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Simpack Modeling and Simulation Fundamentals Guide
What is Multibody Simulation?
Multibody simulation (MBS), also known as multibody system simulation or multibody dynamics, is used to predict and optimize the behavior of any type of multibody system by solving the equations of motion. The name multibody can refer to a wide range of systems including machinery, vehicles, robotics, mechatronics, biomechanics, etc. The bodies of a multibody system are linked by means of joints and kinematic constraints, which allow certain relative motions and restrict others. The bodies themselves can be rigid or flexible. The degrees of freedom (DOF) are represented by a number of independent state variables that define the motion of the body (displacement, deformation). The movements within these degrees of freedom are influenced by arbitrary forces and torques provided by according elements. The system is completed by excitation elements and sensors for measuring the desired outputs. In describing the kinematic behavior, the motion or the position of the multi- body system is studied with respect to the kinematic joints. Dynamic problems describe the motion of the system due to the applied forces and the inertia characteristics of the bodies, i.e. their mass, moments of inertia and position of the center of gravity. The multibody system approach, with the development of computer technology, is clearly an added value in the analysis and design of mechanical and mechatronic systems.
什么是多体仿真？
多体仿真（MBS），也称为多体系统仿真或多体动力学，是通过求解运动方程来预测和优化任何类型多体系统行为的一种方法。"多体"一词可以指代各种系统，包括机械、车辆、机器人、机电一体化、生物力学等。
多体系统的各个部件通过关节和运动约束相互连接，这些连接允许某些相对运动并限制其他运动。这些部件本身可以是刚性的或柔性的。自由度（DOF）由一组独立的状态变量表示，这些变量定义了部件的运动（位移、变形）。这些自由度内的运动受到由相关元件提供的任意力和扭矩的影响。系统通过激励元件和传感器来完成，用于测量所需的输出。
在描述运动行为时，多体系统的运动或位置是相对于运动关节进行研究的。动力学问题则描述了系统由于施加的力和部件的惯性特性（即质量、转动惯量和质心位置）而产生的运动。
随着计算机技术的发展，多体系统方法在机械和机电系统的分析与设计中明显具有附加值。
Basic Modeling Element Categories
Rigid Bodies
Bodies are the Modeling Element to which you can assign mass properties, and rigid Bodies are infinitesimally stiff. Rigid Bodies are generally used to define most Bodies in your model. If you need to consider flexibility in your component Bodies, you can define them as Flexible Bodies. You can find the description of the Simpack Modeling Element category Bodies in Bodies.### 刚体
刚体是您可以分配质量属性的建模元素，并且是无限刚性的。
刚体通常用于定义模型中的大多数实体。 如果您需要考虑组件实体的柔性，则可以将它们定义为柔性体。
您可以在“实体”中找到 Simpack 建模元素类别“实体”的描述。
Flexible Bodies
Modeling the flexibility of a component in a multibody system may be a necessary step in the engineering design process for analyzing the resonance conditions, for obtaining precise solution of the forces that act on the Bodies and how the latter are deformed, as well as for validating purposes. A modal representation is used for simulating Flexible Bodies in Simpack. The modal data describing the flexibility are obtained from a finite element model (known as superelement) provided by the frequently used commercial finite element codes. Thus, to consider the flexibility, the deformation of a Flexible Body is represented by modes. In order to integrate the finite element model into Simpack, the Flexible Body modes in finite element code need to be transformed yielding the reduced finite element model. The mathematical approach is described in Approach in Finite Element Software. The workflow is described in FlexModal: Coupling of FE Models with Simpack. After the reduction, the data (i.e mass, stiffness) are passed in Simpack through the 'FBI File Generation' Utility (see Using the FBI File Generator Utility). In Simpack, Flexible Bodies are contained in the Bodies Modeling Element category.### 柔性体
在多体动力学系统中，对构件的柔性进行建模，可能是工程设计过程中的必要步骤，用于分析共振条件，获得作用于构件的精确力解以及构件变形情况，同时也用于验证目的。
Simpack中使用模态表示法来模拟柔性体。描述柔性的模态数据来源于常用的商业有限元代码提供的有限元模型（称为超单元）。因此，为了考虑柔性，柔性体的变形由模态来表示。
为了将有限元模型集成到Simpack中，有限元代码中的柔性体模态需要进行变换，得到简化的有限元模型。数学方法在有限元软件方法一节中进行描述。工作流程在FlexModal：有限元模型与Simpack耦合一节中进行描述。
在简化后，数据（即质量、刚度）通过“FBI文件生成器”实用工具传递到Simpack中（参见使用FBI文件生成器实用工具）。
在Simpack中，柔性体包含在“构件建模”元素类别中。
Local Coordinate Systems 本地坐标系
Local coordinate systems are required for reference and connection points throughout your model. You define these in Simpack using the Modeling Element category Markers. You can define Markers on both Bodies and Reference Systems. You can find the description of the Simpack Modeling Element category Markers in Markers.
