封闭式行星齿轮传动系统动态特性研究

发布时间：2017-12-31 10:03

本文关键词：封闭式行星齿轮传动系统动态特性研究　出处：《山东大学》2014年博士论文　论文类型：学位论文

【摘要】：行星齿轮传动系统由于其承载能力大、结构紧凑,广泛地应用于航空航天、船舶、汽车等各个领域。由于在承受外部激励的同时又承受着自身参数变化引起的内部激励,行星系统的动力学行为十分复杂,振动和噪声是影响系统可靠性及寿命的关键因素。因此,要提高机械系统的安全性及可靠性,亟需针对机械传动系统的动力学建模、动态响应分析、参数稳定性分析、减振、降噪等动态特征进行深入研究。封闭式行星系统作为行星传动的一种,它所传递的扭矩可以从多个路径传递到负载。因而,封闭式行星传动可承载更大的扭矩,并且结构紧凑,传动比更大,其体积往往比同等额定功率的简单行星系统更小。近年来,封闭式行星传动系统以其独特的优点,越来越多的应用在机械传动领域,对其开展动态特性研究,可为优化设计提供理论基础和指导准则,具有重要的实际意义。本文主要对一种可实现功率分流(汇流)的两级封闭式行星系统的动态特性进行了相关的研究。在传动系统数学模型的建立、固有特性分析、频响特性分析、系统参数对振动特性的影响以及实验研究等方面,取得了一些成果和进展。论文的主要内容包括以下几个方面：根据传动系统各个构件的运动学关系,推导了系统各构件的相对位移。在相关合理假设的前提下,运用集中质量法,基于第二类Lagrange方程分别建立了系统的纯扭转动力学模型和平移-扭转耦合动力学模型。根据所建立的两类动力学模型分析了系统的固有振动特性,并依据固有频率和振型特征进行了归纳和振动模式划分。根据系统子本征值关系式,从数学意义上证明了振动模式划分的完备性。揭示了行星轮数目的变化对系统固有频率的影响规律。所建立的模型易于扩展,可推广至任意行星轮数目和行星传动级数的封闭式行星系统,具有普遍的指导意义。对系统中包含的非线性因素,如时变啮合刚度、齿侧间隙及综合啮合误差等进行了数学意义上的描述,得到非线性、耗散系统的纯扭转模型的动力学微分方程组。对已经无量纲化和去除刚体运动模式的纯扭转模型的非线性动力学微分方程组,利用DFT数值谐波平衡法将其转化成非线性代数方程组。为进一步求解此方程组,运用拟牛顿迭代法(BFS秩2)结合拟弧长算法进行数值求解,综合分析了频响特性曲线的幅值跳跃、多值性以及不稳定解支等典型的非线性特征。通过变化外激励、啮合刚度、系统阻尼等参数值,揭示了重要参数对两级封闭式行星传动系统非线性动态特性的影响规律。本文为深入研究封闭式行星传动系统的动态特性提供了一种新的方法和途径。考虑到由于齿侧间隙属于强非线性因素,多尺度法不能直接应用于齿轮系统非线性动力学模型求解。本文通过分析时变啮合刚度和齿侧间隙两类非线性因的特点,推导了包含两类非线性因素的综合表达式,使多尺度法能合理应用于两级封闭式行星系统非线性模型,并且以此推导了系统主共振幅值的近似解析表达式。对系统相对啮合相位关系进行了深入的研究,推导了任意两对齿轮副的相对啮合相位。基于多尺度近似解析解表达式,揭示了系统结构、相对啮合相位以及系统重合度等几何参数对振动特性的影响规律。构建了两级封闭式行星传动系统的实验平台。通过实验模态分析测试了传动系统的频响函数,获得了系统的固有频率；实验测试结果与理论分析结果对比表明：本文基于集中质量法建立的行星传动系统纯扭转动力学模型和平移-扭转耦合动力学模型是合理的。通过本文的研究揭示了系统设计参数对动态特性的影响规律,为封闭式行星传动系统的动态设计提供了理论依据,对提高我国封闭式行星系统的设计水平有较大的理论意义和实际应用价值。本课题得到国家自然科学基金(51175299)及山东省自然科学基金(ZR2010EM012)的支持。
[Abstract]:Planetary gear transmission system due to its high bearing capacity, compact structure, widely used in aerospace, shipbuilding, automobile and other fields. Due to the internal incentive under the external incentive and bear their own parameters caused by the change of the planet, the dynamic behavior of the system ten is complex, the noise and vibration is a key factor affecting system reliability and life. Therefore, to improve the safety and reliability of the mechanical system dynamics modeling, need for mechanical transmission system, dynamic response analysis, vibration analysis, parameter stability, in-depth study of noise reduction. The dynamic characteristics of the closed planetary system as a planetary transmission, it can load the torque transmitted from multiple paths transfer to the closed planetary transmission. So it can carry more torque, and compact structure, the transmission ratio is bigger, its volume more often than the same power rating is simple The planetary system is smaller. In recent years, closed planetary transmission system has more and more applications in the field of mechanical transmission because of its unique advantages. Its dynamic characteristics can provide theoretical basis and guidance for optimal design, and has important practical significance.
In this paper, a power split (bus) can realize the dynamic characteristics of two stage closed planetary system is studied. The mathematical model of the transmission system is established, the inherent characteristics of analysis, frequency response analysis, influence of system parameters on vibration characteristics and experimental research, made some achievements and progress. The main contents of this paper include the following aspects:
