三维齿轮系统，包括直齿轮、斜齿轮、锥齿轮、齿轮-轴系统以及行星齿轮组等，在航空航天、汽车、风力发电机及机器人等工业中有着十分广泛的应用。齿轮系统通过齿轮对之间的啮合与接触传递运动和力，具有传动效率高、传动误差小、寿命周期长等特点。然而，由于齿轮对之间的动态接触会引发振动、噪声与疲劳问题，极大地影响了齿轮的传动状态以及齿轮箱的寿命，为了处理此类问题，需要在设计阶段对齿轮动力学进行仿真计算。常用的解析方法虽然比较高效，但是其在求解齿轮动力学时做了过多的简化与近似，因而无法求解齿轮系统中诸如多点接触、不均衡受载等复杂三维接触问题；另一方面，有限元方法虽然能够提供高精度的计算工具，但是齿轮系统中大量的自由度会导致计算效率过低，需要占用大量的计算资源。为了解决此类问题，本文提出了一种基于任意拉格朗日方法的适用于多种齿轮系统的高效多体动力学计算方法，在保证仿真精度的基础上，大幅度提高仿真效率，为齿轮箱系统的设计提供高效且准确的仿真工具。本文研究工作如下：1. 提出基于任意拉格朗日欧拉方法的ALE齿轮单元。首先采用Craig-Bampton模态综合法描述齿轮单元的动力学行为；然后，针对单对齿轮在传动过程中存在可能接触齿数非常多而同时发生接触的齿数非常少的传动特点，通过引入ALE齿轮单元，只定义发生接触的齿面节点作为界面节点，从而大幅度缩减模型自由度；最后，提出了基于二叉方向包围盒树的高效接触检测及计算算法，快速排除未发生接触的单元面片，从而提高接触检测的效率，并通过赫兹接触模型高精度地计算三维齿面间的接触力。2. 提出单对齿轮系统的高效建模方法。应用ALE齿轮对单元，进一步对单对齿轮系统，包括单对直齿轮、斜齿轮、锥齿轮及斜齿轮-轴系统实现了高效建模，并以斜齿轮-轴系统为例详细阐述建模过程：首先应用ALE齿轮单元对三维斜齿轮进行建模，高效地解决了齿轮对间的移动接触问题，同时采用Timoshenko梁单元对轴进行有限元划分，在保证计算精度的基础上，实现了对比ABAQUS约一个数量级的仿真效率的提升。在此基础上，进一步提出多对齿轮系统的高效建模方法，在行星齿轮组的建模过程中，应用模型叠加近似方法，将ALE齿轮单元拓展应用到多对齿轮系统中，利用齿轮接触的局部性特点，采用多个单对ALE齿轮接触单元来近似多对齿轮接触系统，从而解决了多对齿轮接触系统中的换齿阈值不一致的问题。仿真结果验证了此方法的准确性，并且实现了对比ABAQUS约5倍仿真。

Three-dimensional gear systems, including spur gear, helical gear, bevel gear, gear-shaft system and planetary gear set, are ubiquitously used in aerospace, automobile, wind energy and robotics industries. Gears are transmitting force and motion through gear meshing and they are characterized by high transmission efficiency, low transmission error, and long life cycles. However, the dynamic meshing forces between gear teeth will also induce the vibration, noise and fatigue problems, greatly reducing the system's transmission capacity and life cycle. Therefore, it is very important to analyze the dynamic behavior of gear systems in the design of gearbox. Available analytical methods, though computationally feasible, cannot consider complex three-dimensional (3D) working conditions like 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 system at high expenses of computation, due to the large amount of degree of freedom (DOFs) in the gear system. To solve this problem, this paper proposes a high-efficiency multibody dynamic model based on the Arbitrary Lagrangian Eulerian (ALE) formulation to predict the dynamic bevavior of a general 3D gear system. This model could greatly improve the computational efficieny of gear system while the accuracy is highly preserved, and it can be used as a reliable tool in the gearbox design. The work of this paper are as follows: 1. The ALE gear element is proposed based on the Arbitrary Lagrangian Eulerian formulation. The Craig-Bampton method is first adopted to reduce the model order of gear system by approximating the dynamic response of gear with mode synthesis. After that, because there are a large amount of DOFs possibly in contact while only a small fraction of them are simultaneously in contact in gear system, the gear dynamics can be regarded as a moving-contact system. Therefore, the ALE formulation is introduced to only define the current contact surface nodes as boundary nodes, thereby greatly reduce the system DOFs. Finally, the hierarchical oriented bounding box tree method is used to accelerate the contact detection process by quickly eliminating the element-face pairs that are not in contact, and the Hertz contact model is then used to predict the contact forces between 3D element-face pairs. 2. The high-efficiency single-contact gear system is established. Using the ALE gear elements, the single-contact gear system is conveniently developed, including spur gears, helical gears, bevel gears and helical gear-shaft system. In the modeling of helical gear-shaft system, the 3D helical gears are modeled with ALE gear elements to solve the moving-contact problem and the shaft are meshed with 3D Timoshenko beam elements. About one order of magnitude acceleration is achieved compared with ABAQUS while the accuracy is highly preserved. In the meanwhile, the high-efficiency multi-contact gear system is established. The model superposition approximation technique is introduced to apply the ALE gear elements in the modeling of multi-contact system like the planetary gear set. This method is made possible by the contact locality of gear system. Therefore, the multi-contact gear system is approximated by multiple single-contact systems, so that the tooth-change thresholds of multiple single-contact systems are independent from each other. Numerical cases are designed to verify the accuracy of this method and about five times acceleration is achieved compared with ABAQUS. 3. The ALE formulation based Patch-Patch moving-contact detection method is proposed. To efficiently solve the contact between flexible bodies, the three-step contact algorithm is established. This algorithm is based on the transmission characteristic of ALE moving-contact problems that only a small fraction of the body is in contact, even though a large number of possible contact scenarios exist when the whole body is considered. Therefore, only a small number of the patch pairs of the whole body are in contact. By defining the contact Patch-Patch pairs as the boundary faces, we can rapidly eliminate the patch pairs that are not possibly in contact and assign much computational resources to the possibly in-contact area, while less resources are assigned in other area. In this way, we could save much computational resources and preserve the accuracy.