少齿差行星减速器动态特性分析及非线性振动研究

发布时间：2018-07-29 06:04

【摘要】：课题来源于国防科工委“十一五”民用航天预研项目—“空间环境下的高性能摩擦副与高效传动机构技术”（C4220061319）、国家教育部“长江学者和创新团队发展计划”项目—“高性能机电传动系统的创新设计理论、方法与技术”（IRT0763）、国家自然科学基金重点项目—“新型高性能传动件及系统的可靠性设计理论与方法”（50735008）。减速器系统的工作状态极其复杂，不仅载荷工况和动力装置多样，且对于齿轮传动系统，由于时变啮合刚度、传动误差、齿侧间隙等因素的影响，引起轮齿接触脱离接触周期性、强非线性耦合振动，对传动系统的平稳性、可靠性产生严重影响。因此对其进行动态特性、间隙非线性振动行为及影响因素的研究，为高性能齿轮系统的设计、分析、制造提供了一定的理论依据与实验参考。论文以NN型少齿差行星减速器为对象，，先分析其结构及传动原理，用有限元法分析其固有频率及模态振型，用集中质量法建立减速器系统非线性振动模型与方程，通过数值求解分析减速器非线性振动特性以及参数对它的影响。最后对其模态特性和振动响应进行实验研究。论文主要研究内容如下：（1）分析该减速器的结构、传动原理，计算某常见工况下各传动件的理论转速。求得两级传动的理论啮合频率、啮合阻尼。详细分析各滚动轴承的变形、刚度、阻尼等动特性参数。（2）推导内齿副单齿刚度计算式，考虑理论重合度，计算多对齿啮合刚度。将两级传动多对齿时变啮合刚度拟合为8阶Fourier级数的形式。分别以各级传动啮合角频率为角速度的正弦函数模拟各级齿轮误差。（3）采用ABAQUS建立该减速器有限元自由模态分析模型，其中轮齿啮合部位采用绑定约束，用弹簧单元模拟轴承。采用Lanczos特征值求解器对该减速器进行自由模态求解，获得该减速器前20阶固有频率及模态振型。（4）综合考虑齿轮啮合刚度、传动误差、齿侧间隙及支撑刚度和阻尼，用集中质量法建立多自由度、多间隙、变参数、弯扭耦合的两级齿轮系统非线性振动模型，用Lagrange方程推导齿轮系统的非线性振动微分方程组。用四阶五级的RKF法对非线性微分方程组求解，系统地分析该减速器各齿轮振动位移、速度响应，以及振动位移速度相图、Poincaré截面。进一步计算得齿轮弹粘啮合力、轴承动载荷、振动加速度响应。最后分析各参数对减速器非线性振动特性的影响。（5）用LMS Test. Lab对该减速器进行锤击法自由模态实验，验证理论分析结果的正确性。用三向加速度传感器采集减速器壳体振动信号，由FFT变换得到相应的振动频率，经1/3倍频处理分析振动加速度级结构噪声，经积分处理得到振动速度及位移响应。
[Abstract]:The subject comes from the "11th Five-Year" Civil Aerospace Pre-Research Program of the National Commission for National Defense Science, Technology of High-Performance friction pairs and High-efficiency Transmission mechanisms in Space Environment (C4220061319), and the National Ministry of Education "Yangtze River Scholars and Innovation team Development Plan" -"innovative design theory for high performance electromechanical transmission systems, Methods and techniques "(IRT0763), key item of National Natural Science Foundation -" Theory and method of Reliability Design for New High performance Transmission parts and Systems "(50735008). The working state of the reducer system is extremely complex, not only the load working conditions and power devices are various, but also the gear transmission system is affected by the time-varying meshing stiffness, transmission error, tooth side clearance and so on. The gear tooth contact is caused by the periodic and strong nonlinear coupling vibration, which has a serious effect on the stability and reliability of the transmission system. Therefore, the study of the dynamic characteristics, the nonlinear vibration behavior of clearance and the influencing factors provide a certain theoretical basis and experimental reference for the design, analysis and manufacture of high performance gear system. In this paper, the structure and transmission principle of NN type planetary reducer with less tooth difference are analyzed, its natural frequency and modal mode are analyzed by finite element method, and the nonlinear vibration model and equation of reducer system are established by means of lumped mass method. The nonlinear vibration characteristics of reducer and the influence of parameters on it are analyzed numerically. Finally, the modal characteristics and vibration response are studied experimentally. The main contents of this paper are as follows: (1) the structure and driving principle of the reducer are analyzed. The theoretical meshing frequency and meshing damping of the two-stage transmission are obtained. The parameters of deformation, stiffness and damping of rolling bearings are analyzed in detail. (2) the calculation formula of single tooth stiffness of internal gear pair is derived, and the meshing stiffness of multiple pairs of teeth is calculated considering the degree of theoretical coincidence. The time-varying meshing stiffness of multi-pair teeth of two-stage transmission is fitted to the form of eighth order Fourier series. The sinusoidal function with the angular frequency of meshing angle of each transmission is used to simulate the errors of gear at all levels. (3) the finite element free modal analysis model of the reducer is established by using ABAQUS, in which the gear tooth meshing part is bound constrained. Use spring element to simulate bearing. The Lanczos eigenvalue solver is used to solve the free mode of the reducer, and the first 20 natural frequencies and modal modes of the reducer are obtained. (4) the gear meshing stiffness, transmission error, tooth side clearance and support stiffness and damping are considered synthetically. The nonlinear vibration model of a two-stage gear system with multiple degrees of freedom, multiple clearances, variable parameters and coupled bending and torsion is established by means of the lumped mass method. The nonlinear vibration differential equations of the gear system are derived by using the Lagrange equation. The fourth order five-stage RKF method is used to solve the nonlinear differential equations. The vibration displacement, velocity response and velocity phase diagram of each gear in the reducer are systematically analyzed. The gear elastic engagement force, bearing dynamic load and vibration acceleration response are further calculated. Finally, the influence of the parameters on the nonlinear vibration characteristics of the reducer is analyzed. (5) LMS Test is used. The free mode experiment of hammering method is carried out by Lab to verify the correctness of the theoretical analysis. The vibration signal of the reducer shell is collected by three direction acceleration sensor and the corresponding vibration frequency is obtained by FFT transform. The structural noise of vibration acceleration level is analyzed by 1 / 3 frequency doubling processing, and the vibration velocity and displacement response are obtained by integral processing.
【学位授予单位】：重庆大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：TH132.46

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