二级锥—斜齿轮系统的非线性动力学特性研究

发布时间：2018-03-28 15:18

本文选题：齿轮系统　切入点：多参数　出处：《兰州交通大学》2017年硕士论文

【摘要】：螺旋锥齿轮和斜齿轮,因为啮合重合度大,承载能力强,使齿轮传动过程趋于平稳,所以是一种广泛的工业机械设备动力传动装置。其力学性能和工作状态直接影响着整个机械设备的正常运行。由于齿轮系统中有很多非线性因素的存在,导致了齿轮系统具有复杂的非线性振动特性,这也是齿轮系统运行过程中出现振动噪声的主要原因。本文以二级锥—斜齿轮系统为研究对象,综合考虑影响齿轮系统的各种非线性因素,建立了系统的实际模型及力学模型,并得到系统的动力学微分方程,之后采用C语言编程,采用四阶Runge-Kutta进行数值模拟仿真。得到了系统在单参数下的分岔图,相图,庞加莱映射图,最大动载荷图及冲击状态图,在系统参数ka1,km1,ζ1,em,ζ11,k11,,b,T1分别与激励频率ω1共同作用下绘制了系统的冲击周期平面双参图,三维分岔图及动载荷平面分布图,占空比分布图,通过分析对比这些图,得到系统参数对齿轮系统运行稳定性的影响规律,得到最优的参数区间。研究分析表明,系统在低频下,系统处于无冲击完全啮合稳定运行状态,各系统参数的变化对系统运行状态影响很小,当激励频率达到一定值后,系统参数变化对系统影响显著。各参数对系统的影响规律可大致总结为.:适当的增加系统的刚度幅值ka1,输入载荷T1,支撑阻尼系数ζ11,支承刚度k11,减小平均啮合刚度km1,综合啮合误差em,都会使得系统在概周期或混沌状态停留区域减小从而扩大了系统的稳定区域,系统的运动规律变得简单,系统更容易进入周期运动,系统的冲击振动特性得到显著减弱。系统啮合阻尼系数ζ1和齿侧间隙b较小时,在一定的频率ω1,的范围内,系统齿轮副1啮合过程出现了齿面冲击和齿背冲击现象,系统可能会发生啮合打齿,断齿的情况,随着ζ1,b这两个参数在适当的范围内变大,齿轮副由双边冲击过渡到单边冲击或无冲击状态,脱啮现象得到明显改善,这有利于系统齿轮传动的准确性,提高齿轮系统的传动寿命。通过研究齿轮系统的动态特性,分析系统各非线性参数,得到参数的最优区间,从而减缓、抑制齿轮系统的分岔和混沌。
[Abstract]:Spiral bevel gear and helical gear, because of the high degree of meshing coincidence and strong bearing capacity, the gear transmission process tends to smooth, Therefore, it is a kind of widely used power transmission device of industrial machinery. Its mechanical properties and working state directly affect the normal operation of the whole mechanical equipment. Because of the existence of many nonlinear factors in the gear system, The gear system has complex nonlinear vibration characteristics, which is the main reason for the vibration and noise in the gear system. In this paper, the two-stage bevel helical gear system is taken as the research object. Considering all kinds of nonlinear factors affecting gear system synthetically, the practical model and mechanical model of the system are established, and the dynamic differential equation of the system is obtained. The bifurcation diagram, phase diagram, Poincare map, maximum dynamic load diagram and impact state diagram of the system under a single parameter are obtained by using fourth-order Runge-Kutta. Under the action of the system parameters ka1km1, 味 1m1, 味 11k11k11 / 1 and excitation frequency 蠅 1 respectively, the biparametric map of the impact period plane, the 3D bifurcation diagram, the dynamic load plane distribution diagram and the duty cycle distribution diagram are drawn, and these diagrams are analyzed and compared. The influence of system parameters on the running stability of gear system is obtained, and the optimal parameter interval is obtained. The research and analysis show that the system is in the condition of complete meshing and stable operation without impact at low frequency. The variation of system parameters has little effect on the operating state of the system. When the excitation frequency reaches a certain value, The effect of system parameters on the system can be summarized as follows: appropriate increase of stiffness amplitude ka 1, input load T 1, support damping coefficient 味 11, support stiffness k 11, and decrease average meshing stiffness, which can be summarized as follows: (1) increase the stiffness amplitude of the system (ka 1), input load (T 1), support damping coefficient (味 11), support stiffness (k 11). KM1, which synthesizes the meshing error eme, makes the system stay in the almost periodic or chaotic state, thus enlarging the stable region of the system. The motion law of the system becomes simple, the system moves more easily into the periodic motion, and the shock vibration characteristic of the system is obviously weakened. The meshing damping coefficient 味 1 and the tooth side clearance b are smaller, and within a certain frequency 蠅 1, the vibration characteristics of the system are greatly weakened. The tooth surface impact and tooth back impact appear in the meshing process of the gear pair 1 of the system, and the teeth may be meshed and broken in the system, with the increase of the parameters 味 1b in a proper range. The gear pair transition from the bilateral impact to the one-sided impact or the non-impact state, the phenomenon of degnaving is obviously improved, which is beneficial to the accuracy of the gear transmission and the increase of the transmission life of the gear system. Through the study of the dynamic characteristics of the gear system, By analyzing the nonlinear parameters of the system, the optimal interval of the parameters is obtained, so as to slow down and suppress the bifurcation and chaos of the gear system.
【学位授予单位】：兰州交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TH132.41

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