基于齿轮系统动力学推导出行星齿轮传动系统的平移-扭转耦合非线性振动微分方程。采用特征值问题求解其固有频率及振型，并进行归类和描述。针对行星齿轮传动系统中内激励频率与转速成正比这一特性，提出一种利用正弦激振扫频模拟其内激励，并通过求解传动系统振动微分方程得到其响应的方法。与传统方法相比，该方法可将系统中复杂的激励分解为若干单一激励，从而量化评价各激励对系统振动响应的影响程度，使各激励与响应形成具体映射关系。研究发现内啮合激励对低阶（1～5阶）与高阶固有频率（16～18阶）影响较小，外啮合激励在低阶固有频率随阶数增加影响递增，并对太阳轮纯扭转振型影响较大，而在中阶固有频率（6～15阶）内外啮合均对行星轮纯扭转振型影响显著，为行星齿轮传动系统固有频率及振型的优化、降振减噪和减小故障发生率提供依据。
Abstract
The translation-rotation coupled nonlinear vibration differential equations is built by using gear system dynamic. natural frequencies and vibration shapes of the system were calculated, the distribution rules of natural frequencies and the characteristic of vibration shapes were described. Aim at the relationship of direct proportion between internal excitation of system and speed. Propose a kind of method which makes use of sine excitation frequency sweep to simulate internal excitation and match with vibration differential equations, so under the excitation vibration response coupling dynamic differential equations is deduced. There are an specific mapping relation between excitation and response. To calculate the meshes excitation effects on response. Find internal meshes excitation have a smaller influence on low（1～5）and high（16～18）natural frequencies, but influence of external meshes increases along with natural frequencies and a larger influence on sun gear rotational modes of high natural frequencies. Internal and external meshes have significant influence on planetary gear rotational modes in intermediate natural frequencies（6～15）. This article lay a foundation for the design of reduce vibration of planetary gears set.
关键词
行星齿轮 /
振动响应 /
啮合激励 /
固有特性
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Key words
planetary gear；vibration response；mesh excitation /
natural characteristics
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