Some Numerical Methods for the Simulation of Geared Transmission Dynamic Behavior Formulation and Assessment
Some Numerical Methods for the Simulation of Geared Transmission Dynamic Behavior Formulation and Assessment
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DOI：
10.1115/1.2826250
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发表时间：
1997-06
影响因子：
3.3
通讯作者：
P. Velex;M. Maatar;J. Raclot
中科院分区：
文献类型：
--
作者：
P. Velex;M. Maatar;J. Raclot
随着对齿轮设计中高速、重载和轻量化要求的提高，动态力和齿轮振动的预测和控制变得至关重要。最近的动态模型的文献通常是弯扭集中参数系统，导致参数激励可能非线性微分方程与外部激励（Blankenship和辛格，1995年;蔡，1995年; Velex和Maatar，1996年）。参数激励的结果接触长度的演变，可以干扰部分或全部接触损失的非线性，而时间和负载依赖的第二个成员通常是由形状偏差，安装误差，变化的扭矩。众所周知，实际齿轮传动的响应谱特别宽，包括与系统基本周期和每转一圈激励相关的低频，由啮合、齿侧偏差以及复杂的振幅和频率调制引起的高频分量。在这种情况下，没有通用的积分技术，最合适的方法取决于研究的目的，即动态齿载荷，齿形修改，轴承传递率，以及要积分的微分方程的数量。时域中的解可以通过时间步长数值积分来评估（Munro，1962; Ichimaru和Hirano，1974; Kubo，1978; Kasuba和Evans，1981; Kumar等人，1985年）。这类方法被广泛使用，但它们的结果依赖于假设给定的初始条件，使得很难找到所有可能的稳定解的强非Unear行为。此外，获得稳态解所需的计算时间，特别是对于轻阻尼系统，可能是显著的。大多数应用在齿轮处理单自由度方程，但扩展到线性多自由度模型与常数和时变啮合刚度使用模态或里兹方法最近已被提出（Kahnovel等人，1989年; Velex和Berthe，1989年; Furukawa，1991年; Velex和Flamand，1996年）。时域中的分析方法包括里兹平均法（Benton和Seireg，1980）和谐波平衡法（Comparin和Singh，1990; Kahnut和Singh，1991; Blankenship和Kahnut，1996），这两种方法都基于通常用傅里叶级数表示的假定周期解。对于线性参数激励微分系统，也可以使用直接幂展开的扰动方法（KiifUkay，1984; Velex和Berthe，1989），但收敛性是不确定的（Nayfeh和穆克，1978）。
With increased requirements for high speeds, heavy loads and light weights in gear design, the prediction and control of dynamic forces and gear vibrations have become critically important. Recent dynamic models of the literature are usually flexural-torsional lumped parameter systems leading to parametrically excited possibly nonlinear differential equations with external excitations (Blankenship and Singh, 1995; Cai, 1995; Velex and Maatar, 1996). Parametric excitations result of contact length evolutions which can interfere with partial or total contact loss nonlinearities while time and load-dependent second members are generally produced by shape deviations, mounting errors, varying torques. It is well known that response spectra on actual gear drives are particularly broad including low frequencies related to the system basic period and onceper-revolution excitations, high frequency components caused by meshings, flank deviations, and complex amplitude and frequency modulations. In such conditions, there is no universal integration technique and the most suitable method depends on the objective of the study ie, dynamic tooth loads, tooth shape modifications, bearing transmissibility, and on the amount of differential equations to be integrated. Solutions in time domain can be evaluated by time-step numerical integrations (Munro, 1962; Ichimaru and Hirano, 1974; Kubo, 1978; Kasuba and Evans, 1981; Kumar et al., 1985). Such methods are widely used but their results depend on the assumed given initial conditions making it difficult to find all possible stable solutions for strongly nonUnear behaviors. Furthermore, computational times required to obtain steady state solutions especially for lightly damped systems may be significant. Most of the applications in gearing deal with single degree of freedom equations but extensions to linear multi-degree of freedom models with constant and time-varying mesh stiffnesses using modal or Ritz methods have been recently proposed (Kahraman et al, 1989; Velex and Berthe, 1989; Furukawa, 1991; Velex and Flamand, 1996). Analytical methods in time domain comprise the Ritz Averaging Method (Benton and Seireg, 1980) and the Harmonic Balance Method (Comparin and Singh, 1990; Kahraman and Singh, 1991; Blankenship and Kahraman, 1996) which are both based on assumed periodic solutions usually expressed in terms of Fourier series. A perturbation method using straight forward power expansions is also possible for linear parametrically excited differential systems (KiifUkay, 1984; Velex and Berthe, 1989) but convergence is uncertain (Nayfeh and Mook, 1978).