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

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.