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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 (DOF) 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. [ABSTRACT FROM AUTHOR]

Understanding the buckling behaviors of rods confined in a finite space is of paramount importance in a diversity of engineering fields. In this paper, theoretical analyses, numerical simulations and experimental measurements are combined to investigate the buckling and postbuckling of a long rod confined in a circular tube. Under uniaxial compression, the initially straight rod first buckles into a sinusoidal shape, followed by the occurrence of snap-through instability or helical buckling, which leads to a complicated, three-dimensional configuration consisting of serially connected sinusoids and helices. A new theoretical model is presented to analyze the sinusoidal and helical buckling processes of the confined rod. The complete load–displacement curve of the buckled system during loading and unloading can be well predicted by the present theory. The critical conditions are obtained for the occurrence of the sinusoidal buckling and the sinusoid–helix transitions of buckling modes. It is found, both theoretically and experimentally, that the morphological evolution during unloading exhibits distinctly different features from that during loading due to the peculiar energetic features of snap-through instability. A flexible multibody dynamics method on the basis of the geometrically exact beam theory is employed to numerically explore the buckling behavior of slender rods and to reveal the underlying energetic mechanisms. The theoretical, numerical, and experimental results agree with each other very well. The theoretical model and the numerical method presented in this work are expected to analyze some other problems of confined rods, beams, and their combined systems. [ABSTRACT FROM AUTHOR]

• An efficient multibody model of 3D helical gear-shaft systems is proposed. • Low-frequency approximation and ALE formulation are used to reduce DOFs. • Dynamic equations are simplified and contact detection process is accelerated. • One order of magnitude acceleration is achieved with high accuracy. The dynamics of helical gear-shaft systems are characterized by three-dimensional (3D) meshing contacts that have significant variations in the location and size of the contact area, resulting in noise that is unavoidably transmitted to the gearbox through the shaft. Accurate and efficient predictions of the dynamic behaviors of helical gear and shaft are indispensable in reliable and cost-effective gearbox design. Available analytical methods, though computationally feasible, cannot consider multi-point contacts and uneven tooth-load distribution. In contrast, the finite element (FE) method provides a high-fidelity approach to compute the dynamic behaviors of a general gear-shaft system at high expenses of computation. This paper aims to establish a high-efficiency multibody dynamic model for 3D contacts in helical gear-shaft systems, in which the helical gear is pertinently represented under the framework of Arbitrary Lagrangian Eulerian formulation and the shaft is discretized by 3D Timoshenko beam elements. The computational efficiency is greatly improved through the following four steps. First, the low-frequency approximation technique is adopted to reduce the degrees of freedom (DOFs) resulting from the fixed boundary normal modes. Second, under the framework of ALE formulation, only the FE nodes of three meshing tooth-faces are defined as boundary nodes. Then, the dynamic equations and Jacobian matrix are simplified by ignoring the inertial forces associated with deformation. Finally, a two-step algorithm is adopted to accelerate the contact detection process. The accuracy and efficiency of the proposed method are demonstrated through five numerical tests with correlation to commercial nonlinear finite element software. [ABSTRACT FROM AUTHOR]