pairs at any timing were determined according to the meshing characteristic of anti-backlash gear. The influences of friction and variations of damping ratio on dynamic transmission error were analyzed finally by numerical calculation and the results show that anti-backlash gear can increase the composite mesh stiffness comparing with the mesh stiffness of the normal gear pair. At the pitch points where the frictions change their signs, additional impulsive effects are observed. The width of impulsive in the same value of center frequency is wider than that without friction, and the amplitude is lower. When gear pairs mesh in and out, damping can reduce the vibration and impact.
基金Project(2021YFB3400903) supported by the National Key R&D Program of ChinaProject(1053320211480) supported by the Science and Technology Innovation Project of Graduate Students of Central South University,China。
文摘Creep ageing forming(CAF)has been widely used in the aerospace engineering,but how to optimize the processing conditions,especially under complex stress state of the CAF process for large-size components produced by friction-stir welding is still a great challenge to now.In this work,the creep ageing behaviors and underlying microstructure evolution of a thick friction-stir welded Al-Cu alloy plate after CAF process under different stress levels are systematically investigated.The creep strain and the strength of the joint are both significantly increased when the stress is close to the average yield strength of the initial weld joint.The grain size reduces while the local strain and dislocation density increase from top to bottom of the NZ;hence,the bottom layer of the weld joint exhibits higher creep strain and steady-stage creep strain rate during the CAF process.The results reveal that the gradient microstructures sensitive to the stress level effectively govern the creep-ageing performance from the upper to the bottom layer in a thick friction stir welded Al-Cu alloy plate.Rationally increasing the initial dislocation density of the weld joint can both enhance the tensile properties and promote the creep deformation of the weld joint for CAF process.