在您的模型中，需要使用本地坐标系作为参考点和连接点。
您可以在 Simpack 中使用“建模元素”类别中的“标记”来定义这些坐标系。 您可以在“刚体”和“参考系”上都定义标记。
有关 Simpack 建模元素类别“标记”的详细描述，请参阅“标记”部分。
Kinematic Joints 运动学连接件
Joints are one of the two kinematic connections between two different Bodies or between a Reference System and a Body. Joints belong to a Body. A Bodyalways has one and only one Joint. You can define kinematic chains where you have a chain of Bodies connected to each other via Joints. Each translational or rotational free motion in a Joint adds a degree of freedom to the system. You can find the description of the Simpack Modeling Element category Joints in Joints.
连接件是两个不同刚体之间或参考坐标系与刚体之间两种运动学连接方式之一。连接件属于一个刚体。 一个刚体始终只有一个且仅有一个连接件。您可以定义运动学链，其中有一系列通过连接件相互连接的刚体。连接件中的每一种平动或转动自由度都会增加系统的自由度。 您可以在“连接件”部分找到 Simpack 建模元素类别“连接件”的描述。
Kinematic Constraints 运动学约束
Constraints are used for creating kinematically closed loops in your system. This means you have more kinematic connections than Bodies. Contrary to Joints, Constraints remove degrees of freedom from the system and add also additional constraining boundary conditions. You will require a solver that can handle differential algebraic equations for solving models containing Constraints. You can find the description of the Simpack Modeling Element category Constraints in Constraints.
约束用于在您的系统中创建运动学闭合回路。 这意味着您的系统具有比刚体（Bodies）更多的运动学连接。与关节（Joints）不同，约束从系统中移除自由度，并添加额外的约束边界条件。 包含约束的模型需要能够处理微分代数方程的求解器。 您可以在“约束”（Constraints）类别中找到 Simpack 建模元素约束的描述。
Topology and Kinematic Tree 拓扑与运动学树
The way how the Modeling Elements described in Basic Modeling Element Categories are connected to each other is called the model topology. So-called topology diagrams visualize the Bodies, Joints, Constraints, Connections, and Force Elements in an abstract way that shows their interconnections but not their geometry or properties.
建模元素之间连接的方式，这些建模元素在基本建模元素类别中定义，被称为模型拓扑。所谓的拓扑图以抽象的方式可视化 Bodies（实体）、Joints（连接）、Constraints（约束）、Connections（连接）和 Force Elements（力元素），展示它们之间的相互连接，但不显示它们的几何形状或属性。
Topology Diagrams 拓扑图
Topology diagrams ease the understandability of the model especially when compared to a three-dimensional visualization: See Figure 1. Simpack generates the topology diagrams automatically (Figure 2) and allows to edit the Modeling Element properties directly from the diagram, see 2D Page.
