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A model order reduction method for the simulation of gear contacts based on Arbitrary Lagrangian Eulerian formulation

机译：基于任意拉格朗日欧拉公式的齿轮接触仿真模型降阶方法

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摘要

Gear contact problems are characterized by a large number of possible contact scenarios while only a few of them are simultaneously active at a given time. When applying the model order reduction method in gear contact problems, the addition of a static shape vector for each possibly-loaded boundary Degree of Freedom (DOE) will enable the contact being accurately described but may be computationally expensive when the number of boundary DOF is large. On the other hand, omission of boundary DOF, though might be computationally efficient, will result in a slow convergence. The objective of this paper is to develop a modeling technique based on Arbitrary Lagrangian Eulerian (ALE) formulation to reduce DOF while providing accurate gear meshing contact simulation. Four techniques are adopted to achieve the critical objective of the paper. First, the low-frequency approximation is attained by ignoring fixed boundary normal modes. Second, under the framework of ALE formulation, only the mesh nodes of four engaging tooth-faces are defined as boundary nodes during the whole process resulting in a great reduction of DOF of the system. Then, the calculation of inertial force and Jacobian matrix are simplified by ignoring the inertial forces resulted from deformation. Finally, a four-step high-efficiency contact algorithm is adopted to reduce the number of contact pairs and accelerate the detection process. The performance of the proposed method is demonstrated with four gear contact problems and correlated with commercial nonlinear finite element software. (C) 2018 Elsevier B.V. All rights reserved.
机译：齿轮接触问题的特征是存在大量可能的接触情况，而在给定时间只有少数几个同时发生。当在齿轮接触问题中应用模型降阶方法时，为每个可能加载的边界自由度（DOE）添加静态形状矢量将使该接触得以精确描述，但是当边界自由度为大。另一方面，省略边界自由度虽然可能在计算上很有效，但会导致收敛缓慢。本文的目的是开发一种基于任意拉格朗日欧拉（ALE）公式的建模技术，以减少自由度，同时提供精确的齿轮啮合接触仿真。采用了四种技术来实现本文的关键目标。首先，通过忽略固定边界法线模式来获得低频近似。其次，在ALE公式化的框架下，整个过程中仅将四个啮合齿面的网格节点定义为边界节点，从而大大降低了系统的自由度。然后，通过忽略变形产生的惯性力，简化了惯性力和雅可比矩阵的计算。最后，采用四步高效接触算法来减少接触对的数量并加快检测过程。通过四个齿轮接触问题证明了该方法的性能，并与商用非线性有限元软件相关联。 （C）2018 Elsevier B.V.保留所有权利。

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