考虑内齿圈柔性的行星齿轮系统动态特性研究

发布时间：2018-01-04 15:49

本文关键词：考虑内齿圈柔性的行星齿轮系统动态特性研究　出处：《郑州大学》2016年硕士论文　论文类型：学位论文

【摘要】：由于行星齿轮系统的诸多优点,所以行星齿轮系统的应用越来越广泛。但是,行星齿轮系统一直受振动和噪声的困扰。在追求低噪声和舒适性生活的今天,这个问题越来越引起人们的关注。因此,为了研究产生振动和噪声的机理和寻求解决方法,人们对行星齿轮系统动态特性的研究孜孜不倦。由于现代机械追求轻量化和高速化,因此内齿圈会减薄,相当于薄壁结构,内齿圈很容易发生较大的变形,尤其是在高速重载的情况下,这势必会给行星齿轮系统的动态特性造成较大的影响,如果再将内齿圈看成刚性的,显然不合适的。所以,本文研究了具有柔性内齿圈行星齿轮系统的动态特性,主要内容如下:第一:建立了集中参数模型,在建立模型过程中,构件与机架之间和齿轮啮合之间的接触均用弹簧阻尼系统代替,运用牛顿第二定律列写系统的动力学方程,并整理成矩阵形式,利用复模态法进行求解,根据方程的数值解分析阻尼对行星齿轮系统动态特性的影响,可以发现行星齿轮系统中阻尼的影响很小,可以忽略不计。第二:建立了具有柔性内齿圈的行星齿轮系统的刚柔耦合模型,将构件间的作用简化为弹簧系统,不再考虑阻尼的影响。利用弹性力学和理论力学的相关知识列写柔性内齿圈的动力学方程并进行处理,与其它刚性构件的动力学方程相结合,列写行星齿轮系统的动力学方程。第三:由于动力学方程组中含有六阶偏微分方程,不能直接求解,所以利用分离变量的方法和δ函数的性质进行降阶处理,将其转化为二阶常微分方程,并将方程整理为矩阵形式,得到方程的刚度矩阵和质量矩阵。第四:利用动力学和线性代数知识将动力学方程的固有频率和振型的求解转化为特征值和特性向量的求解,并利用MATLAB编程求解。用数值解分析了行星齿轮系统的动态特性,与集中参数模型作相比,增加了一种新的振动模式,即内齿圈振动模式,固有频率下降且阶数增多;而且内齿圈柔性越大,系统的固有频率越低;同时本文分析了质量和刚度对行星齿轮系统固有频率的影响。
[Abstract]:Because of the many advantages of the planetary gear system, the planetary gear system is more and more widely used. However, the planetary gear system has been troubled by vibration and noise. This problem has attracted more and more attention. Therefore, in order to study the mechanism of vibration and noise and seek solutions. The dynamic characteristics of planetary gear system have been studied assiduously. Because of the pursuit of lightweight and high-speed in modern machinery, the inner gear ring will be thinned, which is equivalent to thin-walled structure, and the inner gear ring is easy to be deformed. Especially in the case of high speed and heavy load, this will inevitably have a great impact on the dynamic characteristics of the planetary gear system. If the inner gear ring is regarded as rigid, it is obviously inappropriate. In this paper, the dynamic characteristics of planetary gear system with flexible inner gear ring are studied. The main contents are as follows: first, the lumped parameter model is established. The contact between the components and the rack and the gear meshing is replaced by the spring damping system. Newton's second law is used to write the dynamic equation of the system, and the matrix form is arranged, and the complex mode method is used to solve the problem. According to the numerical solution of the equation, the influence of damping on the dynamic characteristics of planetary gear system is analyzed. It can be found that the influence of damping in planetary gear system is very small. Second, the rigid-flexible coupling model of planetary gear system with flexible inner gear ring is established, which simplifies the interaction between components as spring system. The dynamic equations of the flexible inner gear ring are set up and processed by using the relative knowledge of elastic mechanics and theoretical mechanics, and combined with the dynamic equations of other rigid members. The dynamic equations of planetary gear system are listed. Third, because the dynamic equations contain the sixth order partial differential equation, they can not be solved directly, so the method of separating variables and the properties of 未 function are used to reduce the order. It is transformed into a second order ordinary differential equation, and the equation is arranged into a matrix form. The stiffness matrix and mass matrix of the equation are obtained. 4th: by using the knowledge of dynamics and linear algebra, the solution of the natural frequency and mode of the dynamic equation is transformed into the solution of the eigenvalue and characteristic vector. The dynamic characteristics of the planetary gear system are analyzed by using MATLAB programming. Compared with the lumped parameter model, a new vibration mode, the inner gear ring vibration mode, is added. The natural frequency decreases and the order increases; Moreover, the greater the flexibility of the inner gear ring, the lower the natural frequency of the system. At the same time, the influence of mass and stiffness on the natural frequency of planetary gear system is analyzed.
【学位授予单位】：郑州大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TH132.41

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