与三维可视化相比，拓扑图更容易理解模型，如图1所示。Simpack 自动生成拓扑图（如图2所示），并允许直接从图中编辑建模元素的属性，参见 2D 页面。
Kinematic Tree 运动学树
Kinematic connections between Bodies or a Body and a Reference System are made by means of Joints or Constraints. For any model containing more than one Body there are two basic ways to define the kinematic connections: With absolute kinematics, the movement of each Body is described with respect to the global (absolute) coordinate system, called the inertia system, each Joint has its origin there. With relative kinematics, the Bodies' movements are described with respect to another Body, only the first Body relates to the inertia system. Joints connect the Bodies to each other. Of course, mixed topologies within the same model are also possible. See also Figure 3. Using relative kinematics, the model will contain one or more 'kinematic trees'. The name arises from the fact that the kinematic connections form a tree structure, which can well be seen in the bicycle example in Figure 2 by following the blue Joint connection lines. Note: Simpack allows both absolute and relative kinematics but its multibody formalism has been optimized for relative kinematics. In particular for large models, the use of relative kinematics will drastically speed up the solution by taking advantage of a recursive formulation of the equations of motion. Thus, modeling in absolute kinematics is generally not recommended in Simpack, and relative kinematics should be used wherever possible. Another advantage of relative kinematics is the possibility to use a minimal set of degrees of freedom and, thus, equations of motion (see also Degrees of Freedom (DOF)). See again the example in Figure 2: Only the bicycle frame possesses six degrees of freedom. Pedals and wheels are described relative to the frame, which means that they only need one rotational degree of freedom each. In absolute kinematics representation, they would need six degrees of freedom and, additionally, five constraint conditions each to connect them kinematically to the frame. Note: Simpack's recommended concept is to provide only the actually required degrees of freedom by selecting appropriate Joints.
实体之间的运动学连接，或实体与参考系之间的连接，是通过 Joints 或 Constraints 实现的。对于任何包含多个实体的模型，定义运动学连接有两种基本方法：
使用绝对运动学时，每个实体的运动都相对于全局（绝对）坐标系进行描述，该坐标系被称为惯性系，每个 Joint 的原点都在那里。
使用相对运动学时，实体的运动相对于另一个实体进行描述，只有第一个实体与惯性系相关联。Joints 将实体连接在一起。
当然，在同一个模型中也可以使用混合拓扑。参见图3。
使用相对运动学时，模型将包含一个或多个“运动学树”。这个名称源于运动学连接形成树状结构的事实，这在图2中的自行车示例中，沿着蓝色的 Joint 连接线可以清楚地看到。
注意：Simpack 允许使用绝对和相对运动学，但其多体形式已被优化用于相对运动学。特别是对于大型模型，使用相对运动学将通过利用运动方程的递归公式来大大加快求解速度。因此，通常不建议在 Simpack 中使用绝对运动学，而应尽可能使用相对运动学。
相对运动学的另一个优点是可以使用最少的自由度，以及运动方程（参见自由度 (DOF)）。再次查看图2中的示例：只有自行车车架拥有六个自由度。踏板和车轮是相对于车架描述的，这意味着它们只需要每个旋转一个自由度。如果使用绝对运动学表示，它们将需要六个自由度，并且还需要五个约束条件来将它们在运动学上连接到车架。
注意：Simpack 推荐的概念是仅提供实际所需的自由度，通过选择合适的 Joints 来实现。
Closing Kinematic Loops 闭合运动学回路
There are cases where an open kinematic tree structure is not sufficient and some of the branches must be kinematically connected to each other. This is called 'closing a kinematic loop'. In Simpack, Constraints are used in this case. Closing kinematic loops leads to systems which require a solver which can handle DAEs, see also Equations of Motion. Again, this can be seen in Figure 2: There is a kinematic connection between pedals and rear wheel, defined by a rotational Constraint, that ensures that the rotations of these Bodies are coupled. Note that this connection could also be made by using a Force Element (in more detailed models one would even use a detailed chain, belt or cardan shaft modeling). This approach would introduce a stiffness (and damping) between the pedals and wheel rotations, i.e. the Bodies would be dynamically connected but retain their rotational degrees of freedom. In contrast to Force Elements, Constraints actually remove degrees of freedom due to the kinematic nature of the connection they establish, and there is no flexibility in the connection.
在某些情况下，开放的运动学树结构不足以满足要求，一些分支必须在运动学上连接在一起。这被称为“闭合运动学回路”。在 Simpack 中，使用 Constraints 来实现这一点。闭合运动学回路会导致需要能够处理 DAE 的求解器，参见运动方程。
再次，这可以在图2中看到：踏板和后轮之间存在运动学连接，由旋转 Constraint 定义，以确保这些实体的旋转相互耦合。
注意：这种连接也可以通过使用 Force Element 来实现（在更详细的模型中，甚至可以使用详细的链、皮带或万向节建模）。这种方法会在踏板和车轮旋转之间引入刚度和阻尼，即实体将动态连接，但保留其旋转自由度。与 Force Elements 不同，Constraints 实际上由于它们建立的运动学连接而消除了自由度，并且连接中没有柔性。