行星齿轮传动系统的稳定性与分岔特性研究

发布时间：2018-01-15 23:29

本文关键词：行星齿轮传动系统的稳定性与分岔特性研究　出处：《南京航空航天大学》2013年博士论文　论文类型：学位论文

【摘要】：本文对单级行星齿轮传动系统的稳定性与分岔特性进行了研究,主要包括行星齿轮传动系统的非线性动力学建模、运动状态稳定性与分岔以及振动强度的稳定性三方面内容。其中,运动状态的稳定性与分岔包括确定参数下的共存周期轨道及其稳定性判断、周期轨道稳定性的局部分岔特性、运动状态的全局分岔特性、共存周期轨道的全局吸引域;振动强度的稳定性研究内容包括振动强度的参数稳定性域计算、动态均载性能以及啮合冲击特性的研究。在动力学模型的研究中,建立了行星齿轮传动系统的纯扭转非线性动力学模型和弯扭耦合非线性动力学模型,分别用于运动状态的稳定性研究和振动强度的稳定性研究,并通过动力学试验验证了纯扭转非线性动力学模型在运动状态定性研究方面的有效性。在确定参数下共存周期轨道及其稳定性的研究中,采用伪不动点追踪法计算了多组参数组合下行星齿轮传动系统共存的周期轨道,并采用Floquet稳定性理论判断了各共存周期轨道的稳定性。研究表明,在某些确定参数组合下,行星齿轮系统会共存多个周期轨道,这些周期轨道有的稳定,有的不稳定;转速、传递功率以及啮合相对阻尼系数等系统参数会对共存周期轨道的数量、形态以及稳定性产生影响。在周期轨道稳定性局部分岔特性的研究中,采用CPNF方法研究了行星齿轮传动系统周期轨道的稳定性随转速、传递功率以及啮合相对阻尼系数等系统参数的局部分岔规律。获得了行星齿轮非线性动力系统周期轨道的形态和稳定性随系统参数的变化规律以及各种周期轨道之间的分岔途径,确定了不同参数区间与各种周期运动之间的映射关系。在运动状态全局分岔特性的研究中,通过运动时域图、相图、Poincaré映射图、全局分岔图等手段,定性研究了行星齿轮传动系统运动状态的稳定性随转速、传递功率以及啮合相对阻尼系数等参数的全局分岔特性,获得了不同参数组合下系统所呈现的形态丰富的奇怪吸引子,确定了系统通往混沌的道路。在共存周期轨道全局吸引域的研究中,采用Poincaré型胞映射法研究了行星齿轮传动系统在一组典型参数下的具有运动长期稳定性的共存周期轨道及其吸引域,实现了对周期轨道稳定程度的量化评价,给出了行星齿轮传动系统在该组设计参数下的周期轨道所能承受的扰动范围。在振动强度参数稳定域的研究中,提出了一种行星齿轮传动系统参数稳定域的计算方法,并以此定量计算了行星齿轮传动系统关于太阳轮转速、齿侧间隙以及齿轮副啮合相对阻尼系数等不同参数组合下的稳定域、不稳定域以及二者之间的分界线,获得了易于导致振动强度失稳的各种系统参数组合。在动态均载性能以及啮合冲击特性的研究中,采用数值积分分析了系统误差、太阳轮支撑刚度、齿数以及齿侧间隙等设计参数对行星齿轮传动系统动态均载性能的影响规律以及系统误II差、传递功率、太阳轮转速等系统参数对啮合冲击特性的影响规律。
[Abstract]:Stability and bifurcation of the single-stage planetary gear transmission system is studied, including the nonlinear dynamic model of planetary gear transmission system, the motion state of stability and bifurcation and vibration intensity of three aspects. Among them, the stability and bifurcation of the motion state including determination of coexisting periodic orbits parameters and local stability. Bifurcation of periodic orbit stability, the global bifurcation characteristics of the motion state of the global domain of attraction of coexisting periodic orbits; stability research of vibration strength parameters including the stability domain of vibration strength calculation, load balancing performance and study the dynamic characteristics of the meshing impact. In the study of dynamical model, a planetary gear transmission system of pure torsion the nonlinear dynamic model and the lateral torsional coupling nonlinear dynamic model for motion stability respectively. Study on the stability of vibration and strength, and the effectiveness of pure torsion nonlinear dynamics model in the qualitative study on the state of motion is verified by dynamic test. The research and the stability of periodic orbits coexist in the determined parameters in periodic orbits coexist in the planetary gear transmission system using pseudo fixed point tracing method to calculate multiple sets of parameters and, using Floquet stability theory to determine the stability of the coexistence of periodic orbits. The results show that in certain parameter combinations, the planetary gear system will coexist multiple periodic orbits, these periodic orbits have some stability and instability; speed, power transmission and meshing relative damping coefficients of the system parameters such as the number of coexisting periodic orbits the influence of morphology and stability. In the study of bifurcation characteristics of periodic orbit stability bureau, using CPNF method to research the line The stability of periodic orbits of star gear system with speed, transmission power and local bifurcation rules of meshing relative damping coefficient of the system parameters. The bifurcation path between variation of planetary gear nonlinear dynamical system of periodic orbit shape and stability with the system parameters are obtained and a variety of periodic orbits, the mapping relationship between different parameters and different interval periodic motion the study on the state of motion. The global bifurcation characteristics, through the motion graph in time domain, phase diagrams, Poincar maps, global bifurcation diagrams and other means of qualitative research the stability of planetary gear transmission system with motion speed, global bifurcation characteristics of power transmission and meshing relative damping coefficient and other parameters. The strange the attractor under different parameter combination system form rich, determine the system leading to chaos. Coexisted in the week Study on the track in the global domain of attraction, on the planet gear transmission system in a typical set of parameters with long-term stability movement of coexisting periodic orbits and their domains using Poincar cell mapping method, the quantitative evaluation of the degree of stable periodic orbits, periodic orbits are given in the design parameters of the system planetary gear transmission can withstand the disturbance range. In the study of strength parameters in the vibration stability domain, proposes a stability domain of planetary gear transmission system parameter calculation method, and the quantitative calculation of the planetary gear transmission system on the sun wheel speed, the stability domain of backlash and meshing relative damping coefficient with different parameters under the combination, unstable boundary between the domain and the two, get lost easily lead to vibration intensity of various system parameters combination stability. In the dynamic load sharing performance Study and meshing impact characteristics, using numerical analysis of system error, the sun wheel support stiffness, influence of tooth number and tooth clearance design parameters such as load sharing properties of dynamic planetary gear transmission system and the error of II, transmission power, influence of system parameters on the speed of the sun gear meshing impact characteristics.

【学位授予单位】：南京航空航天大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：TH132.425

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