According to the kinematics of each component of the transmission system, the formulas of relative displacement of each component of the system. In the premise of reasonable assumptions, using the lumped mass method, the system dynamics model of pure torsion and translational torsional coupling dynamic model was established based on the Lagrange equation of the second kind. According to the two kinds of the dynamic model analysis the natural vibration characteristics of the system, and based on the natural frequency and vibration characteristics were summarized and classified. According to the vibration mode of system eigenvalue equation, mathematically proved that the complete classification of the vibration modes. The influences of planetary gear changes in the number of the natural frequency of the system. The model is easy to expansion of the closed planetary system can be extended to an arbitrary number of planet gears and planetary gear series, has a universal significance.
The nonlinear factors included in the system, such as time-varying meshing stiffness, backlash and meshing error are mathematically described by nonlinear dynamic differential equation group, pure torsion model of dissipative system. The nonlinear dynamic differential of pure torsion model has dimensionless and remove the rigid motion model of the equations, using DFT numerical harmonic balance method is transformed into nonlinear algebraic equations. In order to further solve the equations, using the quasi Newton method (BFS rank 2) combined with the pseudo arclength algorithm for numerical solution, a comprehensive analysis of the amplitude frequency response curve of the jump, multi value and unstable solution support etc. the typical nonlinear characteristics. By changing the external excitation, the meshing stiffness, damping and other parameters, reveals the important parameters of rule two grade influence dynamic characteristics of nonlinear planetary transmission system in this paper. A new method and way is provided for the thorough study of the dynamic characteristics of the closed planetary transmission system.
Considering the backlash belongs to the strong nonlinear factors, the method of multiple scales cannot be directly applied to solve the nonlinear dynamic model of gear system. Through the analysis of time-varying meshing stiffness and backlash of two kinds of nonlinear factors, including two kinds of nonlinear factors are the comprehensive expression, make the method of multiple scales can be applied reasonably in two grade nonlinear planetary system model, and deduced the approximate analytical expressions of the amplitude of the primary resonance of the system. The system of relative meshing phase are studied, the formulas of relative phase of any two meshing gear pair. The approximate analytic expressions based on multi-scale, reveals the system structure, the relative meshing phase and system the coincidence degree of geometrical parameters on vibration characteristics are studied.
Build the experimental platform of two stage closed planetary transmission system. The frequency response function of transmission system was tested by experimental modal analysis, the natural frequency of the system; comparing test results with the results of theoretical analysis. Based on the lumped mass method of planetary transmission system dynamics model of pure torsion and translational torsional coupling dynamics model based on the reasonable.
The influence of system design parameters on dynamic characteristics is revealed through the research in this paper, which provides a theoretical basis for dynamic design of closed planetary transmission system, and has great theoretical significance and practical application value for improving the design level of closed planetary system in China.
The project has been supported by the National Natural Science Foundation (51175299) and the natural science foundation of Shandong (ZR2010EM012).

【学位授予单位】：山东大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TH132.425

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